explanation blue bibcodes open ADS page with paths to full text
Author name code: toomre
ADS astronomy entries on 2022-09-14
author:"Toomre, Juri"
---------------------------------------------------------
Title: Confinement of the Solar Tachocline by Dynamo Action in the
Radiative Interior
Authors: Matilsky, Loren I.; Hindman, Bradley W.; Featherstone,
Nicholas A.; Blume, Catherine C.; Toomre, Juri
2022arXiv220612920M Altcode:
A major outstanding problem in solar physics is the confinement
of the solar tachocline, the thin shear layer that separates nearly
solid-body rotation in the radiative interior from strong differential
rotation in the convection zone. Here, we present the first 3-D, global
solar simulation in which a tachocline is confined by a self-excited
dynamo. The non-axisymmetric magnetism is initially built in the
convection zone and then diffusively imprints downward. Additionally,
the field is locally amplified throughout the radiative interior by
vigorous horizontal motions that arise from equatorial Rossby waves and
possibly shear instabilities. Our work thus challenges the long-held
notion that the Sun's dynamo magnetic field is amplified only as deep
as the tachocline and stored in a quiescent radiative interior.
---------------------------------------------------------
Title: Longitudinally Modulated Dynamo Action in Simulated M-dwarf
Stars
Authors: Bice, Connor P.; Toomre, Juri
2022ApJ...928...51B Altcode: 2022arXiv220202869B
M-dwarf stars are well known for the intense magnetic activity that many
of them exhibit. In cool stars with near-surface convection zones, this
magnetic activity is thought to be driven largely by the interplay of
convection and the large-scale differential rotation and circulations
it establishes. The highly nonlinear nature of these flows yields
a fascinatingly sensitive and diverse parameter space, with a wide
range of possible dynamics. We report here on a set of three global MHD
simulations of rapidly rotating M2 (0.4 M <SUB>⊙</SUB>) stars. Each of
these three models established nests of vigorous convection that were
highly modulated in longitude at low latitudes. Slight differences in
their magnetic parameters led each model to disparate dynamo states,
but the effect of the convective nest was a unifying feature. In each
case, the action of longitudinally modulated convection led to localized
(and in one case, global) reversals of the toroidal magnetic field,
as well as the formation of an active longitude, with enhanced poloidal
field amplitudes and flux emergence.
---------------------------------------------------------
Title: Powering Stellar Magnetism: Energy Transfers in Cyclic Dynamos
of Sun-like Stars
Authors: Brun, Allan Sacha; Strugarek, Antoine; Noraz, Quentin;
Perri, Barbara; Varela, Jacobo; Augustson, Kyle; Charbonneau, Paul;
Toomre, Juri
2022ApJ...926...21B Altcode: 2022arXiv220113218B
We use the anelastic spherical harmonic code to model the convective
dynamo of solar-type stars. Based on a series of 15 3D MHD simulations
spanning four bins in rotation and mass, we show what mechanisms are
at work in these stellar dynamos with and without magnetic cycles
and how global stellar parameters affect the outcome. We also derive
scaling laws for the differential rotation and magnetic field based
on these simulations. We find a weaker trend between differential
rotation and stellar rotation rate, ( ${\rm{\Delta }}{\rm{\Omega
}}\propto {(| {\rm{\Omega }}| /{{\rm{\Omega }}}_{\odot })}^{0.46}$ )
in the MHD solutions than in their HD counterpart ${\left(| {\rm{\Omega
}}| /{{\rm{\Omega }}}_{\odot }\right)}^{0.66}$ ), yielding a better
agreement with the observational trends based on power laws. We find
that for a fluid Rossby number between 0.15 ≲ Ro <SUB>f</SUB> ≲
0.65, the solutions possess long magnetic cycle, if Ro <SUB>f</SUB>
≲ 0.42 a short cycle and if Ro <SUB>f</SUB> ≳ 1 (antisolar-like
differential rotation), a statistically steady state. We show that
short-cycle dynamos follow the classical Parker-Yoshimura rule
whereas the long-cycle period ones do not. We also find efficient
energy transfer between reservoirs, leading to the conversion of
several percent of the star's luminosity into magnetic energy that
could provide enough free energy to sustain intense eruptive behavior
at the star's surface. We further demonstrate that the Rossby number
dependency of the large-scale surface magnetic field in the simulation
( ${B}_{{\rm{L}},\mathrm{surf}}\sim {{Ro}}_{{\rm{f}}}^{-1.26}$ ) agrees
better with observations ( ${B}_{V}\sim {{Ro}}_{{\rm{s}}}^{-1.4\pm 0.1}$
) and differs from dynamo scaling based on the global magnetic energy
( ${B}_{\mathrm{bulk}}\sim {{Ro}}_{{\rm{f}}}^{-0.5}$ ).
---------------------------------------------------------
Title: Global Confinement Of The Solar Tachocline By A Convective
Dynamo
Authors: Matilsky, L.; Hindman, B.; Toomre, J.
2021AAS...23830401M Altcode:
After more than thirty years, the most striking feature of the internal
rotation profile of the Sun as revealed by helioseismology—the
tachocline of shear at the base of the convection zone (CZ)—remains
poorly understood. Here we present rotating, 3D, spherical-shell
simulations of a CZ overlying a stable radiative zone (RZ) that
confine the tachocline against inward diffusive spreading via a
convective dynamo. In particular, the viscous imprinting of the
differential rotation from the CZ onto the RZ is prevented by the
non-axisymmetric Lorentz torque, producing a tachocline-like shear
layer at all latitudes. The balance remains stable on centuries-long
timescales and overall resembles a more complex (non-axisymmetric)
version of Ferraro's Law of Isorotation, in which isorotation contours
are forced to fall along poloidal magnetic field lines. These results
add an unexpected path toward solving the tachocline confinement
problem. Namely, a dynamo operating mostly in the CZ (and notably
in the absence of a primordial magnetic field confined beneath the
tachocline in the RZ, as suggested in Gough and McIntyre 1998) can by
itself stop the inward burrowing of the differential rotation.
---------------------------------------------------------
Title: Neural network to analyze rising magnetic flux ropes in
M-dwarf stellar convective dynamo simulations
Authors: Bice, C. P.; Toomre, J.
2021AAS...23820805B Altcode:
Despite the central role that rising magnetic flux ropes are thought
to play in the formation of active regions on the surfaces of the
Sun and other stars, global MHD simulations of stellar interiors have
struggled to self-consistently capture their dynamics. By their nature,
these structures tend to be short-lived or wholly absent in all but
the most turbulent high-resolution convective dynamo simulations
— environments which make their hand-identification and study
prohibitively time-consuming. We present here an analysis of hundreds
of self-consistent, rising flux ropes identified autonomously in
global simulations of M-dwarf convective dynamos with the help of
a novel machine-learning pipeline developed for the task. We report
on the details of the neural network models employed, as well as the
variation of flux rope formation rates, locations, and trajectories
across differing stellar parameters.
---------------------------------------------------------
Title: Building and Maintaining a Solar Tachocline through Convective
Dynamo Action
Authors: Matilsky, Loren I.; Toomre, Juri
2021arXiv210505412M Altcode:
For more than thirty years, the dynamical maintenance of the thin
solar tachocline has remained one of the central outstanding problems
of stellar astrophysics. Three main theories have been developed to
explain the tachocline's thinness, but so far none of them has been
shown to work convincingly in the extreme parameter regime of the solar
interior. Here, we present a rotating, 3D, spherical-shell simulation of
a combined solar-like convection zone and radiative zone that achieves
a tachocline built and maintained by convective dynamo action. Because
of numerical constraints, the dynamo prevents the viscous spread of the
tachocline instead of the Eddington-Sweet-time-scale radiative spread
believed to occur in the Sun. Nonetheless, our simulation supports
the scenario of tachocline confinement via the cyclic solar dynamo,
and is the first time one of the main confinement scenarios has been
realized in a global, 3D, spherical-shell geometry including nonlinear
fluid motions and a self-consistently generated dynamo.
---------------------------------------------------------
Title: Machine Learning analysis of self-consistent magnetic flux
ropes realized in M-dwarf dynamo simulations
Authors: Bice, Connor P.; Toomre, Juri
2021csss.confE.300B Altcode:
The dynamical origins of the intense magnetic activity exhibited
by most M-dwarf stars remains an unanswered question in stellar
astrophysics. Despite the central role magnetic flux ropes are
thought to play in the formation of sun and star spots, global MHD
simulations of stellar interiors have historically struggled to
self-consistently capture their dynamics. By their nature, these
structures tend to be short-lived or wholly absent in all but the
most turbulent high-resolution simulations -- environments which make
their hand-identification and study prohibitively time-consuming. We
present here a novel machine learning approach for the identification
and dynamical analysis of the hundreds of self-consistent, rising flux
ropes in our simulations of M-dwarf interiors. We report on the details
of the models developed, as well as the prospects for their continued
use with not only our own simulations, but those of the entire stellar
convection community.
---------------------------------------------------------
Title: Machine Learning Analysis of Self-Consistent Magnetic Flux
Ropes Realized In M-Dwarf Dynamo Simulations
Authors: Bice, Connor; Toomre, Juri
2021csss.confE.327B Altcode:
The dynamical origins of the intense magnetic activity exhibited
by most M-dwarf stars must be tied to their internal convective
dynamos, and yet there remain many unanswered questions concerning
its details. Despite the central role magnetic flux ropes are thought
to play in the formation of solar and stellar starspots, global
MHD simulations of stellar interiors have historically struggled
to self-consistently capture their dynamics. By their nature, these
structures tend to be short-lived or wholly absent in all but the most
turbulent high-resolution simulations -- environments which make their
hand-identification and study prohibitively time-consuming. We present
here a novel machine-learning pipeline for the autonomous identification
and analysis of self-consistent, rising flux ropes found in our global
3D MHD simulations of M-dwarf convective interiors. We report on the
details of the models developed, as well as early results from the
project and its prospects moving forward.
---------------------------------------------------------
Title: Building and maintaining a solar tachocline through convective
dynamo action
Authors: Matilsky, Loren Isaac; Toomre, Juri
2021csss.confE.331M Altcode:
For more than thirty years, the dynamical maintenance of the thin
solar tachocline has remained one of the central outstanding problems
of stellar astrophysics. Three main theories have been developed to
explain the tachocline's thinness, but so far none of them has been
shown to work convincingly in the extreme parameter regime of the solar
interior. Here, we present a rotating, 3D, spherical-shell simulation of
a combined solar-like convection zone and radiative zone that achieves
a tachocline built and maintained by convective dynamo action. Because
of numerical constraints, the dynamo prevents the viscous spread of the
tachocline instead of the Eddington-Sweet-time-scale radiative spread
believed to occur in the Sun. Nonetheless, our simulation supports
the scenario of tachocline confinement via the cyclic solar dynamo,
and is the first time one of the main confinement scenarios has been
realized in a global, 3D, spherical-shell geometry including nonlinear
fluid motions and a self-consistently generated dynamo.
---------------------------------------------------------
Title: Revisiting the Sun's Strong Differential Rotation along
Radial Lines
Authors: Matilsky, Loren I.; Hindman, Bradley W.; Toomre, Juri
2020ApJ...898..111M Altcode: 2020arXiv200400208M
Current state-of-the-art models of the solar convection zone consist
of solutions to the Navier-Stokes equations in rotating, 3D spherical
shells. Such models are highly sensitive to the choice of boundary
conditions. Here we present two suites of simulations differing only in
their outer thermal boundary condition, which is either one of fixed
entropy (FE) or fixed flux (FF; corresponding to a fixed gradient
in the entropy). We find that the resulting differential rotation is
markedly different between the two sets. The FF simulations have strong
differential rotation contrast and isocontours tilted along radial
lines (in good agreement with the Sun's interior rotation revealed by
helioseismology), whereas the FE simulations have weaker contrast and
contours tilted in the opposite sense. We examine in detail the force
balances in our models and find that the poleward transport of heat
by Busse columns drives a thermal wind responsible for the different
rotation profiles. We conclude that the Sun's strong differential
rotation along radial lines may result from the solar emissivity being
invariant with latitude (which is similar to the FF condition in our
models) and the poleward transport of heat by Busse columns. In future
work on convection in the solar context, we strongly advise modelers
to use an FF outer boundary condition.
---------------------------------------------------------
Title: Exploring Bistability in the Cycles of the Solar Dynamo
through Global Simulations
Authors: Matilsky, Loren I.; Toomre, Juri
2020ApJ...892..106M Altcode: 2019arXiv191208158M
The calling card of solar magnetism is the sunspot cycle, during which
sunspots regularly reverse their polarity sense every 11 yr. However,
a number of more complicated time-dependent behaviors have also been
identified. In particular, there are temporal modulations associated
with active longitudes and hemispheric asymmetry, when sunspots appear
at certain solar longitudes or else in one hemisphere preferentially. So
far, a direct link between this asymmetric temporal behavior and the
underlying solar dynamo has remained elusive. In this work, we present
results from global 3D magnetohydrodynamic simulations, which display
both behavior reminiscent of the sunspot cycle (regular polarity
reversals and equatorward migration of internal magnetic field) and
asymmetric, irregular behavior which we interpret as active longitudes
and hemispheric asymmetry in the simulations. The simulations are
thus bistable, in that the turbulent convection can stably support two
distinct flavors of magnetism at different times, in superposition or
with smooth transitions from one state to the other. We discuss this new
family of dynamo models in the context of the extensive observations
of the Sun's surface magnetic field with the Solar and Heliospheric
Observatory and the Solar Dynamics Observatory, as well as earlier
observations of sunspot number and synoptic maps. We suggest that the
solar dynamo itself may be bistable in nature, exhibiting two types
of temporal behavior in the magnetic field.
---------------------------------------------------------
Title: Probing the Influence of a Tachocline in Simulated M-dwarf
Dynamos
Authors: Bice, C. P.; Toomre, J.
2020ApJ...893..107B Altcode: 2020arXiv200105555B
M-type stars are among the best candidates in searches for habitable
Earth-like exoplanets, and yet many M-dwarfs exhibit extraordinary
flaring that would bombard otherwise habitable planets with ionizing
radiation. Observers have found that the fraction of M-stars
demonstrating significant activity transitions from roughly 10% for
main-sequence stars more massive than 0.35 M<SUB>⊙</SUB> to nearly
90% for less massive stars. The latter are typically rotating quite
rapidly, suggesting differing spin-down histories. It is also below
0.35 M<SUB>⊙</SUB> when main-sequence stars become fully convective
and may no longer contain a tachocline. We turn here to the more
massive M-stars to study the impact such a layer may have on their
internal dynamics. Using the global MHD code Rayleigh, we compare the
properties of convective dynamos generated within rapidly rotating 0.4
M<SUB>⊙</SUB> stars, with the computational domain either terminating
at the base of the convection zone or permitting overshoot into the
underlying stable region. We find that a tachocline is not necessary
for the organization of strong toroidal wreaths of magnetism in these
stars, though it can increase the coupling of mean field amplitudes to
the stellar rotation rate. Additionally, we note that the presence of a
tachocline tends to make magnetic cycles more regular than they would
otherwise have been, and can permit alternative field configurations
with much longer cycles. Finally, we find that the tachocline helps
enhance the emergent fields and organize them into larger spatial
scales, providing favorable conditions for more rapid spin-down via
the stellar wind.
---------------------------------------------------------
Title: Dynamo States with Strikingly Different Symmetries Coexisting
in Global Solar Simulations
Authors: Matilsky, Loren I.; Toomre, Juri
2020ASSP...57..197M Altcode:
We present new global 3D MHD simulations of the solar convection
zone that exhibit two distinct states of the dynamo coexisting
simultaneously. We discuss our results in terms of the solar active
longitudes and hemispheric asymmetry.
---------------------------------------------------------
Title: Touching the Interior Structure and Dynamics of Our Nearest
Star
Authors: Toomre, Juri
2020ASSP...57...37T Altcode:
Michael Thompson has had a pivotal and continuing role in developing
and refining inversion techniques to be applied to the great blossoming
of helioseismic data forthcoming from the GONG, MDI (on SOHO) and HMI
(on SDO) observational projects. This has enabled major discoveries
about the internal differential rotation of the Sun, revealing
both a tachocline of shear at the base of its convection zone and
a near-surface shear layer near its surface, and of its temporal
variations. It has also guided efforts to map subsurface flows of many
scales in the convection zone. In parallel with his abiding interests
in helioseismology, Michael was very enthusiastic about recent efforts
in solar convection and dynamo theory to address what he saw as the
outstanding questions about the dynamics proceeding deep within our
nearest star, and thus we touch briefly upon some of these here.
---------------------------------------------------------
Title: Exploring the Origins of Intense Magnetism in Early M-Dwarf
Stars
Authors: Bice, Connor; Toomre, Juri
2020ASSP...57..285B Altcode:
We present the results of new global 3D MHD simulations of early M-Dwarf
stars, exploring the influence that a tachocline of shear has on their
instantaneous and long-term magnetic activity.
---------------------------------------------------------
Title: Probing the Origins of Intense Magnetism in Early M-Dwarf Stars
Authors: Bice, Connor; Toomre, Juri
2019AAS...23412203B Altcode:
M-type stars are quickly stepping into the forefront as some of the
best candidates in searches for habitable Earth-like exoplanets, and
yet many M-dwarfs exhibit extraordinary flaring events which would
bombard otherwise habitable planets with ionizing radiation. In
recent years, observers have found that the fraction of M-stars
demonstrating significant magnetic activity transitions sharply from
roughly 10% for main-sequence stars earlier (more massive) than
spectral type M3.5 (0.35 M<SUB>⊙</SUB>) to nearly 90% for stars
later than M3.5. Stellar dynamos are are driven primarily by fluid
motions in the convection zone, the base of which migrates inward with
decreasing stellar mass. Suggestively, it is also later than M3.5 at
which main-sequence stars become fully convective, and may no longer
contain a tachocline. This layer of rotational shear separating the
convection and radiative zones is thought to play a significant role
in solar magnetism, and so we here investigate its influence on M-dwarf
dynamos. Using the spherical 3D MHD simulation code Rayleigh, we compare
the convective flows, magnetic field configurations and generation,
and time dependencies of dynamos operating within quickly rotating
M2 (0.4 M<SUB>⊙</SUB>) stars spanning a range of rotation rates
and diffusivities, with the computational domain either terminating
at the base of the convection zone or permitting overshoot into the
underlying stable region. We find that a tachocline is not necessary for
the organization of strong (10-20 kG) toroidal wreaths of magnetism in
these stars, though its presence can increase the coupling of mean field
amplitudes to the stellar rotation rate and in some cases drastically
alter the character of the fields produced. Additionally, in stars
that undergo periodic magnetic cycles, we find that the presence of a
tachocline makes these cycles both longer and more regular than they
would have otherwise been. Finally, we find that the tachocline helps
to enhance the surface poloidal fields and organize them into larger
spatial scales, both of which provide favorable conditions for more
rapid angular momentum loss through a magnetized stellar wind.
---------------------------------------------------------
Title: The Relationship Between Differential Rotation and Constant
Effective Temperature in the Sun
Authors: Matilsky, Loren; Hindman, Bradley W.; Toomre, Juri
2019AAS...23431806M Altcode:
Helioseismology has shown that the rotation rate of the solar
interior is constant along radial lines (conical rotation contours)
and has a mostly uniform gradient from equator to pole, facts which
are still not completely understood. Conical rotation contours and
uniform rotation gradients have been reproduced in previous global,
3D, hydrodynamic simulations of the solar convective envelope by
imposing a small temperature gradient at the base of the convective
layer, consistent with thermal wind balance in the tachocline. Here
we show that similar results can be obtained in global simulations
by demanding that the conductive flux through the outer boundary of
the convective layer (corresponding physically to the solar effective
temperature) be constant with latitude. For the Sun, this is in line
with observations that show no significant dependence of the effective
temperature with latitude. By contrast, if instead the entropy at
the outer boundary is fixed (keeping all other simulation parameters
constant), the outward conductive flux is allowed to vary with latitude
and a markedly different rotation profile emerges, namely one that has
cylindrical contours and strong rotation gradients confined mainly to
low latitudes. We discuss in detail how the outer boundary condition
on the entropy (fixed flux vs. fixed entropy) affects the dynamics
responsible for the differential rotation achieved in our simulations.
---------------------------------------------------------
Title: Exploring the Coexistence of Two Distinct Dynamo States in
the Sun through Global Simulations
Authors: Matilsky, Loren; Toomre, Juri
2019AAS...23431803M Altcode:
The origin of the Sun's magnetism remains one of the most pressing
outstanding problems in solar physics. The number of sunspots
(eruptions of magnetic flux through the photosphere) rises and falls
over a regular 11-year cycle. Within each cycle, the sunspots emerge
at mid-latitudes near solar maximum and then closer to the equator
as the cycle progresses. Furthermore, the polarity sense of sunspot
pairs is opposite in the Northern hemisphere compared to the Southern
hemisphere, and this polarity sense flips from one 11-year cycle to the
next. Recently, 3D, global, MHD dynamo simulations have made substantial
contact with observations, yielding regular cycling, polarity reversals,
and in a few cases, equatorward propagation of interior magnetic
field. Here we present a new class of 3D, global simulations of a
solar convection zone that remarkably achieve two distinct states
of the dynamo coexisting simultaneously. One state consists of two
opposite-polarity reservoirs of magnetism in each hemisphere that cycle,
flip polarity, and exhibit equatorward propagation, in remarkable
agreement with the observed solar cycle. Superimposed is another
state, asymmetric about the equator, that consists of one reservoir of
strong toroidal field in a single hemisphere that flips polarity and
migrates poleward with the cycle, in agreement with many other dynamo
simulations. We describe theoretically how our simulated dynamos might
be achieved and whether such processes could be at work in the solar
dynamo. We also investigate the possible observable signatures of two
distinct dynamo states if they were present in the solar interior.
---------------------------------------------------------
Title: Some travels in the land of nonlinear convection and magnetism
Authors: Toomre, J.
2019EAS....82..273T Altcode:
Rotating stars with convection zones are the great builders of magnetism
in our universe. Seeking to understand how turbulent convection actually
operates, and so too the dynamo action that it can achieve, has advanced
through distinctive stages in which Jean-Paul Zahn was often a central
player, or joined by his former students. Some of the opening steps in
dealing with the basic nonlinearity in such dynamics involved modal
equations (with specified horizontal structure) to study convective
amplitudes and heat transports achieved as solutions equilibrated by
feeding back on the mean stratification. These dealt in turn with
laboratory convection, with penetrative convection in Boussinesq
settings, then with compressible penetration via anelastic equations in
simple geometries, and finally with stellar penetrative convection in
A-type stars that coupled two convection zones. Advances in computation
power allowed 2-D fully compressible simulations, and then 3-D modeling
including rotation, to revisit some of these convection and penetration
settings within planar layers. With externally imposed magnetic fields
threading the 2-D layers, magnetoconvection could then be studied to
see how the flows concentrated the fields into complex sheets, or how
new classes of traveling waves could result. The era of considering
turbulent convection in rotating spherical shells had also arrived,
using 3-D MHD codes such as ASH to evaluate how the solar differential
rotation is achieved and maintained. Similarly the manner in which
global magnetic fields could be built by dynamo action within the solar
convection zone took center stage, finding that coherent wreaths of
strong magnetism could be built, and also cycling solutions with field
reversals. The coupling of convection and magnetism continues as a
vibrant research subject. It is also clear that stars like the Sun do
not give up their dynamical mysteries readily when highly turbulent
systems are at play.
---------------------------------------------------------
Title: Rossby and Magnetic Prandtl Number Scaling of Stellar Dynamos
Authors: Augustson, K. C.; Brun, A. S.; Toomre, J.
2019ApJ...876...83A Altcode:
Rotational scaling relationships are examined for the degree of
equipartition between magnetic and kinetic energies in stellar
convection zones. These scaling relationships are approached from two
paradigms, with first a glance at scaling relationship built on an
energy-balance argument and second a look at a force-based scaling. The
latter implies a transition between a nearly constant inertial scaling
when in the asymptotic limit of minimal diffusion and magnetostrophy,
whereas the former implies a weaker scaling with convective Rossby
number. Both scaling relationships are then compared to a suite of 3D
convective dynamo simulations with a wide variety of domain geometries,
stratifications, and range of convective Rossby numbers.
---------------------------------------------------------
Title: Rossby and Magnetic Prandtl Number Scaling of Stellar Dynamos
Authors: ~C. Augustson, K.; ~S. Brun, A.; Toomre, J.
2019arXiv190400225C Altcode:
Rotational scaling relationships are examined for the degree of
equipartition between magnetic and kinetic energies in stellar
convection zones. These scaling relationships are approached from two
paradigms, with first a glance at scaling relationship built upon an
energy-balance argument and second a look at a force-based scaling. The
latter implies a transition between a nearly-constant inertial scaling
when in the asymptotic limit of minimal diffusion and magnetostrophy,
whereas the former implies a weaker scaling with convective Rossby
number. Both scaling relationships are then compared to a suite of 3D
convective dynamo simulations with a wide variety of domain geometries,
stratifications, and range of convective Rossby numbers.
---------------------------------------------------------
Title: The Role of Downflows in Establishing Solar Near-surface Shear
Authors: Matilsky, Loren I.; Hindman, Bradley W.; Toomre, Juri
2019ApJ...871..217M Altcode: 2018arXiv181000115M
The dynamical origins of the Sun’s tachocline and near-surface
shear layer (NSSL) are still not well understood. We have attempted
to self-consistently reproduce an NSSL in numerical simulations of a
solar-like convection zone by increasing the density contrast across
rotating 3D spherical shells. We explore the hypothesis that high
density contrast leads to near-surface shear by creating a rotationally
unconstrained layer of fast flows near the outer surface. Although
our high-contrast models do have near-surface shear, it is confined
primarily to low latitudes (between ±15°). Two distinct types of flow
structures maintain the shear dynamically: rotationally constrained
Busse columns aligned with the rotation axis and fast, rotationally
unconstrained downflow plumes that deplete angular momentum from
the outer fluid layers. The plumes form at all latitudes and, in
fact, are more efficient at transporting angular momentum inward at
high latitudes. The presence of Busse columns at low latitudes thus
appears essential to creating near-surface shear in our models. We
conclude that a solar-like NSSL is unobtainable from a rotationally
unconstrained outer fluid layer alone. In numerical models, the shear is
eliminated through the advection of angular momentum by the meridional
circulation. Therefore, a detailed understanding of how the solar
meridional circulation is dynamically achieved will be necessary to
elucidate the origin of the Sun’s NSSL.
---------------------------------------------------------
Title: Exploring the Role of a Tachocline in M-Dwarf Magnetism
Authors: Bice, Connor; Toomre, Juri
2018csss.confE..27B Altcode: 2018arXiv180902238B
M-type stars are quickly stepping into the forefront as some of the
best candidates in searches for habitable Earth-like exoplanets, and
yet many M-dwarfs exhibit extraordinary flaring events which would
bombard otherwise habitable planets with ionizing radiation. In recent
years, observers have found that the fraction of M-stars demonstrating
significant magnetic activity transitions sharply from roughly 10%
for main-sequence stars earlier (more massive) than spectral type M3.5
(0.35 M_⊙) to nearly 90% for stars later than M3.5. Suggestively,
it is also later than M3.5 at which main-sequence stars become
fully convective, and may no longer contain a tachocline. Using the
spherical 3D MHD simulation code Rayleigh, we compare the peak field
strengths, topologies, and time dependencies of convective dynamos
generated within a quickly rotating (2 Omega_⊙) M2 (0.4 M_⊙) star,
with the computational domain either terminating at the base of the
convection zone or including the tachocline. We find that while both
models generate strong (∼10kG), wreathlike toroidal fields exhibiting
polarity reversals, the tachocline model provided a further reservoir
for the toroidal field, which slowed the average reversal period from
100 rotations to more than 220 rotations and increased the spectral
power of the low-order modes of the near-surface radial field by a
factor of 4.
---------------------------------------------------------
Title: Exploring the Influence of Density Contrast on Solar
Near-Surface Shear
Authors: Matilsky, Loren I.; Hindman, Bradley W.; Toomre, Juri
2018csss.confE..49M Altcode: 2018arXiv181100665M
The advent of helioseismology has determined in detail the average
rotation rate of the Sun as a function of radius and latitude. These
data immediately reveal two striking boundary layers of shear in
the solar convection zone (CZ): a tachocline at the base, where the
differential rotation of the CZ transitions to solid-body rotation in
the radiative zone, and a 35-Mm-thick near-surface shear layer (NSSL)
at the top, where the rotation rate slows by about 5% with increasing
radius. Though asteroseismology cannot probe the differential rotation
of distant stars to the same level of detail that helioseismology
can achieve for the Sun, it is possible that many cool stars with
outer convective envelopes possess similar differential rotation
characteristics, including both a tachocline and a NSSL. Here we present
the results of 3D global hydrodynamic simulations of spherical-shell
convection for a Sun-like star at different levels of density contrast
across the shell. The simulations with high stratification possess
characteristics of near-surface shear, especially at low latitudes. We
discuss in detail the dynamical balance of torques giving rise to the
NSSL in our models and interpret what these balances imply for the
real Sun. We further discuss the dynamical causes that may serve to
wipe out near-surface shear at high latitudes, and conclude by offering
some theories as to how this problem might be tackled in future work.
---------------------------------------------------------
Title: Driving Solar Giant Cells through the Self-organization of
Near-surface Plumes
Authors: Nelson, Nicholas J.; Featherstone, Nicholas A.; Miesch,
Mark S.; Toomre, Juri
2018ApJ...859..117N Altcode: 2018arXiv180401166N
Global 3D simulations of solar giant-cell convection have provided
significant insight into the processes which yield the Sun’s observed
differential rotation and cyclic dynamo action. However, as we move
to higher-resolution simulations a variety of codes have encountered
what has been termed the convection conundrum. As these simulations
increase in resolution and hence the level of turbulence achieved,
they tend to produce weak or even anti-solar differential rotation
patterns associated with a weak rotational influence (high Rossby
number) due to large convective velocities. One potential culprit for
this convection conundrum is the upper boundary condition applied in
most simulations, which is generally impenetrable. Here we present
an alternative stochastic plume boundary condition which imposes
small-scale convective plumes designed to mimic near-surface convective
downflows, thus allowing convection to carry the majority of the outward
solar energy flux up to and through our simulated upper boundary. The
use of a plume boundary condition leads to significant changes in
the convective driving realized in the simulated domain and thus to
the convective energy transport, the dominant scale of the convective
enthalpy flux, and the relative strength of the strongest downflows, the
downflow network, and the convective upflows. These changes are present
even far from the upper boundary layer. Additionally, we demonstrate
that, in spite of significant changes, giant cell morphology in the
convective patterns is still achieved with self-organization of the
imposed boundary plumes into downflow lanes, cellular patterns, and
even rotationally aligned banana cells in equatorial regions. This
plume boundary presents an alternative pathway for 3D global convection
simulations where driving is non-local and may provide a new approach
toward addressing the convection conundrum.
---------------------------------------------------------
Title: The Role of Rotation in Convective Heat Transport: an
Application to Low-Mass Stars
Authors: Matilsky, Loren; Hindman, Bradley W.; Toomre, Juri;
Featherstone, Nicholas
2018AAS...23230603M Altcode:
It is often supposed that the convection zones (CZs) of low-mass stars
are purely adiabatically stratified. This is thought to be because
convective motions are extremely efficient at homogenizing entropy
within the CZ. For a purely adiabatic fluid layer, only very small
temperature variations are required to drive convection, making the
amplitude and overall character of the convection highly sensitive
to the degree of adiabaticity established in the CZ. The presence
of rotation, however, fundamentally changes the dynamics of the CZ;
the strong downflow plumes that are required to homogenize entropy
are unable to penetrate through the entire fluid layer if they are
deflected too soon by the Coriolis force. This talk discusses 3D
global models of spherical-shell convection subject to different
rotation rates. The simulation results emphasize the possibility
that for stars with a high enough rotation rate, large fractions of
their CZs are not in fact adiabatically stratified; rather, there is a
finite superadiabatic gradient that varies in magnitude with radius,
being at a minimum in the CZ’s middle layers. Two consequences of
the varying superadiabatic gradient are that the convective amplitudes
at the largest length scales are effectively suppressed and that there
is a strong latitudinal temperature gradient from a cold equator to a
hot pole, which self-consistently drives a thermal wind. A connection
is naturally drawn to the Sun’s CZ, which has supergranulation
as an upper limit to its convective length scales and isorotational
contours along radial lines, which can be explained by the presence
of a thermal wind.
---------------------------------------------------------
Title: Dynamo Scaling Relationships
Authors: Augustson, Kyle; Mathis, Stéphane; Brun, Sacha; Toomre, Juri
2017IAUS..329..233A Altcode: 2017arXiv170204227A
This paper provides a brief look at dynamo scaling relationships for
the degree of equipartition between magnetic and kinetic energies. Two
simple models are examined, where one that assumes magnetostrophy
and another that includes the effects of inertia. These models are
then compared to a suite of convective dynamo simulations of the
convective core of a main-sequence B-type star and applied to its
later evolutionary stages.
---------------------------------------------------------
Title: On Differential Rotation and Overshooting in Solar-like Stars
Authors: Brun, Allan Sacha; Strugarek, Antoine; Varela, Jacobo; Matt,
Sean P.; Augustson, Kyle C.; Emeriau, Constance; DoCao, Olivier Long;
Brown, Benjamin; Toomre, Juri
2017ApJ...836..192B Altcode: 2017arXiv170206598B
We seek to characterize how the change of global rotation rate
influences the overall dynamics and large-scale flows arising in the
convective envelopes of stars covering stellar spectral types from
early G to late K. We do so through numerical simulations with the
ASH code, where we consider stellar convective envelopes coupled to
a radiative interior with various global properties. As solar-like
stars spin down over the course of their main sequence evolution,
such a change must have a direct impact on their dynamics and rotation
state. We indeed find that three main states of rotation may exist for
a given star: anti-solar-like (fast poles, slow equator), solar-like
(fast equator, slow poles), or a cylindrical rotation profile. Under
increasingly strict rotational constraints, the last profile can
further evolve into a Jupiter-like profile, with alternating prograde
and retrograde zonal jets. We have further assessed how far the
convection and meridional flows overshoot into the radiative zone
and investigated the morphology of the established tachocline. Using
simple mixing length arguments, we are able to construct a scaling of
the fluid Rossby number {R}<SUB>{of</SUB>}=\tilde{ω }/2{{{Ω }}}<SUB>*
</SUB>∼ \tilde{v}/2{{{Ω }}}<SUB>* </SUB>{R}<SUB>* </SUB>, which we
calibrate based on our 3D ASH simulations. We can use this scaling to
map the behavior of differential rotation versus the global parameters
of stellar mass and rotation rate. Finally, we isolate a region on
this map (R <SUB> of </SUB> ≳ 1.5-2) where we posit that stars with
an anti-solar differential rotation may exist in order to encourage
observers to hunt for such targets.
---------------------------------------------------------
Title: Prospects and Challenges for Helioseismology
Authors: Toomre, J.; Thompson, M. J.
2017hdsi.book....7T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Magnetic Furnace: Intense Core Dynamos in B Stars
Authors: Augustson, Kyle C.; Brun, Allan Sacha; Toomre, Juri
2016ApJ...829...92A Altcode: 2016arXiv160303659A
The dynamo action achieved in the convective cores of main-sequence
massive stars is explored here through three-dimensional (3D) global
simulations of convective core dynamos operating within a young
10 {M}<SUB>⊙ </SUB> B-type star, using the anelastic spherical
harmonic code. These simulations capture the inner 65% of this star by
radius, encompassing the convective nuclear-burning core (about 23%
by radius) and a portion of the overlying radiative envelope. Eight
rotation rates are considered, ranging from 0.05% to 16% of the surface
breakup velocity, thereby capturing both convection that barely senses
the effects of rotation and other situations in which the Coriolis
forces are prominent. The vigorous dynamo action realized within all
of these turbulent convective cores builds magnetic fields with peak
strengths exceeding a megagauss, with the overall magnetic energy (ME)
in the faster rotators reaching super-equipartition levels compared
to the convective kinetic energy (KE). The core convection typically
involves turbulent columnar velocity structures roughly aligned with
the rotation axis, with magnetic fields threading through these rolls
and possessing complex linkages throughout the core. The very strong
fields are able to coexist with the flows without quenching them
through Lorentz forces. The velocity and magnetic fields achieve such
a state by being nearly co-aligned, and with peak magnetic islands
being somewhat displaced from the fastest flows as the intricate
evolution proceeds. As the rotation rate is increased, the primary
force balance shifts from nonlinear advection balancing Lorentz forces
to a magnetostrophic balance between Coriolis and Lorentz forces.
---------------------------------------------------------
Title: Magnetoconvection
Authors: Toomre, Juri
2016GApFD.110..458T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Magnetic Furnace: Examining Fully Convective Dynamos And
The Influence Of Rotation
Authors: Augustson, Kyle; Mathis, S.; Brun, A. S.; Toomre, J.
2016csss.confE..29A Altcode:
The dynamo action likely present within fully convective regions
is explored through global-scale 3-D simulations. These simulations
provide a contextual analog for the convective dynamos that are likely
operating deep within the interiors of fully convective low mass
stars. A logarithmic range of rotation rates is considered, thereby
capturing both convection barely sensing the effects of rotation
to others in which the Coriolis forces are prominent. The vigorous
dynamo action realized within all of these turbulent convective cores
builds magnetic fields with peak strengths exceeding a megagauss,
with the overall magnetic energy (ME) in the faster rotators reaching
super-equipartition levels compared to the convective kinetic energy
(KE). Such strong fields are able to coexist with the flows without
quenching them through Lorentz forces. This state is achieved due to
the velocity and magnetic fields being nearly co-aligned, and with
peak magnetic islands being somewhat displaced from the fastest flows
as the intricate evolution of these MHD structures proceeds. As the
rotation rate is increased, the primary force balance shifts from
nonlinear advection balancing Lorentz forces to a magnetostrophic
balance between Coriolis and Lorentz forces.
---------------------------------------------------------
Title: Helioseismic Imaging of Supergranulation throughout the
Sun’s Near-Surface Shear Layer
Authors: Greer, Benjamin J.; Hindman, Bradley W.; Toomre, Juri
2016ApJ...824..128G Altcode:
We present measurements of the Sun’s sub-surface convective flows
and provide evidence that the pattern of supergranulation is driven
at the surface. The pattern subsequently descends slowly throughout
the near-surface shear layer in a manner that is inconsistent with
a 3D cellular structure. The flow measurements are obtained through
the application of a new helioseismic technique based on traditional
ring analysis. We measure the flow field over the course of eleven
days and perform a correlation analysis between all possible pairs of
depths and temporal separations. In congruence with previous studies,
we find that the supergranulation pattern remains coherent at the
surface for slightly less than two days and the instantaneous surface
pattern is imprinted to a depth of 7 Mm. However, these correlation
times and depths are deceptive. When we admit a potential time lag
in the correlation, we find that peak correlation in the convective
flows descends at a rate of 10-40 m s<SUP>-1</SUP> (or equivalently
1-3 Mm per day). Furthermore, the correlation extends throughout all
depths of the near-surface shear layer. This pattern-propagation rate
is well matched by estimates of the speed of downflows obtained through
the anelastic approximation. Direct integration of the measured speed
indicates that the supergranulation pattern that first appears at the
surface eventually reaches the bottom of the near-surface shear layer
a month later. Thus, the downflows have a Rossby radius of deformation
equal to the depth of the shear layer and we suggest that this equality
may not be coincidental.
---------------------------------------------------------
Title: Helioseismic Measurements of the Rossby Number in the Sun's
Near-surface Shear Layer
Authors: Greer, Benjamin J.; Hindman, Bradley W.; Toomre, Juri
2016ApJ...824....4G Altcode:
Through helioseismic measurement of the Sun’s subsurface flows, we
assess the Rossby number associated with the convective motions. The
helioseismic procedure is a new form of the ring-analysis technique
that is capable of resolving supergranulation. The extremely fine
spatial resolution is achieved by deconvolving the set of p-mode
Doppler shifts measured separately within a multitude of densely
overlapping analysis regions. We find that just below the photosphere,
the Rossby number is large ({Ro}≈ 5) and the convective flows are
only weakly influenced by rotation. Below a depth of 10 {Mm}, the flows
become rotationally constrained and the concomitant Rossby number is
small ({Ro}≈ 0.2). These results support the supposition that the
near-surface shear layer is a transition region for the degree of
rotational impact on convective motions.
---------------------------------------------------------
Title: Global Solar Convective Dynamo with Cycles, Equatorward
Propagation and Grand Minima
Authors: Toomre, Juri; Augustson, Kyle C.; Brun, Allan Sacha; Miesch,
Mark S.
2016SPD....47.1013T Altcode:
The 3-D MHD Anelastic Spherical Harmonic (ASH) code, using slope-limited
diffusion, is used to study the interaction of turbulent convection,
rotation and magnetism in a full spherical shell comparable to the solar
convection zone. Here a star of one solar mass, with a solar luminosity,
is considered that is rotating at three times the solar rate. The
dynamo generated magnetic field forms large-scale toroidal wreaths,
whose formation is tied to the low Rossby number of the convection in
this simulation which we have labeled K3S. This case displays prominent
polarity cycles with regular reversals occurring roughly every 6.2
years. These reversals are linked to the weakened differential rotation
and a resistive collapse of the large-scale magnetic field. Distinctive
equatorial migration of the strong magnetic wreaths is seen, arising
from modulation of the differential rotation rather than a dynamo
wave. As the wreaths approach the equator, cross-equatorial magnetic
flux is achieved that permits the low-latitude convection to generate
poloidal magnetic field with opposite polarity. Poleward migration of
such magnetic flux from the equator eventually leads to the reversal of
the polarity of the high-latitude magnetic field. This K3S simulation
also enters an interval with reduced magnetic energy at low latitudes
lasting roughly 16 years (about 2.5 polarity cycles), during which the
polarity cycles are disrupted and after which the dynamo recovers its
regular polarity cycles. An analysis of this striking grand minimum
reveals that it likely arises through the interplay of symmetric and
antisymmetric dynamo families.
---------------------------------------------------------
Title: Helioseismic Imaging of Supergranulation throughout the Sun's
Near-Surface Shear Layer
Authors: Hindman, Bradley; Greer, Benjamin; Toomre, Juri
2016SPD....4720304H Altcode:
We present measurements of the Sun's sub-surface convective flows
and provide evidence that the pattern of supergranulation is driven
at the surface. The pattern subsequently descends slowly throughout
the near-surface shear layer in a manner that is inconsistent with
a 3-D cellular structure. The flow measurements are obtained through
the application of a new helioseismic technique based on traditional
ring analysis. We measure the flow field over the course of eleven
days and perform a correlation analysis between all possible pairs of
depths and temporal separations. In congruence with previous studies,
we find that the supergranulation pattern remains coherent at the
surface for slightly less than two days and the instantaneous surface
pattern is imprinted to a depth of 7 Mm. However, these correlation
times and depths are deceptive. When we admit a potential time lag
in the correlation, we find that peak correlation in the convective
flows descends at a rate of 10 - 30 m s<SUP>-1</SUP> (or equivalently
1 - 3 Mm per day). Furthermore, the correlation extends throughout
all depths of the near-surface shear layer. This pattern-propagation
rate is well matched by estimates of the speed of down flows obtained
through the anelastic approximation. Direct integration of the measured
speed indicates that the supergranulation pattern that first appears
at the surface eventually reaches the bottom of the near-surface shear
layer a month later. Thus, the transit time is roughly equal to a solar
rotation period and we suggest this equality may not be coincidental.
---------------------------------------------------------
Title: Tiny Stars, Strong Fields: Exploring the Origin of Intense
Magnetism in M Stars
Authors: Toomre, Juri
2016atp..prop...15T Altcode:
The M-type stars are becoming dominant targets in searches for
Earth-like planets that could occupy their habitable zones. The
low masses and luminosities of M-dwarf central stars make them
very attractive for such exoplanetary hunts. The habitable zone
of M dwarfs is close to the star due to their low luminosity. Thus
possibly habitable planets will have short orbital periods, making
their detection feasible both with the transit method (used by Kepler,
K2 and soon with TESS) and with the radial velocity approaches. Yet
habitability on a planet likely requires both solid surfaces and
atmospheres, but also a favorable radiation environment. It is here
that the M-dwarf central stars raise major theoretical puzzles, for
many of them exhibit remarkably intense and frequent flaring, despite
their modest intrinsic luminosities. The super-flares release their
energy both in white light and in X-rays, and can be thousands of times
brighter than the strongest solar flares. Such striking events must
have magnetic origins, likely from fields built by convective dynamos
operating in their interiors. Further, recent observations suggest that
the surface of some M stars is carpeted with magnetic fields of 3 kG
or more. Such field strengths are reminiscent of a sunspot, but here
instead cover much of the stellar surface. With M stars now taking
center stage in the search for Earthlike planets, it is crucial to
begin to understand how convective dynamos may be able to build intense
magnetic fields involved with super-flares and vast star spots, and how
they depend upon the mass and rotation rate of these stars. We propose
to use major 3-D MHD simulations with our Anelastic Spherical Harmonic
(ASH) code to study the coupling of turbulent convection, rotation,
and magnetism within full spherical domains such as the interior of
an M dwarf. This permits the exploration of the magnetic dynamos that
must be responsible for the evolving magnetism and intense activity
of many M dwarfs. We bring to this our prior experience with studying
dynamo processes in the outer convective envelopes of G- (the Sun)
and Ftype stars, briefly of M dwarfs, and in full convective cores
within more massive A- and B-type stars. Our previous work suggests
that M dwarfs could display a broad range of dynamo behavior, from
cyclic reversals to more chaotic variations, and further to both weak
and strong dynamo states. We will focus on the latter, exploring how
superequipartition magnetic fields could be achieved by dynamo action
in M dwarfs, as are likely needed to energize super-flares and huge
active regions, and what limits the peak field strengths. M-type
stars are distinctive in becoming fully convective with decreasing
mass at about M3.5 in spectral type (or about 0.35 solar masses). At
this transition, a steep rise in the fraction of magnetically active
stars is observed that is accompanied by an increasing rotational
velocity. Clearly how mass-loss and spin-down can lead to this is of
interest in itself. However, here we propose to study the manner in
which dynamos operating in fully convective M dwarf interiors beyond
the transition may be able to achieve very strong magnetic fields,
and how field strengths and apparent magnetic activity increases
with rotation rate as suggested by observations. We believe that
global connectivity of flows and fields across the core center will
admit new classes of strong behavior, as revealed by our B star core
dynamos, not realized when a convective envelope is bounded below by a
tachocline. These ideas need to be tested in a self-consistent manner
with global ASH simulations to gain theoretical insights into what is
the origin of the fierce magnetic activity in some of M dwarfs that
may be potential hosts to Earth-like planets. Such 3-D MHD simulations,
though challenging, are now feasible and would complement the intensive
observational searches under way.
---------------------------------------------------------
Title: Prospects and Challenges for Helioseismology
Authors: Toomre, J.; Thompson, M. J.
2015SSRv..196....1T Altcode: 2015SSRv..tmp...22T
Helioseismology has advanced considerably our knowledge of the interior
of the Sun over the past three decades. Our understanding of the Sun's
internal structure, its dynamics, rotation, convection and magnetism,
have all been advanced. Yet there are challenges, areas where the
results from helioseismology are tantalizing but inconclusive, and
aspects where the interpretation of the data has still to be put on
a firm footing. In this paper we shall focus on a number of those
challenges and give our assessment of where progress needs to be made
in the next decade.
---------------------------------------------------------
Title: Large-Eddy Simulations of Magnetohydrodynamic Turbulence in
Heliophysics and Astrophysics
Authors: Miesch, Mark; Matthaeus, William; Brandenburg, Axel;
Petrosyan, Arakel; Pouquet, Annick; Cambon, Claude; Jenko, Frank;
Uzdensky, Dmitri; Stone, James; Tobias, Steve; Toomre, Juri; Velli,
Marco
2015SSRv..194...97M Altcode: 2015arXiv150501808M; 2015SSRv..tmp...83M
We live in an age in which high-performance computing is transforming
the way we do science. Previously intractable problems are now becoming
accessible by means of increasingly realistic numerical simulations. One
of the most enduring and most challenging of these problems is
turbulence. Yet, despite these advances, the extreme parameter regimes
encountered in space physics and astrophysics (as in atmospheric and
oceanic physics) still preclude direct numerical simulation. Numerical
models must take a Large Eddy Simulation (LES) approach, explicitly
computing only a fraction of the active dynamical scales. The success
of such an approach hinges on how well the model can represent the
subgrid-scales (SGS) that are not explicitly resolved. In addition
to the parameter regime, heliophysical and astrophysical applications
must also face an equally daunting challenge: magnetism. The presence
of magnetic fields in a turbulent, electrically conducting fluid flow
can dramatically alter the coupling between large and small scales,
with potentially profound implications for LES/SGS modeling. In this
review article, we summarize the state of the art in LES modeling of
turbulent magnetohydrodynamic (MHD) flows. After discussing the nature
of MHD turbulence and the small-scale processes that give rise to energy
dissipation, plasma heating, and magnetic reconnection, we consider how
these processes may best be captured within an LES/SGS framework. We
then consider several specific applications in heliophysics and
astrophysics, assessing triumphs, challenges, and future directions.
---------------------------------------------------------
Title: Grand Minima and Equatorward Propagation in a Cycling Stellar
Convective Dynamo
Authors: Augustson, Kyle; Brun, Allan Sacha; Miesch, Mark; Toomre, Juri
2015ApJ...809..149A Altcode: 2014arXiv1410.6547A
The 3D MHD Anelastic Spherical Harmonic code, using slope-limited
diffusion, is employed to capture convective and dynamo processes
achieved in a global-scale stellar convection simulation for a
model solar-mass star rotating at three times the solar rate. The
dynamo-generated magnetic fields possesses many timescales, with
a prominent polarity cycle occurring roughly every 6.2 years. The
magnetic field forms large-scale toroidal wreaths, whose formation is
tied to the low Rossby number of the convection in this simulation. The
polarity reversals are linked to the weakened differential rotation and
a resistive collapse of the large-scale magnetic field. An equatorial
migration of the magnetic field is seen, which is due to the strong
modulation of the differential rotation rather than a dynamo wave. A
poleward migration of magnetic flux from the equator eventually leads to
the reversal of the polarity of the high-latitude magnetic field. This
simulation also enters an interval with reduced magnetic energy at
low latitudes lasting roughly 16 years (about 2.5 polarity cycles),
during which the polarity cycles are disrupted and after which the
dynamo recovers its regular polarity cycles. An analysis of this grand
minimum reveals that it likely arises through the interplay of symmetric
and antisymmetric dynamo families. This intermittent dynamo state
potentially results from the simulation’s relatively low magnetic
Prandtl number. A mean-field-based analysis of this dynamo simulation
demonstrates that it is of the α-Ω type. The timescales that appear
to be relevant to the magnetic polarity reversal are also identified.
---------------------------------------------------------
Title: Super-equipartition Convective Dynamo Action in the Cores of
B-Type Stars
Authors: Augustson, Kyle C.; Brown, Benjamin P.; Brun, Allan Sacha;
Toomre, Juri
2015IAUGA..2258137A Altcode:
Observations have revealed the presence and topology of magnetic fields
on the surfaces of some main sequence massive stars. These stars
possess a convective core that supports strong dynamo action. This
core is linked to the dynamics of the rest of the star through
overshooting convection and magnetic fields and may influence
the surface magnetism. Such effects are captured through 3-D MHD
simulations of a 10 M<SUB>⊙</SUB> B-type star, using the anelastic
spherical harmonic (ASH) code. These simulations capture the inner 65%
of the star by radius, encompassing the convective core and an extensive
portion of the radiative exterior. Vigorous dynamo action is achieved
in the convective core with self-consistent super-equipartition (SE)
states sustained over a range of rotation rates. Indeed, the ratio
of magnetic to convective kinetic energy shows a distinct scaling
with Elsasser and Coriolis number. The impact of this dynamo action
upon the differential rotation of the core is assessed by contrasting
hydrodynamic and magnetohydrodynamic simulations. The processes that
permit the maintenance of such SE states are examined. We further
study how the magnetic field generated during main-sequence dynamo
action may carry over into later evolutionary stages.
---------------------------------------------------------
Title: Super-equipartition Convective Dynamo Action in the Cores of
B-Type Stars
Authors: Augustson, Kyle C.; Brown, Benjamin P.; Brun, Allan Sacha;
Toomre, Juri
2015IAUGA..2257925A Altcode:
Observations have revealed the presence and topology of magnetic fields
on the surfaces of some main sequence massive stars. These stars
possess a convective core that supports strong dynamo action. This
core is linked to the dynamics of the rest of the star through
overshooting convection and magnetic fields and may influence
the surface magnetism. Such effects are captured through 3-D MHD
simulations of a 10 M<SUB>⊙</SUB> B-type star, using the anelastic
spherical harmonic (ASH) code. These simulations capture the inner 65%
of the star by radius, encompassing the convective core and an extensive
portion of the radiative exterior. Vigorous dynamo action is achieved
in the convective core with self-consistent super-equipartition (SE)
states sustained over a range of rotation rates. Indeed, the ratio
of magnetic to convective kinetic energy shows a distinct scaling
with Elsasser and Coriolis number. The impact of this dynamo action
upon the differential rotation of the core is assessed by contrasting
hydrodynamic and magnetohydrodynamic simulations. The processes that
permit the maintenance of such SE states are examined. We further
study how the magnetic field generated during main-sequence dynamo
action may carry over into later evolutionary stages.
---------------------------------------------------------
Title: Grand Minima and Equatorward Propagation in a Cycling Stellar
Convective Dynamo
Authors: Augustson, Kyle C.; Brun, Allan Sacha; Miesch, Mark;
Toomre, Juri
2015IAUGA..2257912A Altcode:
The 3-D magnetohydrodynamic (MHD) Anelastic Spherical Harmonic (ASH)
code, using slope-limited diffusion, is employed to capture convective
and dynamo processes achieved in a global-scale stellar convection
simulation for a model solar-mass star rotating at three times the solar
rate. The dynamo generated magnetic fields possesses many time scales,
with a prominent polarity cycle occurring roughly every 6.2 years. The
magnetic field forms large-scale toroidal wreaths, whose formation is
tied to the low Rossby number of the convection in this simulation. The
polarity reversals are linked to the weakened differential rotation and
a resistive collapse of the large-scale magnetic field. An equatorial
migration of the magnetic field is seen, which is due to the strong
modulation of the differential rotation rather than a dynamo wave. A
poleward migration of magnetic flux from the equator eventually leads to
the reversal of the polarity of the high-latitude magnetic field. This
simulation also enters an interval with reduced magnetic energy at
low latitudes lasting roughly 16 years (about 2.5 polarity cycles),
during which the polarity cycles are disrupted and after which the
dynamo recovers its regular polarity cycles. An analysis of this
grand minimum reveals that it likely arises through the interplay of
symmetric and antisymmetric dynamo families. This intermittent dynamo
state potentially results from the simulations relatively low magnetic
Prandtl number. A mean-field-based analysis of this dynamo simulation
demonstrates that it is of the α-Ω type. The time scales that appear
to be relevant to the magnetic polarity reversal are also identified.
---------------------------------------------------------
Title: Grand Minima and Equatorward Propagation in a Cycling Stellar
Convective Dynamo
Authors: Augustson, Kyle C.; Brun, Allan Sacha; Miesch, Mark;
Toomre, Juri
2015IAUGA..2258283A Altcode:
The 3-D magnetohydrodynamic (MHD) Anelastic Spherical Harmonic (ASH)
code, using slope-limited diffusion, is employed to capture convective
and dynamo processes achieved in a global-scale stellar convection
simulation for a model solar-mass star rotating at three times the solar
rate. The dynamo generated magnetic fields possesses many time scales,
with a prominent polarity cycle occurring roughly every 6.2 years. The
magnetic field forms large-scale toroidal wreaths, whose formation is
tied to the low Rossby number of the convection in this simulation. The
polarity reversals are linked to the weakened differential rotation and
a resistive collapse of the large-scale magnetic field. An equatorial
migration of the magnetic field is seen, which is due to the strong
modulation of the differential rotation rather than a dynamo wave. A
poleward migration of magnetic flux from the equator eventually leads to
the reversal of the polarity of the high-latitude magnetic field. This
simulation also enters an interval with reduced magnetic energy at
low latitudes lasting roughly 16 years (about 2.5 polarity cycles),
during which the polarity cycles are disrupted and after which the
dynamo recovers its regular polarity cycles. An analysis of this
grand minimum reveals that it likely arises through the interplay of
symmetric and antisymmetric dynamo families. This intermittent dynamo
state potentially results from the simulations relatively low magnetic
Prandtl number. A mean-field-based analysis of this dynamo simulation
demonstrates that it is of the α-Ω type. The time scales that appear
to be relevant to the magnetic polarity reversal are also identified.
---------------------------------------------------------
Title: Helioseismic Imaging of Fast Convective Flows throughout the
Near-surface Shear Layer
Authors: Greer, Benjamin J.; Hindman, Bradley W.; Featherstone,
Nicholas A.; Toomre, Juri
2015ApJ...803L..17G Altcode: 2015arXiv150400699G
Using a new implementation of ring-diagram helioseismology,
we ascertain the strength and spatial scale of convective flows
throughout the near-surface shear layer. Our ring-diagram technique
employs highly overlapped analysis regions and an efficient method
of three-dimensional inversion to measure convective motions with a
resolution that ranges from 3 Mm at the surface to 80 Mm at the base
of the layer. We find the rms horizontal flow speed to peak at 427
m s<SUP>-1</SUP> at the photosphere and fall to a minimum of 124 m
s<SUP>-1</SUP> between 20 and 30 Mm. From the velocity amplitude and
the dominant horizontal scales seen at each depth, we infer the level
of rotational influence on convection to be low near the surface,
but transition to a significant level at the base of the near-surface
shear layer with a Rossby number varying between 2.2 to as low as 0.1.
---------------------------------------------------------
Title: Convective Dynamo Simulation with a Grand Minimum
Authors: Augustson, Kyle C.; Brun, A. S.; Miesch, Mark; Toomre, Juri
2015csss...18..451A Altcode: 2015arXiv150304225A
The global-scale dynamo action achieved in a simulation of a Sun-like
star rotating at thrice the solar rate is assessed. The 3-D MHD
Anelastic Spherical Harmonic (ASH) code, augmented with a viscosity
minimization scheme, is employed to capture convection and dynamo
processes in this G-type star. The simulation is carried out in a
spherical shell that encompasses 3.8 density scale heights of the solar
convection zone. It is found that dynamo action with a high degree of
time variation occurs, with many periodic polarity reversals occurring
roughly every 6.2 years. The magnetic energy also rises and falls with
a regular period. The magnetic energy cycles arise from a Lorentz-force
feedback on the differential rotation, whereas the processes leading
to polarity reversals are more complex, appearing to arise from the
interaction of convection with the mean toroidal fields. Moreover,
an equatorial migration of toroidal field is found, which is linked
to the changing differential rotation, and potentially to a nonlinear
dynamo wave. This simulation also enters a grand minimum lasting roughly
20 years, after which the dynamo recovers its regular polarity cycles.
---------------------------------------------------------
Title: Measuring the Solar Meridional Circulation Using Local
Helioseismology
Authors: Greer, B.; Hindman, B.; Toomre, J.
2014AGUFMSH41B4143G Altcode:
The solar meridional circulation plays an important role in the
transport of angular momentum and magnetic field throughout the
convection zone and is a key component in setting the time-scale
for the solar cycle in flux-transport dynamo models. The meridional
flow is detectable with a variety of methods, including ring-diagram
helioseismology. Many of these methods are plagued with systematic
errors that have only recently been analyzed in detail. For
ring-diagram analysis, the systematic errors introduce a signal that
is easily confused with that of the meridional flow and is often of
significant amplitude. Accurately determining the character of the solar
meridional circulation requires careful attention to these errors. I use
observations from the Helioseismic and Magnetic Imager (HMI) onboard the
Solar Dynamics Observatory (SDO) to measure both the meridional flow and
the associated systematics. I will present recent measurements of the
solar meridional circulation with all known systematics accounted for.
---------------------------------------------------------
Title: Multi-Ridge Fitting for Ring-Diagram Helioseismology
Authors: Greer, Benjamin J.; Hindman, Bradley W.; Toomre, Juri
2014SoPh..289.2823G Altcode: 2014arXiv1402.5166G; 2014SoPh..tmp...46G
Inferences of subsurface flow velocities using local domain ring-diagram
helioseismology depend on measuring the frequency shifts of oscillation
modes seen in acoustic power spectra. Current methods for making
these measurements use maximum-likelihood fitting techniques to
match a model of modal power to the spectra. The model typically
describes a single oscillation mode, and each mode in a given power
spectrum is fit independently. We present a new method that produces
measurements with higher reliability and accuracy by fitting multiple
modes simultaneously. We demonstrate that this method permits measuring
sub-surface flows deeper into the Sun while providing higher uniformity
in data coverage and velocity response closer to the limb of the
solar disk. While the previous fitting method performs better for some
measurements of low phase-speed modes, we find this new method to be
particularly useful for high phase-speed modes and small spatial areas.
---------------------------------------------------------
Title: Towards a Unified Simulation of Convective Dynamo Action and
Flux Emergence in the Sun
Authors: Nelson, Nicholas J.; Brown, Benjamin; Miesch, Mark S.;
Toomre, Juri
2014AAS...22421104N Altcode:
Our global 3D simulations of convection and dynamo action in a
Sun-like star reveal that persistent wreaths of strong magnetism
can be built within the bulk of the convention zone. Our recent
simulations have achieved sufficiently high levels of turbulence to
permit portions of these wreaths to become magnetically buoyant and
rise through the simulated convective layer through a combination of
magnetic buoyancy and advection by convective giant cells. Here we
examine the characteristics of buoyant magnetic structures that are
self-consistently created by dynamo action and turbulent convective
motions. These buoyant loops originate within sections of the magnetic
wreaths in which turbulent flows amplify the fields to much higher
values than is possible through laminar processes. Examining many such
loops over a simulated magnetic activity cycle, we measure statistical
trends in the polarity, twist, and tilt of these loops that mimic
Hale’s Law, Joy’s Law, and the hemispheric helicity rule observed in
sunspots. We further show that these magnetic structures are primarily
generated by non-axisymmetric turbulent amplification on timescales
of about 15 days and not by the Ω-effect which primarily generates
the large-scale wreaths.
---------------------------------------------------------
Title: Buoyant Magnetic Loops Generated by Global Convective Dynamo
Action
Authors: Nelson, Nicholas J.; Brown, Benjamin P.; Sacha Brun, A.;
Miesch, Mark S.; Toomre, Juri
2014SoPh..289..441N Altcode: 2012arXiv1212.5612N
Our global 3D simulations of convection and dynamo action in a
Sun-like star reveal that persistent wreaths of strong magnetism
can be built within the bulk of the convention zone. Here we
examine the characteristics of buoyant magnetic structures that are
self-consistently created by dynamo action and turbulent convective
motions in a simulation with solar stratification but rotating at three
times the current solar rate. These buoyant loops originate within
sections of the magnetic wreaths in which turbulent flows amplify
the fields to much higher values than is possible through laminar
processes. These amplified portions can rise through the convective
layer by a combination of magnetic buoyancy and advection by convective
giant cells, forming buoyant loops. We measure statistical trends
in the polarity, twist, and tilt of these loops. Loops are shown to
preferentially arise in longitudinal patches somewhat reminiscent of
active longitudes in the Sun, although broader in extent. We show
that the strength of the axisymmetric toroidal field is not a good
predictor of the production rate for buoyant loops or the amount of
magnetic flux in the loops that are produced.
---------------------------------------------------------
Title: Center-to-Limb Velocity Systematic in Ring-Diagram Analysis
Authors: Greer, B.; Hindman, B.; Toomre, J.
2013ASPC..478..199G Altcode:
We use HMI ring-diagram pipeline data to measure a center-to-limb
systematic effect seen in velocities. To separate this signal from
persistent flow patterns of physical origin, we perform a least-squares
fit to the data for each wave mode. We fit a model that includes both
the radially symmetric systematic as well as global zonal and meridional
flow components. The resulting measurements of the systematic error
reveal a smooth trend as a function of both mode frequency and phase
speed. The systematic error at 45° from disk center ranges from 20
m/s radially inward to 50 m/s radially outward. The implications for
determining global scale meridional flow is discussed.
---------------------------------------------------------
Title: Dynamo Action and Magnetic Cycles in F-type Stars
Authors: Augustson, Kyle C.; Brun, Allan Sacha; Toomre, Juri
2013ApJ...777..153A Altcode:
Magnetic activity and differential rotation are commonly observed
features on main-sequence F-type stars. We seek to make contact with
such observations and to provide a self-consistent picture of how
differential rotation and magnetic fields arise in the interiors
of these stars. The three-dimensional magnetohydrodynamic anelastic
spherical harmonic code is employed to simulate global-scale convection
and dynamo processes in a 1.2 M <SUB>⊙</SUB> F-type star at two
rotation rates. The simulations are carried out in spherical shells
that encompass most of the convection zone and a portion of the stably
stratified radiative zone below it, allowing us to explore the effects
a stable zone has upon the morphology of the global-scale magnetic
fields. We find that dynamo action with a high degree of time variation
occurs in the star rotating more rapidly at 20 Ω<SUB>⊙</SUB>, with
the polarity of the mean field reversing on a timescale of about 1600
days. Between reversals, the magnetic energy rises and falls with a
fairly regular period, with three magnetic energy cycles required to
complete a reversal. The magnetic energy cycles and polarity reversals
arise due to a linking of the polar-slip instability in the stable
region and dynamo action present in the convection zone. For the more
slowly rotating case (10 Ω<SUB>⊙</SUB>), persistent wreaths of
magnetism are established and maintained by dynamo action. Compared
to their hydrodynamic progenitors, the dynamo states here involve a
marked reduction in the exhibited latitudinal differential rotation,
which also vary during the course of a cycle.
---------------------------------------------------------
Title: Cycling Dynamo in a Young Sun: Grand Minima and Equatorward
Propagation
Authors: Augustson, Kyle; Brun, Allan Sacha; Miesch, Mark Steven;
Toomre, Juri
2013arXiv1310.8417A Altcode:
We assess the global-scale dynamo action achieved in a simulation of
a sun-like star rotating at three times the solar rate. The 3-D MHD
Anelastic Spherical Harmonic code, using slope-limited diffusion,
is employed to capture convection and dynamo processes in such a
young sun. The simulation is carried out in a spherical shell that
encompasses 3.8 density scale heights of the solar convection zone. We
find that dynamo action with a high degree of time variation occurs,
with many periodic polarity reversals every 6.2 years. The magnetic
energy also rises and falls with a regular period, with two magnetic
energy cycles required to complete a polarity cycle. These magnetic
energy cycles arise from a Lorentz-force feedback on the differential
rotation, whereas the polarity reversals are present due to the
spatial separation of the equatorial and polar dynamos. Moreover,
an equatorial migration of toroidal field is found, which is linked
to the changing differential rotation and to a near-surface shear
layer. This simulation also enters a grand minimum lasting roughly 20
years, after which the dynamo recovers its regular polarity cycles.
---------------------------------------------------------
Title: Magnetic Wreaths and Cycles in Convective Dynamos
Authors: Nelson, Nicholas J.; Brown, Benjamin P.; Brun, Allan Sacha;
Miesch, Mark S.; Toomre, Juri
2013ApJ...762...73N Altcode: 2012arXiv1211.3129N
Solar-type stars exhibit a rich variety of magnetic activity. Seeking
to explore the convective origins of this activity, we have carried out
a series of global three-dimensional magnetohydrodynamic simulations
with the anelastic spherical harmonic code. Here we report on the
dynamo mechanisms achieved as the effects of artificial diffusion are
systematically decreased. The simulations are carried out at a nominal
rotation rate of three times the solar value (3 Ω<SUB>⊙</SUB>), but
similar dynamics may also apply to the Sun. Our previous simulations
demonstrated that convective dynamos can build persistent toroidal flux
structures (magnetic wreaths) in the midst of a turbulent convection
zone and that high rotation rates promote the cyclic reversal of
these wreaths. Here we demonstrate that magnetic cycles can also be
achieved by reducing the diffusion, thus increasing the Reynolds and
magnetic Reynolds numbers. In these more turbulent models, diffusive
processes no longer play a significant role in the key dynamical
balances that establish and maintain the differential rotation and
magnetic wreaths. Magnetic reversals are attributed to an imbalance
in the poloidal magnetic induction by convective motions that is
stabilized at higher diffusion levels. Additionally, the enhanced
levels of turbulence lead to greater intermittency in the toroidal
magnetic wreaths, promoting the generation of buoyant magnetic loops
that rise from the deep interior to the upper regions of our simulated
domain. The implications of such turbulence-induced magnetic buoyancy
for solar and stellar flux emergence are also discussed.
---------------------------------------------------------
Title: New Era in 3-D Modeling of Convection and Magnetic Dynamos
in Stellar Envelopes and Cores
Authors: Toomre, J.; Augustson, K. C.; Brown, B. P.; Browning, M. K.;
Brun, A. S.; Featherstone, N. A.; Miesch, M. S.
2012ASPC..462..331T Altcode:
The recent advances in asteroseismology and spectropolarimetry are
beginning to provide estimates of differential rotation and magnetic
structures for a range of F and G-type stars possessing convective
envelopes, and in A-type stars with convective cores. It is essential
to complement such observational work with theoretical studies based
on 3-D simulations of highly turbulent convection coupled to rotation,
shear and magnetic fields in full spherical geometries. We have so
employed the anelastic spherical harmonic (ASH) code, which deals
with compressible magnetohydrodynamics (MHD) in spherical shells, to
examine the manner in which the global-scale convection can establish
differential rotation and meridional circulations under current
solar rotation rates, and these make good contact with helioseismic
findings. For younger G stars rotating 3 to 5 times faster than
the current Sun, the convection establishes ever stronger angular
velocity contrasts between their fast equators and slow poles, and
these are accompanied by prominent latitudinal temperature contrasts as
well. Turning to MHD simulation of magnetic dynamo action within these
younger G stars, the resulting magnetism involves wreaths of strong
toroidal magnetic fields (up to 50 to 100 kG strengths) in the bulk
of the convection zone, typically of opposite polarity in the northern
and southern hemispheres. These fields can persist for long intervals
despite being pummeled by the fast convective downflows, but they can
also exhibit field reversals and cycles. Turning to shallower convective
envelopes in the more luminous F-type stars that range in mass from 1.2
to 1.4 solar masses and for various rotation rates, we find that the
convection can again establish solar-like differential rotation profiles
with a fast equator and slow poles, but the opposite is achieved at
the slower rotation rates. The F stars are also capable of building
strong magnetic fields, often as wreaths, through dynamo action. We
also consider dynamo action within the cores of rotating A-type stars,
finding that striking super-equipartition magnetic fields can be built
there. These families of 3-D simulations are showing that a new era of
detailed stellar modeling is becoming feasible through rapid advances
in supercomputing, and these have the potential to help interpret and
possibly even guide some of the observational efforts now under way.
---------------------------------------------------------
Title: Convection and Differential Rotation in F-type Stars
Authors: Augustson, Kyle C.; Brown, Benjamin P.; Brun, Allan Sacha;
Miesch, Mark S.; Toomre, Juri
2012ApJ...756..169A Altcode:
Differential rotation is a common feature of main-sequence spectral
F-type stars. In seeking to make contact with observations and to
provide a self-consistent picture of how differential rotation is
achieved in the interiors of these stars, we use the three-dimensional
anelastic spherical harmonic (ASH) code to simulate global-scale
turbulent flows in 1.2 and 1.3 M <SUB>⊙</SUB> F-type stars
at varying rotation rates. The simulations are carried out in
spherical shells that encompass most of the convection zone and a
portion of the stably stratified radiative zone below it, allowing
us to explore the effects of overshooting convection. We examine
the scaling of the mean flows and thermal state with rotation rate
and mass and link these scalings to fundamental parameters of the
simulations. Indeed, we find that the differential rotation becomes
much stronger with more rapid rotation and larger mass, scaling as
ΔΩvpropM <SUP>3.9</SUP>Ω<SUP>0.6</SUP> <SUB>0</SUB>. Accompanying the
growing differential rotation is a significant latitudinal temperature
contrast, with amplitudes of 1000 K or higher in the most rapidly
rotating cases. This contrast in turn scales with mass and rotation
rate as ΔTvpropM <SUP>6.4</SUP>Ω<SUP>1.6</SUP> <SUB>0</SUB>. On
the other hand, the meridional circulations become much weaker with
more rapid rotation and with higher mass, with their kinetic energy
decreasing as KE<SUB>MC</SUB>vpropM <SUP>-1.2</SUP>Ω<SUP>-0.8</SUP>
<SUB>0</SUB>. Additionally, three of our simulations exhibit
a global-scale shear instability within their stable regions that
persists for the duration of the simulations. The flow structures
associated with the instabilities have a direct coupling to and impact
on the flows within the convection zone.
---------------------------------------------------------
Title: Effects of Granulation upon Larger-Scale Convection
Authors: Hurlburt, N. E.; DeRosa, M. L.; Augustson, K. C.; Toomre, J.
2012ASPC..454...13H Altcode: 2012arXiv1201.4809H
We examine the role of small-scale granulation in helping to drive
supergranulation and even larger scales of convection. The granulation
is modeled as localized cooling events introduced at the upper boundary
of a 3-D simulation of compressible convection in a rotating spherical
shell segment. With a sufficient number of stochastic cooling events
compared to uniform cooling, we find that supergranular scales are
realized, along with a differential rotation that becomes increasingly
solar-like.
---------------------------------------------------------
Title: Modeling the Dynamical Coupling of Solar Convection with the
Radiative Interior
Authors: Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri
2011ApJ...742...79B Altcode:
The global dynamics of a rotating star like the Sun involves the
coupling of a highly turbulent convective envelope overlying a
seemingly benign radiative interior. We use the anelastic spherical
harmonic code to develop a new class of three-dimensional models
that nonlinearly couple the convective envelope to a deep stable
radiative interior. The numerical simulation assumes a realistic solar
stratification from r = 0.07 up to 0.97R (with R the solar radius),
thus encompassing part of the nuclear core up through most of the
convection zone. We find that a tachocline naturally establishes itself
between the differentially rotating convective envelope and the solid
body rotation of the interior, with a slow spreading that is here
diffusively controlled. The rapid angular momentum redistribution in
the convective envelope leads to a fast equator and slow poles, with a
conical differential rotation achieved at mid-latitudes, much as has
been deduced by helioseismology. The convective motions are able to
overshoot downward about 0.04R into the radiative interior. However,
the convective meridional circulation there is confined to a smaller
penetration depth and is directed mostly equatorward at the base
of the convection zone. Thermal wind balance is established in the
lower convection zone and tachocline but departures are evident in
the upper convection zone. Internal gravity waves are excited by the
convective overshooting, yielding a complex wave field throughout the
radiative interior.
---------------------------------------------------------
Title: Global-scale Magnetism (and Cycles) in Dynamo Simulations of
Stellar Convection Zones
Authors: Brown, B. P.; Browning, M. K.; Brun, A. S.; Miesch, M. S.;
Toomre, J.
2011ASPC..448..277B Altcode: 2011arXiv1101.0171B; 2011csss...16..277B
Young solar-type stars rotate rapidly and are very magnetically
active. The magnetic fields at their surfaces likely originate in their
convective envelopes where convection and rotation can drive strong
dynamo action. Here we explore simulations of global-scale stellar
convection in rapidly rotating suns using the 3-D MHD anelastic
spherical harmonic (ASH) code. The magnetic fields built in these
dynamos are organized on global-scales into wreath-like structures
that span the convection zone. We explore one case rotates five times
faster than the Sun in detail. This dynamo simulation, called case
D5, has repeated quasi-cyclic reversals of global-scale polarity. We
compare this case D5 to the broader family of simulations we have been
able to explore and discuss how future simulations and observations
can advance our understanding of stellar dynamos and magnetism.
---------------------------------------------------------
Title: The 3D Nature of Convective Dynamos
Authors: Miesch, M.; Brown, B.; Nelson, N.; Browning, M.; Brun, A. S.;
Toomre, J.
2011AGUFMSH23D..01M Altcode:
Solar observations throughout the extended minimum between cyles 23 and
24 have highlighted the intrinsically three-dimensional (3D) nature of
the solar magnetic field. These include prominent multipolar components
and low-latitude coronal holes observed with STEREO, asymmetric
surface flux distributions in photospheric magnetograms, ond global,
multi-scale magnetic linkages revealed by SDO. Axisymmetric mean-field
dynamo models cannot capture this complexity, which ultimately arises
from turbulent convection. The solar dynamo is a convective dynamo;
convection is clearly responsible for the diversity of solar magnetic
activity we observe, generating and organizing magnetic fields both
directly by turbulent induction and indirectly via mean flows and MHD
instabilities. Simulations of convective dynamos reveal the 3D nature
of how large-scale magnetic fields are generated and provide insight
into the intricate topology of the solar magnetic field, apparent
even during solar minimum. I will describe recent work on the role of
helicity and shear in magnetic self-organization and promising first
steps toward linking convective dynamos with flux emergence.
---------------------------------------------------------
Title: Exploring the Deep Convection and Magnetism of A-type stars
Authors: Featherstone, Nicholas; Browning, Matthew; Brun, Allan Sacha;
Toomre, Juri
2011APS..DPPN10003F Altcode:
A-type stars have both a near-surface layer of fast convection that
can excite acoustic modes and a deep zone of core convection whose
properties may be probed with asteroseismology. Many A-type stars also
exhibit large magnetic spots that are often attributed to surviving
primordial fields of global scale in the intervening radiative zone. We
have explored the potential for core convection in rotating A-type
stars to build strong magnetic fields through dynamo action. Using the
ASH code, we model the inner 30% by radius of a two solar mass A-type
star, rotating at four times the solar rate and capturing the convective
core and a portion of the overlying radiative envelope. Convection in
these stars drives a strong retrograde differential rotation and yields
a core that is prolate in shape. When dynamo action is admitted, the
convection generates strong magnetic fields largely in equipartition
with the dynamics. Remarkably, introducing a modest but large-scale
external field threading the radiative envelope (which may be of
primordial origin) can substantially alter the turbulent dynamics
of the convective interior. The resulting convection establishes a
complex assembly of helical rolls that link distant portions of the
core and yield magnetic fields of super-equipartition strength.
---------------------------------------------------------
Title: Buoyant Magnetic Loops in a Global Dynamo Simulation of a
Young Sun
Authors: Nelson, Nicholas J.; Brown, Benjamin P.; Brun, Allan Sacha;
Miesch, Mark S.; Toomre, Juri
2011ApJ...739L..38N Altcode: 2011arXiv1108.4697N
The current dynamo paradigm for the Sun and Sun-like stars places the
generation site for strong toroidal magnetic structures deep in the
solar interior. Sunspots and starspots on Sun-like stars are believed
to arise when sections of these magnetic structures become buoyantly
unstable and rise from the deep interior to the photosphere. Here, we
present the first three-dimensional global magnetohydrodynamic (MHD)
simulation in which turbulent convection, stratification, and rotation
combine to yield a dynamo that self-consistently generates buoyant
magnetic loops. We simulate stellar convection and dynamo action in
a spherical shell with solar stratification, but rotating three times
faster than the current solar rate. Strong wreaths of toroidal magnetic
field are realized by dynamo action in the convection zone. By turning
to a dynamic Smagorinsky model for subgrid-scale turbulence, we here
attain considerably reduced diffusion in our simulation. This permits
the regions of strongest magnetic field in these wreaths to rise toward
the top of the convection zone via a combination of magnetic buoyancy
instabilities and advection by convective giant cells. Such a global
simulation yielding buoyant loops represents a significant step forward
in combining numerical models of dynamo action and flux emergence.
---------------------------------------------------------
Title: Convection and dynamo action in B stars
Authors: Augustson, Kyle C.; Brun, Allan S.; Toomre, Juri
2011IAUS..271..361A Altcode: 2010arXiv1011.1016A
Main-sequence massive stars possess convective cores that likely
harbor strong dynamo action. To assess the role of core convection
in building magnetic fields within these stars, we employ the 3-D
anelastic spherical harmonic (ASH) code to model turbulent dynamics
within a 10 M<SUB>solar</SUB> main-sequence (MS) B-type star rotating
at 4 Ω<SUB>solar</SUB>. We find that strong (900 kG) magnetic fields
arise within the turbulence of the core and penetrate into the stably
stratified radiative zone. These fields exhibit complex, time-dependent
behavior including reversals in magnetic polarity and shifts between
which hemisphere dominates the total magnetic energy.
---------------------------------------------------------
Title: Onward from solar convection to dynamos in cores of massive
stars
Authors: Toomre, Juri
2011IAUS..271..347T Altcode:
We reflect upon a few of the research challenges in stellar convection
and dynamo theory that are likely to be addressed in the next five
or so years. These deal firstly with the Sun and continuing study of
the two boundary layers at the top and bottom of its convection zone,
namely the tachocline and the near-surface shear layer, both of which
are likely to have significant roles in how the solar dynamo may be
operating. Another direction concerns studying core convection and
dynamo action within the central regions of more massive A, B and O-type
stars, for the magnetism may have a key role in controlling the winds
from these stars, thus influencing their ultimate fate. Such studies
of the interior dynamics of massive stars are becoming tractable with
recent advances in codes and supercomputers, and should also be pursued
with some vigor.
---------------------------------------------------------
Title: Global-scale wreath-building dynamos in stellar convection
zones
Authors: Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha;
Miesch, Mark S.; Toomre, Juri
2011IAUS..271...78B Altcode: 2010arXiv1011.0445B
When stars like our Sun are young they rotate rapidly and are very
magnetically active. We explore dynamo action in rapidly rotating suns
with the 3-D MHD anelastic spherical harmonic (ASH) code. The magnetic
fields built in these dynamos are organized on global-scales into
wreath-like structures that span the convection zone. Wreath-building
dynamos can undergo quasi-cyclic reversals of polarity and such behavior
is common in the parameter space we have been able to explore. These
dynamos do not appear to require tachoclines to achieve their spatial
or temporal organization. Wreath-building dynamos are present to some
degree at all rotation rates, but are most evident in the more rapidly
rotating simulations.
---------------------------------------------------------
Title: Global magnetic cycles in rapidly rotating younger suns
Authors: Nelson, Nicholas J.; Brown, Benjamin P.; Browning, Matthew
K.; Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri
2011IAUS..273..272N Altcode: 2010arXiv1010.6073N
Observations of sun-like stars rotating faster than our current
sun tend to exhibit increased magnetic activity as well as magnetic
cycles spanning multiple years. Using global simulations in spherical
shells to study the coupling of large-scale convection, rotation,
and magnetism in a younger sun, we have probed effects of rotation
on stellar dynamos and the nature of magnetic cycles. Major 3-D MHD
simulations carried out at three times the current solar rotation
rate reveal hydromagnetic dynamo action that yields wreaths of strong
toroidal magnetic field at low latitudes, often with opposite polarity
in the two hemispheres. Our recent simulations have explored behavior in
systems with considerably lower diffusivities, achieved with sub-grid
scale models including a dynamic Smagorinsky treatment of unresolved
turbulence. The lower diffusion promotes the generation of magnetic
wreaths that undergo prominent temporal variations in field strength,
exhibiting global magnetic cycles that involve polarity reversals. In
our least diffusive simulation, we find that magnetic buoyancy coupled
with advection by convective giant cells can lead to the rise of
coherent loops of magnetic field toward the top of the simulated domain.
---------------------------------------------------------
Title: Magnetic Cycles and Meridional Circulation in Global Models
of Solar Convection
Authors: Miesch, Mark S.; Brown, Benjamin P.; Browning, Matthew K.;
Brun, Allan Sacha; Toomre, Juri
2011IAUS..271..261M Altcode: 2010arXiv1009.6184M
We review recent insights into the dynamics of the solar convection
zone obtained from global numerical simulations, focusing on two recent
developments in particular. The first is quasi-cyclic magnetic activity
in a long-duration dynamo simulation. Although mean fields comprise
only a few percent of the total magnetic energy they exhibit remarkable
order, with multiple polarity reversals and systematic variability
on time scales of 6-15 years. The second development concerns the
maintenance of the meridional circulation. Recent high-resolution
simulations have captured the subtle nonlinear dynamical balances with
more fidelity than previous, more laminar models, yielding more coherent
circulation patterns. These patterns are dominated by a single cell in
each hemisphere, with poleward and equatorward flow in the upper and
lower convection zone respectively. We briefly address the implications
of and future of these modeling efforts.
---------------------------------------------------------
Title: Exploring the deep convection and magnetism of A-type stars
Authors: Featherstone, Nicholas A.; Browning, Matthew K.; Brun,
Allan Sacha; Toomre, Juri
2011IAUS..273..111F Altcode:
A-type stars have both a near-surface layer of fast convection that
can excite acoustic modes and a deep zone of core convection whose
properties may be probed with asteroseismology. Many A-type stars also
exhibit large magnetic spots that are often attributed to surviving
primordial fields of global scale in the intervening radiative zone. We
have explored the potential for core convection in rotating A-type
stars to build strong magnetic fields through dynamo action. These
3-D simulations using the ASH code provide guidance on the nature
of differential rotation and magnetic fields that may be present in
the deep interiors of these stars, thus informing the asteroseismic
deductions now becoming feasible. Our models encompass the inner 30%
by radius of a two solar mass A-type star, rotating at four times
the solar rate and capturing the convective core and a portion of the
overlying radiative envelope. Convection in these stars drives a strong
retrograde differential rotation and yields a core that is prolate in
shape. When dynamo action is admitted, the convection generates strong
magnetic fields largely in equipartition with the dynamics. Remarkably,
introducing a modest but large-scale external field threading the
radiative envelope (which may be of primordial origin) can substantially
alter the turbulent dynamics of the convective interior. The resulting
convection involves a complex assembly of helical rolls that link
distant portions of the core and stretch and advect magnetic field,
ultimately yielding magnetic fields of super-equipartition strength.
---------------------------------------------------------
Title: Probing Subsurface Flows Around Sunspots with 3-Dimensional
Ring Inversions
Authors: Featherstone, Nicholas Andrew; Hindman, Bradley W.; Thompson,
Michael J.; Toomre, Juri
2011shin.confE...7F Altcode:
We examine convective flows around sunspots as inferred through
ring-analysis helioseismology of MDI Dopplergrams. These flow
measurements were obtained using a novel 3-D inversion procedure
termed Adaptively Resolved Ring-Diagram Inversions, or ARRDI, which
uses sensitivity kernels based on the Born approximation. The ARRDI
algorithm is multi-scale in nature, folding together information from
tiles located at different positions on the solar surface and from
tiles of different sizes, thus enabling fine control of the horizontal
resolution and the probing depth. When we apply ARRDI to sunspots,
we measure outflows persisting to depths of at least 7 Mm. In many
instances, the surface outflow diminishes within the upper 3 Mm
of the convection zone. Beyond 3 Mm, such outflows strengthen and
attain peak amplitudes of 200 m/s at depths of 5-7 Mm. We discuss the
implications of such a two-component outflow for understanding the
magneto-hydrodynamic behavior and evolution of sunspots.
---------------------------------------------------------
Title: Magnetic Cycles in a Convective Dynamo Simulation of a Young
Solar-type Star
Authors: Brown, Benjamin P.; Miesch, Mark S.; Browning, Matthew K.;
Brun, Allan Sacha; Toomre, Juri
2011ApJ...731...69B Altcode: 2011arXiv1102.1993B
Young solar-type stars rotate rapidly and many are magnetically
active. Some appear to undergo magnetic cycles similar to the 22 yr
solar activity cycle. We conduct simulations of dynamo action in rapidly
rotating suns with the three-dimensional magnetohydrodynamic anelastic
spherical harmonic (ASH) code to explore dynamo action achieved in
the convective envelope of a solar-type star rotating at five times
the current solar rotation rate. We find that dynamo action builds
substantial organized global-scale magnetic fields in the midst of the
convection zone. Striking magnetic wreaths span the convection zone
and coexist with the turbulent convection. A surprising feature of this
wreath-building dynamo is its rich time dependence. The dynamo exhibits
cyclic activity and undergoes quasi-periodic polarity reversals where
both the global-scale poloidal and toroidal fields change in sense on
a roughly 1500 day timescale. These magnetic activity patterns emerge
spontaneously from the turbulent flow and are more organized temporally
and spatially than those realized in our previous simulations of the
solar dynamo. We assess in detail the competing processes of magnetic
field creation and destruction within our simulations that contribute to
the global-scale reversals. We find that the mean toroidal fields are
built primarily through an Ω-effect, while the mean poloidal fields
are built by turbulent correlations which are not well represented by
a simple α-effect. During a reversal the magnetic wreaths propagate
toward the polar regions, and this appears to arise from a poleward
propagating dynamo wave. As the magnetic fields wax and wane in
strength and flip in polarity, the primary response in the convective
flows involves the axisymmetric differential rotation which varies on
similar timescales. Bands of relatively fast and slow fluid propagate
toward the poles on timescales of roughly 500 days and are associated
with the magnetic structures that propagate in the same fashion. In
the Sun, similar patterns are observed in the poleward branch of the
torsional oscillations, and these may represent poleward propagating
magnetic fields deep below the solar surface.
---------------------------------------------------------
Title: Magnetic Cycles in a Wreath-Building Dynamo Simulation of a
Young Solar-type Star
Authors: Brown, Benjamin; Miesch, M. S.; Browning, M. K.; Brun, A. S.;
Nelson, N. J.; Toomre, J.
2011AAS...21724222B Altcode: 2011BAAS...4324222B
Stars like the Sun build global-scale magnetic fields though dynamo
processes in their convection zones. There, global-scale plasma motions
couple with rotation and likely drive cycles of magnetic activity,
though the exact processes at work in solar and stellar dynamos remain
elusive. Observations of younger suns indicate that they rotate quite
rapidly, have strong magnetic fields at their surfaces, and show
signs of cyclic activity. Here we explore recent 3-D MHD simulations
of younger, more rapidly rotating solar-type stars conducted with
the anelastic spherical harmonic (ASH) code. These simulations of
global-scale convection and dynamo action produce strikingly organized
magnetic structures in the bulk of their convection zones. Wreaths of
magnetic field fill the convection zone and can undergo regular cycles
of polarity reversal. Indeed, we find that cyclic behavior is a common
feature throughout the parameter space we have explored. Though these
magnetic wreaths can coexist with tachoclines of penetration and shear,
they do not rely on that internal boundary layer for their formation or
persistence. Tachoclines may play a less critical role in the stellar
dynamos of younger Suns than has been supposed in solar dynamo theory.
---------------------------------------------------------
Title: Modeling the Near-Surface Shear Layer: Diffusion Schemes
Studied With CSS
Authors: Augustson, Kyle; Rast, Mark; Trampedach, Regner; Toomre, Juri
2011JPhCS.271a2070A Altcode: 2010arXiv1012.4781A
As we approach solar convection simulations that seek to model the
interaction of small-scale granulation and supergranulation and even
larger scales of convection within the near-surface shear layer (NSSL),
the treatment of the boundary conditions and minimization of sub-grid
scale diffusive processes become increasingly crucial. We here assess
changes in the dynamics and the energy flux balance of the flows
established in rotating spherical shell segments that capture much
of the NSSL with the Curved Spherical Segment (CSS) code using two
different diffusion schemes. The CSS code is a new massively parallel
modeling tool capable of simulating 3-D compressible MHD convection with
a realistic solar stratification in rotating spherical shell segments.
---------------------------------------------------------
Title: Magnetic Cycles and Buoyant Magnetic Structures in a Rapidly
Rotating Sun
Authors: Nelson, Nicholas J.; Brown, B. P.; Brun, S.; Miesch, M. S.;
Toomre, J.
2011AAS...21715512N Altcode: 2011BAAS...4315512N
Observations of sun-like stars rotating faster than our current sun
show that they exhibit solar-like magnetic cycles and features, such
as star spots. Using global 3-D simulations to study the coupling
of large-scale convection, rotation, and magnetism in a younger sun,
we have probed the effects of more rapid rotation on stellar dynamos
and the nature of magnetic cycles. Our anelastic spherical harmonics
(ASH) code allows study of the convective envelope, occupying
the outer 30% by radius of a sun-like star. Major MHD simulations
carried out at three times the current solar rotation rate reveal
magnetic dynamo action that can produce wreaths of strong toroidal
magnetic field at low latitudes, often with opposite polarity in the
two hemispheres. The presence of the wreaths is quite surprising, for
they arise as quite persistent global structures amidst the vigorous
and turbulent convection. We have recently explored behavior in
systems with considerably lower diffusivities, achieved with a dynamic
Smagorinsky treatment of unresolved turbulence. The lower levels of
diffusion create magnetic wreaths that undergo prominent variations in
field strength, even exhibiting global magnetic cycles that involve
polarity reversals. Additionally, during the cycle maximum, when
magnetic energies and mean magnetic fields peak, the wreaths possess
buoyant magnetic structures that rise coherently through much of the
convective envelope via a combination of advection by convective upflows
and magnetic buoyancy. We explore aspects of these rising magnetic
structures and the evolving global dynamo action which produces them.
---------------------------------------------------------
Title: Assessing the Deep Interior Dynamics and Magnetism of A-type
Stars
Authors: Featherstone, Nicholas A.; Browning, Matthew K.; Brun,
Allan Sacha; Toomre, Juri
2011JPhCS.271a2068F Altcode:
A-type stars have both a shallow near-surface zone of fast convection
that can excite acoustic modes and a deep zone of core convection
whose properties may be studied through asteroseismology. Many A stars
also exhibit large magnetic spots as they rotate. We have explored the
properties of core convection in rotating A-type stars and their ability
to build strong magnetic fields. These 3-D simulations using the ASH
code may serve to inform asteroseismic deductions of interior rotation
and magnetism that are now becoming feasible. Our models encompass the
inner 30% by radius of a 2 solar mass A-type star, capturing both the
convective core and some of the overlying radiative envelope. Convection
can drive a column of strong retrograde differential rotation and
yield a core prolate in shape. When dynamo action is admitted, the
convection is able to generate strong magnetic fields largely in
equipartition with the dynamics. Introducing a modest external field
(which may be of primordial origin) into the radiative envelope can
substantially alter the turbulent dynamics of the convective core,
yielding magnetic fields of remarkable super-equipartition strength. The
turbulent convection involves a complex assembly of helical rolls that
link distant portions of the core and stretch and advect magnetic field
into broad swathes of strong toroidal field. These simulations reveal
that supercomputing is providing a perspective of the deep dynamics
that may become testable with asteroseismology for these stars.
---------------------------------------------------------
Title: Rotation-rate variations at the tachocline: An update
Authors: Howe, R.; Komm, R.; Hill, F.; Christensen-Dalsgaard, J.;
Larson, T. P.; Schou, J.; Thompson, M. J.; Toomre, J.
2011JPhCS.271a2075H Altcode:
After 15 years of GONG and MDI observations of the solar interior
rotation, we revisit the issue of variations in the rotation rate near
the base of the convection zone. The 1.3-year period seen in the first
few years of the observations disappeared after 2000 and has still
not returned. On the other hand, the agreement between GONG and MDI
observations suggests that variations seen in this region have some
solar origin, whether a true rotation-rate change or possibly mere
stochastic variation; we present a numerical experiment supporting
this contention.
---------------------------------------------------------
Title: The Influence of Tracking Rate on Helioseismic Flow Inferences
Authors: Routh, Swati; Haber, Deborah A.; Hindman, Bradley W.; Bogart,
Richard S.; Toomre, Juri
2011JPhCS.271a2014R Altcode:
Traditionally, most local helioseismic studies of subsurface flows
have removed the large signal due to the Sun's rotation by tracking
the analysis region across the solar surface. In order to work in a
uniformly rotating reference frame, the ring-analysis pipeline of the
recently launched Helioseismic and Magnetic Imager (HMI) will track
all analysis regions at the solid-body Carrington rate. To test this
tracking scheme, we compare flow determinations resulting from two
different tracking schemes. In one scheme we use the HMI pipeline
implementation which tracks at the Carrington rotation rate. In
the other, the tiles are tracked at the local differential surface
rotation rate as measured by Snodgrass (1984). We observe systematic
differences between the flows obtained by the two schemes even after
transforming them to a common frame (Snodgrass frame), with the zonal
flows measured in the Carrington frame being faster by 5-20 m/s.
---------------------------------------------------------
Title: Developing Physics-Based Procedures for Local Helioseismic
Probing of Sunspots and Magnetic Regions
Authors: Birch, Aaron; Braun, D. C.; Crouch, A.; Rempel, M.; Fan,
Y.; Centeno, R.; Toomre, J.; Haber, D.; Hindman, B.; Featherstone,
N.; Duvall, T., Jr.; Jackiewicz, J.; Thompson, M.; Stein, R.; Gizon,
L.; Cameron, R.; Saidi, Y.; Hanasoge, S.; Burston, R.; Schunker, H.;
Moradi, H.
2010AAS...21630805B Altcode:
We have initiated a project to test and improve the local helioseismic
techniques of time-distance and ring-diagram analysis. Our goals are
to develop and implement physics-based methods that will (1) enable the
reliable determinations of subsurface flow, magnetic field, and thermal
structure in regions of strong magnetic fields and (2) be quantitatively
tested with realistic solar magnetoconvection simulations in the
presence of sunspot-like magnetic fields. We are proceeding through a
combination of improvements in local helioseismic measurements, forward
modeling of the helioseismic wavefield, kernel computations, inversions,
and validation through numerical simulations. As improvements over
existing techniques are made they will be applied to the SDO/HMI
observations. This work is funded through the the NASA Heliophysics
Science Division through the Solar Dynamics Observatory (SDO) Science
Center program.
---------------------------------------------------------
Title: Core Convection and Dynamos in Spectral Type O and B Stars
Authors: Augustson, Kyle; Brun, A. S.; Toomre, J.
2010AAS...21642301A Altcode: 2010BAAS...41..835A
Recent observations have revealed that about one-third of O and B type
stars have strong magnetic fields at their surfaces. It is currently
unclear where these fields originate. In order to address this question,
we examine the effects of core convection and magnetic dynamo processes
within massive O and B stars with simulations in rotating spherical
shells using the 3-D Spherical Harmonic (ASH) magnetohydrodynamic code.
---------------------------------------------------------
Title: Modeling the Near-Surface Shear Layer Through Coupled
Simulations of Surface and Deep Convection
Authors: Augustson, Kyle; Hurlburt, N.; DeRosa, M.; Toomre, J.
2010AAS...21640008A Altcode: 2010BAAS...41..855A
We examine the role of small-scale granulation in helping to drive
supergranulation and even larger scales of convection. The granulation
is modeled as localized plumes with statistics taken from surface
convection simulations introduced at the upper boundary of a 3-D
simulation of compressible convection in a rotating spherical shell
segment. With a sufficient number of stochastic plume events compared
to a uniform cooling, we find that supergranular scales are realized,
along with a differential rotation that becomes increasingly solar-like.
---------------------------------------------------------
Title: Persistent Magnetic Wreaths in a Rapidly Rotating Sun
Authors: Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha;
Miesch, Mark S.; Toomre, Juri
2010ApJ...711..424B Altcode: 2010arXiv1011.2831B
When our Sun was young it rotated much more rapidly than
now. Observations of young, rapidly rotating stars indicate that many
possess substantial magnetic activity and strong axisymmetric magnetic
fields. We conduct simulations of dynamo action in rapidly rotating
suns with the three-dimensional magnetohydrodynamic anelastic spherical
harmonic (ASH) code to explore the complex coupling between rotation,
convection, and magnetism. Here, we study dynamo action realized in the
bulk of the convection zone for a system rotating at 3 times the current
solar rotation rate. We find that substantial organized global-scale
magnetic fields are achieved by dynamo action in this system. Striking
wreaths of magnetism are built in the midst of the convection zone,
coexisting with the turbulent convection. This is a surprise, for
it has been widely believed that such magnetic structures should be
disrupted by magnetic buoyancy or turbulent pumping. Thus, many solar
dynamo theories have suggested that a tachocline of penetration and
shear at the base of the convection zone is a crucial ingredient for
organized dynamo action, whereas these simulations do not include
such tachoclines. We examine how these persistent magnetic wreaths
are maintained by dynamo processes and explore whether a classical
mean-field α-effect explains the regeneration of poloidal field. We
find that the global-scale toroidal magnetic fields are maintained by an
Ω-effect arising from the differential rotation, while the global-scale
poloidal fields arise from turbulent correlations between the convective
flows and magnetic fields. These correlations are not well represented
by an α-effect that is based on the kinetic and magnetic helicities.
---------------------------------------------------------
Title: Solar Convective Dynamo Action With A Tachocline
Authors: Featherstone, Nicholas; Brun, A. S.; Miesch, M. S.; Brown,
B. P.; Toomre, J.
2010AAS...21532202F Altcode: 2010BAAS...42..323F
We present continuing simulations of solar-like convection penetrating
into the tachocline at the base of the convection zone and examine
the resulting dynamo action. Prior simulations using the 3-D anelastic
spherical harmonic (ASH) code of convection in a full spherical shell
admitting penetration into a tachocline have yielded differential
rotation profiles whose latitudinal contrast is considerably smaller
than in simulations without penetration. We believe that the relatively
soft stabilizing entropy gradients in the overshooting regions may
have resulted in unusually strong circulations that worked against the
Reynolds stresses, thus diminishing the differential rotation. Here we
turn to ASH simulations with more realistic stiffer entropy gradients
and reduced diffusivities in the radiative zone. We report on the
hydrodynamic balances achieved within the region of penetration that
allows the convection zone to return to differential rotation profiles
in closer accord with helioseismic deductions, including possessing
a tachocline of shear. We then examine the possibilities for dynamo
action in this system and find that weak wreathes of toroidal field,
similar to those found in simulations of faster rotating suns, are
realized in the convection zone. Convective pumping of these fields
into the tachocline leads to the generation of strong axisymmetric
toroidal fields there, with oppositely signed polarities about the
equator. We examine the temporal variation of these magnetic fields
as well as their effects on the angular momentum transport within the
bulk of the convection zone.
---------------------------------------------------------
Title: Wreath-Building Dynamos in Rapidly Rotating Suns
Authors: Brown, Benjamin; Browning, M. K.; Brun, A. S.; Miesch, M. S.;
Toomre, J.
2010AAS...21542415B Altcode: 2010BAAS...42..332B
When stars like our Sun are young, they rotate quite
rapidly. Observations of these young suns indicate that they generally
possess strong magnetic activity. Here we explore 3-D MHD simulations
of dynamo action in rapidly rotating suns. Our simulations with
the anelastic spherical harmonic (ASH) code extend from 0.72 to
0.97 solar radii and thus span the bulk of the stellar convection
zone. We find that these stars achieve strong dynamo action, and
naturally build remarkable global-scale magnetic structures in their
convection zones. These wreaths of magnetism fill the convection zone
and retain coherence over long epochs despite being embedded in the
turbulent convection. This is in striking contrast to many theories
of the global solar dynamo, which is thought to require a tachocline
of shear and penetration at the base of the convection zone to achieve
such structures. Wreath-building dynamos can undergo repeated cycles of
magnetic polarity reversal, with the global-scale magnetic structures
changing their sense on thousand day timescales.
---------------------------------------------------------
Title: Three-Dimensional Simulations of Solar and Stellar Dynamos:
The Influence of a Tachocline
Authors: Miesch, M. S.; Browning, M. K.; Brun, A. S.; Toomre, J.;
Brown, B. P.
2009ASPC..416..443M Altcode: 2008arXiv0811.3032M
We review recent advances in modeling global-scale convection and
dynamo processes with the Anelastic Spherical Harmonic (ASH) code. In
particular, we have recently achieved the first global-scale solar
convection simulations that exhibit turbulent pumping of magnetic
flux into a simulated tachocline and the subsequent organization and
amplification of toroidal field structures by rotational shear. The
presence of a tachocline not only promotes the generation of mean
toroidal flux, but it also enhances and stabilizes the mean poloidal
field throughout the convection zone, promoting dipolar structure with
less frequent polarity reversals. The magnetic field generated by a
convective dynamo with a tachocline and overshoot region is also more
helical overall, with a sign reversal in the northern and southern
hemispheres. Toroidal tachocline fields exhibit little indication of
magnetic-buoyancy instabilities, but may be undergoing magneto-shear
instabilities.
---------------------------------------------------------
Title: Dynamo Action and Wreaths of Magnetism in a Younger Sun
Authors: Brown, B. P.; Browning, M. K.; Brun, A. S.; Miesch, M. S.;
Toomre, J.
2009ASPC..416..369B Altcode:
When our Sun was younger it rotated much more rapidly. Observations of
many young stars indicate that magnetic activity and perhaps dynamo
action are stronger in the rapidly rotating suns. Here we use the
anelastic spherical harmonic (ASH) code to explore 3-D MHD simulations
of the dynamo action that might occur in such younger suns. As a great
surprise, we find that coherent global-scale structures of toroidal
magnetic field are formed in the bulk of the convection zone. These
wreaths of magnetism persist for long periods of time amidst the still
turbulent convection. In contrast to previous solar dynamo simulations,
the wreaths of magnetism formed in these more rapidly rotating suns
do not require a tachocline of penetration and shear at the base of
the convection zone for their creation or survival.
---------------------------------------------------------
Title: Effects of Fossil Magnetic Fields on Convective Core Dynamos
in A-type Stars
Authors: Featherstone, Nicholas A.; Browning, Matthew K.; Brun,
Allan Sacha; Toomre, Juri
2009ApJ...705.1000F Altcode:
The vigorous magnetic dynamo action achieved within the convective cores
of A-type stars may be influenced by fossil magnetic fields within their
radiative envelopes. We study such effects through three-dimensional
simulations that model the inner 30% by radius of a 2 M <SUB>sun</SUB>
A-type star, capturing the convective core and a portion of the
overlying radiative envelope within our computational domain. We
employ the three-dimensional anelastic spherical harmonic code to
model turbulent dynamics within a deep rotating spherical shell. The
interaction between a fossil field and the core dynamo is examined by
introducing a large-scale magnetic field into the radiative envelope
of a mature A star dynamo simulation. We find that the inclusion of
a twisted toroidal fossil field can lead to a remarkable transition
in the core dynamo behavior. Namely, a super-equipartition state can
be realized in which the magnetic energy built by dynamo action is
10-fold greater than the kinetic energy of the convection itself. Such
strong-field states may suggest that the resulting Lorentz forces should
seek to quench the flows, yet we have achieved super-equipartition
dynamo action that persists for multiple diffusion times. This is
achieved by the relative co-alignment of the flows and magnetic fields
in much of the domain, along with some lateral displacements of the
fastest flows from the strongest fields. Convection in the presence of
such strong magnetic fields typically manifests as 4-6 cylindrical rolls
aligned with the rotation axis, each possessing central axial flows that
imbue the rolls with a helical nature. The roll system also possesses
core-crossing flows that couple distant regions of the core. We find
that the magnetic fields exhibit a comparable global topology with
broad, continuous swathes of magnetic field linking opposite sides of
the convective core. We have explored several poloidal and toroidal
fossil field geometries, finding that a poloidal component is essential
for a transition to super-equipartition to occur.
---------------------------------------------------------
Title: Subsurface Circulations Established by Active Regions
Authors: Hindman, Bradley Wade; Haber, Deborah; Toomre, Juri
2009shin.confE..17H Altcode:
Using the local helioseismic technique of ring analysis we deduce
subsurface flows within and surrounding magnetic active regions. We
apply this technique to data from MDI and analyze the resulting flow
fields for durations of several months from each of three consecutive
years. We compute the mean motion of magnetic plage, mean inflow
rates into magnetic complexes and mean circulation speeds around
active regions. We find that the plage within active regions rotates
more rapidly than quiet sun by roughly 20 m/s, yet advects poleward
at the same rate as quiet sun. We also find that almost all active
regions possess a mean inflow (20-30 m/s) and a cyclonic circulation
( 5 m/s) at their peripheries; whereas their cores, where the sunspots
are located, are zones of strong anticyclonic outflow ( 50 m/s).
---------------------------------------------------------
Title: Subsurface Circulations within Active Regions
Authors: Hindman, Bradley W.; Haber, Deborah A.; Toomre, Juri
2009ApJ...698.1749H Altcode: 2009arXiv0904.1575H
Using high-resolution ring analysis, we deduce subsurface flows within
magnetic active regions and within the quiet Sun. With this procedure,
we are capable of measuring flows with a horizontal spatial resolution
of 2° in heliographic angle (or roughly 20 Mm). From the resulting flow
fields we deduce mean inflow rates into active regions, mean circulation
speeds around active regions, and probability density functions (PDFs)
of properties of the flow field. These analyses indicate that active
regions have a zonal velocity that exceeds that of the quiet Sun at
the same latitude by 20 m s<SUP>-1</SUP>, yet active regions advect
poleward at the same rate as the quiet Sun. We also find that almost
all active regions possess a mean inflow (20-30 m s<SUP>-1</SUP>) and
a cyclonic circulation (≈5 m s<SUP>-1</SUP>) at their peripheries,
whereas their cores, where the sunspots are located, are zones of
strong anticyclonic outflow (≈50 m s<SUP>-1</SUP>). From the PDFs,
we find that active regions modify the structure of convection with
a scale greater than that of supergranulation. Instead of possessing
an asymmetry between inflows and outflows (with a larger percentage
of the surface occupied by outflows), as is seen in the quiet Sun,
active regions possess symmetric distributions.
---------------------------------------------------------
Title: Wreathes of Magnetism in Rapidly Rotating Suns
Authors: Brown, Benjamin P.; Browning, Matthew K.; Miesch, Mark S.;
Brun, Allan Sacha; Toomre, Juri
2009arXiv0906.2407B Altcode:
When our Sun was young it rotated much more rapidly than
now. Observations of young, rapidly rotating stars indicate that
many possess substantial magnetic activity and strong axisymmetric
magnetic fields. We conduct simulations of dynamo action in rapidly
rotating suns with the 3-D MHD anelastic spherical harmonic (ASH)
code to explore the complex coupling between rotation, convection
and magnetism. Here we study dynamo action realized in the bulk of
the convection zone for two systems, rotating at three and five times
the current solar rate. We find that substantial organized global-scale
magnetic fields are achieved by dynamo action in these systems. Striking
wreathes of magnetism are built in the midst of the convection zone,
coexisting with the turbulent convection. This is a great surprise,
for many solar dynamo theories have suggested that a tachocline of
penetration and shear at the base of the convection zone is a crucial
ingredient for organized dynamo action, whereas these simulations do
not include such tachoclines. Some dynamos achieved in these rapidly
rotating states build persistent global-scale fields which maintain
amplitude and polarity for thousands of days. In the case at five
times the solar rate, the dynamo can undergo cycles of activity,
with fields varying in strength and even changing polarity. As the
magnetic fields wax and wane in strength, the primary response in
the convective flows involves the axisymmetric differential rotation,
which begins to vary on similar time scales. Bands of relatively fast
and slow fluid propagate toward the poles on time scales of roughly 500
days. In the Sun, similar patterns are observed in the poleward branch
of the torsional oscillations, and these may represent a response to
poleward propagating magnetic field deep below the solar surface.
---------------------------------------------------------
Title: Mean-Field Generation in Turbulent Convective Dynamos: The
Role of a Tachocline
Authors: Miesch, Mark S.; Browning, M. K.; Brun, A. S.; Brown, B. P.;
Toomre, J.
2009SPD....40.0406M Altcode:
Turbulent dynamos tend to generate turbulent magnetic fields. The
Sun exhibits such disordered fields but it also exhibits large-scale
magnetic activity patterns of striking order, including cyclically
varying sunspot distributions and a reversing dipole moment. The
challenge of global solar dynamo theory is to account for such
order. Rotational shear almost certainly plays an essential role,
placing the solar tachocline at center stage. Here we present global
simulations of convective dynamos with and without a tachocline,
focusing on how the presence of a tachocline alters mean field
generation. The presence of a tachocline not only promotes the
generation of mean toroidal flux, but it also enhances and stabilizes
the mean poloidal field throughout the convection zone, promoting
dipolar structure with less frequent polarity reversals. Magnetic fields
generated in the presence of a tachocline are more helical overall,
with opposite senses among hemispheres and among mean and fluctuating
components. Toroidal tachocline fields exhibit little indication of
magnetic buoyancy instabilities but may be undergoing magneto-shear
instabilities.
---------------------------------------------------------
Title: Stochastic Effects of Granulation and Supergranulation Upon
Deep Convection
Authors: Augustson, Kyle; De Rosa, M. L.; Hurlburt, N. E.; Toomre, J.
2009SPD....40.0805A Altcode:
Vigorous fluid motions associated with the observed patterns of
supergranulation, mesogranulation, and granulation play a large
role in the turbulent transport of heat to the solar surface. The
downflows associated with these convective motions plunge from the
surface into the near-surface layers of the Sun bringing cooler,
low entropy material with them. These flow structures may provide
some stochastic effects upon the dynamics of the giant cells of deep
convection that extend into the near-surface regions. To investigate
such dynamics, we have carried out several 3-D numerical simulations of
fully compressible fluids within curved, spherical segments that, at
this stage, approximate conditions near the top of the rotating solar
convection zone. The upper boundary of the segment is stochastically
driven with cool plumes that approximate the spatial and temporal
scales of supergranular cell downflows, in essence creating a network
of supergranular cells. The segment spans 30° in latitude and 30°
in longitude, and has a radial extent of 15% of the solar radius. We
explore the formation and evolution of the boundary layer resulting
from such stochastic driving, and discuss these dynamics in the context
of the near-surface shear layer of the solar convection zone.
---------------------------------------------------------
Title: Marching Toward More Realistic Penetration of Convection into
a Tachocline
Authors: Featherstone, Nicholas; Brun, A. S.; Miesch, M. S.; Toomre, J.
2009SPD....40.0803F Altcode:
The solar convection zone has provided many challenges for the
theoretical modeling of dynamics within our nearest star. The
tachocline, a region of strong shear near the base of the convection
zone, has received much attention due to its likely role in the
generation of the global-scale magnetic fields. The establishment and
maintenance of the solar tachocline has been variously attributed to
angular momentum transport via gravity waves, magnetic torques and
anisotropic mixing processes. Self consistently capturing the turbulent
dynamics of the convection zone and underlying radiative zone through
3-D numerical modeling is difficult due to the wide range of scales
involved. Prior simulations using the 3-D anelastic spherical harmonic
(ASH) code of convection in a full spherical shell admitting penetration
into a stable region below have yielded differential rotation profiles
whose latitudinal contrast is considerably smaller than in simulations
without penetration. We believe that the relatively soft stabilizing
entropy gradients in the overshooting regions may have resulted
in unusually strong circulations that worked against the Reynolds
stresses, thus diminishing the differential rotation. Here we turn
to ASH simulations with more realistic stiffer entropy gradients and
reduced diffusivities in the radiative zone. We report on the balances
achieved within the region of penetration that allows the convection
zone to return to differential rotation profiles in closer accord with
helioseismic deductions, including possessing a tachocline of shear.
---------------------------------------------------------
Title: Global Magnetic Reversal in a Rapidly Rotating Sun
Authors: Nelson, Nicholas J.; Brown, B. P.; Toomre, J.
2009SPD....40.0804N Altcode:
Global MHD simulations of the solar convection zone and a tachocline
of shear at its base have demonstrated that strong bands of toroidal
magnetic field can be built in the tachocline through stretching and
organizing of small-scale fields that have been pumped downward into
it. Recent 3-D simulations of more rapidly rotating suns have revealed
that global-scale wreathes of toroidal magnetic field can even be
achieved in the bulk of the convection zone itself, remarkably without
a tachocline of shear present at its base. Continuing this work, we
simulate a sun without a tachocline, rotating at three times the solar
rate, and at a higher turbulence level than previous simulations. We
find toroidal magnetic wreathes which have large temporal variations
in field strength as they interact with turbulent convection and global
differential rotation, yet rebuild themselves, persisting in the bulk of
the convection zone for thousands of days. These magnetic structures can
even undergo a reversal of global magnetic polarity, and may persist in
this state for some time. We describe here the nature of such a reversal
and the relative timing of changes in the poloidal and toroidal fields.
---------------------------------------------------------
Title: Turbulence, Magnetism, and Shear in Stellar Interiors
Authors: Miesch, Mark S.; Toomre, Juri
2009AnRFM..41..317M Altcode:
Stars can be fascinating settings in which to study intricate couplings
among convection, rotation, magnetism, and shear, usually under
distinctly nonlinear conditions that yield vigorous turbulence. The
emerging flux and the rotation rates of stars can vary widely,
yet there are common elements that must contribute to building and
maintaining the vibrantly evolving magnetic activity they exhibit. Some
of these elements, such as the rotational shear and meridional flows
established by the coupling of convection with rotation, can now be
studied in detail within our nearest star using helioseismology. Major
three-dimensional numerical simulations help refine our intuitions
about such interior dynamics, aided by rapid advances in supercomputing
that are improving the fidelity of the modeling. These developments,
combined with intense thrusts at new high resolution and continuous
observations of solar magnetism and solar oscillations, herald a
promising era for exploring such astrophysical fluid dynamics.
---------------------------------------------------------
Title: Rapidly Rotating Suns and Active Nests of Convection
Authors: Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha;
Miesch, Mark S.; Toomre, Juri
2008ApJ...689.1354B Altcode: 2008arXiv0808.1716B
In the solar convection zone, rotation couples with intensely turbulent
convection to drive a strong differential rotation and achieve complex
magnetic dynamo action. Our Sun must have rotated more rapidly in
its past, as is suggested by observations of many rapidly rotating
young solar-type stars. Here we explore the effects of more rapid
rotation on the global-scale patterns of convection in such stars and
the flows of differential rotation and meridional circulation, which
are self-consistently established. The convection in these systems is
richly time-dependent, and in our most rapidly rotating suns a striking
pattern of localized convection emerges. Convection near the equator in
these systems is dominated by one or two nests in longitude of locally
enhanced convection, with quiescent streaming flow in between them at
the highest rotation rates. These active nests of convection maintain a
strong differential rotation despite their small size. The structure of
differential rotation is similar in all of our more rapidly rotating
suns, with fast equators and slower poles. We find that the total
shear in differential rotation Δ Ω grows with more rapid rotation,
while the relative shear Δ Ω/Ω<SUB>0</SUB> decreases. In contrast,
at more rapid rotation, the meridional circulations decrease in energy
and peak velocities and break into multiple cells of circulation in
both radius and latitude.
---------------------------------------------------------
Title: Structure and Evolution of Giant Cells in Global Models of
Solar Convection
Authors: Miesch, Mark S.; Brun, Allan Sacha; DeRosa, Marc L.;
Toomre, Juri
2008ApJ...673..557M Altcode: 2007arXiv0707.1460M
The global scales of solar convection are studied through
three-dimensional simulations of compressible convection carried out
in spherical shells of rotating fluid that extend from the base of
the convection zone to within 15 Mm of the photosphere. Such modeling
at the highest spatial resolution to date allows study of distinctly
turbulent convection, revealing that coherent downflow structures
associated with giant cells continue to play a significant role in
maintaining the differential rotation that is achieved. These giant
cells at lower latitudes exhibit prograde propagation relative to
the mean zonal flow, or differential rotation, that they establish,
and retrograde propagation of more isotropic structures with vortical
character at mid and high latitudes. The interstices of the downflow
networks often possess strong and compact cyclonic flows. The
evolving giant-cell downflow systems can be partly masked by the
intense smaller scales of convection driven closer to the surface,
yet they are likely to be detectable with the helioseismic probing that
is now becoming available. Indeed, the meandering streams and varying
cellular subsurface flows revealed by helioseismology must be sampling
contributions from the giant cells, yet it is difficult to separate
out these signals from those attributed to the faster horizontal flows
of supergranulation. To aid in such detection, we use our simulations
to describe how the properties of giant cells may be expected to vary
with depth and how their patterns evolve in time.
---------------------------------------------------------
Title: Rapid rotation, active nests of convection and global-scale
flows in solar-like stars
Authors: Brown, B. P.; Browning, M. K.; Brun, A. S.; Miesch, M. S.;
Toomre, J.
2007AN....328.1002B Altcode: 2008arXiv0801.1672B
In the solar convection zone, rotation couples with intensely turbulent
convection to build global-scale flows of differential rotation and
meridional circulation. Our sun must have rotated more rapidly in its
past, as is suggested by observations of many rapidly rotating young
solar-type stars. Here we explore the effects of more rapid rotation
on the patterns of convection in such stars and the global-scale
flows which are self-consistently established. The convection in
these systems is richly time dependent and in our most rapidly
rotating suns a striking pattern of spatially localized convection
emerges. Convection near the equator in these systems is dominated by
one or two patches of locally enhanced convection, with nearly quiescent
streaming flow in between at the highest rotation rates. These active
nests of convection maintain a strong differential rotation despite
their small size. The structure of differential rotation is similar
in all of our more rapidly rotating suns, with fast equators and
slower poles. We find that the total shear in differential rotation,
as measured by latitudinal angular velocity contrast, \Delta \Omega,
increases with more rapid rotation while the relative shear, \Delta
\Omega/ \Omega, decreases. In contrast, at more rapid rotation the
meridional circulations decrease in both energy and peak velocities and
break into multiple cells of circulation in both radius and latitude.
---------------------------------------------------------
Title: Dynamo action in simulations of penetrative solar convection
with an imposed tachocline
Authors: Browning, M. K.; Brun, A. S.; Miesch, M. S.; Toomre, J.
2007AN....328.1100B Altcode:
We summarize new and continuing three-dimensional spherical shell
simulations of dynamo action by convection allowed to penetrate
downward into a tachocline of rotational shear. The inclusion
of an imposed tachocline allows us to examine several processes
believed to be essential in the operation of the global solar dynamo,
including differential rotation, magnetic pumping, and the stretching
and organization of fields within the tachocline. In the stably
stratified core, our simulations reveal that strong axisymmetric
magnetic fields (of ∼ 3000 G strength) can be built, and that those
fields generally exhibit a striking antisymmetric parity, with fields
in the northern hemisphere largely of opposite polarity to those in
the southern hemisphere. In the convection zone above, fluctuating
fields dominate over weaker mean fields. New calculations indicate
that the tendency toward toroidal fields of antisymmetric parity
is relatively insensitive to initial magnetic field configurations;
they also reveal that on decade-long timescales, the magnetic fields
can briefly enter (and subsequently emerge from) states of symmetric
parity. We have not yet observed any overall reversals of the field
polarity, nor systematic latitudinal propagation.
---------------------------------------------------------
Title: Dynamo action in the presence of an imposed magnetic field
Authors: Featherstone, N. A.; Browning, M. K.; Brun, A. S.; Toomre, J.
2007AN....328.1126F Altcode:
Dynamo action within the cores of Ap stars may offer intriguing
possibilities for understanding the persistent magnetic fields observed
on the surfaces of these stars. Deep within the cores of Ap stars,
the coupling of convection with rotation likely yields magnetic dynamo
action, generating strong magnetic fields. However, the surface fields
of the magnetic Ap stars are generally thought to be of primordial
origin. Recent numerical models suggest that a primordial field in
the radiative envelope may possess a highly twisted toroidal shape. We
have used detailed 3-D simulations to study the interaction of such a
twisted magnetic field in the radiative envelope with the core-dynamo
operating in the interior of a 2 solar mass A-type star. The resulting
dynamo action is much more vigorous than in the absence of such a
fossil field, yielding magnetic field strengths (of order 100 kG)
much higher than their equipartition values relative to the convective
velocities. We examine the generation of these fields, as well as the
growth of large-scale magnetic structure that results from imposing
a fossil magnetic field.
---------------------------------------------------------
Title: Strong Dynamo Action in Rapidly Rotating Suns
Authors: Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha;
Miesch, Mark S.; Nelson, Nicholas J.; Toomre, Juri
2007AIPC..948..271B Altcode: 2008arXiv0801.1684B
Stellar dynamos are driven by complex couplings between rotation and
turbulent convection, which drive global-scale flows and build and
rebuild stellar magnetic fields. When stars like our sun are young,
they rotate much more rapidly than the current solar rate. Observations
generally indicate that more rapid rotation is correlated with stronger
magnetic activity and perhaps more effective dynamo action. Here
we examine the effects of more rapid rotation on dynamo action in a
star like our sun. We find that vigorous dynamo action is realized,
with magnetic field generated throughout the bulk of the convection
zone. These simulations do not possess a penetrative tachocline of shear
where global-scale fields are thought to be organized in our sun, but
despite this we find strikingly ordered fields, much like sea-snakes
of toroidal field, which are organized on global scales. We believe
this to be a novel finding.
---------------------------------------------------------
Title: Convective Core Dynamos of A-type Stars in the Presence of
Fossil Magnetic Fields
Authors: Featherstone, N. A.; Browning, M. K.; Brun, A. S.; Toomre, J.
2007AIPC..948..279F Altcode:
The persistent magnetic fields of Ap stars are generally thought to
be of primordial origin, but dynamo generation of magnetic fields may
offer alternative possibilities. Deep within the interiors of such
stars, vigorous core convection likely couples with rotation to yield
magnetic dynamo action, generating strong magnetic fields. Recent
numerical models suggest that a primordial field remaining from the
star's formation may possess a highly twisted toroidal shape in the
radiative interior. We have used detailed 3-D simulations to study the
interaction of such a magnetic field with a dynamo generated within the
core of a 2 solar mass A-type star. Dynamo action realized under these
circumstances is much more vigorous than in the absence of a fossil
field in the radiative envelope, yielding magnetic field strengths (of
order 100 kG) much higher than their equipartition values relative to
the convective velocities. We examine the generation of these fields,
as well as their effect on the complex dynamics of the convective core.
---------------------------------------------------------
Title: Global Models of Solar Convection
Authors: Miesch, Mark S.; Browning, Matthew K.; Brun, Allan Sacha;
Toomre, Juri
2007AIPC..948..149M Altcode:
Convection is fundamental and enigmatic enough to rank high on any
pundit's list of unsolved problems in stellar physics. It is responsible
in large part for why stars shine since most stellar interiors are
at least partially convective. Furthermore, convection plays an
essential role in how stars build magnetic fields. Magnetism in turn
accounts for most short-term solar and stellar variability. Despite
its ubiquity, stellar convection is challenging to model theoretically
or numerically. In this paper we provide an overview of some recent
insights into solar and stellar convection obtained from high-resolution
numerical simulations. Thanks to continuing advances in high performance
computing technology, such simulations continue to achieve unprecedented
parameter regimes revealing turbulent dynamics inaccessible to previous
models. Here we focus in particular on the subtle and profound influence
of the complex boundary layers which exist near the top and bottom of
the solar convection zone.
---------------------------------------------------------
Title: Challenges of magnetism in the turbulent Sun
Authors: Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri
2007IAUS..239..488B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Simulations of solar magnetic dynamo action in the convection
zone and tachocline
Authors: Browning, Matthew K.; Miesch, Mark S.; Brun, Allan Sacha;
Toomre, Juri
2007IAUS..239..510B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Magnetic Dynamo Action In The Convective Cores Of A-type
Stars In The Presence Of Fossil Fields
Authors: Featherstone, Nicholas; Browning, M. K.; Brun, A. S.;
Toomre, J.
2007AAS...210.1702F Altcode: 2007BAAS...39Q.117F
The intense surface magnetism of Ap stars has attracted much
scrutiny. The observed persistent fields are generally thought to be
of primordial origin, but dynamo generation of magnetic fields may
offer alternative possibilities. Deep within the interiors of such
stars, vigorous core convection likely couples with rotation to yield
magnetic dynamo action, generating strong magnetic fields. Recent
numerical models suggest that a primordial field remaining from the
star’s formation may possess a highly twisted toroidal shape in the
radiative interior. We have used detailed 3-D simulations to study the
interaction of such a magnetic field with a dynamo generated within the
core of a 2 solar mass A-type star. Dynamo action realized under these
circumstances is much more vigorous than in the absence of a fossil
field in the radiative envelope, yielding magnetic field strengths (of
order 100 kG) much higher than their equipartition values relative to
the convective velocities. We examine the generation of these fields,
as well as their effect on the complex dynamics of the convective core.
---------------------------------------------------------
Title: Structure and Evolution of Giant Cells in Global Models of
Solar Convection
Authors: Miesch, Mark S.; Brun, A. S.; De Rosa, M. L.; Toomre, J.
2007AAS...210.2217M Altcode: 2007BAAS...39..127M
We present the highest-resolution simulations of global-scale solar
convection so far achieved, dealing with turbulent compressible
flows interacting with rotation in a full spherical shell. The
three-dimensional simulation domain extends from 0.71R-0.98R, close
enough to the photosphere to overlap with solar subsurface weather
(SSW) maps inferred from local helioseismology. The convective patterns
achieved are complex and continually evolving on a time scale of several
days. However, embedded within the intricate downflow network near
the surface are coherent downflow lanes associated with giant cells
which persist for weeks to months and which extend through much of the
convection zone. These coherent downflow lanes are generally confined
to low latitudes and are oriented in a north-south direction. The low
dissipation in these simulations permits a more realistic balance of
forces which yields differential rotation and meridional circulation
profiles in good agreement with those inferred from helioseismology.
---------------------------------------------------------
Title: Round table discussion of session G: MHD convection and dynamos
Authors: Toomre, Juri
2007IAUS..239..494T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Rapid Rotation And Nests Of Convection In Solar-like Stars
Authors: Brown, Benjamin; Browning, M. K.; Brun, A. S.; Miesch, M. S.;
Toomre, J.
2007AAS...210.1703B Altcode: 2007BAAS...39..117B
Earlier in its life our Sun must have rotated considerably more
rapidly, given that its magnetized wind slowly carries away angular
momentum. Indeed many G-type stars are found to rotate rapidly, and
their deep convective envelopes and the dynamos operating there must
sense the effects of rotation. Here we use 3-D simulations to study
the differential rotation and patterns of convection established in
these more rapidly rotating stars. Our simulations with the anelastic
spherical harmonic (ASH) code capture the deep solar convection
zone with a solar-like radial stratification and within a spherical
geometry, which admits global-scale flows. We explore a range of
rotation rates from 1 to 10 times the solar rotation rate. Convection
in the equatorial regions of these rapidly rotating stars shows strong
longitudinal modulation. At the fastest rotation rates, convection is
restricted to active nests spanning compact regions in longitude, with
quiescent streaming flow filling the regions in between. These nests
of convection persist for long periods and drive a strong differential
rotation. Convection at high latitudes is more isotropic but couples
to the equatorial regions through the meridional circulations present
throughout the shell.
---------------------------------------------------------
Title: Dynamo Action, Magnetic Activity, And Rotation In F Stars
Authors: Augustson, Kyle; Brown, B. P.; Brun, A. S.; Toomre, J.
2007AAS...210.1701A Altcode: 2007BAAS...39..117A
The origin of stellar magnetic fields must rest with dynamo
processes occurring deep within a star. Observations of F-type stars
suggest unusual relations between their rotation rates and magnetic
activity. Generally in cooler stars, magnetic activity increases with
more rapid rotation, but, in F-type stars, there is observational
evidence for a sharp transition from this behavior around spectral
type F5. Stars hotter than F5 show an anti-correlation between
magnetic activity and rotation: more rapidly rotating stars seem
to possess weaker magnetic fields, possibly because they have less
efficient dynamos. We have conducted 3-D simulations of compressible
MHD convection with the anelastic spherical harmonic (ASH) code,
in order to study F-type star convection zone dynamics in rotating
spherical shells. Our initial radial stratification is based on stellar
models of stars in the narrow mass range between 1.2 and 1.4 solar
masses. We exhibit the resulting differential rotation profiles and
rich convective behavior realized as the rotation rates of the stars
are increased. We also discuss our preliminary foray into studying
the magnetic dynamo achieved within several models, considering the
effects of rotation rates.
---------------------------------------------------------
Title: Helioseismic Searches for the Elusive Giant Cells of Convection
Authors: Featherstone, Nicholas; Hindman, B. W.; Haber, D. A.;
Toomre, J.
2007AAS...210.2216F Altcode: 2007BAAS...39..127F
The turbulent solar convection zone exhibits a range of scales of
convection which are visible at the solar surface, ranging from
granules ( 1 Mm) to supergranules ( 30 Mm). Numerical simulations of
solar convection carried out in full-spherical shells consistently
reveal even larger scales of convection, termed giant cells, which
may span a few hundred Mm in the horizontal and extend throughout
the depth of the convection zone. Recent correlation tracking of
supergranular motions has revealed the tendency of supergranules to
align themselves in the north-south direction. This alignment may be
due to organization by larger-scale giant-cell motions and is generally
weak, with the strongest alignment occurring at low latitudes. Using
f-mode time-distance helioseismology, we have probed the flow signals
associated with the presence of these giant cells and have found
good agreement with the results from previous correlation tracking
studies. Moreover, we find that the horizontal divergence of our
measured flows exhibit particularly striking alignment at larger scales.
---------------------------------------------------------
Title: Strong Global Dynamo Action in a Younger Sun
Authors: Brown, Benjamin; Brun, A. S.; Miesch, M. S.; Toomre, J.
2007AAS...210.2414B Altcode: 2007BAAS...39..130B
Stellar dynamos are powered by the coupling of rotation, convection and
the global scale flows which are established in these systems. Our Sun
has lost angular momentum through its magnetized wind and once rotated
more rapidly than it currently does. We explore the nature of dynamo
action in a younger sun rotating five times its current rate. Our
explorations employ 3-D simulations of compressible MHD convection
within a spherical shell extending from 0.72 to 0.97 solar radii using
the anelastic spherical harmonic (ASH) code on massively parallel
supercomputers. The dynamo which naturally arises in this convective
system is vigorous and builds organized magnetic structures which
fill the bulk of the convection zone. This is in striking contrast
to the global dynamo thought to operate in the current sun, which
appears to require the pumping of magnetic field into a tachocline of
shear at the base of the convection zone to generate similar magnetic
structures. Particularly in the equatorial regions, we find strong
toroidal fields ( 30 kG) coexisting with the turbulent convection. This
dynamo system exhibits cyclic behavior, with the large-scale toroidal
and poloidal fields switching their polarity.
---------------------------------------------------------
Title: Temporal variations in solar rotation at the bottom of the
convection zone: The current status
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R.;
Schou, J.; Thompson, M. J.; Toomre, J.
2007AdSpR..40..915H Altcode:
We present the most recent results on the short-period variations
in the solar rotation rate near the base of the convection zone. The
1.3-year period which was reported in the early years of solar cycle 23
appears not to persist after 2001, but there are hints of fluctuations
at a different period during the declining phase of the cycle.
---------------------------------------------------------
Title: Helioseismically Determined Near-Surface Flows Underlying a
Quiescent Filament
Authors: Hindman, Bradley W.; Haber, Deborah A.; Toomre, Juri
2006ApJ...653..725H Altcode:
The extended filaments seen in Hα images of the solar disk, and the
corresponding prominences when viewed at the solar limb, are one of
the great hallmarks of solar magnetism. Such arches of magnetic field
and the coronal plasma structures they support are both beautiful and
enigmatic. Many models of filament formation and maintenance invoke the
existence of surface plasma flows, which are used to drive the magnetic
reconnection needed to form twisted loops of flux held down by a coronal
arcade. These flows are typically composed of a converging flow, which
brings flux elements of opposite polarity together, combined with a
tangential shear that stresses the coronal arcade. In this paper we
present helioseismic measurements of near-surface flows underlying a
single quiescent filament lying within a decayed active region. Newly
devised high-resolution ring analyses (HRRA) with both 2° and 4°
spatial resolution were applied to Doppler imaging data provided by the
Michelson Doppler Imager (MDI) instrument on the SOHO spacecraft. A
long-lived filament appearing in 2002 May and April was studied. We
find that the filament channel is a region of vigorous subphotospheric
convection. The largest observed scales of such convection span
the region of weak magnetic field separating the active region's two
polarities. Thus, the magnetic neutral line that forms the spine of the
filament channel tends to lie along the centers of large convection
cells. In temporal and spatial averages of the flow field, we do not
find a systematic converging flow. However, we do detect a significant
shearing flow parallel to the neutral line. This shear takes the form
of two oppositely directed jets, one to either side of the neutral line
and within 20 Mm of the line. The jets produce a net shear in the flow
speed of 30 m s<SUP>-1</SUP> occurring over a distance of 20 Mm.
---------------------------------------------------------
Title: Helioseismic probing of giant-cell convection
Authors: Featherstone, N. A.; Haber, D. A.; Hindman, B. W.; Toomre, J.
2006ESASP.624E.133F Altcode: 2006soho...18E.133F
No abstract at ADS
---------------------------------------------------------
Title: Subsurface convective flows within active regions
Authors: Hindman, B. W.; Haber, D. A.; Toomre, J.
2006ESASP.624E..11H Altcode: 2006soho...18E..11H
No abstract at ADS
---------------------------------------------------------
Title: Large-scale circulations using ring analysis
Authors: Haber, D.; Hindman, B.; Toomre, J.; Bogart, R. S.
2006ESASP.624E..45H Altcode: 2006soho...18E..45H
No abstract at ADS
---------------------------------------------------------
Title: Various dynamical puzzle pieces in the seismic Rubik's cube
Authors: Toomre, J.
2006ESASP.624E...1T Altcode: 2006soho...18E...1T
No abstract at ADS
---------------------------------------------------------
Title: Dynamo Action in the Solar Convection Zone and Tachocline:
Pumping and Organization of Toroidal Fields
Authors: Browning, Matthew K.; Miesch, Mark S.; Brun, Allan Sacha;
Toomre, Juri
2006ApJ...648L.157B Altcode: 2006astro.ph..9153B
We present the first results from three-dimensional spherical shell
simulations of magnetic dynamo action realized by turbulent convection
penetrating downward into a tachocline of rotational shear. This permits
us to assess several dynamical elements believed to be crucial to the
operation of the solar global dynamo, variously involving differential
rotation resulting from convection, magnetic pumping, and amplification
of fields by stretching within the tachocline. The simulations reveal
that strong axisymmetric toroidal magnetic fields (about 3000 G in
strength) are realized within the lower stable layer, unlike in the
convection zone where fluctuating fields are predominant. The toroidal
fields in the stable layer possess a striking persistent antisymmetric
parity, with fields in the northern hemisphere largely of opposite
polarity to those in the southern hemisphere. The associated mean
poloidal magnetic fields there have a clear dipolar geometry, but
we have not yet observed any distinctive reversals or latitudinal
propagation. The presence of these deep magnetic fields appears to
stabilize the sense of mean fields produced by vigorous dynamo action
in the bulk of the convection zone.
---------------------------------------------------------
Title: Introductory - Overview: Close interplay between global
helioseismology and dynamical models
Authors: Toomre, J.
2006IAUJD..17E...1T Altcode:
The nearly continuous full-disk imaging of solar resonant oscillations
with both the ground-based Global Oscillation Network Group (GONG)
and the space-based Michelson Doppler Imager (MDI) on SOHO have
yielded detailed inferences about differential rotation, meridional
circulations, and large-scale streaming flows within the solar
convection zone. Of particular interest has been the evolution of such
dynamical structures, and their coupling to magnetism, variously in the
tachocline of rotational shear at its base and in the near-surface shear
layer. We review properties of such dynamics involving variations in
rotation rates near the tachocline, of propagating banded features in
the differential rotation in the upper reaches of the convection zone,
and of evolving patterns in the circulations there. In addition, local
helioseismic probing shows the presence of striking subsurface flows
appearing variously as meandering jets and a wide range of structured
and possibly cellular flows. These samplings of dynamics proceeding
within the solar convection zone provides challenges and inspiration
for three-dimensional simulations of turbulent convection, rotation
and magnetism in spherical shells now enabled by massively-parallel
supercomputers. We review the interplay between features emerging
from such high-resolution simulations of the solar convection zone and
the richness of dynamics being revealed by helioseismic probing. The
simulations now make good contact with differential rotation profiles
so deduced in the bulk of the convection zone. Yet all models possess
complex downflow structures that extend over most of that zone. Such
large-scale convection so evident in global simulations may now have
been identified in the helioseismic data, with simulations guiding
the manner in which the elusive giant cells may be detected amidst
the intense flows of supergranulation.
---------------------------------------------------------
Title: Solar-Cycle Variations of Internal Structure, Rotation and
Circulations
Authors: Toomre, J.
2006IAUJD...8E..67T Altcode:
Helioseismology is permitting detailed study of structure and dynamics
in the solar interior as the magnetic cycle advances. Although
many International helioseismic projects have contributed, the
nearly continuous Doppler imaging provided for over ten years by the
ground-based Global Oscillation Network Group (GONG) project and the
Michelson Doppler Imager (MDI) on the SOHO spacecraft allow us to
evaluate changes within the sun over a significant fraction of the
22-year activity cycle. Nearly 10 million resonant acoustic modes of
oscillation observable in the solar atmosphere provide probes of flows
and structures over a wide range of depths within the solar convection
zone and the tachocline of rotational shear at its base. The global
magnetic dynamo responsible for the activity cycles is believed to
operate in a distributed manner throughout these regions, but the
principal stretching to achieve strong toroidal magnetic fields
(responsible for the eventual emergence of sunspot pairs) proceeds
in the tachocline. We review the evidence for variations in the
differential rotation observed near the tachocline, of propagating
bands of zonal flow speedup observed in the near-surface shear layer,
and of changes in the meridional circulations as the cycle advances. We
also discuss the evolving patterns of streaming flows known as solar
subsurface weather (SSW) and of their interactions with magnetic active
regions, often exhibiting prominent inflows at shallow depths and strong
outflows deeper down within that near-surface shear layer. Such a range
of clues being provided by helioseismology about the complex dynamics
proceeding with the convection zone are serving to guide efforts to
build self-consistent models of the solar global dynamo.
---------------------------------------------------------
Title: Solar Filament Evolution in the Presence of Subsurface Flows
Authors: Haber, Deborah A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.
2006SPD....37.3202H Altcode: 2006BAAS...38..257H
Many models of filament formation and evolution are driven by
converging and shearing flows in the photosphere and upper convection
zone, where the gas is dense enough to move the magnetic footpoints
of a filament. With our recent development of High-Resolution Ring
Analysis (HRRA) procedures, we are now able to measure flows below
the surface with a horizontal resolution of 2 heliographic degrees
(∼20 Mm). With this HRRA analysis of the flows underlying filaments
and filament channels, we have found evidence of shearing flows along
the neutral line in at least one instance and will be presenting the
results from several more filaments. This research is funded in part
by NASA grants NAG5-12491 and NNG05GM83G.
---------------------------------------------------------
Title: Helioseismic Probing of Giant-Cell Convection
Authors: Featherstone, Nicholas; Haber, D. A.; Hindman, B. W.;
Toomre, J.
2006SPD....37.3201F Altcode: 2006BAAS...38R.257F
The turbulent solar convection zone exhibits a range of scales
of convection which are visible at the solar surface, ranging from
granules ( 1 Mm) to supergranules ( 30 Mm). Numerical simulations of
solar convection carried out in full spherical shells consistently
reveal even larger scales of convection, termed giant cells, which
may span a few hundreds of Mm in the horizontal and extend over much
of the convection zone. Recent correlation tracking of supergranular
motions has revealed the tendency of supergranules to align themselves
in the north-south direction. This alignment is possibly due to
organization by larger-scale giant cell motions and is generally weak,
with the strongest alignment occurring at the equator. Using f-mode
time-distance and specialized averaging and tracking techniques, we
probe for the possible flow signals associated with the presence of
these giant cells near the solar equator.
---------------------------------------------------------
Title: Localized Nests of Convection in Rapidly Rotating Suns
Authors: Brown, Benjamin; Browning, M.; Brun, A.; Toomre, J.
2006SPD....37.3205B Altcode: 2006BAAS...38..258B
Many solar-like stars rotate more rapidly than the sun. Through
their magnetized winds, these stars gradually lose angular momentum
and spin down. By similar processes, our Sun must have rotated more
rapidly in the past than it currently does. We explore the effects
of more rapid rotation upon turbulent stellar convection, studying
full spherical shells that admit global scale flows. We conduct 3-D
simulations of compressible turbulent convection with the anelastic
spherical harmonic (ASH) code on massively parallel supercomputers. For
simplicity, we adopt the radial stratification of the present-day sun
and examine global scale convection in a zone extending from 0.72 to
0.97 solar radii, and consider a range of rotation rates from 1 to 5
times the solar rotation rate. With increasing rotation we observe
that convection at low latitudes becomes spatially modulated in
strength, yielding localized nests of strong convection. These nests
are persistent over very long periods and propagate in longitude at
slower rates than individual convective structures within them. It
is striking that a strong differential rotation is achieved by these
modulated states. The convection at high latitudes is more isotropic
but influenced by the meridional circulations present throughout the
shell. Weak modulation can be recognized even at the solar rotation
rate, with some implications for active magnetic longitudes in the Sun.
---------------------------------------------------------
Title: Solar Differential Rotation Influenced by Latitudinal Entropy
Variations in the Tachocline
Authors: Miesch, Mark S.; Brun, Allan Sacha; Toomre, Juri
2006ApJ...641..618M Altcode:
Three-dimensional simulations of solar convection in spherical shells
are used to evaluate the differential rotation that results as thermal
boundary conditions are varied. In some simulations a latitudinal
entropy variation is imposed at the lower boundary in order to take
into account the coupling between the convective envelope and the
radiative interior through thermal wind balance in the tachocline. The
issue is whether the baroclinic forcing arising from tachocline-induced
entropy variations can break the tendency for numerical simulations of
convection to yield cylindrical rotation profiles, unlike the conical
profiles deduced from helioseismology. As the amplitude of the imposed
variation is increased, cylindrical rotation profiles do give way to
more conical profiles that exhibit nearly radial angular velocity
contours at midlatitudes. Conical rotation profiles are maintained
primarily by the resolved convective heat flux, which transmits entropy
variations from the lower boundary into the convective envelope, giving
rise to baroclinic forcing. The relative amplitude of the imposed
entropy variations is of order 10<SUP>-5</SUP>, corresponding to a
latitudinal temperature variation of about 10 K. The role of thermal
wind balance and tachocline-induced entropy variations in maintaining
the solar differential rotation is discussed.
---------------------------------------------------------
Title: Simulations of Core Convection in Rotating A-Type Stars:
Magnetic Dynamo Action
Authors: Brun, Allan Sacha; Browning, Matthew K.; Toomre, Juri
2005ApJ...629..461B Altcode: 2006astro.ph.10072B
Core convection and dynamo activity deep within rotating A-type
stars of 2 M<SUB>solar</SUB> are studied with three-dimensional
nonlinear simulations. Our modeling considers the inner 30% by
radius of such stars, thus capturing within a spherical domain the
convective core and a modest portion of the surrounding radiative
envelope. The magnetohydrodynamic (MHD) equations are solved using the
anelastic spherical harmonic (ASH) code to examine turbulent flows and
magnetic fields, both of which exhibit intricate time dependence. By
introducing small seed magnetic fields into our progenitor hydrodynamic
models rotating at 1 and 4 times the solar rate, we assess here how
the vigorous convection can amplify those fields and sustain them
against ohmic decay. Dynamo action is indeed realized, ultimately
yielding magnetic fields that possess energy densities comparable to
that of the flows. Such magnetism reduces the differential rotation
obtained in the progenitors, partly by Maxwell stresses that transport
angular momentum poleward and oppose the Reynolds stresses in the
latitudinal balance. In contrast, in the radial direction we find
that the Maxwell and Reynolds stresses may act together to transport
angular momentum. The central columns of slow rotation established in
the progenitors are weakened, with the differential rotation waxing and
waning in strength as the simulations evolve. We assess the morphology
of the flows and magnetic fields, their complex temporal variations,
and the manner in which dynamo action is sustained. Differential
rotation and helical convection are both found to play roles in
giving rise to the magnetic fields. The magnetism is dominated by
strong fluctuating fields throughout the core, with the axisymmetric
(mean) fields there relatively weak. The fluctuating magnetic fields
decrease rapidly with radius in the region of overshooting, and the
mean toroidal fields less so due to stretching by rotational shear.
---------------------------------------------------------
Title: Helioseismic Ring Analyses of Artificial Data Computed for
Two-dimensional Shearing Flows
Authors: Hindman, Bradley W.; Gough, Douglas; Thompson, Michael J.;
Toomre, Juri
2005ApJ...621..512H Altcode:
The local helioseismological technique of ring analysis has been
crucial in the discovery of complex large-scale flows in the Sun's
near-surface shear layer. However, current implementations of
ring-analysis procedures assume that the flow field is horizontally
homogeneous over the analysis region. This assumption is certainly
incorrect, and in the present paper we assess the significance of this
approximation by analyzing artificial data sets computed from models of
horizontal shear flows. We consider the simple case of purely horizontal
and unidirectional flow that varies solely in the horizontal direction
orthogonal to the flow in a piecewise-constant manner. An ensemble
of plane waves is incident on the flow, and the scattered wave field
produced by the prescribed two-dimensional flow is computed to generate
an artificial helioseismic power spectrum. The artificial spectrum
is processed in a manner similar to standard ring analysis, and the
flow field that is thereby inferred is compared with the known imposed
flow. We find that the inferred flow velocity is essentially an average
of the true flow velocity over the region of the analysis, weighted by
the square of the spatial apodization function used in processing the
oscillation signal. Furthermore, the shape of a p-mode line profile
is determined by the distribution of speeds across the analysis region.
---------------------------------------------------------
Title: Simulations of core convection and resulting dynamo action
in rotating A-type stars
Authors: Browning, Matthew K.; Brun, Allan S.; Toomre, Juri
2004IAUS..224..149B Altcode: 2004astro.ph..9703B
We present the results of 3-D nonlinear simulations of magnetic dynamo
action by core convection within A-type stars of 2 M<SUB>⊙</SUB> with
a range of rotation rates. We consider the inner 30% by radius of such
stars, with the spherical domain thereby encompassing the convective
core and a portion of the surrounding radiative envelope. The
compressible Navier-Stokes equations, subject to the anelastic
approximation, are solved to examine highly nonlinear flows that span
multiple scale heights, exhibit intricate time dependence, and admit
magnetic dynamo action. Small initial seed magnetic fields are found
to be amplified greatly by the convective and zonal flows. The central
columns of strikingly slow rotation found in some of our progenitor
hydrodynamic simulations continue to be realized in some simulations
to a lesser degree, with such differential rotation arising from the
redistribution of angular momentum by the nonlinear convection and
magnetic fields. We assess the properties of the magnetic fields thus
generated, the extent of the convective penetration, the magnitude of
the differential rotation, and the excitation of gravity waves within
the radiative envelope.
---------------------------------------------------------
Title: Evolution of Solar Supergranulation
Authors: De Rosa, Marc L.; Toomre, Juri
2004ApJ...616.1242D Altcode:
The structure and evolution of solar supergranulation is studied using
horizontal velocity fields, deduced from applying local correlation
tracking (LCT) techniques to full-disk, line-of-sight Doppler velocity
data observed by the Michelson Doppler Imager on board the Solar
and Heliospheric Observatory spacecraft. Two 45° square regions
of photospheric plasma, one of the quiet Sun and one with increased
magnetic activity, are tracked for as long as they remain visible on
the disk of the Sun (about 6 days), enabling a determination of the
complete life histories of over 3000 supergranules in each region. With
this method, the horizontal outflows associated with the pattern of
supergranulation are revealed with clarity, even for locations near
disk center where little of the horizontal velocity field is projected
into the line of sight. The LCT flow mappings are of sufficient temporal
extent that they can be used to study the complex evolution of a broad
spectrum of supergranules, revealing that merging and fragmentation
events figure prominently in the life histories of more than half of the
supergranules in each data set. Such dynamics lead to many short-lived
supergranules (about 75% of the total population) having lifetimes of
less than 24 hr, coexisting among numerous long-lived supergranules,
many of which exist for several days. Average supergranular lifetimes
lie in the 16-23 hr range, although about 7% of all are recognizable
for time periods of 48 hr or more. The average supergranular cell
diameter lies in the 12-20 Mm range, with smaller cells more prevalent
in areas of greater magnetism. There exists a tendency for larger cells
to preferentially have longer lifetimes when embedded in a region of
increased magnetic flux.
---------------------------------------------------------
Title: Core Convection and Dynamo Action in Rotating A-type Stars
Authors: Browning, M. K.; Brun, A. S.; Toomre, J.
2004AAS...205.3403B Altcode: 2004BAAS...36.1402B
We have carried out 3-D simulations of core convection and dynamo
activity within A-type stars of two solar masses at a range of rotation
rates. Our models consider the inner 30% by radius of such stars, thus
capturing the entire convective core and a portion of the surrounding
radiative envelope within the spherical computational domain. Using
the anelastic spherical harmonic (ASH) code on massively parallel
supercomputers, we solve the compressible MHD equations to examine
highly nonlinear and evolving flows and magnetic fields. Vigorous
dynamo action is realized, with initial seed magnetic fields amplified
by many orders of magnitude and sustained against ohmic decay. The
resulting complex magnetism possesses energy densities comparable to
that in the flows, is structured on many scales, and serves to modify
the convective and zonal flows that gave rise to it. The differential
rotation established in progenitor hydrodynamic simulations is weakened,
and waxes and wanes in strength as the simulations evolve. We discuss
the morphology and evolution of the flows and magnetic fields,
the penetrative properties of the convection, and the nature of the
dynamo process.
---------------------------------------------------------
Title: Simulations of Core Convection and Dynamo Activity in Rotating
A-Type Stars
Authors: Browning, M. K.; Brun, A. S.; Toomre, J.
2004ESASP.559..349B Altcode: 2004soho...14..349B
No abstract at ADS
---------------------------------------------------------
Title: Subphotospheric Flows Near Active Region NOAA 10486
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
Thompson, M. J.
2004ESASP.559..148H Altcode: 2004soho...14..148H
No abstract at ADS
---------------------------------------------------------
Title: Cause of Shrinking Sun Effect in Local Correlation Tracking
and Impacts on the Mapping of Ssw Flows
Authors: Lisle, J.; Toomre, J.
2004ESASP.559..556L Altcode: 2004soho...14..556L
No abstract at ADS
---------------------------------------------------------
Title: Differential Rotation when the Sun Spun Faster
Authors: Brown, B. P.; Browning, M. K.; Brun, A. S.; Toomre, J.
2004ESASP.559..341B Altcode: 2004soho...14..341B
No abstract at ADS
---------------------------------------------------------
Title: Comparison of Solar Subsurface Flows Assessed by Ring and
Time-Distance Analyses
Authors: Hindman, Bradley W.; Gizon, Laurent; Duvall, Thomas L., Jr.;
Haber, Deborah A.; Toomre, Juri
2004ApJ...613.1253H Altcode:
The solar near-surface shear layer exhibits a rich medley of flows
that are now being measured by a variety of local helioseismic
techniques. We present comparisons of the horizontal flows obtained
with two of these techniques, ring and time-distance analyses, applied
to Michelson Doppler Imager (MDI) Dynamics Program data from the years
1998 and 1999. The ring analyses use the frequencies of both f and
p modes in inversions to obtain flows within the near-surface shear
layer as a function of depth. The f-mode time-distance analyses make
velocity inferences just beneath the photosphere. After degrading
the spatial resolution of the time-distance analyses to match the
coarser resolution of the ring analyses, we find that the flows deduced
with the two methods are remarkably similar, with common inflow and
outflow sites as well as agreement in flow direction. The flows from
ring and time-distance analyses are highly correlated with each other
(correlation coefficients ~0.8) direct correspondence of features
in the flows is largely realized in both the quiet-Sun and magnetic
active regions.
---------------------------------------------------------
Title: Time-Distance Helioseismology: a Fourier Transform Method
and Measurement of Reynolds Stresses
Authors: Featherstone, N. A.; Hindman, B. W.; Haber, D. A.; Toomre, J.
2004ESASP.559..428F Altcode: 2004soho...14..428F
No abstract at ADS
---------------------------------------------------------
Title: Comparison of Local Helioseismic Techniques Applied to MDI
Doppler Data
Authors: Hindman, B. W.; Featherstone, N. A.; Haber, D. A.; Musman,
S.; Toomre, J.
2004ESASP.559..460H Altcode: 2004soho...14..460H
No abstract at ADS
---------------------------------------------------------
Title: Global-Scale Turbulent Convection and Magnetic Dynamo Action
in the Solar Envelope
Authors: Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri
2004ApJ...614.1073B Altcode: 2006astro.ph.10073B
The operation of the solar global dynamo appears to involve many
dynamical elements, including the generation of fields by the intense
turbulence of the deep convection zone, the transport of these fields
into the tachocline region near the base of the convection zone,
the storage and amplification of toroidal fields in the tachocline by
differential rotation, and the destabilization and emergence of such
fields due to magnetic buoyancy. Self-consistent magnetohydrodynamic
(MHD) simulations that realistically incorporate all of these processes
are not yet computationally feasible, although some elements can now
be studied with reasonable fidelity. Here we consider the manner in
which turbulent compressible convection within the bulk of the solar
convection zone can generate large-scale magnetic fields through dynamo
action. We accomplish this through a series of three-dimensional
numerical simulations of MHD convection within rotating spherical
shells using our anelastic spherical harmonic (ASH) code on massively
parallel supercomputers. Since differential rotation is a key ingredient
in all dynamo models, we also examine here the nature of the rotation
profiles that can be sustained within the deep convection zone as strong
magnetic fields are built and maintained. We find that the convection
is able to maintain a solar-like angular velocity profile despite the
influence of Maxwell stresses, which tend to oppose Reynolds stresses
and thus reduce the latitudinal angular velocity contrast throughout
the convection zone. The dynamo-generated magnetic fields exhibit a
complex structure and evolution, with radial fields concentrated in
downflow lanes and toroidal fields organized into twisted ribbons
that are extended in longitude and achieve field strengths of up to
5000 G. The flows and fields exhibit substantial kinetic and magnetic
helicity although systematic hemispherical patterns are only apparent in
the former. Fluctuating fields dominate the magnetic energy and account
for most of the back-reaction on the flow via Lorentz forces. Mean
fields are relatively weak and do not exhibit systematic latitudinal
propagation or periodic polarity reversals as in the Sun. This may
be attributed to the absence of a tachocline, i.e., a penetrative
boundary layer between the convection zone and the deeper radiative
interior possessing strong rotational shear. The influence of such a
layer will await subsequent studies.
---------------------------------------------------------
Title: Variations of Solar Subsurface Weather in the Vicinity of
Active Regions
Authors: Brown, B. P.; Haber, D. A.; Hindman, B. W.; Toomre, J.
2004ESASP.559..345B Altcode: 2004soho...14..345B
No abstract at ADS
---------------------------------------------------------
Title: Solar Differential Revealed by Helioseismology and Simulations
of Deep Shells of Turbulent Convection
Authors: Toomre, J.; Brun, A. S.
2004IAUS..215..326T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Spectrum of the Solar Supergranulation: Multiple Nonwave
Components
Authors: Rast, Mark P.; Lisle, Jason P.; Toomre, Juri
2004ApJ...608.1156R Altcode:
It has recently been suggested that the solar supergranulation undergoes
oscillations, with a spectrum of superposed traveling waves of unknown
origin showing excess prograde power to yield superrotation. We show
here that the observed supergranular spectrum does not necessarily
imply a wave origin but is instead consistent with two components of
nonoscillatory bulk motions having differing rotation rates and somewhat
asymmetrically distributed in space. The two components are identified
with solar mesogranulation and supergranulation, and the spatial
asymmetry is shown to be caused by a weak north-south alignment of the
supergranular flows. The source of both the supergranular alignment and
its enhanced rotation is likely underlying giant cell motions. Because
no single rotation rate characterizes all components of a solar image,
the spectral properties, including the Fourier dispersion relation, are
extremely sensitive to the rate at which the solar disk is tracked when
making up the time series. A spuriously wavelike spectrum is obtained
when the image tracking rate falls between the actual mesogranular
and supergranular rotation rates.
---------------------------------------------------------
Title: Looking Deep Within an A-type Star: Core Convection Under
the Influence of Rotation
Authors: Brun, A. S.; Browning, M.; Toomre, J.
2004IAUS..215..388B Altcode: 2003astro.ph..2598B
The advent of massively parallel supercomputing has begun to permit
explicit 3--D simulations of turbulent convection occurring within the
cores of early-type main sequence stars. Such studies should complement
the stellar structure and evolution efforts that have so far largely
employed 1--D nonlocal mixing length descriptions for the transport,
mixing and overshooting achieved by core convection. We have turned
to A-type stars as representative of many of the dynamical challenges
raised by core convection within rotating stars. The differential
rotation and meridional circulations achieved deep within the star by
the convection, the likelihood of sustained magnetic dynamo action
there, and the bringing of fresh fuel into the core by overshooting
motions, thereby influencing main sequence lifetimes, all constitute
interesting dynamical questions that require detailed modelling
of global-scale convection. Using our anelastic spherical harmonic
(ASH) code tested on the solar differential rotation problem, we have
conducted a series of 3--D spherical domain simulations that deal with
a simplified description of the central regions of rotating A-type
stars, i.e a convectively unstable core is surrounded by a stable
radiative envelope. A sequence of 3--D simulations are used to assess
the properties of the convection (its global patterns, differential
rotation, meridional circulations, extent and latitudinal variation of
the overshooting) as transitions are made between laminar and turbulent
states by changing the effective diffusivities, rotation rates, and
subadiabaticity of the radiative exterior. We report on the properties
deduced from these models for both the extent of penetration and the
profile of rotation sustained by the convection.
---------------------------------------------------------
Title: Simulations of Core Convection Dynamos in Rotating A-type Stars
Authors: Browning, M.; Brun, A. S.; Toomre, J.
2004IAUS..215..376B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Persistent North-South Alignment of the Solar Supergranulation
Authors: Lisle, Jason P.; Rast, Mark P.; Toomre, Juri
2004ApJ...608.1167L Altcode:
We have found evidence of an alignment of the solar supergranulation
in the direction parallel to the Sun's rotation axis. Signatures
of the alignment are apparent in both time-averaged images and in
three-dimensional power spectra. The north-south organization is
persistent in time, extending over many supergranular lifetimes. It
occurs over a wide latitudinal extent, to +/-60°, and shows variation
on a 10°-30° scale. These properties, as well as the rotation rate
of the pattern, suggest a underlying larger scale dynamical cause. We
examine a mechanism by which giant cell motions may contribute to
such alignment.
---------------------------------------------------------
Title: Subphotospheric Flows Around Active Region NOAA 10486
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
Thompson, M. J.; LoHCo Team
2004AAS...204.0211H Altcode: 2004BAAS...36Q.669H
We have used MDI Dynamics Program Doppler data taken between October
18th and November 15th 2003 to study the interaction of solar subsurface
flows with NOAA 10486, one of the most dynamic active regions of the
past solar cycle. Using the local helioseismic techniques of ring and
time-distance analyses, we assess the horizontal flows that surrounded
and permeated this region and how they varied with depth in the upper
14 Mm of the convection zone. We examine and identify structures in the
flow field that may have been associated with the energetic flares that
occurred during the period of observation. This research is in part
supported by NASA through grants NAG5-11920, NAG5-10917, and NAG5-12491.
---------------------------------------------------------
Title: Simulations of Core Convection and Dynamo Activity in A-type
Stars at a Range of Rotation Rates
Authors: Browning, M. K.; Brun, A. S.; Toomre, J.
2004AAS...204.0707B Altcode: 2004BAAS...36..786B
We present the results of nonlinear 3--D simulations of magnetic dynamo
action by core convection within A-type stars of 2 solar masses, at a
range of rotation rates. We consider the inner 30% by radius of such
stars, with the spherical domain thereby encompassing the convective
core and a portion of the surrounding radiative envelope. We solve the
compressible Navier-Stokes equations in the anelastic approximation to
examine highly nonlinear flows that span multiple scale heights, exhibit
intricate time dependence, and admit magnetic dynamo action. Small
initial seed magnetic fields are found to be amplified greatly by the
convective and zonal flows. The central columns of strikingly slow
rotation found in some of our progenitor hydrodynamic simulations
continue to be realized in some simulations to a lesser degree,
with such differential rotation arising from the redistribution of
angular momentum by the nonlinear convection and magnetic fields. We
assess the properties of the magnetic fields thus generated and the
magnitude of the differential rotation sustained as the rotation rate
in our simulations is varied.
---------------------------------------------------------
Title: Organized Subsurface Flows near Active Regions
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Thompson, M. J.
2004SoPh..220..371H Altcode:
Local helioseismic techniques, such as ring analysis and time-distance
helioseismology, have already shown that large-scale flows near the
surface converge towards major active regions. Ring analysis has further
demonstrated that at greater depths some active regions exhibit strong
outflows. A critique leveled at the ring-analysis results is that the
Regularized Least Squares (RLS) inversion kernels on which they are
based have negative sidelobes near the surface. Such sidelobes could
result in a surface inflow being misidentified as a diverging outflow
at depth. In this paper we show that the Optimally Located Averages
(OLA) inversion technique, which produces kernels without significant
sidelobes, generates flows markedly similar to the RLS results. Active
regions are universally zones of convergence near the surface, while
large complexes evince strong outflows deeper down.
---------------------------------------------------------
Title: Simulations of Core Convection in Rotating A-Type Stars:
Differential Rotation and Overshooting
Authors: Browning, Matthew K.; Brun, Allan Sacha; Toomre, Juri
2004ApJ...601..512B Altcode: 2003astro.ph.10003B
We present the results of three-dimensional simulations of core
convection within A-type stars of 2 M<SUB>solar</SUB>, at a range of
rotation rates. We consider the inner 30% by radius of such stars,
thereby encompassing the convective core and some of the surrounding
radiative envelope. We utilize our anelastic spherical harmonic
code, which solves the compressible Navier-Stokes equations in the
anelastic approximation, to examine highly nonlinear flows that can
span multiple scale heights. The cores of these stars are found to
rotate differentially, with central cylindrical regions of strikingly
slow rotation achieved in our simulations of stars whose convective
Rossby number (R<SUB>oc</SUB>) is less than unity. Such differential
rotation results from the redistribution of angular momentum by the
nonlinear convection that strongly senses the overall rotation of
the star. Penetrative convective motions extend into the overlying
radiative zone, yielding a prolate shape (aligned with the rotation
axis) to the central region in which nearly adiabatic stratification
is achieved. This is further surrounded by a region of overshooting
motions, the extent of which is greater at the equator than at the
poles, yielding an overall spherical shape to the domain experiencing
at least some convective mixing. We assess the overshooting achieved
as the stability of the radiative exterior is varied and the weak
circulations that result in that exterior. The convective plumes
serve to excite gravity waves in the radiative envelope, ranging from
localized ripples of many scales to some remarkable global resonances.
---------------------------------------------------------
Title: Simulations of core convection in rotating A-type stars:
Magnetic dynamo action
Authors: Browning, M. K.; Brun, A. S.; Toomre, J.
2003AAS...203.8502B Altcode: 2003BAAS...35.1342B
We present the results of 3--D simulations of core convection dynamos
within A-type stars of 2 solar masses, at a range of rotation rates. The
inner 30% by radius of such stars are considered in our calculations,
with the spherical domain thereby encompassing the convective core and
some of the surrounding radiative envelope. We utilize our anelastic
spherical harmonic (ASH) code to examine highly nonlinear flows that can
admit magnetic dynamo action. Small initial seed magnetic fields are
found to be amplified greatly by the convective and zonal flows. The
resulting global fields possess structure on many scales, are strong
enough to influence the convective flows themselves, and persist for
as long as we have continued our calculations. The central columns of
strikingly slow rotation found in some of our progenitor hydrodynamic
simulations continue to be realized here to a lesser degree, with
such differential rotation arising from the redistribution of angular
momentum by the nonlinear convection and magnetic fields. We assess the
properties of the magnetic fields, the extent of convective penetration,
and the excitation of gravity waves within the radiative envelope.
---------------------------------------------------------
Title: The LoHCo Project. 1 -- Comparison of Ring-Diagram Local
Helioseismology on GONG++, MDI and Mt. Wilson Data Sets
Authors: Bogart, R. S.; Schou, J.; Basu, S.; Bolding, J.; Hill, F.;
Howe, R.; Komm, R. W.; Leibacher, J. W.; Toner, C. G.; Corbard, T.;
Haber, D. A.; Hindman, B. W.; Toomre, J.; Rhodes, E. J.; Rose, P. J.;
LoHCo Project Team
2003SPD....34.0804B Altcode: 2003BAAS...35..822B
Full deployment of the GONG+ enhanced observing network in October
2001 and implementation of ring-diagram helioseismology in the
GONG++ analysis pipeline this year has enabled us to make a detailed
intercomparison of results obtained through multiple paths, from
observation through each of the analysis steps. Such comparisons
can provide a certain degree of validation of the implementations
of the analysis procedures, hints of systematic errors, and better
characterization of the observations, possibly leading to improved
calibrations. The Local Helioseismology Comparison (LoHCo) Project
has been established to provide standards for intercomparison of
results obtained with different local helioseismic analysis techniques
applied to the available observational data sources. We present here
a detailed comparison of ring-diagram determinations of localized
sub-surface flows and frequency shifts obtained from both MDI and
GONG in common observing intervals during Carrington Rotation 1988
(2002/3/30 -- 2002/4/26), using both the MDI and the GONG analysis
pipelines. We also present preliminary results of similar analyses of
data obtained by the Mt. Wilson MOF during the same times. <P />This
work is partially supported by grants from NASA and NSF.
---------------------------------------------------------
Title: Comparison of Solar Subsurface Weather Obtained with
Time-Distance Tomography and Ring Analysis
Authors: Hindman, B. W.; Zhao, J.; Haber, D. A.; Kosovichev, A. G.;
Toomre, J.
2003SPD....34.0806H Altcode: 2003BAAS...35R.822H
The near-surface shear layer exhibits a rich medley of flows that
vary in size from granular and supergranular flows to flows of global
scale. The largest of these flows have been dubbed Solar Surface Weather
(SSW), and have been detected with both time-distance tomography and
ring analysis. We present comparisons of synoptic maps of SSW flows
obtained with both techniques from SOI-MDI Dynamics Program data. Both
techniques provide measurements of the flows as a function of depth
through inversion. The time-distance method utilizes only p-mode
oscillations, while the ring analysis uses f modes as well. We find that
the flows obtained with the two helioseismic techniques are remarkably
similar, with common inflow and outflow sites as well as agreement in
the general flow direction. At a depth of roughly 1.5 Mm the Spearman
rank correlation coefficient between maps is on the order of 0.80. As
the depth increases the correlation become weaker. The reduction in the
correlation coefficient with depth is due to the increasing difference
between the vertical resolution kernel of the two seismic techniques.
---------------------------------------------------------
Title: Overview - where do we stand with helioseismology?
Authors: Toomre, Juri
2003ESASP.517....3T Altcode: 2003soho...12....3T
The advent of GONG+ and the selection of the Helioseismic and Magnetic
Imager (HMI) for the Solar Dynamics Observatory (SDO) together promise
a high-resoluton future for helioseismology in probing the internal
dynamics and structure of the sun. We address some of the dynamical
issues in the upper reaches of the solar convection zone that inspire
these observational efforts which seek to understand the complex
couplings between the highly turbulent convection and the intense
magnetism exhibited by the sun. We examine findings to date about
the evolving flows, called Solar Subsurface Weather (SSW), and their
interaction with magnetism deduced from various local helioseismic
approaches. We discuss the substantial efforts that appear to be
required to make these procedures capable of subsurface flows with
GONG+ and HMI over a wide range of depths for much of the visible solar
disk. We shall also review some recent evidence for variability with
advancing solar cycle both within the body of the convection zone and
within its upper shear layer.
---------------------------------------------------------
Title: Comparison of near-surface flows assessed by ring-diagram
and f-mode time-distance analyses
Authors: Hindman, Bradley; Gizon, Laurent; Haber, Deborah; Duval,
Thomas, Jr.; Toomre, Juri
2003ESASP.517..299H Altcode: 2003soho...12..299H
The near-surface shear layer exhibits a rich medley of flows that are
now being measured by time-distance and ring analysis techniques. We
present comparisons of the flows obtained with the two techniques
using SOI-MDI Dynamics Program data from the years 1998 and 1999. The
time-distance analyses utilize f-mode data without depth inversion. The
flows deduced with the two methods are remarkably similar, with common
inflow and outflow sites as well as agreement in the general flow
directions. The direct correspondence of features in the flows is
realized in both quiet and active regions.
---------------------------------------------------------
Title: Transient oscillations near the solar tachocline
Authors: Toomre, Juri; Christensen-Dalsgaard, Jorgen; Hill, Frank;
Howe, Rachel; Komm, Rudolf W.; Schou, Jesper; Thompson, Michael J.
2003ESASP.517..409T Altcode: 2003soho...12..409T
We report on further developments in the 1.3-yr quasi-periodic
oscillations reported by Howe et al. (2000). These are small (6 to 8
nHz peak-to-peak) oscillations in the inferred rotation rate near the
bottom of the convection zone and in the outer part of the radiative
interior. The oscillations are strongest and most coherent at about a
fractional radius of 0.72 in the equatorial region. Further monitoring
of the oscillations near the equator shows that they continued for a
period after the end of the data analyzed by Howe et al., but appear to
have now diminished in amplitude. This is reminiscent of the transient
behavior of similar (1.3 to 1.4 yr) periodicities in solar-wind and
geomagnetic datasets previously reported. We speculate that the near
tachocline oscillation is associated with the rising phase of the
solar cycle. We discuss tests performed to eliminate various possible
explanations of the oscillations due to systematic errors in the data
and in their analyses.
---------------------------------------------------------
Title: Interaction of solar subsurface flows with major active regions
Authors: Haber, Deborah A.; Hindman, Bradley W.; Toomre, Juri
2003ESASP.517..103H Altcode: 2003soho...12..103H
Solar Subsurface Weather (SSW), which consists of complex and meandering
large-scale horizontal flows below the solar surface, has been studied
in detail with ring analyses of SOI-MDI data from SOHO. SSW flows are of
particular significance since they appear to interact and influence the
magnetic fields visible at the surface, with active regions appearing as
zones of convergent flow and possible downflows. Such subsurface flows
over a range of depths can mechanically twist and displace field lines,
possibly leading to unstable magnetic configurations that may flare or
erupt as coronal mass ejections. It is highly likely that such flows
and magnetic fields are broadly linked in their evolution. We have
studied in detail horizontal flow fields in the vicinity of several
major active regions observed during 2001 and 2002, finding that at
shallow depths there is general flow convergence toward these regions
and noticeable flow deflections in the large-scale zonal and meridional
circulations. We have detected strengthening of jet-like features in
the converging flows occurring over the course of several days. These
features are accompanied by prominent diverging outflows at greater
depths. It appears that the large-scale flow fields surrounding active
complexes have a distinct cellular structure that may contribute to both
the overall cohesion of active regions as well as to the movement of
magnetic flux within those regions that can lead to flares and other
eruptive phenomena.
---------------------------------------------------------
Title: Solar Differential Rotation and Magnetism: a 3--D MHD View
Authors: Brun, Allan Sacha; Toomre, Juri
2003IAUJD..12E...7B Altcode:
We discuss recent progresses made in modelling the complex
magnetohydrodynamics of the Sun using our anelastic spherical harmonics
(ASH) code on massively parallel computers. We have conducted 3--D
MHD simulations of compressible convection in spherical shells to
study the coupling between convection rotation and magnetic field
in seeking to understand how the solar differential rotation is
established and maintained. The resulting convection within domains
that capture a good fraction of the bulk of the solar convection zone
is highly time dependent and intricate and is dominated by intermittent
upflows and networks of strong downflows (i.e. plumes). These plumes
play a significant role in yielding Reynolds stresses that serve to
redistribute angular momentum leading to angular velocity profiles
that make good contact with helioseismic deductions. Such complex
convective flows are efficient in amplifying the magnetic energy near
equipartition. The resulting magnetic fields are found to concentrate
around the downflowing networks and to have significant north-south
asymmetry and helicity. But these strong fields yield Maxwell stresses
that seek to speed up the poles and destroy the agreement with
helioseismic observations. So for a given angular velocity profile
the level of magnetism that the Sun can sustain is likely to be limited
---------------------------------------------------------
Title: Bridges between helioseismology and models of convection
zone dynamics
Authors: Toomre, Juri
2003safd.book..299T Altcode:
The sun is a magnetic star whose variable activity has a profound
effect on our technological society. The high speed solar wind and
its energetic particles, mass ejections and flares that affect the
solar-terrestrial interaction all stem from the variability of the
underlying solar magnetic fields. We are in an era of fundamental
discovery about the overall dynamics of the solar interior and its
ability to generate magnetic fields through dynamo action. This has
come about partly through guidance and challenges to theory from
helioseismology as we now observationally probe the interior of this
star. It also rests on our increasing ability to conduct simulations
of the crucial solar turbulent processes using the latest generation
of supercomputers.
---------------------------------------------------------
Title: Solar Turbulence and Magnetism Studied Within a Rotating
Convective Spherical Shell
Authors: Brun, A. S.; Toomre, J.
2003ASPC..293..134B Altcode: 2003astro.ph..2593B; 2003tdse.conf..134B
We discuss recent advances made in modelling the complex
magnetohydrodynamics of the Sun using our anelastic spherical harmonics
(ASH) code. We have conducted extensive 3--D simulations of compressible
convection in rotating spherical shells with and without magnetic
fields, to study the coupling between global-scale convection and
rotation in seeking to understand how the solar differential rotation
is established and maintained. Such simulations capable of studying
fairly turbulent convection have been enabled by massively parallel
supercomputers. The resulting convection within domains that capture
a good fraction of the bulk of the convection zone is highly time
dependent and intricate, and is dominated by intermittent upflows and
networks of strong downflows. A high degree of coherent structures
involving downflowing plumes can be embedded in otherwise chaotic flow
fields. These vortical structures play a significant role in yielding
Reynolds stresses that serve to redistribute angular momentum, leading
to differential rotation profiles with pole-to-equator contrasts of
about 30% in angular velocity, Omega, and some constancy along radial
lines at mid latitudes, thereby making good contact with deductions
from helioseismology. When a magnetic field is introduced, a dynamo
regime can be found that does not destroy the strong differential
rotation achieved in pure hydrodynamics cases. The magnetic fields
are found to concentrate around the downflowing networks and to have
significant north-south asymmetry and helicity.
---------------------------------------------------------
Title: The Internal Rotation of the Sun
Authors: Thompson, Michael J.; Christensen-Dalsgaard, Jørgen; Miesch,
Mark S.; Toomre, Juri
2003ARA&A..41..599T Altcode:
Helioseismology has transformed our knowledge of the Sun's
rotation. Earlier studies revealed the Sun's surface rotation,
but now a detailed observational picture has been built up of the
internal rotation of our nearest star. Unlike the predictions of
stellar-evolution models, the radiative interior is found to rotate
roughly uniformly. The rotation within the convection zone is also
very different from prior expectations, which had been that the
rotation rate would depend primarily on the distance from the rotation
axis. Layers of rotational shear have been discovered at the base of
the convection zone and in the subphotospheric layers. Studies of the
time variation of rotation have uncovered zonal-flow bands, extending
through a substantial fraction of the convection zone, which migrate
over the course of the solar cycle, and there are hints of other
temporal variations and of a jet-like structure. At the same time,
building on earlier work with mean-field models, researchers have made
great progress in supercomputer simulations of the intricate interplay
between turbulent convection and rotation in the Sun's interior. Such
studies are beginning to transform our understanding of how rotation
organizes itself in a stellar interior.
---------------------------------------------------------
Title: Solar Multiscale Convection and Rotation Gradients Studied
in Shallow Spherical Shells
Authors: De Rosa, Marc L.; Gilman, Peter A.; Toomre, Juri
2002ApJ...581.1356D Altcode: 2002astro.ph..9054D
The differential rotation of the Sun, as deduced from helioseismology,
exhibits a prominent radial shear layer near the top of the convection
zone wherein negative radial gradients of angular velocity are
evident in the low- and midlatitude regions spanning the outer 5%
of the solar radius. Supergranulation and related scales of turbulent
convection are likely to play a significant role in the maintenance
of such radial gradients and may influence dynamics on a global scale
in ways that are not yet understood. To investigate such dynamics, we
have constructed a series of three-dimensional numerical simulations
of turbulent compressible convection within spherical shells, dealing
with shallow domains to make such modeling computationally tractable. In
all but one case, the lower boundary is forced to rotate differentially
in order to approximate the influence that the differential rotation
established within the bulk of the convection zone might have upon a
near-surface shearing layer. These simulations are the first models
of solar convection in a spherical geometry that can explicitly
resolve both the largest dynamical scales of the system (of order the
solar radius) as well as smaller scale convective overturning motions
comparable in size to solar supergranulation (20-40 Mm). We find that
convection within these simulations spans a large range of horizontal
scales, especially near the top of each domain, where convection
on supergranular scales is apparent. The smaller cells are advected
laterally by the larger scales of convection within the simulations,
which take the form of a connected network of narrow downflow lanes that
horizontally divide the domain into regions measuring approximately
100-200 Mm across. We also find that the radial angular velocity
gradient in these models is typically negative, especially in the low-
and midlatitude regions. Analyses of the angular momentum transport
indicate that such gradients are maintained by Reynolds stresses
associated with the convection, transporting angular momentum inward
to balance the outward transport achieved by viscous diffusion and
large-scale flows in the meridional plane, a mechanism first proposed
by Foukal & Jokipii and tested by Gilman & Foukal. We suggest
that similar mechanisms associated with smaller scale convection in
the Sun may contribute to the maintenance of the observed radial shear
layer located immediately below the solar photosphere.
---------------------------------------------------------
Title: Solar Subsurface Weather and Possible Giant Cell Signatures
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
Hill, F.
2002AAS...200.0414H Altcode: 2002BAAS...34Q.645H
Helioseismic observations taken with SOI-MDI aboard SOHO have led to
a new era of discovery about complex and evolving dynamics within the
upper solar convection zone. The data now span nearly six years. Using
the technique of ring-diagram analysis applied to MDI Dynamics Program
Doppler data over a large number of regions on the solar disk, we have
generated synoptic maps of horizontal flows at a variety of depths
below the photosphere. These maps have been assembled for all of the
years for which the SOI-MDI Dynamics Program data are available, with
the latest data coming from March 2002. Flows associated with Solar
Subsurface Weather (SSW) are observed to vary from month to month and
year to year, with the largest flows occurring in and around regions
of intense magnetic activity. Longitudinal averages of the flows reveal
that the fast banded zonal flows seen in previous years have now merged
at the equator while the multiple cell structure found in the meridional
circulation within the northern hemisphere over the last four years is
still present at a reduced level in 2002. When the average flows are
removed, it is possible to see areas of cyclonic flow in regions of
quiet sun as well as divergent cells on the order of 30 to 40 degrees
in diameter that might be signatures of giant convection cells. This
research was supported by NAG5-7996.
---------------------------------------------------------
Title: Turbulent Convection under the Influence of Rotation:
Sustaining a Strong Differential Rotation
Authors: Brun, Allan Sacha; Toomre, Juri
2002ApJ...570..865B Altcode: 2002astro.ph..6196B
The intense turbulence present in the solar convection zone is a major
challenge to both theory and simulation as one tries to understand the
origins of the striking differential rotation profile with radius and
latitude that has been revealed by helioseismology. The differential
rotation must be an essential element in the operation of the solar
magnetic dynamo and its cycles of activity, yet there are many
aspects of the interplay between convection, rotation, and magnetic
fields that are still unclear. We have here carried out a series
of three-dimensional numerical simulations of turbulent convection
within deep spherical shells using our anelastic spherical harmonic
(ASH) code on massively parallel supercomputers. These studies of the
global dynamics of the solar convection zone concentrate on how the
differential rotation and meridional circulation are established. We
have addressed two issues raised by previous simulations with
ASH. First, can solutions be obtained that possess the apparent
solar property that the angular velocity Ω continues to decrease
significantly with latitude as the pole is approached? Prior
simulations had most of their rotational slowing with latitude
confined to the interval from the equator to about 45°. Second, can a
strong latitudinal angular velocity contrast ΔΩ be sustained as the
convection becomes increasingly more complex and turbulent? There was
a tendency for ΔΩ to diminish in some of the turbulent solutions
that also required the emerging energy flux to be invariant with
latitude. In responding to these questions, five cases of increasingly
turbulent convection coupled with rotation have been studied along
two paths in parameter space. We have achieved in one case the slow
pole behavior comparable to that deduced from helioseismology and
have retained in our more turbulent simulations a consistently strong
ΔΩ. We have analyzed the transport of angular momentum in establishing
such differential rotation and clarified the roles played by Reynolds
stresses and the meridional circulation in this process. We have found
that the Reynolds stresses are crucial in transporting angular momentum
toward the equator. The effects of baroclinicity (thermal wind) have
been found to have a modest role in the resulting mean zonal flows. The
simulations have produced differential rotation profiles within the bulk
of the convection zone that make reasonable contact with ones inferred
from helioseismic inversions, namely, possessing a fast equator, an
angular velocity difference of about 30% from equator to pole, and
some constancy along radial lines at midlatitudes. Future studies must
address the implications of the tachocline at the base of the convection
zone, and the near-surface shear layer, on that differential rotation.
---------------------------------------------------------
Title: Evolving Submerged Meridional Circulation Cells within the
Upper Convection Zone Revealed by Ring-Diagram Analysis
Authors: Haber, Deborah A.; Hindman, Bradley W.; Toomre, Juri; Bogart,
Richard S.; Larsen, Rasmus M.; Hill, Frank
2002ApJ...570..855H Altcode:
Using the local helioseismic technique of ring-diagram analysis
applied to Michelson Doppler Imager (MDI) Dynamics Program data from
the Solar and Heliospheric Observatory, we have discovered that the
meridional flow within the upper convection zone can develop additional
circulation cells whose boundaries wander in latitude and depth as
the solar cycle progresses. We report on the large-scale meridional
and zonal flows that we observe from 1996 to 2001. In particular, we
discuss the appearance and evolution of a submerged meridional cell
during the years 1998-2001, which arose in the northern hemisphere
and disrupted the orderly poleward flow and symmetry about the equator
that is typically observed. The meridional flows in the southern and
northern hemispheres exhibit striking asymmetry during the past four
years of the advancing solar cycle. Such asymmetry and additional
circulation cells should have profound impact on the transport of
angular momentum and magnetic field within the surface layers. These
flows may have a significant role in the establishment and maintenance
of the near-surface rotational shear layer.
---------------------------------------------------------
Title: Solar Subsurface Weather: Recent Measurements of Flows Using
Ring-Diagram Analysis
Authors: Hindman, B. W.; Haber, D. A.; Toomre, J.; Bogart, R. S.
2002AAS...200.7904H Altcode: 2002BAAS...34..780H
Continuous helioseismic observations from SOI-MDI on SOHO have led to
a new era of discovery about complex and evolving dynamics within the
solar convection zone. Local probing of the Sun's acoustic wave field,
using ring-diagram analysis, has revealed the presence of large-scale
horizontal flows within the near-surface layers of the Sun. These
remarkable weather-like flow patterns, called Solar Subsurface Weather
(SSW), possess intricate patterns that change from one day to the next,
accompanied by more gradually evolving patterns such as banded zonal
flows and meridional circulation cells. Synoptic maps of these flow
structures reveal that solar magnetism strongly modulates flow speeds
and directions with an effect that varies with depth. I will present
out latest measurements of the flows associated with SSW and briefly
discuss the implications of these measurements on the redistribution of
angular momentum and magnetic fields. This research has been supported
by NASA and NSF.
---------------------------------------------------------
Title: Penetration and Overshooting in Turbulent Compressible
Convection
Authors: Brummell, Nicholas H.; Clune, Thomas L.; Toomre, Juri
2002ApJ...570..825B Altcode:
We present the results of a series of high-resolution, three-dimensional
numerical experiments that investigate the nature of turbulent
compressible convective motions extending from a convection zone into
a stable layer below. In such convection, converging flows in the
near-surface cellular convecting network create strong downflowing
plumes that can traverse the multiple scale heights of the convection
zone. Such structures can continue their downward motions beyond the
convecting region, piercing the stable layer, where they are decelerated
by buoyancy braking. If these motions mix entropy to an adiabatic
state below the convection zone, the process is known as penetration;
otherwise it is termed overshooting. We find that in three-dimensional
turbulent compressible convection at the parameters studied, motions
generally overshoot a significant fraction of the local pressure scale
height but do not establish an adiabatic penetrative region, even at
the highest Péclet numbers considered. This is mainly due to the low
filling factor of the turbulent plumes. The scaling of the overshooting
depth with the relative stability S of the two layers is affected by
this lack of true penetration. Only an S<SUP>-1</SUP> dependence is
exhibited, reflecting the existence of a thermal adjustment region
without a nearly adiabatic penetration zone. Rotation about a vertical
axis decreases the depth of overshooting, owing to horizontal mixing
induced by the rotation. For rotation about an inclined axis, turbulent
rotational alignment of the strong downflow structures decreases
the overshooting further at mid-latitudes, but the laminar effects
of cellular roll solutions take over at low latitudes. Turbulent
penetrative convection is quite distinct from its laminar counterpart
and from the equivalent motions in a domain confined by impenetrable
horizontal boundaries. Although overshooting would not be so deep in
the solar case, the lack of true penetration extending the adiabatic
region may explain why helioseismic inferences show little evidence of
the expected abrupt change between the convection zone and the radiative
interior. These results may also provide insight into how overshooting
motions can provide a coupling between the solar convection zone and
the tachocline.
---------------------------------------------------------
Title: Eddies and vortices in ocean basin dynamics
Authors: Siegel, A.; Weiss, Jeffrey B.; Toomre, Juri; McWilliams,
James C.; Berloff, Pavel S.; Yavneh, Irad
2001GeoRL..28.3183S Altcode:
A wind-driven, closed-basin quasi-geostrophic ocean model is computed
at very high horizontal resolution to study the effect of increasing
Reynolds number (Re) on eddy variability. Five numerical simulations
are performed with identical configurations, varying only in horizontal
resolution and viscosity coefficient (and therefore Re). Qualitative
changes in the structure of eddy variability are evident in the dramatic
increase of isolated vortex structures at the highest Re. While the
time-mean kinetic energy is relatively independent of Re, the vortex
emergence contributes to a continual increase with Re of eddy kinetic
energy and meridional vorticity flux. The rate of increase slows
somewhat at the highest Re, indicating the possibility of a regime
where eddy variability becomes insensitive to further increases in Re.
---------------------------------------------------------
Title: Evolving Large-Scale Flows With Advancing Solar Cycle Using
Helioseismic Dense-Pack Ring-Diagram Analyses
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
Hill, F.
2001AGUSM..SP22A02H Altcode:
We have recently completed the first local helioseismic ring-diagram
analysis of the entire SOI-MDI Dynamics Program data. These data sets
include up to three months of continuous Doppler velocity data from
each of the years 1996 through 2000. A single ring-diagram analysis
over a 15<SUP>o</SUP> region of the sun, followed by an inversion
of the frequency shifts thus obtained, yields measurements of the
horizontal velocity field as a function of depth within the upper 14 Mm
of the convection zone beneath that region. By performing the analysis
over a Dense-Pack mosaic of 189 overlapping tiles and repeating the
procedure for each day of data, we have mapped the velocity field as
a function of time over a substantial fraction of the solar disk for
a number of full Carrington rotations. Our studies of the dynamics
of the upper convection zone have revealed the presence of striking
north-south asymmetries in both the zonal and meridional flows as a
function of depth. For example, a small second meridional flow cell
appeared at depths below 10 Mm at latitudes north of 45<SUP>o</SUP>N
in 1998, expanded upwards to 3 Mm in depth at all latitudes above
22<SUP>o</SUP>N in 1999, and then receded again in 2000. Synoptic maps,
formed from nearly 4500 ring-diagram analyses per Carrington rotation,
show that active regions are sites of convergent flow and appear at
the boundaries of the northern meridional cells in 1999. Even finer
sampling grids show that there are steep gradients in the flows within
active regions. Our work has also revealed a relationship between the
fast zonal "torsional oscillation" bands that migrate towards the
equator and the meridional flow as the solar cycle progresses. The
dominantly poleward meridional flow reaches maxima in both hemispheres
at the latitudes at which the zonal fast belts occur. As the zonal fast
belts drift towards the equator, the latitudes of maximal meridional
flow also drift equatorward.
---------------------------------------------------------
Title: Variations in Rotation Rate Within the Solar Convection Zone
From GONG and MDI 1995-2000
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.;
Schou, J.; Thompson, M. J.; Toomre, J.
2001AGUSM..SP31A15H Altcode:
Helioseismic measurements with the Michelson Doppler Imager (MDI)
instrument aboard SOHO, and complementary measurements from the Global
Oscillation Network Group (GONG) project, are revealing changes deep
within the Sun as the solar cycle progresses. We will present the
latest results based on recent data from both experiments, including
flows in the upper part of the convection zone and variations in the
rotation rate near its base.
---------------------------------------------------------
Title: Transport and Storage of Magnetic Field by Overshooting
Turbulent Compressible Convection
Authors: Tobias, Steven M.; Brummell, Nicholas H.; Clune, Thomas L.;
Toomre, Juri
2001ApJ...549.1183T Altcode:
We present the results of a series of numerical experiments that
investigate the transport of magnetic fields by turbulent penetrative
compressible convection. We find that magnetic flux is preferentially
transported downward out of a turbulent convecting region and stored in
a stably stratified region below. This pumping mechanism is believed
to be a crucial component for the operation of a large-scale solar
interface dynamo since it may be responsible for the transport
of flux from the solar convection zone to the stable overshoot
region. The high-resolution three-dimensional simulations show that
efficient pumping occurs as a result of the action of strong coherent
downflowing plumes. The properties of the transport are evaluated as a
function of magnetic field strength, rotation rate, supercriticality,
stiffness of the interface, and configuration. The turbulent pumping of
magnetic flux is remarkably robust and more efficient than its laminar
counterpart. The turbulent convection naturally amplifies magnetic
energy from any existing mean field. The transport of flux from the
convection zone removes the source for this local amplification there,
and thus the peak magnetic energy also comes to reside in the stable
region. This is important for an effective interface dynamo.
---------------------------------------------------------
Title: Fractional Frequency Shifts of Local Helioseismic Modes With
Magnetic Activity Using Ring-Diagram Analysis
Authors: Hindman, B.; Haber, D.; Toomre, J.; Bogart, R. S.
2001IAUS..203..215H Altcode:
Using full-disk Doppler velocity data from SOI-MDI during the advancing
solar cycle from 1996 through 1999, we have computed the local
frequencies of high-degree p modes and f modes over a dense mosaic of
localized regions of the sun using ring-diagram analysis. The motion of
active regions as they rotate across the solar disk is well traced by
changes in the frequencies. Active regions appear as locations of large
positive frequency shifts. Depending on the radial order and wavenumber
of the observed acoustic modes the frequency shifts can be as much as
10 to 30 microHz. Shifts of this amplitude are 20 to 60 times larger
than the shifts in global acoustic oscillations. The magnitude and
frequency dependence of the large frequency shifts are consistent with
those measured in global modes provided the local frequency shifts
are averaged over the solar disk and are scaled to the appropriate
wavenumber regimes. The frequency dependence of the shifts indicates
that the physical phenomena inducing them is largely confined to the
surface layers of the sun, although there is some indication that
there may be a deeper structural component as well. These local area
samplings may help to understand the restructuring of the near-surface
layers of the convection zone by magnetic fields.
---------------------------------------------------------
Title: Comparing local frequency shifts measured through ring-diagram
analysis with global frequency shifts
Authors: Hindman, Bradley W.; Haber, Deborah A.; Toomre, Juri; Bogart,
Richard S.
2001ESASP.464..143H Altcode: 2001soho...10..143H
Using ring-diagram mode fitting of a subset of the MDI Dynamics Program
data called the dense-pack data set (Haber et al. 2000), we measure
the frequencies of high-degree p modes and f modes as a function of
position on the solar disk and of time. Daily maps of the resulting
frequencies reveal that high-degree mode frequencies are spatially and
temporally variable and are composed of the sum of two components. One
component is stationary and is produced primarily by imperfections in
the MDI optics, while the other component is spatially intermittent,
rotates with the solar surface, and is associated with the presence of
active regions. The frequency shifts within active regions can exceed 60
μHz for some wavelengths and mode orders. We remove the instrumentally
dependent portion of the signal and average the resulting frequency
shifts over the solar disk and over time producing a global average. The
frequency and wavenumber dependence of these average frequency shifts
indicates that the physical phenomena inducing the shifts is largely
confined to the surface layers of the sun, although there is evidence
that a small contribution from deeper layers exists. The average
frequency shifts strongly resemble the solar cycle variations that
are observed in the frequencies of global p-mode oscillations of low
harmonic degree.
---------------------------------------------------------
Title: Comparing mode frequencies from MDI and GONG
Authors: Howe, R.; Hill, F.; Basu, S.; Christensen-Dalsgaard, J.;
Komm, R. W.; Munk Larsen, R.; Roth, M.; Schou, J.; Thompson, M. J.;
Toomre, J.
2001ESASP.464..137H Altcode: 2001soho...10..137H
We present results of analyses of MDI and GONG time series covering
the same time intervals, and using both the MDI and GONG peakbagging
algorithms. We discuss some of the likely causes of differences between
the inferred frequencies and frequency splittings. In addition, we
consider the effect of these differences on the results of inversions
for the solar internal rotation and sound speed.
---------------------------------------------------------
Title: Daily variations of large-scale subsurface flows and global
synoptic flow maps from dense-pack ring-diagram analyses
Authors: Haber, Deborah A.; Hindman, Bradley W.; Toomre, Juri; Bogart,
Richard S.; Hill, Frank
2001ESASP.464..209H Altcode: 2001soho...10..209H
Ring-diagram analyses carried out daily on a mosaic of sites spanning
much of the solar disk have allowed the mapping of large-scale flows in
the upper portion of the solar convection zone. Inversion of frequency
splittings from such local helioseismic analyses reveal large-scale
flows, in addition to the mean zonal and meridional flows, that vary
from day-to-day and with depth. We contrast such flow behavior in
regions of active and quiet sun. We also provide synoptic maps based
on dense-pack studies covering three full solar rotations in 1999.
---------------------------------------------------------
Title: Solar cycle changes in convection zone dynamics from MDI and
GONG 1995 - 2000
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.;
Munk Larsen, R.; Schou, J.; Thompson, M. J.; Toomre, J.
2001ESASP.464...19H Altcode: 2001soho...10...19H
The combined GONG and MDI medium-degree helioseismic data sets now cover
just over 5 years and allow us to probe the changing dynamics of the
convection zone in unprecedented detail. Here we present the latest
results from both projects, showing the evolution of the migrating
zonal flows close to the surface and also changes close to and below
the base of the convection zone.
---------------------------------------------------------
Title: Comparison of phase inversion and time-distance analysis of
one-dimensional artificial seismic data
Authors: Gough, D. O.; Sekii, T.; Toomre, J.
2001ESASP.464..207G Altcode: 2001soho...10..207G
We have studied the application of a phase inversion technique (Gough,
Merryfield and Toomre 1991, 1993, 1998; Gough, Sekii and Toomre 1998,
2000) to stochastically excited damped oscillations in an inhomogeneous
one-dimensional loop, using artificial seismic data (Gough, Sekii and
Toomre 2000). It has been found that within a parameter range that might
be relevant to the solar case, strong damping can significantly degrade
inversions for the wave propagation speed. Here we analyse the same
artificial data by a time-distance technique, to compare how the two
techniques differ in their response to the presence of strong damping.
---------------------------------------------------------
Title: Development of multiple cells in meridional flows and evolution
of mean zonal flows from ring-diagram analyses
Authors: Haber, Deborah A.; Hindman, Bradley W.; Toomre, Juri; Bogart,
Richard S.; Hill, Frank
2001ESASP.464..213H Altcode: 2001soho...10..213H
Meridional flows within the solar convection zone have been observed
with both direct Doppler measurements and with local helioseismic
techniques based on ring-diagram analyses and time-distance
methods. Typically these mean flows are poleward with speeds of
roughly 20 m s<SUP>-1</SUP>. Using ring-diagram analyses on a subset
of the MDI Dynamics Program data, called the dense-pack data set, we
find that a deviation from this general behavior occurs in 1999. A
second meridional cell appears below the surface in the northern
hemisphere. At the same time, the mean zonal flows do not reveal any
evidence of this cell. The zonal bands or "torsional oscillations"
continue their steady migration toward the equator.
---------------------------------------------------------
Title: Numerical simulations of supergranular scales of convection
in shallow spherical shells
Authors: De Rosa, Marc L.; Toomre, Juri
2001ESASP.464..595D Altcode: 2001soho...10..595D
The differential rotation of the sun, as deduced from helioseismology,
exhibits a prominent radial shear layer near the top of the convection
zone. Supergranulation and related scales of turbulent convection
are likely to play a significant role in the maintenance of strong
radial gradients in angular velocity which vary with latitude near
the surface. We present results from 3-D numerical simulations of such
turbulent convection in shallow spherical shells, using the anelastic
spherical harmonic (ASH) code running on massively parallel computers
to study the effects of rotation and compressibility on the resulting
highly nonlinear convection. Convection of supergranular nature is
driven by imposing the solar heat flux at the bottom of a shallow
spherical shell located near the top of the convection zone which is
rotating at the mean solar rate. The angular momentum balance in the
shell is studied for cases where a solar-like differential rotation
profile is imposed at the lower boundary. Convection spanning a large
range of horizontal scales is driven within the shell, especially near
the top of the domain. The resulting radial angular velocity gradient
is negative for all latitudes, suggesting that fluid parcels partially
conserve their angular momentum while moving radially.
---------------------------------------------------------
Title: Mean flows in rotating turbulent convective shells
Authors: Brun, Allan Sacha; Toomre, Juri
2001ESASP.464..619B Altcode: 2001soho...10..619B
We conduct numerical simulations of turbulent compressible convection
within rotating spherical shells to model solar differential rotation
and meridional circulation. These 3-D simulations are carried out on
massively parallel computers using the Anelastic Spherical Harmonic
(ASH) code. The evolution of such convection is studied in four cases
which sample several paths in achieving highly turbulent flows that are
able to drive a strong differential rotation from equator to pole. The
resulting angular velocity Ω profiles make reasonable contact with
many aspects of the solar rotation profiles inferred from helioseismic
inversions of both MDI and GONG data. The substantial contrast in Ω
of order 30% achieved in our simulations of turbulent convection is
considerably greater than realized in previous studies.
---------------------------------------------------------
Title: Magnetic Pumping at the Base of the Solar Convection Zone
Authors: Tobias, S. M.; Brummell, N. H.; Toomre, J.
2001IAUS..203..156T Altcode:
We present the results of a series of numerical experiments that
investigate the pumping of magnetic fields by turbulent penetrative
convection. This pumping mechanism, which is responsible for the
transport of flux from the solar convection zone to the stable overshoot
region, is believed to be a crucial component for the operation
of a large-scale solar interface dynamo. The high-resolution three
dimensional simulations show that efficient pumping occurs due to the
action of strong coherent downwards plumes. The pumping depth is then
calculated as a function of magnetic field strength, rotation rate,
supercriticality and stiffness of the interface.
---------------------------------------------------------
Title: Turbulent Convection and Subtleties of Differential Rotation
Within the Sun
Authors: Toomre, J.; Brun, A. Sacha; De Rosa, M.; Elliott, J. R.;
Miesch, M. S.
2001IAUS..203..131T Altcode:
Differential rotation and cycles of magnetic activity are
intimately linked dynamical processes within the deep shell of
highly turbulent convection occupying the outer 200 Mm below the
solar surface. Helioseismology has shown that the angular velocity
Ω within the solar convection zone involves strong shear layers
both near the surface and especially at its base near the interface
with the radiative interior. The tachocline of radial shear there
that varies with latitude is thought to be the site of the global
magnetic dynamo. Most recent continuous helioseismic probing with
MDI on SOHO and from GONG have revealed systematic temporal changes
in Ω with the advancing solar cycle. These include propagating bands
of zonal flow speedup extending from the surface to a depth of about
70 Mm, distinctive out-of-phase vacillations in Ω above and below the
tachocline with a period of about 1.3 years near the equator, a changing
pattern of meridional circulation cells with broken symmetries in the
two hemispheres, and complex speedups and slowdowns in the bulk of
the convection zone. We review these helioseismic findings and their
implications. We also describe current 3-D numerical simulations of
anelastic rotating convection in full spherical shells used to study
the differential rotation that can be established by such turbulence
exhibiting coherent structures. These simulations enabled by massively
parallel computers are making promising contact with aspects of the
Ω profiles deduced from helioseismology, but challenges remain.
---------------------------------------------------------
Title: Interior Solar-Cycle Changes Detected by Helioseismology
Authors: Howe, R.; Hill, F.; Komm, R. W.; Christensen-Dalsgaard, J.;
Munk Larsen, R.; Schou, J.; Thompson, M. J.; Toomre, J.
2001IAUS..203...40H Altcode:
Helioseismic measurements with the MDI instrument aboard SOHO,
and complementary measurements from the GONG network, are revealing
changes deep within the Sun as the solar cycle progresses. We will
present results based on recent data from both experiments, including
variations in the rotation rate deep inside the convection zone.
---------------------------------------------------------
Title: Subsurface Flows with Advancing Solar Cycle Using Dense-Pack
Ring-Diagram Analyses
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
Hill, F.
2001IAUS..203..211H Altcode:
Large-scale horizontal flows within the upper convection zone of
the sun are analyzed using the helioseismic technique of ring-diagram
analysis applied to data from SOI-MDI. We map the velocity field over a
substantial fraction of the solar disk by carrying out local inversion
analyses over a Dense-Pack mosaic of many overlapping sites. There
are substantial changes in subsurface flows at any given site from
one day to the next that appear to be of solar origin. Such mosaics
are processed almost daily for at least two solar rotations during
each of the MDI Dynamics Campaigns from 1996 through 1999. We find
that longitudinally-averaged zonal velocity possess bands of fast and
slow flow. As the solar cycle progresses, the latitudes at which the
fast bands occur migrate towards the equator and vary in their flow
amplitudes. These bands are not symmetric about the solar equator, and
their asymmetry changes with time. The average meridional flow for the
years 1996 to 1998 is primarily poleward, reaching maxima in the two
hemispheres at the latitudes at which the zonal fast belts occur. The
latitudes of maximal meridional flow drift equatorward in time much as
the zonal fast belts. However, in 1999, the meridional circulation in
the northern hemisphere develops a two-celled structure with latitude,
whereas in the southern hemisphere it remains single celled.
---------------------------------------------------------
Title: Solar Interior: Convection Zone
Authors: Toomre, J.
2000eaa..bookE1995T Altcode:
The Sun, like all main sequence stars of moderate mass, possesses a
deep convective envelope just below its surface in which turbulent
fluid motions serve to carry outward the energy flux that results from
nuclear burning within its core. Observations of the Sun reveal complex
flows and magnetic structures that are evidence of highly turbulent
convection just below the surface of this rotating s...
---------------------------------------------------------
Title: New Approach to Study Extended Evolution of Supergranular
Flows and Their Advection of Magnetic Elements
Authors: Lisle, Jason; De Rosa, Marc; Toomre, Juri
2000SoPh..197...21L Altcode:
Using velocity and magnetogram data extracted from the full-disk field
of view of MDI during the 1999 Dynamics Program, we have studied the
dynamics of small-scale magnetic elements (3-7 Mm in size) over time
periods as long as six days while they are readily visible on the
solar disk. By exploiting concurrent time series of magnetograms and
Doppler images, we have compared the motion of magnetic flux elements
with the supergranular velocity field inferred from the correlation
tracking of mesogranular motions. Using this new method (which combines
the results from correlation tracking of mesogranules with detailed
analysis of simultaneous magnetograms), it is now possible to correlate
the motions of the velocity field and magnetic flux for long periods of
time and at high temporal resolution. This technique can be utilized
to examine the long-term evolution of supergranulation and associated
magnetic fields, for it can be applied to data that span far longer
time durations than has been possible previously. As tests of its
efficacy, we are able to use this method to verify many results of
earlier investigations. We confirm that magnetic elements travel at
approximately 350 m s <SUP>−1</SUP> throughout the duration of their
lifetime as they are transported by supergranular outflows. We also
find that the positions of the magnetic flux elements coincide with
the supergranular network boundaries and adjust as the supergranular
network itself evolves over the six days of this data set. Thus
we conclude that this new method permits us to study the extended
evolution of the supergranular flow field and its advection of magnetic
elements. Since small-scale magnetic elements are strongly advected
by turbulent convection, their dynamics can give important insight
into the properties of the subsurface convection.
---------------------------------------------------------
Title: Phase inversion of one-dimensional artificial seismic data
Authors: Gough, D. O.; Sekii, T.; Toomre, J.
2000SoPh..195....1G Altcode:
Oscillations of an inhomogeneous one-dimensional loop have been
simulated for the purpose of examining the effect of excitation and
damping on the sound-speed inversion based on phase analysis. It has
been demonstrated that the procedure is robust against the realization
noise arising from frequent, stochastic excitation of weakly damped
waves, but that strong damping can spoil the inversion.
---------------------------------------------------------
Title: Turbulent Convection, Rotation, and the Solar Dynamo
Authors: Tobias, Steve; Toomre, Juri; Weiss, Nigel
2000astu.progE..30T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Global Models of Turbulent Convection
Authors: Toomre, Juri
2000astu.confE..35T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Local Fractional Frequency Shifts of Helioseismic Modes
Associated With Magnetic Activity Using Ring-Diagram Analyses
Authors: Hindman, B. W.; Haber, D. A.; Toomre, J.; Bogart, R. S.
2000SPD....31.0109H Altcode: 2000BAAS...32..802H
Using full-disk velocity data from SOI-MDI during the advancing solar
cycle from 1996 through 1999, we have computed the local frequencies of
high-degree p modes and f modes over localized regions of the sun. The
frequencies are obtained through ring-diagram mode fitting over
Dense-Pack data sets consisting of mosaics of 189 overlapping tiles,
each tracked separately at the surface rotation rate over 1664-minute
time intervals during the MDI Dynamics Programs. Each tile is 16 degrees
square, and the tile centers are separated by 7.5 degrees in latitude
and longitude. For each observational day and for each tile, we have
computed the frequency shift measured relative to the temporal and
spatial average of the entire set of frequencies sampled over a full
rotation. The magnetic field is computed for each of the 189 regions
using the magnetograms supplied every 90 min by MDI. The motion of
active regions as they rotate across the solar disk is vividly traced by
changes in the frequencies. Active regions appear as locations of large
positive frequency shifts. Depending on the radial order and wavenumber
of the observed acoustic modes the frequency shifts can be as much as
10 to 30 microHz. The magnitude and frequency dependence of the large
frequency shifts are consistent with the far smaller changes measured
in global oscillation frequencies over the solar cycle, provided the
local frequency shifts are averaged over the solar disk and are scaled
to the appropriate wavenumber regimes. The frequency dependence of
the shifts indicates that the physical phenomena inducing the shifts
is largely confined to the surface layers of the sun, although there
is some indication that there may be a deeper structural component as
well. This research was supported by NASA through grants NAG 5-8133
and NAG 5-7996, and by NSF through grant ATM-9731676.
---------------------------------------------------------
Title: Solar-Cycle Changes in Convection-Zone Dynamics from SOI and
GONG Data
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.;
Larsen, R. M.; Schou, J.; Thompson, M. J.; Toomre, J.
2000SPD....31.0113H Altcode: 2000BAAS...32..803H
The combined GONG and MDI medium-degree helioseismic data sets now cover
more than 4.5 years and allow us to probe the changing dynamics of the
convection zone in unprecedented detail. Here we present the latest
results from both projects, showing the evolution of the migrating zonal
flows close to the surface and also changes close to and below the base
of the convection zone. This work utilizes data obtained by the Global
Oscillation Network Group (GONG) project, managed by the National Solar
Observatory, a Division of the National Optical Astronomy Observatories,
which is operated by AURA, Inc. under a cooperative agreement with the
National Science Foundation. SOHO is a joint project of ESA and NASA.
---------------------------------------------------------
Title: Evolving Dynamics of the Supergranular Flow Field
Authors: De Rosa, M. L.; Lisle, J. P.; Toomre, J.
2000SPD....31.0106D Altcode: 2000BAAS...32..802D
We study several large (45-degree square) fields of supergranules
for as long as they remain visible on the solar disk (about 6 days)
to characterize the dynamics of the supergranular flow field and its
interaction with surrounding photospheric magnetic field elements. These
flow fields are determined by applying correlation tracking methods
to time series of mesogranules seen in full-disk SOI-MDI velocity
images. We have shown previously that mesogranules observed in this
way are systematically advected by the larger scale supergranular
flow field in which they are embedded. Applying correlation tracking
methods to such time series yields the positions of the supergranular
outflows quite well, even for locations close to disk center. These
long-duration datasets contain several instances where individual
supergranules are recognizable for time scales as long as 50 hours,
though most cells persist for about 25 hours that is often quoted as a
supergranular lifetime. Many supergranule merging and splitting events
are observed, as well as other evolving flow patterns such as lanes
of converging and diverging fluid. By comparing the flow fields with
the corresponding images of magnetic fields, we confirm the result
that small-scale photospheric magnetic field elements are quickly
advected to the intercellular lanes to form a network between the
supergranular outflows. In addition, we characterize the influence
of larger-scale regions of magnetic flux, such as active regions,
on the flow fields. Furthermore, we have measured even larger-scale
flows by following the motions of the supergranules, but these flow
fields contain a high noise component and are somewhat difficult to
interpret. This research was supported by NASA through grants NAG
5-8133 and NAG 5-7996, and by NSF through grant ATM-9731676.
---------------------------------------------------------
Title: Helioseismic Dense-Pack Ring Diagram Analyses to Study
Evolution of Subsurface Flows With Advancing Solar Cycle
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
Larsen, R. M.; Hill, F.
2000SPD....31.0103H Altcode: 2000BAAS...32..801H
We analyze data obtained from the Michelson Doppler Imager (MDI) on
SOHO in 1996-1999 using the helioseismic ring-diagram technique to
infer large-scale horizontal flows within the upper solar convection
zone. Each separate ring analysis deduces the average flow components
below a 16 degree square region on the solar surface. We map the
velocity field over a substantial fraction of the solar disk by
repeating the analysis over a Dense-Pack mosaic of 189 overlapping
tiles, with each sampling interval spanning 1664 minutes. We process
such a mosaic on a nearly daily schedule and have analyzed two
Carrington rotations (48 days) in 1996 and one or two rotations each
in 1997, 1998, and 1999. There are substantial changes in subsurface
flows at any given site from one day to the next that appear to be of
solar origin. The mean zonal and meridional flows display gradual and
systematic changes. We find that the longitudinally-averaged zonal
velocity, after removing a smooth differential rotation component,
possesses bands of fast and slow flow, much like `torsional
oscillations' first reported from surface Doppler measurements and
recently from global helioseismic assessments. As the solar cycle
progresses, the latitudes at which the fast bands occur migrate towards
the equator. The amplitudes of these banded zonal flows increase with
magnetic activity. Our local-area analyses reveal that these belts
of fast and slow flow are not symmetric about the solar equator, and
their asymmetry changes with time. The average meridional flow (of
typical amplitudes 10-20 m/s) deduced from our samplings for 1996,
1997 and 1998 is primarily poleward and reaches maxima in the two
hemispheres at the latitudes at which the zonal fast belts occur. As
these zonal fast belts drift towards the equator, the latitudes of
maximal meridional flow also drift equatorward. We further find that
in 1999 the meridional circulation in the northern hemisphere has
developed a two-celled structure with latitude, whereas that in the
southern hemisphere is still single celled. This research was supported
by NASA through grants NAG 5-8133 and NAG 5-7996, and by NSF through
grant ATM-9731676.
---------------------------------------------------------
Title: Deeply Penetrating Banded Zonal Flows in the Solar Convection
Zone
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.;
Larsen, R. M.; Schou, J.; Thompson, M. J.; Toomre, J.
2000ApJ...533L.163H Altcode: 2000astro.ph..3121H
Helioseismic observations have detected small temporal variations
of the rotation rate below the solar surface that correspond to the
so-called “torsional oscillations” known from Doppler measurements of
the surface. These appear as bands of slower- and faster-than-average
rotation moving equatorward. Here we establish, using complementary
helioseismic observations over 4 yr from the GONG network and from
the MDI instrument on board SOHO, that the banded flows are not
merely a near-surface phenomenon: rather, they extend downward at
least 60 Mm (some 8% of the total solar radius) and thus are evident
over a significant fraction of the nearly 200 Mm depth of the solar
convection zone.
---------------------------------------------------------
Title: Turbulent Solar Convection and Its Coupling with Rotation:
The Effect of Prandtl Number and Thermal Boundary Conditions on the
Resulting Differential Rotation
Authors: Elliott, J. R.; Miesch, M. S.; Toomre, J.
2000ApJ...533..546E Altcode:
The dynamics of the vigorous convection in the outer envelope of the Sun
must determine the transport of energy, angular momentum, and magnetic
fields and must therefore be responsible for the observed surface
activity and the angular velocity profile inferred helioseismically
from SOI-MDI p-mode frequency splittings. Many different theoretical
treatments have been applied to the problem, ranging from simple
physical models such as mixing-length theory to sophisticated numerical
simulations. Although mixing-length models provide a good first
approximation to the structure of the convection zone, recent progress
has mainly come from numerical simulations. Computational constraints
have until now limited simulations in full spheres to essentially
laminar convection. The angular velocity profiles have shown constancy
on cylinders, in striking contrast to the approximately constant angular
velocity on radial lines inferred for the Sun. In an effort to further
our understanding of the dynamics of the solar convection zone, we have
developed a new computer code that, by exploiting massively parallel
architectures, enables us to study fully turbulent spherical shell
convection. Here we present five fully evolved solutions. Motivated
by the fact that a constant entropy upper boundary condition produces
a latitudinal modulation of the emergent energy flux (of about 10%,
i.e., far larger than is observed for the Sun), three of these solutions
have a constant energy flux upper boundary condition. This leads to a
latitudinal modulation of the specific entropy that breaks the constancy
of the angular velocity on cylinders, making it more nearly constant
on radial lines at midlatitudes. The effect of lowering the Prandtl
number is also considered-highly time-dependent, vortical convective
motions are revealed, and the Reynolds stresses are altered, leading to
a reduced differential rotation. The differential rotation in all of
our simulations shows a balance between driving by Reynolds stresses
and damping by viscosity. This contrasts with the situation in the
Sun, where the effect of viscosity on the mean differential rotation
is almost negligible.
---------------------------------------------------------
Title: Near-Surface Flow Fields Deduced Using Correlation Tracking
and Time-Distance Analyses
Authors: De Rosa, Marc; Duvall, T. L., Jr.; Toomre, Juri
2000SoPh..192..351D Altcode:
Near-photospheric flow fields on the Sun are deduced using two
independent methods applied to the same time series of velocity images
observed by SOI-MDI on SOHO. Differences in travel times between f
modes entering and leaving each pixel measured using time-distance
helioseismology are used to determine sites of supergranular
outflows. Alternatively, correlation tracking analysis of mesogranular
scales of motion applied to the same time series is used to deduce
the near-surface flow field. These two approaches provide the means to
assess the patterns and evolution of horizontal flows on supergranular
scales even near disk center, which is not feasible with direct
line-of-sight Doppler measurements. We find that the locations of the
supergranular outflows seen in flow fields generated from correlation
tracking coincide well with the locations of the outflows determined
from the time-distance analysis, with a mean correlation coefficient
after smoothing of <SUB>s</SUB>=0.890. Near-surface velocity field
measurements can be used to study the evolution of the supergranular
network, as merging and splitting events are observed to occur in these
images. The data consist of one 2048-min time series of high-resolution
(0.6” pixels) line-of-sight velocity images taken by MDI on 1997
January 16 -18 at a cadence of one minute.
---------------------------------------------------------
Title: Solar shear flows deduced from helioseismic dense-pack
samplings of ring diagrams
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
Thompson, M. J.; Hill, F.
2000SoPh..192..335H Altcode:
We report on large-scale horizontal flows in the solar convection zone
and their variability in time and space using a local-helioseismology
technique known as ring-diagram analysis. By performing this analysis
on a dense mosaic of individual regions on the solar disk, i.e.,
a `Dense-Pack' sampling, and repeating the analysis periodically on
several time scales, we are able to assess the variation of horizontal
flows from day-to-day, week-to-week, and year-to-year. We find that
although there are changes in the flows on all these time scales,
there are also basic patterns that persist. On a daily time scale we
observe that the flow is reduced in those areas which are occupied
by large active regions. On somewhat longer time-scales we see bands
of persistent fast and slow zonal flow that are identifiable as
torsional oscillations. As we examine these bands during a series of
years, we find that these bands migrate toward the equator as solar
activity increases. Similarly, the latitudes at which the meridional
flow reaches maximum follow these regions of fast zonal flow as they
migrate equatorwards. These Dense-Pack samplings also reveal substantial
differences in the zonal and meridional flow patterns in the northern
and southern hemispheres.
---------------------------------------------------------
Title: Time Variability of Rotation in Solar Convection Zone From
soi-mdi
Authors: Toomre, J.; Christensen-Dalsgaard, J.; Howe, R.; Larsen,
R. M.; Schou, J.; Thompson, M. J.
2000SoPh..192..437T Altcode:
The variation of rotation in the convection zone over a period of two
years from mid-1996 is studied using inversions of SOI-MDI data. We
confirm the existence of near-surface banded zonal flows migrating
towards the equator from higher latitudes, and reveal that these banded
flows extend substantially beneath the surface, possibly to depths
as great as 70 Mm (10% of the solar radius). Our results also reveal
apparently significant temporal variations in the rotation rate at
high latitudes and in the vicinity of the tachocline over the period
of study.
---------------------------------------------------------
Title: Dynamic Variations at the Base of the Solar Convection Zone
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.;
Larsen, R. M.; Schou, J.; Thompson, M. J.; Toomre, J.
2000Sci...287.2456H Altcode:
We have detected changes in the rotation of the sun near the base of
its convective envelope, including a prominent variation with a period
of 1.3 years at low latitudes. Such helioseismic probing of the deep
solar interior has been enabled by nearly continuous observation of
its oscillation modes with two complementary experiments. Inversion of
the global-mode frequency splittings reveals that the largest temporal
changes in the angular velocity Ω are of the order of 6 nanohertz
and occur above and below the tachocline that separates the sun's
differentially rotating convection zone (outer 30% by radius) from
the nearly uniformly rotating deeper radiative interior beneath. Such
changes are most pronounced near the equator and at high latitudes and
are a substantial fraction of the average 30-nanohertz difference in Ω
with radius across the tachocline at the equator. The results indicate
variations of rotation close to the presumed site of the solar dynamo,
which may generate the 22-year cycles of magnetic activity.
---------------------------------------------------------
Title: Three-dimensional Spherical Simulations of Solar
Convection. I. Differential Rotation and Pattern Evolution Achieved
with Laminar and Turbulent States
Authors: Miesch, Mark S.; Elliott, Julian R.; Toomre, Juri; Clune,
Tom L.; Glatzmaier, Gary A.; Gilman, Peter A.
2000ApJ...532..593M Altcode:
Rotationally constrained convection possesses velocity correlations
that transport momentum and drive mean flows such as differential
rotation. The nature of this transport can be very complex in turbulent
flow regimes, where large-scale, coherent vorticity structures and mean
flows can be established by smaller scale turbulence through inverse
cascades. The dynamics of the highly turbulent solar convection
zone therefore may be quite different than in early global-scale
numerical models, which were limited by computational resources to
nearly laminar flows. Recent progress in high-performance computing
technology and ongoing helioseismic investigations of the dynamics of
the solar interior have motivated us to develop more sophisticated
numerical models of global-scale solar convection. Here we report
three-dimensional simulations of compressible, penetrative convection
in rotating spherical shells in both laminar and turbulent parameter
regimes. The convective structure in the laminar case is dominated
by “banana cells,” but the turbulent case is much more complex,
with an intricate, rapidly evolving downflow network in the upper
convection zone and an intermittent, plume-dominated structure in
the lower convection zone and overshoot region. Convective patterns
generally propagate prograde at low latitudes and retrograde at high
latitudes relative to the local rotation. The differential rotation
profiles show some similarity with helioseismic determinations of
the solar rotation but still exhibit significantly more cylindrical
alignment. Strong, intermittent, vortical downflow lanes and plumes
play an important dynamical role in turbulent flow regimes and are
responsible for significant differences relative to laminar flows with
regard to momentum and energy transport and to the structure of the
overshoot region at the base of the convection zone.
---------------------------------------------------------
Title: Local Fractional Frequency Shifts Used as Tracers of Magnetic
Activity
Authors: Hindman, Bradley; Haber, Deborah; Toomre, Juri; Bogart, Rick
2000SoPh..192..363H Altcode:
Using data from SOI-MDI (Haber et al., 2000), we compute the local
frequencies of high-degree p modes and f modes. The frequencies are
obtained through ring-diagram mode fitting. The Dense-Pack data set
consists of a mosaic of 189 overlapping tiles, each tracked separately
at the surface rotation rate over 1664-min time intervals during the
Dynamics Programs. Each tile is 16° square and the tile centers are
separated by 7.5° in latitude and longitude. For each sampling day and
for each tile, we have computed the frequency shift measured relative to
the temporal and spatial average of the entire set of frequencies. The
motion of active regions as they rotate across the solar disk is vividly
traced by these measurements. Active regions appear as locations of
large positive frequency shifts. If the shifts are averaged over the
solar disk and are scaled down to the appropriate wave number regime,
the magnitude and frequency dependence of the shifts are consistent
with the measured changes in global oscillation frequencies that occur
over the solar cycle. As with the frequency shifts of low-degree global
oscillations, the frequency dependence of the shifts indicates that
the physical phenomena inducing the shifts is confined to the surface
layers of the Sun.
---------------------------------------------------------
Title: Helioseismic detection of temporal variations of solar rotation
rate near the base of the convection zone
Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.;
Larsen, R. M.; Schou, J.; Thompson, M. J.; Toomre, J.
1999AAS...19510702H Altcode: 1999BAAS...31R1530H
The differential rotation of the Sun and its ability to generate
large-scale magnetic fields through cyclic dynamo action appear to be
intimately linked. It is now commonly thought that the global dynamo
behavior responsible for the emergence of active regions is derived
from strong organized toroidal magnetic fields generated by rotational
shear in a thin region (the tachocline) at the base of the convection
zone. The magnetic field could well have a feedback effect on the fluid
motions in the region. We are thus motivated to use helioseismology
to look for changes in rotation profiles near the tachocline as the
Sun's magnetic cycle progresses. This approach has become possible
using frequency-splitting data for p- and f-mode oscillations derived
over four years (from May 1995 to Sept 1999) of full-disk Doppler
observations from the ground-based Global Oscillation Network Group
(GONG) project and from the Michelson Doppler Imager (MDI) experiment
aboard the SOHO spacecraft. Inversions using two different methods of
the splittings from these two independent data sets reveal systematic
variations of the rotation rate close to the base of the convection
zone, with different behavior at low and high latitudes. Notable
are variations of order 6 nHz in rotation rates near the equator,
to be compared with the radial angular velocity contrast across the
tachocline of about 30 nHz. These exhibit several nearly repetitive
changes with a period of about 1.2-1.4 years and appear to be real
changes in the deep convection zone and tachocline rotation rates that
need to be followed as the solar cycle progresses. The GONG project is
managed by the National Solar Observatory, a Division of the National
Optical Astronomy Observatories, which is operated by AURA, Inc. under
a cooperative agreement with the National Science Foundation. SOHO is
a joint project of ESA and NASA.
---------------------------------------------------------
Title: Evolution of Subsurface Zonal and Meridional Flows With
Advancing Solar Cycle Using Helioseismic Dense-Pack Samplings of
Ring Diagrams
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
Larsen, R. M.; Hill, F.
1999AAS...19510701H Altcode: 1999BAAS...31Q1530H
We report on the behavior of large-scale horizontal flows within the
upper convection zone of the sun, using the helioseismic technique of
ring-diagram analysis applied to data from the Michelson Doppler Imager
(MDI) on the SOHO spacecraft. Horizontal flows yield displacements in
the rings of power (at fixed frequency) associated with solar acoustic
waves propagating in different directions below a localized area being
studied. We pass these shifts through an inversion procedure and obtain
measurements of the zonal and meridional flows as a function of depth to
about 10 Mm below the surface. Each separate ring analysis deduces the
average flow below a 16 degree square region on the solar surface. We
map the velocity field over a substantial fraction of the solar disk by
repeating the analysis over a densely packed mosaic of 189 overlapping
tiles (called a Dense-Pack). We process such a mosaic on a nearly daily
schedule and have fully analyzed two Carrington rotations (48 days) in
1996 and one rotation each in 1997, 1998, and 1999 during MDI Dynamics
Campaigns. We find that the longitudinally-averaged zonal velocity,
after removing a smooth differential rotation component, possesses
bands of fast and slow flow, much like `torsional oscillations'
first reported from surface Doppler measurements and recently from
global helioseismic assessments. As the solar cycle progresses,
the latitudes at which the fast bands occur migrate towards the
equator. The amplitudes of these banded zonal flows increase with
magnetic activity. Our local-area analyses reveal that these belts of
fast and slow flow are not symmetric about the solar equator, and their
asymmetry changes with time. The average meridional flow is primarily
poleward and reaches maxima in the two hemispheres at the latitudes
at which the zonal fast belts occur. As these zonal fast belts drift
towards the equator, the latitudes of maximal meridional flow also drift
equatorward. This research was supported by NASA grants NAG 5--8133,
NAG 5--7996 and NAG 5--3077 and by NSF grant ATM-9731676.
---------------------------------------------------------
Title: Daily Variations and Average Structure of Solar Shear Flows
Deduced from Helioseismic Dense-Pack Samplings of Ring Diagrams
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
Schou, J.; Hill, F.
1999AAS...194.5611H Altcode: 1999BAAS...31..913H
We report on the daily variations and average behavior of large-scale
flows in the upper convection zone as determined by ring-diagram
helioseismic analysis applied to SOI-MDI full-disk velocity data from
the 1996 and 1998 Dynamics Campaigns. We have tracked many small regions
of 15 degrees diameter whose centers are spaced 7.5 degrees apart in
latitude and longitude, creating a mosaic of tiles that oversample
the spatial domain. The tiles cover the solar disk out to a distance
of 52.5 degrees from disk center. An individual dense-pack mosaic
is prepared by tracking each of 189 regions for 1664 minutes (27.7
hrs). Successive mosaics are prepared every 15 degrees in Carrington
longitude, roughly once every 1633 minutes. Such mosaics now cover
more than two full Carrington rotations in 1996 and one rotation in
1998. This is the best spatial and temporal coverage of any ring-diagram
study carried out to date. The longitudinally averaged meridional flow
varies with latitude but remains relatively constant with depth below
the upper shear layer at 2 Mm down to a depth of about 16 Mm. The
averaged zonal flow increases with depth within this same layer and
agrees well with the rotation rates found from global modes. However
with the high-degree wave field data from this analysis we are better
able to resolve that shear layer within the upper convection zone. We
see bands of faster averaged zonal flow near 30 degrees latitude both
in the northern and southern hemisphere that are present at all depths
studied. We also present movies of the daily variations in the flows
within this dense pack for given depths that show the evolution of
the complex velocity field. This research was supported by NASA grants
NAG5-3077 and NAG5-7996, and NSF grant AST-9417337.
---------------------------------------------------------
Title: Comparison Between Near-Surface Flow Fields Deduced from
Correlation Tracking and Time-Distance Helioseismology Methods
Authors: De Rosa, M. L.; Toomre, J.; Duvall, T. L., Jr.
1999AAS...194.5608D Altcode: 1999BAAS...31..913D
Near-photospheric flow fields deduced using two independent methods
applied to the same SOI-MDI time series of images from SOHO are
compared. Differences in travel times between incoming and outgoing
f modes measured using time-distance helioseismology are used to
determine the sites of supergranule outflows. Alternatively, correlation
tracking analysis is applied to granular and mesogranular structures
seen in time series of Doppler and intensity images. We find that the
locations of the supergranular outflows seen in flow fields generated
from correlation tracking coincide well with the locations of the
outflows determined from the time-distance analysis. The near-surface
flow fields provide us with insight in understanding the dyanmics
of the turbulent convection occurring below the photosphere. The data
consist of four 512-minute time series of high-resolution (0.6” pixels)
Doppler images and continuum intensity images taken by MDI on 17--18
January 1997 at a cadence of one minute.
---------------------------------------------------------
Title: Time-Variability of the Inferred Rotation in the Upper
Convection Zone
Authors: Toomre, J.; Christensen-Dalsgaard, J.; Howe, R.; Larsen,
R. M.; Schou, J.; Thompson, M. J.
1999soho....9E..87T Altcode:
We present results of inverting for the rotation of the upper convection
zone, using frequency splittings derived from successive 72-day time
series of SOI-MDI observations. Schou (1999; also Schou et al. 1998)
has studied the evolution of the pattern of small-scale zonal flows
in the near-surface layers using f-mode splittings and has found that
this flow pattern migrates equatorward in a manner similar to that seen
in the so-called torsional oscillation observed in surface Doppler
measurements. In the present work we look at the time variability
of the rotation at greater depth, in the upper convection zone, by
inverting both f- and p-mode splittings. The evolution of the flow is
less regular than is seen at the surface, but we do observe apparently
significant variations in the inferred flow pattern, on latitudinal
scales similar to those seen at the surface. In particular, in the
subsurface shear layer we see intriguing variations, with the first
year's data showing apparent emergence of zonal flows of some 10-15
m/s amplitude at around 20 degrees latitude.
---------------------------------------------------------
Title: Large-Eddy Simulations of Turbulent Solar Convection and its
Coupling with Rotation
Authors: Elliott, J. R.; Miesch, M.; Toomre, J.
1999soho....9E..54E Altcode:
Turbulent fluid motions in the sun's convection zone must play a
large part in setting up the observed differential rotation. Studies
of convection have either been based on the parametrizations of the
effects of turbulent motions (for example the Reynolds stresses),
or upon numerical simulations. Most of the recent progress has come
from numerical simulations. In this poster we present results from
anelastic convection simulations carried out in a spherical shell
geometry, and calculated with a code specifically optimized for high
performance on Massively Parallel machines. Whereas early simulations
tended to show angular velocity approximately constant on cylinders
aligned with the rotation axis (in disagreement with deductions from
helioseismology), our latest simulations show a differential rotation
in much closer agreement with helioseismic inversions. This results from
several improvements over earlier models, including the use of a higher
resolution coupled with longer integration times, and the implementation
of the idea of large-eddy simulation. We hope to demonstrate convergence
of our results as the resolution of the shell is increased.
---------------------------------------------------------
Title: Comparison Between Near-Surface Flow Fields Deduced from
Correlation Tracking and Time-Distance Helioseismology Methods
Authors: de Rosa, Marc; Toomre, Juri; Duvall, T. L., Jr.
1999soho....9E..51D Altcode:
Near-photospheric flow fields deduced using two independent methods
applied to the same SOI-MDI time series of images from SOHO are
compared. Differences in travel times between incoming and outgoing f
modes measured using time-distance helioseismology are used to determine
the sites of supergranule outflows. Alternatively, correlation tracking
analysis is applied to granular and mesogranular structures seen in time
series of Doppler and intensity images. We find that the locations
of the supergranular outflows seen in flow fields generated from
correlation tracking coincide well with the locations of the outflows
determined from the time-distance analysis. The near-surface flow fields
provide us with insight in understanding the dynamics of the turbulent
convection occurring below the photosphere. The data consist of four
512-minute time series of high-resolution (0.6 arc-second pixels)
Doppler images and continuum intensity images taken by MDI on 17-18
January 1997 at a cadence of one minute.
---------------------------------------------------------
Title: Long-Term Dynamics of Small-Scale Magnetic Flux Elements
Embedded in the Near-Surface Velocity Field
Authors: Lisle, Jason; de Rosa, Marc; Toomre, Juri
1999soho....9E..72L Altcode:
Using velocity and magnetogram data generated by SOI-MDI during the
1999 Dynamics Program, we have studied the dynamics of small-scale
magnetic elements over time periods of several days. By exploiting
concurrent time series of MDI magnetograms and velocity images, we
have correlated the motions of the magnetic flux elements with the
supergranular velocity field inferred from tracking of mesogranular
motions. We confirm that these magnetic elements travel at approximately
200 m/s throughout the duration of their lifetime (10-20 hours) as they
are transported by supergranular outflows. We also find that boundaries
of supergranules traced by magnetic flux elements coincide with the
boundaries determined from the tracking of mesogranules. In addition,
we have studied the association between magnetic flux emergence and
destruction events and the evolution of the supergranular network. The
data consist of several tracked regions of corresponding magnetogram and
photospheric velocity images extracted from full-disk SOI-MDI images
taken during the 1999 Dynamics Program when the MDI instrument was at
best focus. Time series were created by following these individual
patches as they rotated across the solar disk. Individual magnetic
elements were identified by thresholding the magnetograms, while the
supergranular flow fields were determined by applying a correlation
tracking algorithm to time series of mesogranules. The mesogranules
were isolated by removing the signal due to solar rotation, p-mode
oscillations, and supergranulation from the velocity data.
---------------------------------------------------------
Title: Phase Inversion of One-Dimensional Artificial Seismic Data
Authors: Gough, D. O.; Sekii, T.; Toomre, J.
1999soho....9E..30G Altcode:
It has been pointed out (Sekii 1997; Gough, Sekii & Toomre 1998,
1999) that the application of the phase inversion technique (Gough,
Merryfield & Toomre 1991, 1993, 1998) to the solar high-degree
sectoral data, for detecting the background inhomogeneity in the
solar equatorial region, may be facing difficulty arising from the
presence of excitation and damping. We have studied the implication of
the effects of these, using a simple model of stochastically excited
damped oscillations of a one-dimensional loop. The results of phase
inversions for various cases will be presented and various strategies
to overcome the difficulty will be discussed.
---------------------------------------------------------
Title: Simulation of Wave Fields to Assess the Sensitivity of
Ring-Diagram Analyses to Shearing Flows
Authors: Hindman, B. W.; Gough, D. O.; Haber, D. A.; Thompson, M. J.;
Toomre, J.
1999soho....9E..64H Altcode:
Ring-diagram analyses of acoustic-wave distortion by flows map
horizontal motions within the solar convection beneath the localized
regions where the observations are taken. To leading order, the
flow field responsible for the advection of waves is taken to be
horizontally uniform across the region. Current ring-diagram analyses
are only carried out to this order, although in reality the flow
is likely to vary across the local patch of the Sun. It is crucial
for the interpretation of the results of ring-diagram analyses that
the effects of shearing flows be assessed. Furthermore, the present
analyses ignore any influence on the ring parameters of flows exterior
to the region being studied. We present a progress report on the
forward calculation of the modification of ring parameters produced
by spatially varying flow fields. We examine effects of flow fields
both inside and outside the region of observation. Additionally,
we assess the influence of the non-uniform flow on the maps of the
velocity field obtained by inverting the ring-parameter data. The
effect of the inhomogeneous flow can be studied as a scattering
problem. We have developed Green functions connecting an underlying
inhomogeneous horizontal flow to the scattered wave field that results
when an incident plane wave encounters the flow. By considering an
ensemble of such incident waves, ring parameters can be inferred from
the wave field. One application is to analyze artificial data sets,
computed from models that contain horizontal shear flows. The scattered
wave field produced by a prescribed 3-D shearing flow is computed,
and the original and scattered wave fields are combined to generate an
artificial helioseismic data set. The artificial data so produced should
then be passed through a ring-diagram analysis and the deduced velocity
field compared to the known imposed flow. Another application is to
compute 3-D kernels relating the ring parameters to the underlying flow:
these will in the future permit 3-D inversions for the flows within
the solar convection zone, using mosaics of many ring-diagram samplings.
---------------------------------------------------------
Title: Changes in High-Degree Oscillation Frequencies from 1996 to
1999 Determined from Ring-Diagram Analysis
Authors: Bogart, R. S.; Schou, J.; Haber, D. A.; Hindman, B. W.;
Toomre, J.; Hill, F.
1999soho....9E..45B Altcode:
Ring-diagram analysis has traditionally been used primarily as a
diagnostic for large-scale flows in the upper convection zone. It
also yields values for the unperturbed (rest) frequencies of the
local high-degree p-mode oscillations. These frequencies, positioned
predominantly in a regime where ridge-fitting of traditional
global modes is difficult, possess information about the average
near-surface temperature profile in the region being analyzed. As
the solar magnetic activity level increased from 1996 through 1999,
we might expect these frequencies to have changed correspondingly. We
present spatially and temporally averaged rest frequencies determined
from ring-diagram analysis of full-disk Doppler data for selected
intervals from each of the four annual SOI Dynamics campaigns covering
the rise in solar activity from 1996 through 1999. These analyses are
performed on a `dense-pack' mosaic of tracked tiles that oversample
the spatial domain with a resolution of 15 heliographic degrees (180
Mm). Tiles are individually tracked over time spans of 1664 minutes
(27.7 hr), so a given physical region on the Sun is sampled from 7 to
15 times depending on its latitude as it rotates across the visible
hemisphere. We discuss the frequency changes seen for comparable areas
on the disc over the years analyzed. This research is supported by
NASA grant NAG5-3077 at Stanford University.
---------------------------------------------------------
Title: Local p-Mode Frequency Shifts Used as Tracers of Solar Activity
Authors: Hindman, B. W.; Haber, D. A.; Toomre, J.
1999soho....9E...5H Altcode:
The Dense-Pack data set from SOI-MDI was originally devised for
ring-diagram analyses. Each day of data consists of 189 separately
tracked tiles on the solar surface. Each tile is 16 degrees square
and the tile centers are separated by 7.5 degrees in latitude and
longitude. The tiling extends out to roughly 52.5 degrees from disk
center. I have computed the local frequency of low order p modes in each
of the Dense-Pack tiles. The frequencies were calculated once a day for
a period of roughly two months during the 1996 dynamics campaign and
for a period of more than week during the 1998 dynamics campaign. For
each day of data and for each latitude and longitude in the Dense-Pack
grid, I have computed the fractional frequency shift by subtracting
the spatial and temporal average of the entire set of frequencies. The
motion of active regions as they rotate across the solar disk is
vividly tracked by these measurement of the local fractional frequency
shift. Active regions are locations with a positive frequency shift,
indicating a region of higher wave propagation speed. To demonstrate
this correspondence, I will present animations of the fractional
frequency shift overlaid with contemporaneous magnetograms.
---------------------------------------------------------
Title: Solar Shear Flows Deduced From Helioseismic Dense-Pack
Samplings of Ring Diagrams
Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.;
Schou, J.; Hill, F.
1999soho....9E..62H Altcode:
Large-scale flows in the upper convection zone can be inferred
by ring-diagram helioseismic analysis, permitting the study of
both their daily variations and their longer temporal means. We use
selected full-disk SOI-MDI velocity data from the 1996, 1997, and 1998
Dynamics campaigns. We have tracked sets of regions (each 15 degrees
in diameter and spaced 7.5 degrees apart in latitude and longitude),
creating a `dense-pack' mosaic of such tiles that oversamples the
spatial domain. The tiles cover the solar disc to a distance of up to
52.5 degrees from center. A single dense-pack mosaic is prepared by
tracking each of 189 regions for 1664 minutes (27.7 hrs). Such mosaics
now cover more than two full Carrington rotations in 1996 and one-third
of a rotation each in both 1997 and 1998. This is the best spatial and
temporal coverage of any ring-diagram study carried out to date. We
are able to compare the mean flows determined over 9-day averages
for data from the different SOI-MDI Dynamics campaigns, as well as
examine the daily flow maps, allowing us to study possible changes
in the convection during the rising magnetic activity of the current
solar cycle. We also present movies of the daily variations in the
flows within this dense pack for given depths that show the evolution
of the complex velocity field. The longitudinally-averaged meridional
flow varies with latitude but remains relatively constant with depth
below the upper shear layer at 2 Mm down to a depth of about 16 Mm. The
averaged zonal flow increases with depth within this same layer and
agrees well with the rotation rates found from global modes. However,
with the high-degree wave-field data from this analysis we are better
able to resolve the shear layer within the upper convection zone. We
see bands of faster and slower average zonal flows in both hemispheres;
these are present at all depths studied.
---------------------------------------------------------
Title: Helioseismic Studies of Differential Rotation in the Solar
Envelope by the Solar Oscillations Investigation Using the Michelson
Doppler Imager
Authors: Schou, J.; Antia, H. M.; Basu, S.; Bogart, R. S.; Bush,
R. I.; Chitre, S. M.; Christensen-Dalsgaard, J.; Di Mauro, M. P.;
Dziembowski, W. A.; Eff-Darwich, A.; Gough, D. O.; Haber, D. A.;
Hoeksema, J. T.; Howe, R.; Korzennik, S. G.; Kosovichev, A. G.;
Larsen, R. M.; Pijpers, F. P.; Scherrer, P. H.; Sekii, T.; Tarbell,
T. D.; Title, A. M.; Thompson, M. J.; Toomre, J.
1998ApJ...505..390S Altcode:
The splitting of the frequencies of the global resonant acoustic modes
of the Sun by large-scale flows and rotation permits study of the
variation of angular velocity Ω with both radius and latitude within
the turbulent convection zone and the deeper radiative interior. The
nearly uninterrupted Doppler imaging observations, provided by the
Solar Oscillations Investigation (SOI) using the Michelson Doppler
Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft
positioned at the L<SUB>1</SUB> Lagrangian point in continuous sunlight,
yield oscillation power spectra with very high signal-to-noise ratios
that allow frequency splittings to be determined with exceptional
accuracy. This paper reports on joint helioseismic analyses of
solar rotation in the convection zone and in the outer part of the
radiative core. Inversions have been obtained for a medium-l mode set
(involving modes of angular degree l extending to about 250) obtained
from the first 144 day interval of SOI-MDI observations in 1996. Drawing
inferences about the solar internal rotation from the splitting data
is a subtle process. By applying more than one inversion technique
to the data, we get some indication of what are the more robust
and less robust features of our inversion solutions. Here we have
used seven different inversion methods. To test the reliability and
sensitivity of these methods, we have performed a set of controlled
experiments utilizing artificial data. This gives us some confidence
in the inferences we can draw from the real solar data. The inversions
of SOI-MDI data have confirmed that the decrease of Ω with latitude
seen at the surface extends with little radial variation through much
of the convection zone, at the base of which is an adjustment layer,
called the tachocline, leading to nearly uniform rotation deeper
in the radiative interior. A prominent rotational shearing layer in
which Ω increases just below the surface is discernible at low to
mid latitudes. Using the new data, we have also been able to study the
solar rotation closer to the poles than has been achieved in previous
investigations. The data have revealed that the angular velocity
is distinctly lower at high latitudes than the values previously
extrapolated from measurements at lower latitudes based on surface
Doppler observations and helioseismology. Furthermore, we have found
some evidence near latitudes of 75° of a submerged polar jet which
is rotating more rapidly than its immediate surroundings. Superposed
on the relatively smooth latitudinal variation in Ω are alternating
zonal bands of slightly faster and slower rotation, each extending
some 10° to 15° in latitude. These relatively weak banded flows
have been followed by inversion to a depth of about 5% of the solar
radius and appear to coincide with the evolving pattern of “torsional
oscillations” reported from earlier surface Doppler studies.
---------------------------------------------------------
Title: Pumping of Magnetic Fields by Turbulent Penetrative Convection
Authors: Tobias, Steven M.; Brummell, Nicholas H.; Clune, Thomas L.;
Toomre, Juri
1998ApJ...502L.177T Altcode:
A plausible scenario for solar dynamo action is that the large-scale
organized toroidal magnetic field is generated by the action of strong
radial shear at the base of the solar convection zone, whereas the
weaker poloidal field is regenerated by cyclonic convection throughout
the convection zone. We show, using high-resolution three-dimensional
numerical simulations, that the required transport of magnetic field
from the convection zone to the overshoot region can be achieved on
a convective rather than diffusive timescale by a pumping mechanism
in turbulent penetrative compressible convection. A layer of magnetic
field initially placed in the convection zone is swept down by strong
sinking plumes, locally amplified, and deposited in the stable region
at the base of the convection zone, despite the opposing action of
magnetic buoyancy. The rate of transport is insensitive to the strength
of the initial imposed field.
---------------------------------------------------------
Title: Phase Inversion: Inferring Solar Subphotospheric Flow and
Other Asphericity from the Distortion of Acoustic Waves
Authors: Gough, Douglas; Merryfield, William J.; Toomre, Juri
1998ApJ...501..882G Altcode:
A method is proposed for analyzing an almost monochromatic train of
waves propagating in a single direction in an inhomogenous medium that
is not otherwise changing in time. An effective phase is defined in
terms of the Hilbert transform of the wave function, which is related,
via the JWKB approximation, to the spatial variation of the background
state against which the wave is propagating. The contaminating effect
of interference between the truly monochromatic components of the train
is eliminated using its propagation properties. Measurement errors,
provided they are uncorrelated, are manifest as rapidly varying noise;
although that noise can dominate the raw phase-processed signal, it can
largely be removed by low-pass filtering. The intended purpose of the
analysis is to determine the distortion of solar oscillations induced by
horizontal structural variation and material flow. It should be possible
to apply the method directly to sectoral modes. The horizontal phase
distortion provides a measure of longitudinally averaged properties
of the Sun in the vicinity of the equator, averaged also in radius
down to the depth to which the modes penetrate. By combining such
averages from different modes, the two-dimensional variation can be
inferred by standard inversion techniques. After taking due account
of horizontal refraction, it should be possible to apply the technique
also to locally sectoral modes that propagate obliquely to the equator
and thereby build a network of lateral averages at each radius, from
which the full three-dimensional structure of the Sun can, in principle,
be determined as an inverse Radon transform.
---------------------------------------------------------
Title: Subphotospheric Convective Flows Determined by Ring-Diagram
Analyses of SOI-MDI Observations
Authors: Haber, D.; Hindman, B.; Toomre, J.; Bogart, R.; Schou, J.;
Hill, F.
1998ESASP.418..791H Altcode: 1998soho....6..791H
The variation of large-scale velocity flows with depth and location
on the sun places important constraints on theoretical models of the
solar convection zone and dynamo. High-degree oscillations can be
viewed as nearly plane waves that are advected and distorted by the
underlying flows. By conducting observations over limited regions
of the solar surface to obtain `ring diagram' power spectra, we can
deduce spatially-averaged horizontal flows with depth below that
region. Previous analyses of ring diagrams have already suggested
the presence of strong shearing flows below the surface. We have
now implemented a highly efficient technique for determining these
horizontal flows with depth and report here on a systematic analysis of
full-disk Doppler velocity data taken continuously with a one-minute
cadence during portions of the two-month dynamics observing program
with SOI-MDI in 1996. The square regions examined span about 15-circ,
and are studied for time intervals each of about 1536 mins (~25 hrs). A
lattice of such squares is considered: their centers are spaced 15-circ
apart in longitude and there are seven such regions across the solar
disk at +20-circ, 0-circ, -20-circ latitude. Another set of regions
is placed along the central meridian at 10-circ and 15-circ intervals
in latitude. Properties of the underlying large-scale subphotospheric
flows and their temporal variations so revealed are presented in detail.
---------------------------------------------------------
Title: Slow Poles and Shearing Flows from Heliospheric Observations
with MDI and GONG Spanning a Year
Authors: Schou, J.; Christensen-Dalsgaard, J.; Howe, R.; Larsen,
R. M.; Thompson, M. J.; Toomre, J.
1998ESASP.418..845S Altcode: 1998soho....6..845S
We invert one year of coeval high-resolution rotational splitting data
(up to degree l 250) from GONG and SOI-MDI. The first 4 months of
MDI data uncovered several new features in the rotation of the solar
convective envelope: surface and subsurface zonal bands corresponding
to the so-called torsional oscillations, superimposed on the overall
smooth latitudinal surface rotation; a drop in the near-polar surface
rotation rate below the rate extrapolated from lower latitudes; and an
indication of a prograde jet-like feature at high latitudes at a depth
of about 5 percent of the solar radius. Using the 1 year of data from
the MDI and GONG instruments, we test the robustness and stationarity of
these features. As an aid to testing the robustness of our inferences,
we use two independent inversion methods (2-D regularized least squares
and SOLA) and apply them to the splitting data obtained from both GONG
and MDI.
---------------------------------------------------------
Title: Helioseismology: What are We Learning About the Sun?
Authors: Toomre, Juri
1998ASPC..154..275T Altcode: 1998csss...10..275T
Helioseismology studies the internal structure and dynamics of the
Sun, utilizing very precise measurements of the frequencies of sound
waves that propagate throughout the solar interior and are observed
at the surface. Efforts to accurately and precisely measure the mode
frequencies from a single observing site have met with fundamental
limitations imposed by the day-night cycle. Such difficulties
have recently been overcome as nearly uninterrupted Doppler imaged
observations of the full solar disk have become available both from
the ground-based six-station Global Oscillation Network Group (GONG)
project and from the SOI Michelson Doppler Imager (SOI-MDI) aboard
the SOHO spacecraft in continuous sunlight orbiting the Sun-Earth L_1
Lagrangian point. Thus helioseismology has entered a major new phase
of intensive scientific study as coordinated scientific teams have
started to analyze both the GONG and SOI data. We review some of the
basic principles and motivations of helioseismology, and then discuss
some of the preliminary scientific results obtained by the teams through
inversion of the global-mode frequencies and their splittings, dealing
with the structure of the solar interior and the physics of stellar
models, and an assessment of the differential rotation profile with
depth and latitude. The inversions confirm that the surface latitudinal
variation of the rotation rate carries through much of the convection
zone. At the base of the convection zone there is a currently unresolved
adjustment layer with latitudinally independent rotation at greater
depths. A shearing layer just below the surface is discernible at low
to mid latitudes. Such global investigations are supplemented by local
area analyses via ring diagrams and time-distance methods, which enable
one to probe the subsurface variation of large-scale flows and thermal
structures with depth beneath selected regions of the Sun.
---------------------------------------------------------
Title: Correlation Tracking of Mesogranules from SOI-MDI Doppler
Images to Reveal Supergranular Flow Fields
Authors: De Rosa, Marc L.; Toomre, Juri
1998ESASP.418..753D Altcode: 1998soho....6..753D
We present evidence that mesogranules on the sun are advected
horizontally by the underlying supergranular flow field. Correlation
tracking of mesogranules, as observed in full-disk SOI-MDI Doppler
images, reveal that the flow field experienced by the mesogranules is
composed of several long-lived regions of divergent fluid. These outflow
regions correlate well with the locations of supergranules present on
related Doppler images. The flow fields also contain regions where the
fluid is converging or is moving slowly, both corresponding to areas of
the related Doppler images where no organized supergranular outflows
exist. Typical velocities are of order 200 m s<SUP>-1</SUP>. The data
used in this study consist of 30-circ-square patches of the photospheric
velocity field extracted from full-disk SOI-MDI Dopplergrams. Time
series were created by tracking each patch in a frame corotating
with the surface plasma. Images of mesogranulation superimposed on
supergranulation were created by removing the velocity signals due
to rotation and acoustic oscillations. The supergranular signal is
isolated by spatially smoothing each image, while the mesogranular
signal is isolated by taking the residual of the smoothed and unsmoothed
images. The correlation tracking calculation was performed on the time
series of mesogranulation, from which the surface flow-fields analyzed
in this study were deduced.
---------------------------------------------------------
Title: Turbulent Solar Convection and its Coupling with Rotation
Authors: Elliott, J. R.; Miesch, M. S.; Toomre, J.; Cluney, T. C.;
Glatzmaier, G. A.
1998ESASP.418..765E Altcode: 1998soho....6..765E
Previous numerical simulations of global-scale solar convection in
rotating spherical shells of fluid have been restricted by computational
resources to deal with nearly laminar flow regimes. Disparities between
the differential rotation profiles that such models predict and those
deduced from helioseismology, coupled with recent advances in high
performance computing, encouraged us to begin pursuing numerical
simulations of global-scale convection in turbulent parameter
regimes. We anticipate that rotationally-constrained turbulence can
possess inverse cascades that yield large-scale coherent vorticity
structures and strong mean flows which coexist with less persistent
smaller-scale turbulence, and yield angular velocity profiles that
may be quite different than those obtained with laminar convection. We
have developed a new code for studying penetrative anelastic convection
in rotating spherical shells which is highly optimized for massively
parallel supercomputer architechtures, and as a result, is capable
of achieving more turbulent flow regimes than previously possible. We
present results from such simulations, which are providing new insight
into the nature of turbulent solar convection and its coupling to
differential rotation.
---------------------------------------------------------
Title: Some Comments on Phase Inversions
Authors: Gough, D. O.; Sekii, T.; Toomre, J.
1998ESASP.418..789G Altcode: 1998soho....6..789G
The method of phase inversion have been proposed and tested for simple
cases by Gough, Merryfield and Toomre(1991,1993,1998) for detection of
inhomogeneity in media by observing wave propagation. We discuss some of
the difficulties that are encountered with the procedure in practice,
and what might be done to overcome them in transferring the technique
to the solar case, such as in the study of horizontal inhomogeneity in
the solar cavity along the equator using the MDI sectoral-mode data. A
complication seems to arise, aside from observational problems, from
the fact that the waves are not only scattered by inhomogeneity, but
are also excited and damped, as is observed in the broadening of the
ridges in the k-ω diagram.
---------------------------------------------------------
Title: Turbulent Compressible Convection with Rotation. II. Mean
Flows and Differential Rotation
Authors: Brummell, Nicholas H.; Hurlburt, Neal E.; Toomre, Juri
1998ApJ...493..955B Altcode:
The effects of rotation on turbulent, compressible convection within
stellar envelopes are studied through three-dimensional numerical
simulations conducted within a local f-plane model. This work
seeks to understand the types of differential rotation that can
be established in convective envelopes of stars like the Sun, for
which recent helioseismic observations suggest an angular velocity
profile with depth and latitude at variance with many theoretical
predictions. This paper analyzes the mechanisms that are responsible
for the mean (horizontally averaged) zonal and meridional flows that are
produced by convection influenced by Coriolis forces. The compressible
convection is considered for a range of Rayleigh, Taylor, and Prandtl
(and thus Rossby) numbers encompassing both laminar and turbulent flow
conditions under weak and strong rotational constraints. <P />When the
nonlinearities are moderate, the effects of rotation on the resulting
laminar cellular convection leads to distinctive tilts of the cell
boundaries away from the vertical. These yield correlations between
vertical and horizontal motions that generate Reynolds stresses that
can drive mean flows, interpretable as differential rotation and
meridional circulations. Under more vigorous forcing, the resulting
turbulent convection involves complicated and contorted fluid particle
trajectories, with few clear correlations between vertical and
horizontal motions, punctuated by an evolving and intricate downflow
network that can extend over much of the depth of the layer. Within
such networks are some coherent structures of vortical downflow that
tend to align with the rotation axis. These yield a novel turbulent
alignment mechanism, distinct from the laminar tilting of cellular
boundaries, that can provide the principal correlated motions and thus
Reynolds stresses and subsequently mean flows. The emergence of such
coherent structures that can persist amidst more random motions is a
characteristic of turbulence with symmetries broken by rotation and
stratification. Such structure is here found to play a crucial role
in defining the mean zonal and meridional flows that coexist with the
convection. Though they are subject to strong inertial oscillations,
the strength and type of the mean flows are determined by a combination
of the laminar tilting and the turbulent alignment mechanisms. Varying
the parameters produces a wide range of mean motions. Among these,
some turbulent solutions exhibit a mean zonal velocity profile that
is nearly constant with depth, much as deduced by helioseismology
at midlatitudes within the Sun. The solutions exhibit a definite
handedness, with the direction of the persistent mean flows often
prescribing a spiral with depth near the boundaries, also in accord
with helioseismic deductions. The mean helicity has a profile that is
positive in the upper portion of the domain and negative in the lower
portion, a property bearing on magnetic dynamo processes that may be
realized within such rotating layers of turbulent convection.
---------------------------------------------------------
Title: Differential rotation in turbulent compressible convection
Authors: Brummell, N. H.; Toomre, J.; Hurlburt, N.
1997ASSL..225..223B Altcode: 1997scor.proc..223B
Numerical simulations of 3D compressible convection in a local
rectilinear geometry show that zonal and meridional mean flows,
$\overline{u}(z)$ and $\overline{v}(z)$, can be produced when rotation
is included. A wide variety of mean profiles can be achieved depending
upon the parameters, including behaviour equivalent (within the
limitations of the model) to that inferred from helioseismic solar
observations.
---------------------------------------------------------
Title: Rotation and Zonal Flows in the Solar Envelope from the
SOHO/MDI Observations
Authors: Scherrer, P. H.; Schou, J.; Bogart, R. S.; Bush, R. I.;
Hoeksema, J. T.; Kosovichev, A. G.; Antia, H. M.; Chitre, S. M.;
Christensen-Dalsgaard, J.; Larsen, R. M.; Pijpers, F. P.; Eff-Darwich,
A.; Korzennik, S. G.; Gough, D. O.; Sekii, T.; Howe, R.; Tarbell,
T.; Title, A. M.; Thompson, M. J.; Toomre, J.
1997AAS...191.7310S Altcode: 1997BAAS...29.1322S
We report on the latest inferences concerning solar differential
rotation that have been drawn from the helioseismic data that are now
available from the Solar Oscillations Investigation (SOI) using the
Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory
(SOHO). That spacecraft is positioned in a halo orbit near the Sun-Earth
Lagrangian point L_1, in order to obtain continuous Doppler-imaged
observations of the sun with high spatial fidelity. Doppler velocity,
intensity and magnetic field images are recorded, based on modulations
of the 676.8 nm Ni I solar absorption line. The high spatial resolution
of MDI thereby permits the study of many millions of global resonant
modes of solar oscillation. Determination and subsequent inversion
of the frequencies of these modes, including the degeneracy-splitting
by the rotation of the sun, enables us to infer how the sun's angular
velocity varies throughout much of the interior. The current MDI data
are providing substantial refinements to the helioseismic deductions
that can be made about differential rotation both within the convection
zone and in its transition to the radiative interior. The shearing
layer evident in the angular velocity Omega just below the solar
surface is becoming better defined, as is the adjustment layer or
tachocline near the base of the convection zone. The MDI data are also
revealing a prominent decrease in Omega at high latitudes from the
rotation rate expressed by a simple three-term expansion in latitude
that was originally deduced from surface Doppler measurements. Further,
there are indications that a submerged polar vortex involving somewhat
faster Omega than its surroundings exists at about 75(deg) in latitudes.
---------------------------------------------------------
Title: Global-scale numerical simulation of solar turbulent convection
and its coupling to rotation
Authors: Elliott, J. R.; Miesch, M.; Toomre, J.; Clune, T. C.;
Glatzmaier, G. A.
1997AAS...191.7403E Altcode: 1997BAAS...29.1324E
The larger scales of convection in the sun are influenced by
rotation, leading to a redistribution of angular momentum which
is seen as differential rotation. Previous numerical simulations
of such global-scale convection in rotating spherical shells of
fluid have been restricted by computational resources to deal with
nearly laminar flow regimes for the resolved scales of motion, though
provisions were made for diffusive transport by nominally turbulent
unresolved scales. The disparities between the differential rotation
profiles that those models predict (angular velocity nearly constant on
cylinders) and those deduced from the frequency splittings of p modes
(nearly constant on radii in the convection zone), coupled with recent
advances in high performance computing, encouraged us to begin pursuing
numerical simulations of global-scale convection in turbulent parameter
regimes. We anticipate that rotationally-constrained turbulence can
possess inverse cascades that yield large-scale coherent vorticity
structures and strong mean flows which coexist with less persistent
smaller-scale turbulence, and yield angular velocity profiles that may
be quite different than those obtained with laminar convection. The
dominant challenge to all turbulence simulations is to be able to
explicitly describe the dynamics over a broad enough range of length
scales. To this end, we have developed a new code for studying rotating
anelastic convection in spherical shells, employing expansions in
spherical harmonics to resolve horizontal structures and in Chebyshev
polynomials to resolve radial structures. Appropriate optimization
techniques, including expedient use of inter-processor transposes
and sophisticated load balancing, enable the code to achieve high
performance on massively parallel architectures, and currently to reach
a speed of around 100Mflop/s per node on the Cray T3E. The new code is
enabling us to perform simulations of convection at spatial resolutions
significantly higher than those of earlier studies, and thereby to
begin to investigate fully turbulent parameter regimes. We present the
results from such a simulation, which includes the important effects
of penetration into the stable interior, and discuss the corresponding
differential-rotation profile obtained.
---------------------------------------------------------
Title: The Nature of Supergranulation from SOI-MDI Dopplergrams
Authors: De Rosa, Marc L.; Toomre, Juri
1997SPD....28.0257D Altcode: 1997BAAS...29..903D
We discuss the distribution of supergranule cell areas and
evolutionary characteristics as determined from a series of SOI-MDI
dopplergrams. Patches of the photospheric velocity field 30(deg)
x30(deg) (heliographic) in size were tracked as they rotated across the
disk of the sun. Supergranule boundaries were identified on each tracked
image by a pattern recognition algorithm, from which supergranule area
distributions and evolutionary trends are found.
---------------------------------------------------------
Title: Persistence of Large-Scale Flows Beneath Quiet Sun: Local-Area
Analysis Using MDI Doppler Data
Authors: Haber, D.; Toomre, J.; Bogart, R.; Schou, J.; Gonzalez, I.;
Hill, F.
1997SPD....28.0201H Altcode: 1997BAAS...29..893H
Knowing the large-scale flows that occur in the upper convection zone
is critical to our understanding of the processes that govern the
solar cycle. Here we apply solar oscillation ring-diagram analysis to
several small tracked regions on the sun, approximately 15(deg) on a
side, as they rotate across the solar disk, in order to determine the
persistence and depth variation of the large-scale flows beneath these
regions. We use the Doppler velocity images from the Michelson Doppler
Imager (MDI) instrument aboard the Solar Heliospheric Observatory
(SOHO) satellite using quiet-sun data taken during the MDI Dynamics
campaign of 1996. Three regions at different latitudes were extracted
from full-disk Doppler images of 1024 x 1024 pixels (pixel size ~
2” square) with a one-minute temporal cadence. Eight sequential
1536-minute time intervals were tracked, remapped onto great-circle
grids, spatially and temporally filtered, and apodized in space and
time. They were then Fourier transformed in two spatial dimensions
and time. The resulting power spectra show characteristic rings at
each frequency slice. Shifts in the center positions of the rings are
caused by underlying flow fields and can be inverted to map these flows
with depth. We use several techniques to fit these shifts in order to
assess the stability of the results.
---------------------------------------------------------
Title: Structure and Rotation of the Solar Interior: Initial Results
from the MDI Medium-L Program
Authors: Kosovichev, A. G.; Schou, J.; Scherrer, P. H.; Bogart, R. S.;
Bush, R. I.; Hoeksema, J. T.; Aloise, J.; Bacon, L.; Burnette, A.; de
Forest, C.; Giles, P. M.; Leibrand, K.; Nigam, R.; Rubin, M.; Scott,
K.; Williams, S. D.; Basu, Sarbani; Christensen-Dalsgaard, J.; Dappen,
W.; Rhodes, E. J., Jr.; Duvall, T. L., Jr.; Howe, R.; Thompson, M. J.;
Gough, D. O.; Sekii, T.; Toomre, J.; Tarbell, T. D.; Title, A. M.;
Mathur, D.; Morrison, M.; Saba, J. L. R.; Wolfson, C. J.; Zayer, I.;
Milford, P. N.
1997SoPh..170...43K Altcode:
The medium-l program of the Michelson Doppler Imager instrument on board
SOHO provides continuous observations of oscillation modes of angular
degree, l, from 0 to ∽ 300. The data for the program are partly
processed on board because only about 3% of MDI observations can be
transmitted continuously to the ground. The on-board data processing,
the main component of which is Gaussian-weighted binning, has been
optimized to reduce the negative influence of spatial aliasing of the
high-degree oscillation modes. The data processing is completed in a
data analysis pipeline at the SOI Stanford Support Center to determine
the mean multiplet frequencies and splitting coefficients. The initial
results show that the noise in the medium-l oscillation power spectrum
is substantially lower than in ground-based measurements. This enables
us to detect lower amplitude modes and, thus, to extend the range of
measured mode frequencies. This is important for inferring the Sun's
internal structure and rotation. The MDI observations also reveal the
asymmetry of oscillation spectral lines. The line asymmetries agree
with the theory of mode excitation by acoustic sources localized in the
upper convective boundary layer. The sound-speed profile inferred from
the mean frequencies gives evidence for a sharp variation at the edge
of the energy-generating core. The results also confirm the previous
finding by the GONG (Gough et al., 1996) that, in a thin layer just
beneath the convection zone, helium appears to be less abundant than
predicted by theory. Inverting the multiplet frequency splittings from
MDI, we detect significant rotational shear in this thin layer. This
layer is likely to be the place where the solar dynamo operates. In
order to understand how the Sun works, it is extremely important to
observe the evolution of this transition layer throughout the 11-year
activity cycle.
---------------------------------------------------------
Title: Plane-wave analysis of 501 data
Authors: Bogart, R. S.; Discher de Sá, L. A.; González Hernández,
I.; Patrón Recio, J.; Haber, D. A.; Toomre, J.; Hill, F.; Rhodes,
E. J., Jr.; Xue, Y.; SOI Ring Diagrams Team
1997IAUS..181..111B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Internal structure and rotation of the Sun: First results
from MDI data
Authors: Kosovichev, A. G.; Schou, J.; Scherrer, P. H.; Bogart, R. S.;
Bush, R. I.; Hoeksema, J. T.; Aloise, J.; Bacon, L.; Burnette, A.;
De Forest, C.; Giles, P. M.; Leibrand, K.; Nigam, R.; Rubin, M.;
Scott, K.; Williams, S. D.; Basu, Sarbani; Christensen-Dalsgaard,
J.; Däppen, W.; Rhodes, E. J., Jr.; Duvall, T. L., Jr.; Howe, R.;
Thompson, M. J.; Gough, D. O.; Sekii, T.; Toomre, J.; Tarbell, T. D.;
Title, A. M.; Mathur, D.; Morrison, M.; Saba, J. L. R.; Wolfson,
C. J.; Zayer, I.; Milford, P. N.
1997IAUS..181..203K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Dynamics of the solar convection zone
Authors: Toomre, J.
1997ppvs.conf..343T Altcode:
Introduction Multiple discrete scales of convection Probing of structure
and flows with helioseismology Multitude of magnetic structures and
dynamo action Structures and inverse cascades in turbulence Dynamical
range of solar turbulence Local models of rotating compressible
convection Formulation of local ƒ-plane models Nature of rotating
turbulent convection Driving of mean flows and implications for
differential rotation Penetrative convection and intermittency in
transport of heat Global models of spherical convection Formulation
of anelastic convection in rotating shells Nature of global convection
and the mean flows Reflections
---------------------------------------------------------
Title: Internal rotation and dynamics of the Sun from GONG data
Authors: Korzennik, S.; Thompson, M. J.; Toomre, J.; GONG Internal
Rotation Team
1997IAUS..181..211K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The seismic structure of the Sun from GONG
Authors: Anderson, E.; Antia, H. M.; Basu, S.; Chaboyer, B.; Chitre,
S. M.; Christensen-Dalsgaard, J.; Eff-Darwich, A.; Elliott, J. R.;
Giles, P. M.; Gough, D. O.; Guzik, J. A.; Harvey, J. W.; Hill,
F.; Leibacher, J. W.; Kosovichev, A. G.; Monteiro, M. J. P. F. G.;
Richard, O.; Sekii, T.; Shibahashi, H.; Takata, M.; Thompson, M. J.;
Toomre, J.; Vauclair, S.; Vorontsov, S. V.
1997IAUS..181..151A Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Turbulent Compressible Convection with Rotation. I. Flow
Structure and Evolution
Authors: Brummell, Nicholas H.; Hurlburt, Neal E.; Toomre, Juri
1996ApJ...473..494B Altcode:
The effects of Coriolis forces on compressible convection are studied
using three-dimensional numerical simulations carried out within a
local modified f-plane model. The physics is simplified by considering
a perfect gas occupying a rectilinear domain placed tangentially to a
rotating sphere at various latitudes, through which a destabilizing
heat flux is driven. The resulting convection is considered for a
range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers,
evaluating conditions where the influence of rotation is both weak
and strong. Given the computational demands of these high-resolution
simulations, the parameter space is explored sparsely to ascertain
the differences between laminar and turbulent rotating convection. The
first paper in this series examines the effects of rotation on the flow
structure within the convection, its evolution, and some consequences
for mixing. Subsequent papers consider the large-scale mean shear flows
that are generated by the convection, and the effects of rotation on
the convective energetics and transport properties. <P />It is found
here that the structure of rotating turbulent convection is similar to
earlier nonrotating studies, with a laminar, cellular surface network
disguising a fully turbulent interior punctuated by vertically coherent
structures. However, the temporal signature of the surface flows is
modified by inertial motions to yield new cellular evolution patterns
and an overall increase in the mobility of the network. The turbulent
convection contains vortex tubes of many scales, including large-scale
coherent structures spanning the full vertical extent of the domain
involving multiple density scale heights. Remarkably, such structures
align with the rotation vector via the influence of Coriolis forces on
turbulent motions, in contrast with the zonal tilting of streamlines
found in laminar flows. Such novel turbulent mechanisms alter the
correlations which drive mean shearing flows and affect the convective
transport properties. In contrast to this large-scale anisotropy,
small-scale vortex tubes at greater depths are randomly orientated by
the rotational mixing of momentum, leading to an increased degree of
isotropy on the medium to small scales of motion there. Rotation also
influences the thermodynamic mixing properties of the convection. In
particular, interaction of the larger coherent vortices causes a loss of
correlation between the vertical velocity and the temperature leaving
a mean stratification which is not isentropic.
---------------------------------------------------------
Title: Angular Momentum Transport in Turbulent Compressible Convection
Authors: Hurlburt, N. E.; Brummell, N. H.; Toomre, J.
1996AAS...188.6907H Altcode: 1996BAAS...28R.936H
We consider the dynamics of compressible convection within a curved
local segment of a rotating spherical shell, aiming to resolve the
disparity between the differential rotation profiles predicted by
previous laminar simulations (angular velocity constant on cylinders)
and those deduced from helioseismic inversion of the observed frequency
splitting of p modes. By limiting the horizontal extent of the domain
under study, we can utilize the available spatial degrees of freedom
on current supercomputers to attain more turbulent flows than in the
full shell. Our previous study of three-dimensional convection within
a slab geometry of an f-plane neglected the effects of curvature,
and thus did not admit the generation of Rossby waves. These waves
propagate in the longitudinal direction and thus produce rather
different spectral characteristics and mean flows in the north-south
and east-west directions. By considering motions in a curvilinear
geometry in which the Coriolis parameter varies with latitude, we
admit the possibility of Rossby waves which couple to the turbulent
convection. Here we present simulations with Rayleigh numbers in excess
of 10(6) , and Prandtl numbers less than 0.1 in such a curved local
segment of a spherical shell using a newly developed code based on
compact finite differences. This computational domain takes the form of
a curved, periodic channel in longitude with stress-free sidewalls in
latitude and radius. Despite the differences in geometry and boundary
conditions, the flows maintain similarities with those of our previous
f-plane simulations. The surface flows form broad, laminar networks
which mask the much more turbulent flows of the interior. The dynamics
within this turbulent region is controlled by the interactions of a
tangled web of strong vortex tubes. These interactions are further
complicated by the effects of curvature. The differential rotation
generated by the turbulent convection typically increases with depth
and attains a maximum at the base of the layer of about 10 % over the
imposed rotation rate.
---------------------------------------------------------
Title: Perspectives in Helioseismology
Authors: Gough, D. O.; Leibacher, J. W.; Scherrer, P. H.; Toomre, J.
1996Sci...272.1281G Altcode:
Helioseismology is probing the interior structure and dynamics of
the sun with ever-increasing precision, providing a well-calibrated
laboratory in which physical processes can be studied under conditions
that are unattainable on Earth. Nearly 10 million resonant modes
of oscillation are observable in the solar atmosphere, and their
frequencies need to be known with great accuracy in order to gauge the
sun's interior. The advent of nearly continuous imaged observations
from the complementary ground-based Global Oscillation Network Group
(GONG) observatories and the space-based Solar and Heliospheric
Observatory instruments augurs a new era of discovery. The flow of
early results from GONG resolves some issues and raises a number of
theoretical questions whose answers are required for understanding
how a seemingly ordinary star actually operates.
---------------------------------------------------------
Title: Preliminary Ring-Diagram Analysis of Doppler Velocity Fields
Observed with MDI on SOHO
Authors: Haber, D. A.; Bogart, R. S.; Sa, L. A. D.; Hill, F.; Toomre,
J.; Duvall, T. L., Jr.
1996AAS...188.3710H Altcode: 1996BAAS...28Q.879H
We analyze properties of high-degree acoustic wave fields over small
patches of the sun using high-resolution Doppler velocity observations
with the Michelson Doppler Imager (MDI) on the Solar Heliospheric
Observatory (SOHO). By studying asymmetric frequency shifts in the
acoustic waves that propagate in different horizontal directions,
we can make inferences about the underlying large-scale flows which
contribute to these shifts. We here analyze two different sets of
data obtained from early observations with MDI. One is a continuous
80-hour sequence of full-disk Doppler images with a 60 s cadence and 4”
resolution, the other is an 8-hour sequence of high-resolution images
that have 1.2” resolution. Both sets have 1024 x 1024 pixels but the
second set only covers about 36deg on the sun and is centered on the
central meridian and somewhat above disk center. In both cases we remap
a number of smaller areas of the data and compute three-dimensional
Fourier transforms (two in space, one in time) over each patch. The
resulting power diagrams have cross-sections in frequency that exhibit
power distributed along rings. The detailed shapes and displacements
of the rings depend upon the averaged velocities and their gradients,
which can be estimated by theory. We measure the displacements of the
rings using two different analysis techniques, thereby determining
the frequency splittings which are then used in inversion procedures
to deduce the underlying smoothed flow fields in each region. The
results from the various patches provide preliminary estimates of the
flow structures present in the upper convection zone.
---------------------------------------------------------
Title: The Seismic Structure of the Sun
Authors: Gough, D. O.; Kosovichev, A. G.; Toomre, J.; Anderson,
E.; Antia, H. M.; Basu, S.; Chaboyer, B.; Chitre, S. M.;
Christensen-Dalsgaard, J.; Dziembowski, W. A.; Eff-Darwich, A.;
Elliott, J. R.; Giles, P. M.; Goode, P. R.; Guzik, J. A.; Harvey,
J. W.; Hill, F.; Leibacher, J. W.; Monteiro, M. J. P. F. G.; Richard,
O.; Sekii, T.; Shibahashi, H.; Takata, M.; Thompson, M. J.; Vauclair,
S.; Vorontsov, S. V.
1996Sci...272.1296G Altcode:
Global Oscillation Network Group data reveal that the internal
structure of the sun can be well represented by a calibrated standard
model. However, immediately beneath the convection zone and at the
edge of the energy-generating core, the sound-speed variation is
somewhat smoother in the sun than it is in the model. This could be a
consequence of chemical inhomogeneity that is too severe in the model,
perhaps owing to inaccurate modeling of gravitational settling or to
neglected macroscopic motion that may be present in the sun. Accurate
knowledge of the sun's structure enables inferences to be made about
the physics that controls the sun; for example, through the opacity,
the equation of state, or wave motion. Those inferences can then be
used elsewhere in astrophysics.
---------------------------------------------------------
Title: The Global Oscillation Network Group (GONG) Project
Authors: Harvey, J. W.; Hill, F.; Hubbard, R. P.; Kennedy, J. R.;
Leibacher, J. W.; Pintar, J. A.; Gilman, P. A.; Noyes, R. W.; Title,
A. M.; Toomre, J.; Ulrich, R. K.; Bhatnagar, A.; Kennewell, J. A.;
Marquette, W.; Patron, J.; Saa, O.; Yasukawa, E.
1996Sci...272.1284H Altcode:
Helioseismology requires nearly continuous observations of the
oscillations of the solar surface for long periods of time in
order to obtain precise measurements of the sun's normal modes of
oscillation. The GONG project acquires velocity images from a network
of six identical instruments distributed around the world. The GONG
network began full operation in October 1995. It has achieved a duty
cycle of 89 percent and reduced the magnitude of spectral artifacts by
a factor of 280 in power, compared with single-site observations. The
instrumental noise is less than the observed solar background.
---------------------------------------------------------
Title: Differential Rotation and Dynamics of the Solar Interior
Authors: Thompson, M. J.; Toomre, J.; Anderson, E. R.; Antia, H. M.;
Berthomieu, G.; Burtonclay, D.; Chitre, S. M.; Christensen-Dalsgaard,
J.; Corbard, T.; De Rosa, M.; Genovese, C. R.; Gough, D. O.; Haber,
D. A.; Harvey, J. W.; Hill, F.; Howe, R.; Korzennik, S. G.; Kosovichev,
A. G.; Leibacher, J. W.; Pijpers, F. P.; Provost, J.; Rhodes, E. J.,
Jr.; Schou, J.; Sekii, T.; Stark, P. B.; Wilson, P. R.
1996Sci...272.1300T Altcode:
Splitting of the sun's global oscillation frequencies by large-scale
flows can be used to investigate how rotation varies with radius
and latitude within the solar interior. The nearly uninterrupted
observations by the Global Oscillation Network Group (GONG) yield
oscillation power spectra with high duty cycles and high signal-to-noise
ratios. Frequency splittings derived from GONG observations confirm
that the variation of rotation rate with latitude seen at the surface
carries through much of the convection zone, at the base of which is
an adjustment layer leading to latitudinally independent rotation at
greater depths. A distinctive shear layer just below the surface is
discernible at low to mid-latitudes.
---------------------------------------------------------
Title: High Resolution Numerical Simulations of Global Solar
Convection
Authors: Miesch, M.; Clune, T.; Toomre, J.; Glatzmaier, G.
1996AAS...188.6908M Altcode: 1996BAAS...28..936M
We present a new computer code for simulating anelastic stellar
convection in a rotating spherical shell which is based on an existing
algorithm, but redesigned to take full advantage of the higher
resolution possible on currently available parallel super-computing
platforms. Similar previous studies have led to important insights into
the dynamics of the solar convection zone, but are unable to reproduce
several important features, in particular the latitudinal and radial
angular velocity profile inferred from helioseismological inversion. The
results from helioseismology imply a differential rotation which is
constant on radial lines at mid latitudes in the convection zone,
while numerical simulations generally exhibit profiles which tend
to be constant on cylindrical surfaces aligned with the rotation
axis. Spherical shell simulations by Glatzmaier and other results from
convection in plane-parallel geometries suggest that the answer may
lie in increasing the spatial resolution of the model. The relatively
low resolutions of previous simulations only admit predominantly
laminar flows, which are known to exhibit significantly different
transport properties than turbulent flows, and which are therefore
less applicable to the highly turbulent conditions in solar convection
zone. To achieve the highest possible resolution, and therefore the most
turbulent flows, on current (and near future) computational resources,
our new implementation of Glatzmaier's earlier code is specifically
suited to the hierarchical memories characteristic of MPPs, with
careful consideration given to achieving both good serial performance
as well as good scalability on this class of machines. The former is
largely achieved through an extremely efficient implementation of the
Legendre transform which constitutes the majority of the computational
workload, while the latter is achieved primarily by a relatively complex
load-balancing scheme. We discuss the implementation as well as the
flow characteristics and transport properties of several simulations
achieved on our initial target platform, the IBM SP-2 at the Cornell
Theory Center, with spatial resolutions of up to 768 x 1536 x 129
(latitude, longitude, radial).
---------------------------------------------------------
Title: First Helioseismic Results from the Global Oscillation
Network Group
Authors: Toomre, Juri
1996AAS...188.2901T Altcode: 1996BAAS...28..861T
Helioseismology studies the internal structure and dynamics of the
sun, utilizing very precise measurements of the frequencies of sound
waves that propagate throughout the solar interior and are observed
at the surface. Efforts to accurately and precisely measure the mode
frequencies from a single observing site have met with fundamental
limitations imposed by the inevitable interruptions arising from the
day-night cycle. To address such problems, the NSF-sponsored Global
Oscillation Network Group (GONG) project has developed a network of
six identical instruments around the world providing velocity images
nearly continuously, a data processing system that can keep up with the
massive data flow, and is supported by a vigorous scientific community
structured around GONG teams that have shared in all aspects of the
development of the project. Though the primary helioseismic data deals
with the frequencies and their splittings for the nearly half-million
global acoustic modes detectable with the GONG instruments, the
data also allows study of how wave fields are locally influenced by
flows and magnetic structures below the solar surface, and further
provides direct measures of larger-scale flows at the surface. We
shall briefly describe the network, instruments, and data analysis,
and then review some of the preliminary scientific results obtained
by the teams through inversion of the frequency data, dealing with
the structure of the solar interior and the physics of stellar models,
and an assessment of the differential rotation profile with depth and
latitude. Early results will also be presented concerning nearly steady
surface flows of the solar surface.
---------------------------------------------------------
Title: Solar Internal Rotation and Dynamics from GONG Frequency
Splittings
Authors: Thompson, M. J.; Toomre, J.; GONG Dynamics Inversion Team
1996AAS...188.5305T Altcode: 1996BAAS...28..903T
The splitting of the Sun's global mode frequencies by large-scale flows
can be used to investigate the rotation profile in both radius and
latitude within the convection zone and deeper radiative interior. The
inversion of GONG data confirms that the surface latitudinal variation
of the rotation rate carries through much of the convection zone. At the
base of the convection zone there is a currently unresolved adjustment
layer with latitudinally independent rotation at greater depths. A
shearing layer just below the surface is discernable at low to mid
latitudes. Such global investigations are supplemented by local area
analyses via ring diagrams, which enable us to probe the subsurface
variation of rotation with depth beneath selected regions of the Sun.
---------------------------------------------------------
Title: First Scientific Results from the GONG Helioseismology Network
Authors: Toomre, Juri
1995AAS...18711402T Altcode: 1995BAAS...27.1447T
The GONG helioseismology project involves a broad international
collaboration among experimentalists and theoreticians keenly
interested in studying the internal dynamics and structure of our
nearest star. Much of the scientific work is being done by teams of GONG
members working together to assess the scientific inferences that can be
drawn from the nearly continuous Doppler imaging of the sun that is now
available from this network of identical instruments. Though the primary
helioseismic data deals with the frequencies and their splittings for
the nearly half-million global acoustic modes detectable with the GONG
instruments, the data also allows study of how wave fields are locally
influenced by flows and magnetic structures below the solar surface,
and further provides direct measures of larger-scale flows at the
surface. We shall review some of the preliminary scientific results
obtained by the teams through inversion of the frequency data obtained
from the early operation of the full network, dealing with assessment
of differential rotation profiles with depth and latitude deduced from
inversion of frequency splittings and of the sound speed profiles,
and thus mean structure deduced from the basic mode frequencies. Early
results will also be presented concerning nearly steady surface flows,
and of magnetic effects seen in the wave fields.
---------------------------------------------------------
Title: Turbulent Dynamics in the Solar Convection Zone
Authors: Brummell, Nicholas; Cattaneo, Fausto; Toomre, Juri
1995Sci...269.1370B Altcode:
Observations of the sun reveal highly complex flows and magnetic
structures that must result from turbulent convection in the solar
envelope. A remarkable degree of large-scale coherence emerges
from the small-scale turbulent dynamics, as seen in the cycles of
magnetic activity and in the differential rotation profile of this
star. High-performance computing now permits numerical simulations
of compressible turbulence and magnetohydrodynamics with sufficient
resolution to show that compact structures of vorticity and magnetic
fields can coexist with larger scales. Such structured turbulence
is yielding transport properties for heat and angular momentum at
considerable variance with earlier models. These simulations are
elucidating the coupling of turbulent fluid motions with rotation
and magnetic fields, which must control the interlinked differential
rotation and magnetic dynamo action.
---------------------------------------------------------
Title: Local-Area Simulations of Rotating Compressible Convection
and Associated Mean Flows
Authors: Hurlburt, N. E.; Brummel, N. H.; Toomre, J.
1995ESASP.376b.245H Altcode: 1995soho....2..245H; 1995help.confP.245H
No abstract at ADS
---------------------------------------------------------
Title: The Sensitivity of Various Mode Sets for Probing Differential
Rotation Shear Zones
Authors: Christensen-Dalsgaard, J.; Schou, J.; Thompson, M. J.;
Toomre, J.
1995ESASP.376b..41C Altcode: 1995soho....2...41C; 1995help.confP..41C
The potential of forthcoming datasets from GONG and SOI for resolving
long-lived azimuthal jets and shearing flows is investigated. The
authors construct various artificial datasets, containing noise
resembling that for a one-year observing run. These are then inverted,
using a 2-D regularized least squares (RLS) inversion. In particular,
the authors investigate the ability of the RLS method to form
well-localized averages of the rotation rate, as measured by the
averaging kernels, using an extensive mode set as well as subsets
thereof. The authors show that it is possible to keep the noise in
the solution down to a few nanohertz in much of the solar interior,
while obtaining very reasonable resolution, for a GONG-like dataset.
---------------------------------------------------------
Title: Analysis of Helioseismic Wave Fields to Examine Horizontal
Structures
Authors: Julien, K. A.; Gough, D. O.; Toomre, J.
1995ESASP.376b.155J Altcode: 1995help.confP.155J; 1995soho....2..155J
Presents and evaluates a preliminary inversion procedure for carrying
out a local area analysis on simulated oscillation data to deduce
two-dimensional subsurface structures in the horizontal, representative
of thermal variations, potentially as function of depth.
---------------------------------------------------------
Title: Non-Local Transport in Turbulent MHD Convection
Authors: Miesch, M.; Brandenburg, A.; Zweibel, E.; Toomre, J.
1995ESASP.376b.253M Altcode: 1995help.confP.253M; 1995soho....2..253M
No abstract at ADS
---------------------------------------------------------
Title: Plane-Wave Analysis of Solar Acoustic-Gravity Waves: a
(slightly) New Approach
Authors: Bogart, R. S.; Sá, L. A. D.; Duvall, T. L.; Haber, D. A.;
Toomre, J.; Hill, F.
1995ESASP.376b.147B Altcode: 1995soho....2..147B; 1995help.confP.147B
Plane-wave decomposition of acoustic-gravity wave effects observed
in the photosphere provides a computationally efficient technique for
probing the structure of the upper convective zone and boundary, where
the flat-Sun approximation is reasonably accurate. The authors describe
the technique to be used for systematic plane-wave analysis of MDI
data as part of the SOI data analysis pipeline, and the SOI analysis
plan. The authors present estimates of sensitivity and discuss the
effects of using different planar mappings. The technique is compared
with previous approaches to the 3-dimensional plane-wave problem.
---------------------------------------------------------
Title: Local-Area Analysis of High-Degree Solar Oscillations: New
Ring-Fitting Procedures
Authors: Haber, D. A.; Toomre, J.; Hill, F.; Gough, D. O.
1995ESASP.376b.141H Altcode: 1995help.confP.141H; 1995soho....2..141H
Local-area analysis of five-minute solar oscillations using ring
diagrams to determine subphotospheric velocity flows is on the brink
of becoming an important tool in understanding convective zone
dynamics. One of the main problems up to this point has been the
large computational burden of fitting the rings. The authors present a
faster method for carrying out the ring fits using data obtained with
the High-l Helioseismometer at Kitt Peak. The authors first eliminate
serious sources of noise, then use a perturbation approach to fit the
azimuthally averaged spectrum. The parameters so determined are held
constant while fitting the entire ring diagram.
---------------------------------------------------------
Title: Turbulent Rotating Compressible Convection in Spherical Domains
Authors: Hurlburt, N. E.; Brummell, N. H.; Toomre, J.
1995SPD....26..406H Altcode: 1995BAAS...27..955H
No abstract at ADS
---------------------------------------------------------
Title: Inversion for Background Inhomogeneity from Phase Distortion
of Two-Dimensional Wave Fields
Authors: Julien, K.; Gough, D.; Toomre, J.
1995ASPC...76..196J Altcode: 1995gong.conf..196J
No abstract at ADS
---------------------------------------------------------
Title: Global-Scale Solar Turbulent Convection and its Coupling
to Rotation
Authors: Glatzmaier, G. A.; Toomre, J.
1995ASPC...76..200G Altcode: 1995gong.conf..200G
No abstract at ADS
---------------------------------------------------------
Title: Spherical Core Convection in Rotating A-Type Stars
Authors: Dolez, N.; Glatzmaier, G. A.; Toomre, J.
1995ASPC...76..653D Altcode: 1995gong.conf..653D
No abstract at ADS
---------------------------------------------------------
Title: Maintenance of Differential Rotation in Turbulent Compressible
Convection with Rotation
Authors: Brummell, N. H.; Xie, X.; Toomre, J.; Baillie, C.
1995ASPC...76..192B Altcode: 1995gong.conf..192B
No abstract at ADS
---------------------------------------------------------
Title: Modelling Astrophysical Turbulent Convection
Authors: Brummell, N.; Toomre, J.
1995ASPC...77...15B Altcode: 1995adass...4...15B
Numerical simulations of highly turbulent flows in astrophysics
benefit greatly from recent advances in high performance computing. Yet
such three-dimensional modelling raises major problems in capturing,
moving, and analyzing the resulting massive data sets necessary to
sample the evolving intricate dynamics. Thus archiving, networking,
and visualization are as essential as the actual act of computing when
it comes to real scientific progress.
---------------------------------------------------------
Title: Solar Convection Zone Dynamics and Rotation
Authors: Toomre, J.; Brummell, N. H.
1995ESASP.376a..47T Altcode: 1995soho....1...47T; 1995heli.conf...47T
Reviews a range of approaches to study the basic dynamics of convection,
along with its ability to redistribute angular momentum in rotating
systems. The authors then describe results of three-dimensional
simulations of turbulent compressible convection constrained by
effects of rotation, both within spherical shells and within local
area f-planes. The turbulence possesses intense vortex tubes with
intricate interactions and instabilities, and more persistent and
spatially-coherent downflow networks, along with strong mean flows
when the rotational constraint is prominent. These theoretical
studies reveal that transition to turbulent states have associated
with them significant changes in flow asymmetries and transports,
and that such turbulent convection can drive substantial mean flows
which are distinctly different from those in which the convection is
dominantly laminar.
---------------------------------------------------------
Title: Hunting for Azimuthal Jets and Shearing Flows in the Solar
Convection Zone
Authors: Christensen-Dalsgaard, J.; Schou, J.; Thompson, M. J.;
Toomre, J.
1995ASPC...76..212C Altcode: 1995gong.conf..212C
No abstract at ADS
---------------------------------------------------------
Title: Solar Oscillation Ring Diagrams: Benefits of Great Circle
Remapping
Authors: Haber, D.; Toomre, J.; Hill, F.; Gough, D.
1995ASPC...76..272H Altcode: 1995gong.conf..272H
No abstract at ADS
---------------------------------------------------------
Title: Astrophysical Convection and Turbulence
Authors: Toomre, J.
1994AAS...184.5002T Altcode: 1994BAAS...26..942T
The vigorous turbulence that results from convective instability
within rotating stars serves to not only transport heat but also
redistribute angular momentum and chemical species, and can yield
magnetic dynamo action. A hallmark of such turbulence constrained by
rotation and stratification is that large-scale coherent structures
and strong mean flows can coexist with the intense smaller-scale
turbulence. Helioseismology is suggesting that the resulting
differential rotation within the convection zone of a star like the
sun yields serious puzzles about the interaction of convection and
rotation. Understanding such nonlinear dynamics at a fundamental
level raises formidable challenges because of the broad range of
scales of motion that must be resolved. High-performance computing
offers the opportunity to make substantial inroads in studying the
properties of such astrophysical turbulence. An interdisciplinary team
of researchers at several institutions is working jointly on problems
in geophysical and astrophysical fluid dynamics (GAFD) turbulence
to utilize massively parallel architectures to increase the spatial
resolution in three-dimensional simulations employing variously
pseudo-spectral, finite-difference, multi-grid and PPM approaches
in studying the intense turbulence encountered in both planetary and
stellar settings. The scale of these simulations requires corresponding
progress in the computational sciences, both in order to develop and
optimize software for massively-parallel computers and to capture and
visualize the resulting massive data sets. A selection of highlights
from our turbulence research will be presented, turning for instance to
local-area models of turbulent compressible convection within stellar
envelopes. The turbulence possesses both intense vortex filaments
with intricate interactions and instabilities, and more persistent
and spatially-coherent downflow networks, along with strong mean
flows when the rotational constraint is prominent. We also consider
the convective turbulence and mixing achieved within the full nuclear
burning cores of rotating A-type stars, finding that such penetrative
convection drives substantial differential rotation.
---------------------------------------------------------
Title: Penetration below a Convection Zone
Authors: Hurlburt, Neal E.; Toomre, Juri; Massaguer, Josep M.; Zahn,
Jean-Paul
1994ApJ...421..245H Altcode:
Two-dimensional numerical simulations are used to investigate how fully
compressible nonlinear convection penetrates into a stably stratified
zone beneath a stellar convection zone. Estimates are obtained of the
extent of penetration as the relative stability S of the stable to
the unstable zone is varied over a broad range. The model deals with
a perfect gas possessing a constant dynamic viscosity. The dynamics
is dominated by downward-directed plumes which can extend far into
the stable material and which can lead to the excitation of a broad
spectrum of internal gravity waves in the lower stable zone. The
convection is highly time dependent, with the close coupling between
the lateral swaying of the plumes and the internal gravity waves they
generate serving to modulate the strength of the convection. The depth
of penetration delta, determined by the position where the time-averaged
kinetic flux has its first zero in the stable layer, is controlled by
a balance between the kinetic energy carried into the stable layer by
the plumes and the buoyancy braking they experience there. A passive
scalar is introduced into the unstable layer to evaluate the transport
of chemical species downward. Such a tracer is effectively mixed
within a few convective overturning times down to a depth of delta
within the stable layer. Analytical estimates based on simple scaling
laws are used to interpret the variation of delta with S, showing that
it first involves an interval of adiabatic penetration if the local
Peclet number of the convection exceeds unity, followed by a further
thermal adjustment layer, the depths of each interval scaling in turn
as S<SUP>-1</SUP> and S<SUP>-1/4</SUP>. These estimates are in accord
with the penetration results from the simulations.
---------------------------------------------------------
Title: Seismology of the Sun
Authors: Christensen-Dalsgaard, J.; Gough, D. O.; Toomre, J.
1994snft.book..418C Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Compressible Convection with Ionization. II. Thermal
Boundary-Layer Instability
Authors: Rast, Mark P.; Toomre, Juri
1993ApJ...419..240R Altcode:
Rast & Toomre (1993, Paper I) examined the effects of
ionization-state changes on the stability, flow asymmetry,
and flux transport properties of two-dimensional compressible
convection. Here we employ the same single-atomic-level hydrogen model
and analyze vigorously time-dependent nonlinear solutions. Ionization-
state-dependent variations in thermal diffusivity of the fluid can
result in thermal boundary-layer instability and plume formation. The
interval between pluming events depends on the growth rate of the
instability and both the scale and the velocity of the underlying
convective motions. Such instabilities can occur at either boundary,
depending on the positioning of the partially ionized region within the
domain. Here we concentrate on simulations in which the instability is
manifest in the upper thermal boundary layer, and results in cool plume
formation. Temperature fluctuations and associated buoyancy forces in
the plumes are maintained as long as heat exchange and compressional
heating result primarily in ionization of the fluid rather than in
temperature equilibration, and this can lead to supersonic vertical
flows in an otherwise subsonic flow field. These flows serve to excite
acoustic oscillations, the phase of which can be abruptly altered
by subsequent plume events. For high rates of plume initiation, the
fundamental acoustic period of the domain is greater than the time
span between two descents. Such ionization effects are expected to
influence the dynamics of granulation and acoustic mode excitation
in the Sun and other stars, and likewise the coupling of convection
with pulsations that occurs in stars such as white dwarfs and Cepheid
variables. Additionally, it is possible that thermal instabilities
analogous to those seen in these simulations occur not only in the
photosphere but also at the base of stellar convective envelopes owing
to temperature-sensitive variations in the radiative conductivity of
fluid there.
---------------------------------------------------------
Title: Compressible Convection with Ionization. I. Stability, Flow
Asymmetries, and Energy Transport
Authors: Rast, Mark P.; Toomre, Juri
1993ApJ...419..224R Altcode:
The influence of nonideal effects associated with ionization
upon the dynamics and thermodynamics of compressible convection
is studied. Linear and finite-amplitude analyses and fully
nonlinear two-dimensional simulations of a plane-parallel layer
of single-atomic-level hydrogen fluid are undertaken. Ionization
significantly influences both the global transport properties and
the local dynamics of convective flows by modifying the particle
number density, specific heat, and internal energy content of the
fluid. Strong temperature fluctuations and corresponding buoyancy
forces develop locally in the fluid wherever rapid changes in
ionization state occur. These can result in narrow regions of
intense vertical flow. The flow asymmetries seen in simulations of
compressible ideal-gas convection can either be enhanced or diminished
depending on the vertical positioning of the partially ionized
region within the domain. Additionally, the enthalpy flux achieved
by ionizing convection is dominated in regions of partial ionization
by latent-heat transport. The enthalpy carried by downflow plumes can
be considerably elevated, and the cancellation between kinetic energy
and enthalpy fluxes observed in the downflows in some simulations of
ideal gas turbulence may thus be offset by partial ionization of the
fluid. Such ionization effects are likely to influence the character
of convective motions within stellar envelopes. Convective transport
properties may differ substantially between the partially ionized and
the deeper fully ionized regions of a star, and since ionization zone
placement also varies with respect to both the photosphere and the
lower thermal boundary, between stellar types and during the course
of stellar evolution.
---------------------------------------------------------
Title: Turbulent Compressible Convection with Rotation
Authors: Brummell, N. H.; Toomre, J.; Hurlburt, N. E.
1993BAAS...25.1192B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Ionization Effects in Three-dimensional Solar Granulation
Simulations
Authors: Rast, Mark P.; Nordlund, Ake; Stein, Robert F.; Toomre, Juri
1993ApJ...408L..53R Altcode:
These numerical studies show that ionization influences both the
transport and dynamical properties of compressible convection
near the surface of the Sun. About two-thirds of the enthalpy
transported by convective motions in the region of partial hydrogen
ionization is carried as latent heat. The role of fast downflow
plumes in total convective transport is substantially elevated
by this contribution. Instability of the thermal boundary layer
is strongly enhanced by temperature sensitive variations in the
radiative properties of the fluid, and this provides a mechanism for
plume initiation and cell fragmentation in the surface layers. As
the plumes descend, temperature fluctuations and associated buoyancy
forces are maintained because of the increased specific heat of the
partially ionized material. This can result is supersonic vertical
flows. At greater depths, ionization effects diminish, and the plumes
are decelerated by significant entrainment of surrounding fluid.
---------------------------------------------------------
Title: Large-Eddy Simulations of Compressible Convection on Massively
Parallel Computers
Authors: Xie, Xin; Toomre, Juri
1993ApJ...405..747X Altcode:
We report preliminary implementation of the large-eddy simulation (LES)
technique in 2D simulations of compressible convection carried out
on the CM-2 massively parallel computer. The convective flow fields
in our simulations possess structures similar to those found in a
number of direct simulations, with roll-like flows coherent across the
entire depth of the layer that spans several density scale heights. Our
detailed assessment of the effects of various subgrid scale (SGS) terms
reveals that they may affect the gross character of convection. Yet,
somewhat surprisingly, we find that our LES solutions, and another in
which the SGS terms are turned off, only show modest differences. The
resulting 2D flows realized here are rather laminar in character,
and achieving substantial turbulence may require stronger forcing and
less dissipation.
---------------------------------------------------------
Title: Interaction of Externally-Driven Acoustic Waves with
Compressible Convection
Authors: Jones, P.; Merryfield, W.; Toomre, J.
1993ASPC...42...45J Altcode: 1993gong.conf...45J
No abstract at ADS
---------------------------------------------------------
Title: Inversion for Background Inhomogeneity from Phase Distortions
of One-Dimensional Wave Trains
Authors: Gough, D. O.; Merryfield, W. J.; Toomre, J.
1993ASPC...42..257G Altcode: 1993gong.conf..257G
No abstract at ADS
---------------------------------------------------------
Title: Acoustic Excitation by Thermal Boundary Layer Instability in
a Partially Ionized Convecting Fluid
Authors: Rast, M. P.; Toomre, J.
1993ASPC...42...41R Altcode: 1993gong.conf...41R
No abstract at ADS
---------------------------------------------------------
Title: Thermal convection and penetration.
Authors: Toomre, J.
1993afd..conf..325T Altcode:
Contents: 1. Introduction. 2. Boussinesq convection in simple
geometries. 3. Anelastic modal convection. 4. Two-dimensional fully
compressible convection. 5. Three-dimensional fully compressible
convection. 6. Final reflections.
---------------------------------------------------------
Title: Ionization Effects on Solar Granulation Dynamics
Authors: Rast, M. P.; Nordlund, A.; Stein, R. F.; Toomre, J.
1993ASPC...42...57R Altcode: 1993gong.conf...57R
No abstract at ADS
---------------------------------------------------------
Title: Turbulent Compressible Convection with Rotation
Authors: Brummell, N. H.; Hurlburt, N. E.; Toomre, J.
1993ASPC...42...61B Altcode: 1993gong.conf...61B
No abstract at ADS
---------------------------------------------------------
Title: Laboratory and theoretical models of planetary-scale
instabilities and waves
Authors: Hart, John E.; Toomre, Juri
1991gsap.rept...47H Altcode:
Meteorologists and planetary astronomers interested in large-scale
planetary and solar circulations recognize the importance of rotation
and stratification in determining the character of these flows. The
two outstanding problems of interest are: (1) the origins and nature
of chaos in baroclinically unstable flows; and (2) the physical
mechanisms responsible for high speed zonal winds and banding on
the giant planets. The methods used to study these problems, and the
insights gained, are useful in more general atmospheric and climate
dynamic settings. Because the planetary curvature or beta-effect
is crucial in the large scale nonlinear dynamics, the motions of
rotating convecting liquids in spherical shells were studied using
electrohydrodynamic polarization forces to generate radial gravity and
centrally directed buoyancy forces in the laboratory. The Geophysical
Fluid Flow Cell (GFFC) experiments performed on Spacelab 3 in 1985 were
analyzed. The interpretation and extension of these results have led to
the construction of efficient numerical models of rotating convection
with an aim to understand the possible generation of zonal banding on
Jupiter and the fate of banana cells in rapidly rotating convection as
the heating is made strongly supercritical. Efforts to pose baroclinic
wave experiments for future space missions using a modified version of
the 1985 instrument have led us to develop theoretical and numerical
models of baroclinic instability. Some surprising properties of both
these models were discovered.
---------------------------------------------------------
Title: Simulation of Effects of Atmospheric Seeing on the Observation
of High-Degree Solar Oscillations
Authors: Hill, Frank; Gough, Douglas; Merryfield, William J.;
Toomre, Juri
1991ApJ...369..237H Altcode:
Numerical simulations of the effects of atmospheric seeing distortions
on observations of solar oscillations of intermediate and high degree
are performed. The simulations involve a representation of about 100
p-modes of oscillation, with degrees l = 50-150 (intermediate-degree)
and 150-450 (high-degree), formed from the complement of a sexated mode
set. These modes are superposed on a steady large-scale convective
background, and projected onto the plane of the sky. Image motion is
modeled by displacement maps generated from two-dimensional turbulence
power spectra; the maps are scaled so that the rms amplitude of the
displacements has values of 2-5 arcsec. The distorted velocity field is
then Fourier analyzed to produce simulated (l, nu) power diagrams, where
nu is the temporal cyclic frequency. The results show that power in the
mode ridges is diminished as atmospheric seeing worsens, particularly
at high degrees. Redistribution of power produces an apparent decrease
in the frequencies of the oscillations as measured by the centroids
of the ridges in the power spectra. It is found that time-averaging
the observations is quite effective in reducing the noise.
---------------------------------------------------------
Title: Turbulent Compressible Convection
Authors: Cattaneo, Fausto; Brummell, Nicholas H.; Toomre, Juri;
Malagoli, Andrea; Hurlburt, Neal E.
1991ApJ...370..282C Altcode:
Numerical simulations with high spatial resolution (up to 96-cubed
gridpoints) are used to study three-dimensional, compressible
convection. A sequence of four models with decreasing viscous
dissipation is considered in studying the changes in the flow structure
and transport properties as the convection becomes turbulent.
---------------------------------------------------------
Title: Nonlinear Behavior of Solar Gravity Modes Driven by 3He in
the Core. II. Numerical Simulations
Authors: Merryfield, William J.; Toomre, Juri; Gough, Douglas
1991ApJ...367..658M Altcode:
The nonlinear behavior of gravity-mode oscillations driven by
He-3-destroying reactions in the solar core has been examined
by numerically integrating equations describing a very simplified
model. The results of a previous bifurcation analysis, which suggest
that such oscillations are unlikely to attain amplitudes sufficient
to trigger core convection, are verified. These results are extended
to models whose nuclear reaction rates and thermal stratification
represent the core somewhat more accurately. Nonlinear processes give
rise to a preference for the oscillations to develop as standing waves
rather than traveling waves, thus breaking the degeneracy between
these two types of motion which exists in linearized theory. Study
of the large-amplitude behavior of the oscillations is hindered by a
tendency for the model to become thermally unstable.
---------------------------------------------------------
Title: On the Analysis of Physical Wave Trains
Authors: Gough, D. O.; Merryfield, W. J.; Toomre, J.
1991LNP...388..265G Altcode: 1991ctsm.conf..265G
When a wave train whose constituent frequencies and wave numbers are
unresolved by observation propagates through an inhomogeneous medium,
beating between the components can contaminate deductions one might
naively draw about the inhomogeneous background. This is a severe
problem to anyone confronted with analysing helioseismic data with
a view to determining the structure of giant convective cells. We
propose a procedure for analysing wave trains, based on approximating
a packet as a single representative pure wave. We present some
preliminary results of analysing artificial data. For simplicity, we
have deliberately excluded some of the effects of wave interference,
which must be faced by any means of analysis. Therefore we do not
claim to have found a complete procedure for analysing real data.
---------------------------------------------------------
Title: Challenges to Theories of the Structure of Moderate-Mass Stars
Authors: Gough, Douglas; Toomre, Juri
1991LNP...388.....G Altcode: 1991ctsm.conf.....G
No abstract at ADS
---------------------------------------------------------
Title: The Organization of Turbulent Convection
Authors: Brummell, Nicholas; Cattaneo, Fausto; Malagoli, Andrea;
Toomre, Juri; Hurlburt, Neal E.
1991LNP...388..187B Altcode: 1991ctsm.conf..187B
Highly resolved numerical simulations are used to study
three-dimensional, compressible convection. The viscous dissipation is
sufficiently low that the flow divides itself in depth into two distinct
regions: (i) an upper thermal boundary layer containing a smooth flow
with a granular appearance, and (ii) a turbulent interior pierced
by the strongest downflows from the surface layer. Such downflows
span the whole depth of the unstable layer, are temporally coherent,
and are thermodynamically well correlated. A remarkable property of
such convection, once it becomes turbulent, is that the enthalpy and
kinetic fluxes carried by the strong downflows nearly cancel, for they
are of opposite sense and nearly equal in amplitude. Thus, although the
downflows serve to organize the convection and are the striking feature
that emerges from effects of compressibility, it is the small-scale,
disorganized turbulent motions (between the coherent downflow structures
that serve as the principal carriers of net convected flux.
---------------------------------------------------------
Title: The role of f modes in the inversion of high-ℓ rotational
splittings
Authors: Haber, Deborah A.; Hill, Frank; Toomre, Juri
1991LNP...388...87H Altcode: 1991ctsm.conf...87H
The contribution of the solar f modes of oscillation to the inversion
of high-degree rotational splitting data is examined. We find that
the f modes play an important role in such inversions as revealed
by the magnitude of their weighting coefficients c i . This may be
attributed to the single-peaked structure of the f-mode kernels,
which is similar to that of the desired averaging kernels and in
contrast to the many-peaked shape of the higher-order kernels. The
high weight placed on the f modes in the inversions raises issues for
observational techniques since the f modes possess modest power levels
and their detection is influenced by the choice of spatial filtering.
---------------------------------------------------------
Title: Program at ITP: Helioseismology — Probing the interior of
a star
Authors: Gough, Douglas; Toomre, Juri
1991LNP...388....1G Altcode: 1991ctsm.conf....1G
The research program in helioseismology carried out at the Institute
for Theoretical Physics (ITP) at the University of California, Santa
Barbara during the six-month interval from January to June 1990
involved 61 scientists of diverse disciplines: theorists, observers
and instrumentalists in physics, astrophysics and geophysics. The main
topics of research and joint discussion included mode excitation and
decay, the internal structure of the sun and its sensitivity to the
physics of the equation of state and opacity, seismological inverse
procedures, and solar rotation and convection-zone dynamics.
---------------------------------------------------------
Title: Vertically Coherent Compressible Convective Flows in a Layer
with a High Density Contrast
Authors: Xie, Xin; Toomre, Juri
1991LNP...388..171X Altcode: 1991ctsm.conf..171X
Two-dimensional simulations are used to study compressible convection
in a plane-parallel layer of ideal gas with a high density contrast
across the layer. The convective flows are found to consist of rolls
which are coherent throughout the entire vertical domain, similar to the
results of a number of earlier investigations. Motions near the upper
boundary are supersonic, though the Rayleigh number is moderate. The
major effect of a high density stratification is to significantly
rarefy the fluid in the upper part of the domain, hence increase its
thermal diffusivity. The consequence appears to be twofold: Firstly,
enhanced thermal diffusion makes non-adiabatic cooling more efficient,
thus helps the flows to become supersonic more easily. Secondly,
sufficient diffusion can broaden shocks to such an extent that it
actually turns them into smooth transition regions.
---------------------------------------------------------
Title: Effects of spatial filtering on high-ℓ power spectra and
rotational splitting inversions
Authors: Haber, Deborah A.; Hill, Frank; Toomre, Juri
1991LNP...388..259H Altcode: 1991ctsm.conf..259H
The effects of the spatial filtering algorithm on the results of an
inversion of high-degree solar oscillation data are examined. In
attempting to isolate sectoral modes, the Fourier transforms in
longitude are accompanied by three different spatial filterings in
the orthogonal direction. The filters are: simple averaging in the
plane of the sky, averaging along lines of constant heliographic
longitude with uniform weighting, and another with weighting based
on appropriate Legendre functions. The choice of spatial filter
changes the distribution of power in the two-dimensional spectrum
of the oscillations, particularly in the f and p 1 ridges. These
variations in the power distribution affect the determination of the
rotational splittings, thereby influencing the results of inversions
which emphasize information contained in the low-order ridges.
---------------------------------------------------------
Title: Seismic observations of the solar interior.
Authors: Gough, Douglas; Toomre, Juri
1991ARA&A..29..627G Altcode:
Contents: 1. Introduction. 2. Solar evolution. 3. Properties of
modes. 4. Observational principles. 5. Inversion of data. 6. Inference
of hydrostatic structure. 7. The neutrino problem. 8. Rotation and
other subsurface flows. 9. Mode excitation and decay. 10. Solar cycle
variations. 11. Asteroseismology.
---------------------------------------------------------
Title: Interaction of Acoustic Oscillations with Time-Dependent
Compressible Convection
Authors: Jones, P. W.; Merryfield, W. J.; Toomre, J.
1991LNP...388..213J Altcode: 1991ctsm.conf..213J
We present the results of numerical simulations in which acoustic waves
are driven into a two-dimensional layer of compressible fluid which
is undergoing convection. The energetics of the waves are analyzed by
computing the work integrals associated with the modulation of the
gas and turbulent pressures. We find that the relative importance
of the turbulent pressure component of the work integral increases
prominently with increasing wave frequency. Also, the time dependence
of the convection leads to temporal irregularity in the component
of wave driving and damping associated with the convection-pulsation
coupling. We speculate that such irregularity may contribute to the
aperiodicity observed in the light curves of Mira variables and other
pulsating red giant stars.
---------------------------------------------------------
Title: Large Eddy Simulations of Compressible Convection
Authors: Xie, Xin; Toomre, Juri
1991LNP...388..147X Altcode: 1991ctsm.conf..147X
Large-eddy simulation (LES) technique has been applied to
two-dimensional compressible convection in a plane-parallel layer
of ideal gas with intermediate density contrast. The general flow
patterns consist of a series of rolls in the horizontal which are
coherent throughout the entire vertical domain, much like findings by a
number of investigators. The horizontal component of the subgrid-scale
(SGS) force appears to enhance fluctuations of pressure and density,
which in turn cause the resultant force, say f pg arising from pressure
gradient and gravity terms, to increase in magnitude in such a way that
f pg, besides balancing the inertial terms, can essentially offset
the vertical component of the SGS force. Consequently, compared to a
solution obtained omitting the SGS terms, the flow field of the LES
solution only shows moderate differences. There is some indication
that the overall SGS effect tends to reduce the asymmetry between the
vertical flows in the interior of the domain while enhancing it in
the base region.
---------------------------------------------------------
Title: Three-dimensional compressible convection at low Prandtl
numbers.
Authors: Toomre, Juri; Brummell, Nicholas; Cattaneo, Fausto; Hurlburt,
Neal E.
1990CoPhC..59..105T Altcode:
Numerical simulations are used to study fully compressible thermal
convection at large Rayleigh numbers. The authors present results from a
sequence of three-dimensional simulations that reveal a transition from
gradually-evolving laminar convection to nearly turbulent convection
as the Prandtl number is reduced from a value of unity to one-tenth.
---------------------------------------------------------
Title: Nonlinear Behavior of Solar Gravity Modes Driven by 3He in
the Core. I. Bifurcation Analysis
Authors: Merryfield, William J.; Toomre, Juri; Gough, Douglas
1990ApJ...353..678M Altcode:
The nonlinear development of solar gravity modes driven by He-3 burning
in the solar core is investigated by means of an idealized dynamical
model. Possible outcomes that have been suggested in the literature
include the triggering of subcritical direct convection, leading to
core mixing, and the saturation of the excitation processes, leading
to sustained finite-amplitude oscillations. The present simple model
suggests that the latter is the more likely. The limiting amplitude
of the oscillations is estimated, ignoring possible resonances with
other gravity modes, to be of order 10 km/s at the solar surface. Such
oscillations would be easily observable. That large-amplitude gravity
modes have not been observed suggests either that these modes are not
unstable in the present era or that they are limited to much smaller
amplitudes by resonant coupling.
---------------------------------------------------------
Title: Supersonic Convection
Authors: Cattaneo, Fausto; Hurlburt, Neal E.; Toomre, Juri
1990ApJ...349L..63C Altcode:
Numerical simulations with high spatial resolution are used to study
that the combined effects of stratification, pressure gradients,
and nonadiabatic processes can lead to the formation of regions of
supersonic motions near the upper thermal boundary layer. Within
these regions, the dynamics is dominated by nonstationary shock
structures. These form near the downflow sites and propagate upstream
along the boundary layer to the upflow regions where they weaken and
eventually disappear. The shock cycle, consisting of the formation,
propagation, and disappearance of shock structures, has a time scale
comparable to the sound crossing time over a portion of the convective
cell, giving rise to vigorous time dependence in the convection.
---------------------------------------------------------
Title: Laboratory and theoretical models of planetary-scale
instabilities and waves
Authors: Hart, John E.; Toomre, Juri
1989gsap.rept...59H Altcode:
The continuous low-g environment of the orbiting space shuttle provided
a setting for conducting geophysical fluid model experiments with a
completely consistent representation of sphericity and the resultant
radial gravity found on astrogeophysical objects. This is possible
because in zero gravity an experiment can be constructed that has
its own radial buoyancy forces. The dielectric forces in a liquid,
which are linearly dependent on fluid temperature, give rise to an
effectively radial buoyancy force when a radial electrostatic field
is applied. The Geophysical Fluid Flow Cell (GFFC) experiment is an
implementation of this idea in which fluid is contained between two
rotating hemispheres that are differentially heated and stressed with a
large ac voltage. The GFFC flew on Spacelab 3 in May 1985. Data in the
form of global Schlieren images of convective patterns were obtained
for a large variety of configurations. These included situations of
rapid rotation (large Taylor numbers), low rotation, large and small
thermal forcing, and situations with applied meridional temperature
gradients. The analysis and interpretation of the GFFC-85 data are
being conducted. Improvements were developed to the GFFC instrument
that will allow for real-time (TV) display of convection data and for
near-real-time interactive experiments. These experiments, on the
transition to global turbulence, the breakdown of rapidly rotating
convective planforms and other phenomena, are scheduled to be carried
out on the International Microgravity Laboratory (IML-1) aboard the
shuttle in June 1990.
---------------------------------------------------------
Title: Preflare activity.
Authors: Priest, E. R.; Gaizauskas, V.; Hagyard, M. J.; Schmahl, E. J.;
Webb, D. F.; Cargill, P.; Forbes, T. G.; Hood, A. W.; Steinolfson,
R. S.; Chapman, G. A.; Deloach, A. C.; Gary, G. A.; Jones, H. P.;
Karpen, J. T.; Martres, M. -J.; Porter, J. G.; Schmieder, B.; Smith,
J. B., Jr.; Toomre, J.; Woodgate, B.; Waggett, P.; Bentley, R.;
Hurford, G.; Schadee, A.; Schrijver, J.; Harrison, R.; Martens, P.
1989epos.conf....1P Altcode:
Contents: 1. Introduction. 2. Magnetohydrodynamic
instability. 3. Preflare magnetic and velocity fields. 4. Coronal
manifestations of preflare activity.
---------------------------------------------------------
Title: Two and Three-Dimensional Simulations of Compressible
Convection
Authors: Cattaneo, F.; Hurlburt, N. E.; Toomre, J.
1989ASIC..263..415C Altcode: 1989ssg..conf..415C
No abstract at ADS
---------------------------------------------------------
Title: Nonlinear studies of solar gravity modes driven by nuclear
burning of the <SUP>3</SUP>He in the core.
Authors: Merryfield, W. J.; Toomre, J.; Gough, Douglas O.
1988ESASP.286...21M Altcode: 1988ssls.rept...21M
The finite-amplitude behavior of gravity-mode oscillations driven
within the deep interior of the sun has been studied by means of a
simple idealized model. Such g modes may be self-excited by their
ability to extract energy from the nuclear burning of <SUP>3</SUP>He
in the core. Both a nonlinear bifurcation analysis and numerical
simulations of the behavior of this instability suggest that the
growth of <SUP>3</SUP>He-driven oscillations is likely be limited to
an amplitude which is insufficient to induce convective instability
in the core, a process which has been proposed as a mechanism for core
mixing. The numerical results also indicate that if the oscillations are
linarly unstable then the degeneracy in linear theory between standing
and travelling g modes is broken by nonlinear effects. The oscillations
thus develop into a left- or right-travelling wave rather than a
standing wave or other superposition of horizontally propagating waves.
---------------------------------------------------------
Title: Local effects of a major flare on solar five-minute
oscillations.
Authors: Haber, D. A.; Toomre, J.; Hill, Frank; Gough, Douglas O.
1988ESASP.286..301H Altcode: 1988ssls.rept..301H
Doppler velocity images of the full Sun were obtained both during and
after a major white-light flare. These velocities were interpolated onto
a cylindrical coordinate system centered on the flare and decomposed
into radially propagating waves defined by Hankel functions. For
a similar analysis of quiet Sun regions the authors find fairly
comparable power in incoming and outgoing waves irrespective of the
presence of the flare. However, for the flaring region, there is 14%
greater power in incoming as opposed to outgoing waves when there
is no flare, but 5% greater power in outgoing than in incoming waves
during the flare. This result suggests that the flare may have excited
outgoing waves which counteracted the more usual absorption of incoming
acoustic waves by sunspots.
---------------------------------------------------------
Title: Whirlpool traced by granulation
Authors: Toomre, Juri
1988Natur.335..202T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Magnetic Fields Interacting with Nonlinear Compressible
Convection
Authors: Hurlburt, Neal E.; Toomre, Juri
1988ApJ...327..920H Altcode:
Two-dimensional numerical simulations are used to study fully
compressible convection in the presence of an imposed magnetic
field. Highly nonlinear flows are considered that span multiple density
scale heights. The convection tends to sweep the initially uniform
vertical magnetic field into concentrated flux sheets with significant
magnetic pressures. These flux sheets are partially evacuated, and
effects of buoyancy and Lorentz forces there can serve to suppress
motions. The flux sheets can be surrounded by a sheath of descending
flow. If the imposed magnetic field is sufficiently strong, the
convection can become oscillatory. The unstably stratified fluid layer
has an initial density ratio (bottom to top of layer) of 11. Surveys of
solutions at fixed Rayleigh number sample Chandrasekhar numbers from 1
to 1000 and magnetic Prandtl numbers from 1/16 to 1. These nonlinear
simulations utilize a two-dimensional numerical scheme based on a
modified two-step Lax-Wendroff method.
---------------------------------------------------------
Title: Simulations of the Interaction of Radial Stellar Pulsations
with Compressible Convection
Authors: Merryfield, W. J.; Toomre, J.
1988BAAS...20..702M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Topology of Plumes in Nonlinear Compressible Convection
Authors: Toomre, J.; Cattaneo, F.; Hurlburt, N. E.
1988BAAS...20..678T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Helioseismology: Theoretical Background and Challenges
Authors: Toomre, J.
1988BAAS...20..729T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solar Equatorial Rotation Rate Inferred from Inversion of
Frequency Splitting of High-Degree Modes
Authors: Hill, F.; Gough, D. O.; Toomre, J.; Haber, D. A.
1988IAUS..123...45H Altcode:
The equatorial rotation rate has been inferred as a function of depth
through the outer 16 Mm of the Sun from observations of high-degree
five-minute oscillations. The results imply that the solar rotation
rate increases with depth by 0.023 μHz reaching a maximum at about
2 Mm below the surface, then decreases by 0.037 μHz down to 16 Mm.
---------------------------------------------------------
Title: Response of the Solar 5-MINUTE Oscillations to a Major Flare
Authors: Haber, D. A.; Toomre, J.; Hill, F.
1988IAUS..123...59H Altcode:
Solar five-minute oscillations of intermediate-degree l were observed
both before and after a very strong white-light flare. The data
were projected onto both equatorial and polar sectoral modes and
Fourier transformed in time. Comparing the resulting power spectra,
the authors find a substantial increase in power in the p<SUB>5</SUB>
ridge of the equatorial modes on the day after the flare. When data
from all the ridges are considered, there is an average increase in
power of only a few percent the day after the flare.
---------------------------------------------------------
Title: Traveling waves and chaos in thermosolutal convection
Authors: Deane, A. E.; Knobloch, E.; Toomre, J.
1987PhRvA..36.2862D Altcode:
Numerical experiments on two-dimensional thermosolutal convection reveal
oscillations in the form of traveling, standing, modulated, and chaotic
waves. Transitions between these wave forms and steady convection are
investigated and compared with theory. Such rich nonlinear behavior
is possible in fluid layers of wide horizontal extent, and provides
an explanation for waves observed in recent laboratory experiments
with binary fluid mixtures.
---------------------------------------------------------
Title: Solar oscillations and convective flows as probes of structure
in the subphotosphere
Authors: Toomre, Juri; Gebbie, Katharine B.
1987jila.rept.....T Altcode:
Application of inverse theory to the observation of high-degree
five-minute solar oscillations has led to the detection of horizontal
flows below the solar surface that are a combination of solar
rotation and giant convection cells. The distinctive displacements
in the centroids of the ridges evident in the power diagrams of the
oscillations from one observing day to the next arise from different
patterns of giant cells being rotated into view. Such observation
of frequency splittings for the high degree oscillation modes,
combined with refinements in the inversion of the data using optimal
averaging and spectral expansions, has shown that helioseismology
should permit detailed mapping of velocity and thermal structures
below the solar surface. Extensive theoretical studies of fully
compressible magnetoconvection have shown that flows are indeed able
to concentrate magnetic fields into concentrated flux sheets that are
substantially evacuated of gas. The magnetic buoyancy instabilities
have been extensively studied.
---------------------------------------------------------
Title: A laboratory model of planetary and stellar convection
Authors: Hart, J. E.; Toomre, J.; Deane, A. E.; Hurlburt, N. E.;
Glatzmaier, G. A.; Fichtl, G. H.; Leslie, F.; Fowlis, W. W.; Gilman,
P. A.
1987STIN...8722108H Altcode:
Experiments on thermal convection in a rotating, differentially-heated
spherical shell with a radial buoyancy force were conducted in an
orbiting microgravity laboratory. A variety of convective structures,
or planforms, were observed depending on the magnitude of the rotation
and the nature of the imposed heating distribution. The results are in
agreement with numerical simulations that can be conducted at modest
parameter values, and suggest possible regimes of motion in rotating
planets and stars.
---------------------------------------------------------
Title: Vector array processor computer equipment
Authors: Toomre, Juri
1987colo.rept.....T Altcode:
To support the on-going research on Solar Oscillations and Convective
Flows as Probes of Structure in the Subphotosphere, a vector array
processor system was acquired to augment the existing DEC VAX-11/750
computer system. The fifty-fold average increase in computing speed
offered by the array processor would make it feasible to invert
solar oscillation data on a regular basis, and thereby permit us to
use the five-minutes oscillations of the Sun to probe the turbulent
convection zone below the surface of this star. The array processor
would also permit us to carry out detailed numerical experiments
with compressible convection in the presence of magnetic fields,
for the speed and memory of the machine makes it a formidable tool
for direct numerical simulations of two- and three-dimensional fluid
dynamics. Such theoretical simulations are also needed to study the
solar dynamo and its ability to build and transform magnetic fields,
an issue central to solar-terrestrial variability and predictions of
solar activity. Attached as Appendix A is a cover article in Science
Magazine that describes the importance of the work on the Seismology of
the Sun that is beginning to emerge from the class of array processors.
---------------------------------------------------------
Title: Spacelab experiments on convection in a rotating spherical
shell with radial gravity
Authors: Toomre, J.; Hart, J. E.; Glatzmaier, G. A.
1987ASSL..137...27T Altcode: 1987isav.symp...27T
Experiments on thermal convection in a rotating, differentially-heated
hemispherical shell of fluid with a radial gravity field were carried
out in the microgravity environment of Spacelab 3 which was flown on the
space shuttle Challenger in May 1985. Schlieren visualizations of these
laboratory flows are compared briefly to three-dimensional nonlinear
simulations that can be conducted at the more modest heating rates.
---------------------------------------------------------
Title: Nonlinear Compressible Convection Penetrating into Stable
Layers and Producing Internal Gravity Waves
Authors: Hurlburt, Neal E.; Toomre, Juri; Massaguer, Josep M.
1986ApJ...311..563H Altcode:
Penetrative convection spanning multiple scale heights is studied
within a simple stellar envelope consisting of three layers: a
convectively unstable middle layer bounded above and below by stably
stratified polytropes. Two-dimensional numerical simulations are
used to investigate the fully compressible nonlinear motions that
ensue. The cellular flows display prominent downward-directd plumes
surrounded by broader regions of upflow. Such asymmetry arises because
pressure fluctuations accentuate buoyancy driving in the concentrated
plumes and can even lead to weak buoyancy braking in the surrounding
ascending flows. As the plumes plunge downward into a region of stable
stratification, they serve to excite a broad spectrum of internal
gravity waves there. The induced waves are not passive, for they feed
back upon the plumes by deflecting them sideways, thereby modulating
the amplitude of the convection in time even in the unstable layer. The
penetrative motions that billow upward into the upper stable zone are
distinctly weaker, and they cascade back downward toward the unstable
zone over a broad horizontal scale. The strong excitation of gravity
waves by the convection has implications for gradual mixing deep within
a star.
---------------------------------------------------------
Title: Space-laboratory and numerical simulations of thermal
convection in arotating hemispherical shell with radial gravity.
Authors: Hart, John E.; Glatzmaier, Gary A.; Toomre, Juri
1986JFM...173..519H Altcode:
The flight of the Spacelab 3 microgravity laboratory onboard the
Space Shuttle Challenger in May 1985 enabled electroconvection
experiments to be conducted using the goephysical fluid flow cell
instrument. Experimental results are presented which illustrate the
variety of convection achieved by varying the imposed radial and
latitudinal temperature gradients, rotation rates, and the strength
of the electrostatic gravity. These results are compared with those
obtained from nonlinear three-dimensional simulations and good agreement
is found.
---------------------------------------------------------
Title: Laboratory Experiments on Planetary and Stellar Convection
Performed on Spacelab 3
Authors: Hart, J. E.; Toomre, J.; Deane, A. E.; Hurlburt, N. E.;
Glatzmaier, G. A.; Fichtl, G. H.; Leslie, F.; Fowlis, W. W.; Gilman,
P. A.
1986Sci...234...61H Altcode:
Experiments on thermal convection in a rotating, differentially heated
hemispherical shell with a radial buoyancy force were conducted in an
orbiting microgravity laboratory. A variety of convective structures,
or planforms, were observed, depending on the magnitude of the rotation
and the nature of the imposed heating distribution. The results are
compared with numerical simulations that can be conducted at the more
modest heating rates, and suggest possible regimes of motion in rotating
planets and stars.
---------------------------------------------------------
Title: Local Response of the Five-Minute Oscillations to a Major
Solar Flare
Authors: Haber, D. A.; Toomre, J.; Hill, F.; Gough, D. O.
1986BAAS...18Q1011H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Preflare activity.
Authors: Priest, E. R.; Gaizauskas, V.; Hagyard, M. J.; Schmahl, E. J.;
Webb, D. F.; Cargill, P.; Forbes, T. G.; Hood, A. W.; Steinolfson,
R. S.; Chapman, G. A.; Deloach, A. C.; Gary, G. A.; Jones, H. P.;
Karpen, J. T.; Martres, M. -J.; Porter, J. G.; Schmieder, B.; Smith,
J. B., Jr.; Toomre, J.; Woodgate, B.; Waggett, P.; Bentley, R.;
Hurford, G.; Schadee, A.; Schrijver, J.; Harrison, R.; Martens, P.
1986NASCP2439....1P Altcode:
Contents: 1. Introduction: the preflare state - a review of previous
results. 2. Magnetohydrodynamic instability: magnetic reconnection,
nonlinear tearing, nonlinear reconnection experiments, emerging flux and
moving satellite sunspots, main phase reconnection in two-ribbon flares,
magnetic instability responsible for filament eruption in two-ribbon
flares. 3. Preflare magnetic and velocity fields: general morphology of
the preflare magnetic field, magnetic field shear, electric currents in
the preflare active region, characterization of the preflare velocity
field, emerging flux. 4. Coronal manifestations of preflare activity:
defining the preflare regime, specific illustrative events, comparison
of preflare X-rays and ultraviolet, preflare microwave intensity and
polarization changes, non-thermal precursors, precursors of coronal
mass ejections, short-lived and long-lived HXIS sources as possible
precursors.
---------------------------------------------------------
Title: Influence of spatial filtering on possible anisotropies in
solar oscillations.
Authors: Hill, Frank; Haber, Deborah A.; Toomre, Juri; November,
Laurence J.
1986ASIC..169...85H Altcode: 1986ssds.proc...85H
The authors have used full disk Doppler observations of solar
oscillations to compare the amplitudes of sectoral modes propagating
along the equator with those of similar modes propagating along a
great circle aligned with the poles. They find that the amplitudes are
generally not equal for the two classes of modes, but the results are
sensitive to analysis procedures attempting to isolate the different
modes of oscillation. Spatial filtering of the data using spherical
harmonics suggests that greater amplitudes are associated with "polar"
sectoral modes than with "equatorial" sectoral modes.
---------------------------------------------------------
Title: Properties of solar oscillations.
Authors: Toomre, Juri
1986ASIC..169....1T Altcode: 1986ssds.proc....1T
Many of the oscillations that can be observed in the atmosphere of the
Sun are resonant acoustic or gravity modes of the interior. Accurate
measurement of the frequencies of these p and g modes permits deductions
about the internal structure and dynamics of this star. Some of
the methods of interpretation, involving a close interplay between
observation and theory, can be carried over to the study of more
distant stars.
---------------------------------------------------------
Title: Theoretical and experimental studies in support of the
geophysical fluid flow experiment
Authors: Hart, J.; Toomre, J.
1985aprr.nasa.....H Altcode:
Meteorologists and astrophysicists interested in large scale planetary
and solar circulations have come to recognize the importance of
rotation and stratification in determining the character of these
flows. In particular, the effect of latitude-dependent Coriolis force on
nonlinear convection is thought to play a crucial role in such phenomena
as differential rotation on the Sun, cloud band orientation on Jupiter,
and the generation of magnetic fields in thermally driven dynamos. The
continuous low-gravity environment of the orbiting space shuttle offers
a unique opportunity to make laboratory studies of such large-scale
thermally driven flows under the constraint imposed by rotation
and sphericity. This is possible because polarization forces in a
dielectric liquid, which are linearly dependent on fluid temperature,
give rise to an effectively radial buoyancy force when a radial
electrostatic field is imposed. The Geophysical Fluid Flow Cell (GFFC)
is an implementation of this ideal in which fluid is contained between
two rotating hemispheres that are differentially heated and stressed
with a large a-c voltage. The experiment, to be flown on Spacelab III
(currently set for launch April 29, 1985), will explore non-linear mode
selection and high Rayleigh number turbulence in a rotating convecting
spherical shell of liquid. Experiments will be carried out in a low
driving parameter range where some limited numerical experimentation
is currently feasible, as well as in a parameter range significantly
beyond numerical computation for many years.
---------------------------------------------------------
Title: Seismology of the Sun
Authors: Christensen-Dalsgaard, J.; Gough, D.; Toomre, J.
1985Sci...229..923C Altcode:
Oscillations of the sun make it possible to probe the inside of a
star. The frequencies of the oscillations have already provided measures
of the sound speed and the rate of rotation throughout much of the solar
interior. These quantities are important for understanding the dynamics
of the magnetic cycle and have a bearing on testing general relativity
by planetary precession. The oscillation frequencies yield a helium
abundance that is consistent with cosmology, but they reinforce the
severity of the neutrino problem. They should soon provide an important
standard by which to calibrate the theory of stellar evolution.
---------------------------------------------------------
Title: Helioseismology
Authors: Leibacher, J. W.; Noyes, R. W.; Toomre, J.; Ulrich, R. K.
1985SciAm.253c..48L Altcode: 1985SciAm.253...48L
Oscillations of the sun's surface are due to sound waves resonating in
the solar interior. In actual observations, such surface displacements
are evidenced in the form of Doppler shifts in the wavelengths of
light that are absorbed by the moving gases, and as variations in
brightness. The spatial pattern and period of surface oscillation
allows investigators to deduce the three-dimensional structure of the
resonance, and to infer properties of the solar interior. Reflection
and refraction below the solar surface confine sound waves within
acoustic cavities. Such trapped waves interfere constructively with
themselves as they circle the sun, creating the resonances that are
detectable as solar surface oscillations.
---------------------------------------------------------
Title: Helioseismology.
Authors: Leibacher, J. W.; Noyes, R. W.; Toomre, J.; Ulrich, R. K.
1985SciAm.253c..34L Altcode: 1985SciAm.253...34L
Acoustic waves within the sun are visible as oscillations on the solar
surface. Their pattern and period hold clues to structure, composition
and dynamics in the sun's interior.
---------------------------------------------------------
Title: Frequent Ultraviolet Brightenings in Solar Active Regions
Authors: Porter, J. G.; Toomre, J.; Gebbie, K. B.
1985BAAS...17..629P Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Changes in Subsurface Horizontal Velocities Inferred from
Observations of High Degree 5-Minute Solar Oscillations
Authors: Hill, F.; Toomre, J.; Gough, D. O.
1985BAAS...17..643H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Turbulence and wave particle interactions in solar-terrestrial
plasmas
Authors: Dulk, G. A.; Goldman, M. V.; Toomre, J.
1985colo.reptQ....D Altcode:
Activities in the following study areas are reported: (1) particle and
wave processes in solar flares; (2) solar convection zone turbulence;
and (3) solar radiation emission. To investigate the amplification of
cyclotron maser radiation in solar flares, a radio frequency. (RF)
heating model was developed for the corona surrounding the energy
release site. Then nonlinear simulations of compressible convection
display prominent penetration by plumes into regions of stable
stratification at the base of the solar convection zone, leading to the
excitation of internal gravity waves there. Lastly, linear saturation
of electron-beam-driven Langmuir waves by ambient density fluctuations,
nonlinear saturation by strong turbulence processes, and radiation
emission mechanisms are examined. An additional section discusses
solar magnetic fields and hydromagnetic waves in inhomogeneous media,
and the effect of magnetic fields on stellar oscillation.
---------------------------------------------------------
Title: Sensitivity of inferred subphotospheric velocity field to
mode selection, analysis technique and noise.
Authors: Hill, F.; Gough, D.; Toomre, J.
1984sses.nasa...95H Altcode: 1984sss..conf...95H
The horizontal velocity immediately below the photosphere can be
inferred from observations of high-degree solar oscillations by an
optimal-averaging inversion technique. The authors investigate the
sensitivity of the results to various details of both the inversion
and the determination of the frequencies. The results are shown to be
quite stable to the choice of most parameters, suggesting that this
procedure produces reliable estimates of the subsurface velocity.
---------------------------------------------------------
Title: Solar Seismology From Space. A conference at Snowmass, Colorado
Authors: Ulrich, R. K.; Harvey, J.; Rhodes, E. J., Jr.; Toomre, J.
1984sses.nasa.....U Altcode: 1984sss..conf.....U
No abstract at ADS
---------------------------------------------------------
Title: Overview of solar seismology: oscillations as probes of
internal structure and dynamics in the Sun.
Authors: Toomre, J.
1984sses.nasa....7T Altcode: 1984sss..conf....7T
The physical nature of solar oscillations is reviewed. The nomenclature
of the subject and the techniques used to interpret the oscillations
are discussed. Many of the acoustic and gravity waves that can be
observed in the atmosphere of the Sun are actually resonant or standing
modes of the interior; precise measurements of the frequencies of
such modes allow deductions of the internal structure and dynamics of
this star. The scientific objectives of such studies of solar seismic
disturbances, or of solar seismology, will be outlined. The reasons
for why it would be very beneficial to carry out further observations
of solar oscillations both from ground-based networks and from space
will be discussed.
---------------------------------------------------------
Title: Penetrative cellular convection in a stratified atmosphere
Authors: Massaguer, J. M.; Latour, J.; Toomre, J.; Zahn, J. -P.
1984A&A...140....1M Altcode:
In the present investigation of penetrative convection within a simple
compressible model, the middle one of the three layers of differing
stratification prior to the onset of convection is a convectively
unstable polytrope bounded above and below by two stably stratified
polytropes. One- and two-mode steady solutions with hexagonal planforms
have been studied for Rayleigh numbers up to aobut 1000 times critical,
and for a range of Prandtl numbers, horizontal wavenumbers, and
stratifications. These indicate that the penetration into the lower
stable layer by downward plumes is substantially larger in a stratified
medium than in a Boussinesq fluid, and produces an extended region
of adiabatic stratification. The strong asymmetry between upward and
downward penetration in compressible media has major implications for
the mixing of stable regions above and below stellar convection zones.
---------------------------------------------------------
Title: Frequent ultraviolet brightenings observed in a solar active
region with solar maximum mission
Authors: Porter, J. G.; Toomre, J.; Gebbie, K. B.
1984ApJ...283..879P Altcode:
Observations of the temporal behavior of ultraviolet emission from
bright points within an active region of the sun are reported. Frequent
and rapid brightenings in Si IV and O IV line emission are seen. The
observations suggest that intermittent heating events of modest
amplitude are occurring at many sites within an active region. By
selecting the brightest site at any given time within an active region
and then sampling its behavior in detail within a 120 s interval, it
is found that about two-thirds of the samples show variations of the
Si IV line intensity. The brightenings typically last about 40-60 s;
intensity increases of about 20-100 percent are frequently observed. The
results suggest that heating due to magnetic field reconnection within
an active region is proceeding almost stochastically. Events involving
only a modest release of energy occur the most frequently.
---------------------------------------------------------
Title: Two-dimensional compressible convection extending over multiple
scale heights
Authors: Hurlburt, N. E.; Toomre, J.; Massaguer, J. M.
1984ApJ...282..557H Altcode:
The theoretical description of the dynamics of a stellar convection
zone is considered, taking into account one of the most basic issues
by studying compressible convection extending over multiple scale
heights. A revised version of a code reported by Graham (1975) is
employed. Two-dimensional simulations show that nonlinear compressible
convection possesses cellular structures with strong localized
downward-directed plumes and broader upflows. The horizontal flows
which close the circulation within the cell satisfy an approximate
Bernoulli integral along a considerable portion of the horizontal
trajectory. Attention is given to details regarding the numerical
methods, the properties of the numerical solutions, the overall effects
of compressibility on nonlinear convection, and a comparison with
anelastic modal solutions.
---------------------------------------------------------
Title: Attempt to measure the solar subsurface velocity
Authors: Hill, F.; Gough, D.; Toomre, J.
1984MmSAI..55..153H Altcode:
Five-minute oscillation modes are advected by horizontal velocities
below the solar surface, and thus can be used as probes of rotation
and large-scale convective flows. Results of inverse theory applied
to observations of high-degree modes carried out on six separate days
reveal variations in horizontal velocities with depth from day to day
that may be the result of giant convection cells, through noise in
the data makes this interpretation somewhat tentative.
---------------------------------------------------------
Title: Solar convection
Authors: Toomre, J.; Gebbie, K. B.
1984colo.rept.....T Altcode:
A thorough study of convective penetration into the solar atmosphere
and convective motions in sub-atmospheric layers on the sun was
made. Non-linear anelastic and Boussinesq modal equations were developed
and solved to describe solar and stellar convection. An explanation was
developed for the lack of penetration of large-scale convective motions
into the observable solar atmosphere through the discovery of buoyancy
braking near the top of a supposedly unstable layer. Observations
of motions in the solar atmosphere led to the discovery of a new
scale of solar motion, the so-called mesogranulation. A technique was
developed to use changes in the solar five-minute oscillations as a
probe of internal solar structure. Using this technique, large-scale,
subatmospheric convective eddies were discovered.
---------------------------------------------------------
Title: Simulation of Effects of Atmospheric Seeing on Observations
of Solar Five-Minute Oscillations
Authors: Merryfield, W. J.; Toomre, J.; Hill, F.; Gough, D. O.
1984BAAS...16..532M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Horizontal Velocities in the Solar Convection Zone Inferred
from High Degree 5-Minute Oscillations
Authors: Hill, F.; Toomre, J.; Gough, D. O.
1984BAAS...16R.451H Altcode: 1984BAAS...16..451H
No abstract at ADS
---------------------------------------------------------
Title: Effects of Spherical Harmonic Filtering on Analysis of
Five-Minute Solar Oscillations of High-Degree
Authors: Haber, D.; Toomre, J.; Hill, F.
1984BAAS...16Q.533H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Strong Downward Plumes Resulting from Compressibility in
Nonlinear Convection and Their Coupling to Gravity Waves
Authors: Toomre, J.; Hurlburt, N. E.; Massaguer, J. M.
1984ssdp.conf..222T Altcode:
Two-dimensional numerical simulations are used to model fully
compressible nonlinear convection spanning multiple scale heights
within a stellar envelope.
---------------------------------------------------------
Title: Solar seismology from space. A conference at Snowmass,
Colorado, August 17 - 19, 1983.
Authors: Ulrich, R. K.; Harvey, J.; Rhodes, E. J., Jr.; Toomre, J.
1984ssfs.book.....U Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On the Detection of Subphotospheric Convective Velocities
and Temperature Fluctuations
Authors: Gough, D. O.; Toomre, J.
1983SoPh...82..401G Altcode: 1983IAUCo..66..401G
A procedure is outlined for estimating the influence of large-scale
convective eddies on the wave patterns of five-minute oscillations
of high degree. The method is applied to adiabatic oscillations, with
frequency ω and wave number k, of a plane-parallel polytropic layer
upon which is imposed a low-amplitude convective flow. The distortion to
the k - ω relation has two constituents: one depends on the horizontal
component of the convective velocity and has a sign which depends on
the sign of ω/k; the other depends on temperature fluctuations and
is independent of the sign of ω/k. The magnitude of the distortion
is just at the limit of present observational sensitivity. Thus there
is reasonable hope that it will be possible to reveal some aspects of
the large-scale flow in the solar convection zone.
---------------------------------------------------------
Title: Nonlinear Anelastic Modal Theory for Solar Convection
Authors: Latour, J.; Toomre, J.; Zahn, J. -P.
1983SoPh...82..387L Altcode: 1983IAUCo..66..387L
Preliminary solar envelope models have been computed using the
single-mode anelastic equations as a description of turbulent
convection. This approach provides estimates for the variation
with depth of the largest convective cellular flows, akin to giant
cells, with horizontal sizes comparable to the total depth of the
convection zone. These modal nonlinear treatments are capable of
describing compressible motions occurring over many density scale
heights. Single-mode anelastic solutions have been constructed for a
solar envelope whose mean stratification is nearly adiabatic over most
of its vertical extent because of the enthalpy (or convective) flux
explicitly carried by the big cell; a sub-grid scale representation of
turbulent heat transport is incorporated into the treatment near the
surface. The single-mode equations admit two solutions for the same
horizontal wavelength, and these are distinguished by the sense of
the vertical velocity at the center of the three-dimensional cell. It
is striking that the upward directed flows experience large pressure
effects when they penetrate into regions where the vertical scale height
has become small compared to their horizontal scale. The fluctuating
pressure can modify the density fluctuations so that the sense of the
buoyancy force is changed, with buoyancy braking actually achieved near
the top of the convection zone. The pressure and buoyancy work in the
shallow but unstable H<SUP>+</SUP> and He<SUP>+</SUP> ionization regions
can serve to decelerate the vertical motions and deflect them laterally,
leading to strong horizontal shearing motions. It appears that such
dynamical processes may explain why the amplitudes of flows related to
the largest scales of convection are so feeble in the solar atmosphere.
---------------------------------------------------------
Title: Variability in the power spectrum of solar five-minute
oscillations
Authors: Hill, F.; Toomre, J.; November, L. J.
1983SoPh...82..411H Altcode: 1983IAUCo..66..411H
Two-dimensional power spectra of solar five-minute oscillations
display prominent ridge structures in (k, ω) space, where k is the
horizontal wavenumber and ω is the temporal frequency. The positions
of these ridges in k and ω can be used to probe temperature and
velocity structures in the subphotosphere. We have been carrying out a
continuing program of observations of five-minute oscillations with the
diode array instrument on the vacuum tower telescope at Sacramento Peak
Observatory (SPO). We have sought to establish whether power spectra
taken on separate days show shifts in ridge locations; these may arise
from different velocity and temperature patterns having been brought
into our sampling region by solar rotation. Power spectra have been
obtained for six days of observations of Doppler velocities using the
MgIλ5173 and FeIλ5434 spectral lines. Each data set covers 8 to 11
hr in time and samples a region 256″ × 1024″ in spatial extent,
with a spatial resolution of 2″ and temporal sampling of 65 s. We have
detected shifts in ridge locations between certain data sets which are
statistically significant. The character of these displacements when
analyzed in terms of eastward and westward propagating waves implies
that changes have occurred in both temperature and horizontal velocity
fields underlying our observing window. We estimate the magnitude of
the velocity changes to be on the order of 100 m s<SUP>-1</SUP>; we may
be detecting the effects of large-scale convection akin to giant cells.
---------------------------------------------------------
Title: Search for Solar Giant Cells Using Five-Minute Oscillations
as Probes of Velocity Structures
Authors: Toomre, J.
1983EOSTr..64..303T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Time-dependent solutions of multimode convection equations
Authors: Toomre, J.; Gough, D. O.; Spiegel, E. A.
1982JFM...125...99T Altcode:
Truncated modal equations are used to study the time evolution of
thermal convection. In the Boussinesq approximation these nonlinear
equations are obtained by expanding the fluctuating velocity and
temperature fields in a finite set of planforms of the horizontal
coordinates. Numerical studies dealing with two or three modes with
triad interactions are discussed. Rich time dependence was found
in these cases: periodic and aperiodic solutions can be obtained,
along with various steady solutions. Three-mode solutions reproduce
the qualitative appearance of spoke-pattern convection as observed in
experiments at high Prandtl numbers. Though the values of the periods of
the time-dependent solutions do not agree with those of the experiments,
their variation with Rayleigh number compares favorably. Except at
the highest Rayleigh number considered (10,000,000), the theoretical
Nusselt numbers agree well with experiment.
---------------------------------------------------------
Title: Internal gravity waves in the solar atmosphere. II - Effects
of radiative damping
Authors: Mihalas, B. W.; Toomre, J.
1982ApJ...263..386M Altcode:
In the solar photosphere, temperature fluctuations associated
with acoustic-gravity waves may be rapidly smoothed by the transfer
mechanism of radiation between hotter and cooler regions. The present
investigation of the radiative effects on internal gravity waves takes
into account the parameterization of the radiative energy, employing the
Newtonian cooling approximation. A linear analysis of the propagation of
internal gravity waves is carried out in a model of the solar atmosphere
which is taken to be homogeneous in the horizontal coordinates. Linear
wave properties both with and without radiative cooling are summarized,
and the variation with height of energy fluxes and of nonlinearities
in the waves is discussed. Attention is given to the significance of
the obtained results in terms of energy balance in the chromosphere
and in relation to spectral line observations.
---------------------------------------------------------
Title: Single-mode theory of diffusive layers in thermohaline
convection
Authors: Gough, D. O.; Toomre, J.
1982JFM...125...75G Altcode:
A two-layer configuration of thermohaline convection is studied,
with the principal aim of explaining the observed independence of
the buoyancy-flux ratio on the stability parameter when the latter is
large. Temperature is destabilizing and salinity is stabilizing, so
diffusive interfaces separate the convecting layers. The convection is
treated in the single-mode approximation, with a prescribed horizontal
planform and wavenumber. Surveys of numerical solutions are presented
for a selection of Rayleigh numbers R, stability parameters lambda
and horizontal wavenumbers. The solutions yield a buoyancy flux
ratio chi that is insensitive to lambda, in accord with laboratory
experiments. However chi increases with increasing R, in contradiction
to laboratory observations.
---------------------------------------------------------
Title: Nonlinear modal analysis of penetrative convection
Authors: Zahn, J. -P.; Toomre, J.; Latour, J.
1982GApFD..22..159Z Altcode:
It is pointed out that thermal convection in many astrophysical and
geophysical settings occurs in an unstable layer bounded above and
below by regions which are stably stratified. The convective motions
may extend a substantial distance into the adjacent stable zones. If
the motions have little direct effect upon the mean stratification
of the stable zone, then they are usually referred to as convective
overshooting. The primary objective of the present investigation is
to study the dynamics of overshooting at very large Rayleigh numbers,
mainly with stellar applications in mind. Numerically this is only
feasible if severe simplifications are made in the description of
what are likely to be turbulent motions. The approach employed in the
investigation utilizes nonlinear modal equations in which the vertical
and temporal structure of the convection is described accurately at
the expense of the horizontal structure. A summary of the salient
properties of penetrative convection is provided on the basis of the
results of the conducted studies.
---------------------------------------------------------
Title: Relation of Ephemeral Magnetic Regions to the Low Amplitude
Branch of Persistent Vertical Velocities
Authors: Gebbie, K. B.; Toomre, J.; Haber, D. A.; Hill, F.; Simon,
G. W.; November, L. J.; Gurman, J. B.; Shine, R. A.
1982BAAS...14R.939G Altcode: 1982BAAS...14..939G
No abstract at ADS
---------------------------------------------------------
Title: The Lateral Deflection of Large-Scale Convective Flows by
Scale Height Effects below the Solar Surface
Authors: Hurlburt, N.; Toomre, J.
1982BAAS...14..938H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solar Five-Minute Oscillations, Subsurface Velocities and
Inverse Theory
Authors: Gough, D. O.; Hill, F.; Toomre, J.
1982BAAS...14..938G Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Vertical flows of supergranular and mesogranular scale observed
on the sun with OSO 8
Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W.
1982ApJ...258..846N Altcode:
A program of observations was carried out in order to study the
penetration of supergranular flows over a broad range of heights in
the solar atmosphere. Steady Doppler velocities are determined from
observations of a Si II spectral line using the Ultraviolet Spectrometer
on the Orbiting Solar Observatory 8 (OSO 8) satellite and Fe I and
Mg I lines with the diode-array instrument on the vacuum telescope at
Sacramento Peak Observatory (SPO). The heights of formation of these
spectral lines span about 1400 km or nearly 11 density scale heights
from the photosphere to the middle chromosphere. Steady vertical flows
on spatial scales typical of supergranulation and mesogranulation have
been detected in the middle chromosphere with OSO 8. The patterns of
intensity and steady velocity of granular scale are reproducible in
successive data sets. The patterns appear to evolve slowly over the
9 hr period spanned by six orbits.
---------------------------------------------------------
Title: University of Colorado, Boulder, Colorado 80309. Report.
Authors: Dulk, G. A.; Shull, J. M.; Toomre, J.
1982BAAS...14..122D Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solar 5-MINUTE Oscillations as Probes of Structure in the
Subphotosphere
Authors: Hill, F.; Toomre, J.; November, L. J.
1982pccv.conf..139H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Review of Time-Dependent Convection and Attempts to Couple
it to Pulsation in Stars
Authors: Toomre, J.
1982pccv.conf..170T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Steady flows in the solar transition region observed with SMM
Authors: Gebbie, K. B.; Hill, F.; November, L. J.; Gurman, J. B.;
Shine, R. A.; Woodgate, B. E.; Athay, R. G.; Tandberg-Hanssen, E. A.;
Toomre, J.; Simon, G. W.
1981ApJ...251L.115G Altcode:
Steady flows in the quiet solar transition region have been observed
with the Ultraviolet Spectrometer and Polarimeter experiment on the
Solar Maximum Mission (SMM) satellite. The persistent vertical motions
seen at disk center have spatial rms amplitudes of 1.4 km/s in the C
II line, 3.9 km/s in Si IV, and 4.2 km/s in C IV. The amplitudes of
the more horizontal flows seen toward the limb tend to be somewhat
higher. Plots of steady vertical velocity versus intensity seen at
disk center in Si IV and C IV show two distinct branches.
---------------------------------------------------------
Title: Internal gravity waves in the solar atmosphere. I - Adiabatic
waves in the chromosphere
Authors: Mihalas, B. W.; Toomre, J.
1981ApJ...249..349M Altcode:
The properties of adiabatic and linear internal gravity waves
propagating in a solar wind model are discussed, using nonlinearity
criteria unique to gravity waves to estimate wave-breaking heights. The
results are used to deduce information on the possible role of gravity
waves in the chromospheric energy balance. Maximum vertical velocity
amplitudes for gravity waves are estimated to be on the order of 2
km/sec or less, and maximum horizontal velocity amplitudes are less than
6 km/sec, with temperature perturbations as large as 1000-2000 K. It
is also estimated that gravity waves with an incident energy flux of
one million ergs/sq cm-sec can propagate upward to a maximum height
of 900-1000 km above the visible surface before nonlinearities lead
to wave breaking, while those with an energy flux of 100,000 ergs/sq
cm-sec can reach maximum heights of 1400-1600 km.
---------------------------------------------------------
Title: Stellar convection theory. III - Dynamical coupling of the
two convection zones in A-type stars by penetrative motions
Authors: Latour, J.; Toomre, J.; Zahn, J. -P.
1981ApJ...248.1081L Altcode:
The thermal convection occurring over many density scale heights in an
A-type star outer envelope, encompassing both the hydrogen and helium
convectively unstable zones, is examined by means of anelastic modal
equations. The single-mode anelastic equations for such compressible
convection display strong overshooting of the motions into adjacent
radiative zones, which would preclude diffusive separation of
elements in the supposedly quiescent region between the two unstable
zones. In addition, the anelastic solutions reveal that the two zones
of convective instability are dynamically coupled by the overshooting
motions. The two solutions that the nonlinear single-mode equations
admit for the same horizontal wavelength are distinguished by the
sense of the vertical velocity at the center of the three-dimensional
cell. It is suggested that strong horizontal shear flows should be
present just below the surface of the star, and that the large-scale
motions extending into the stable atmosphere would appear mainly as
horizontal flows.
---------------------------------------------------------
Title: The detection of mesogranulation on the sun.
Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W.
1981ApJ...245L.123N Altcode:
Time averages of velocity measurements at disk center on the quiet sun
reveal the presence of a fairly stationary pattern of cellular flow
with a spatial scale of 5-10 Mm. Such mesogranulation has a spatial rms
vertical velocity amplitude of about 60 m/s superposed on the larger
scale supergranular flows. The lifetimes of mesogranules appear to be
at least 2 hr.
---------------------------------------------------------
Title: Nonlinear Penetrative Convection in a Compressible Medium
Authors: Hurlburt, N.; Toomre, J.; Massaguer, J. M.
1981BAAS...13..912H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solar Five-Minute Oscillations as Probes of Velocity and
Temperature Fields
Authors: Hill, F.; Toomre, J.; November, L. J.
1981BAAS...13Q.860H Altcode: 1981BAAS...13..860H
No abstract at ADS
---------------------------------------------------------
Title: Nonlinear Anelastic Models of Solar Convection
Authors: Toomre, J.; Latour, J.; Zahn, J. -P.
1981BAAS...13Q.907T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Height Dependence of Steady Flows Determined from Coordinated
SMM and SPO Observations
Authors: Gebbie, K. B.; Hill, F.; Toomre, J.; November, L. J.; Simon,
G. W.; Gurman, J. B.; Shine, R. A.; Woodgate, B. E.
1981BAAS...13..914G Altcode:
No abstract at ADS
---------------------------------------------------------
Title: OSO 8 Observations of Coherent Chromospheric Oscillations
Authors: Hill, F.; Toomre, J.; November, L. J.
1980BAAS...12R.894H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Nonlinear Simulations of Rotational Effects in Supergranules
Authors: Hathaway, D. H.; Toomre, J.
1980BAAS...12Q.894H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Steady Flows in the Solar Transition Region Observed with
the UVSP Experiment on SMM
Authors: Gebbie, K. B.; Hill, F.; Toomre, J.; November, L. J.; Simon,
G. W.; Athay, R. G.; Bruner, E. C.; Rehse, R.; Gurman, J. B.; Shine,
R. A.; Woodgate, B. E.; Tandberg-Hanssen, E. A.
1980BAAS...12..907G Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Two Dimensional Compressible Convection Extending Over Multiple
Scale Heights
Authors: Hurlburt, N. E.; Toomre, J.; Massaguer, J. M.; Graham, E.
1980BAAS...12S.894H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Anelastic Modal Theory Applied to the Solar Convection Zone
Authors: Toomre, J.; Latour, J.; Zahn, J. P.
1980BAAS...12..895T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Lifetime of Solar Mesogranulation
Authors: November, L. J.; Gebbie, K. B.; Hill, F.; Toomre, J.; Simon,
G. W.
1980BAAS...12..895N Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Axisymmetric Convection Driven by Latitudinal Temperature
Gradients in Rotating Spherical Shells.
Authors: Hathaway, D. H.; Gilman, P. A.; Miller, J.; Toomre, J.
1980BAAS...12..686H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Overshooting Motions from the Convection Zone and Their Role
in Atmospheric Heating
Authors: Toomre, J.
1980HiA.....5..571T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Convective instability when the temperature gradient and
rotation vector are oblique to gravity. II. Real fluids with effects
of diffusion
Authors: Hathaway, D. H.; Toomre, J.; Gilman, P. A.
1980GApFD..15....7H Altcode:
The linear stability analysis of Hathaway, Gilman and Toomre (1979)
(hereafter referred to as Paper I) is repeated for Boussinesq fluids
with viscous and thermal diffusion. As in Paper I the fluid is confined
between plane parallel boundaries and the rotation vector is oblique
to gravity. This tilted rotation vector introduces a preference
for roll-like disturbances whose axes are oriented north-south;
the preference is particularly strong in the equatorial region. The
presence of a latitudinal temperature gradient produces a thermal
wind shear which favors axisymmetric convective rolls if the gradient
exceeds some critical value. For vanishingly small diffusivities the
value of this transition temperature gradient approaches the inviscid
value found in Paper I. For larger diffusivities larger gradients are
required particularly in the high latitudes. These results are largely
independent of the Prandtl number. Diffusion tends to stabilize the
large wavenumber rolls with the result that a unique wavenumber can
be found at which the growth rate is maximized. These preferred rolls
have widths comparable to the depth of the layer and tend to be broader
near the equator. The axisymmetric rolls are similar in many respects
to the cloud bands on Jupiter provided they extend to a depth of about
15,000 km.
---------------------------------------------------------
Title: Mesogranulation -- An Intermediate Scale of Motion on the Sun
Authors: Toomre, J.; November, L. J.; Gebbie, K. B.; Simon, G. W.
1979BAAS...11..641T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Convective Instability in Rotating Layers with Thermal Winds
and Application to Jupiter
Authors: Hathaway, D. H.; Gilman, P. A.; Toomre, J.
1979BAAS...11Q.618H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The height variation of supergranular velocity fields
determined from simultaneous OSO 8 satellite and ground-based
observations.
Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W.
1979ApJ...227..600N Altcode:
Results are reported for simultaneous satellite and ground-based
observations of supergranular velocities in the sun, which were made
using a UV spectrometer aboard OSO 8 and a diode-array instrument
operating at the exit slit of an echelle spectrograph attached to a
vacuum tower telescope. Observations of the steady Doppler velocities
seen toward the limb in the middle chromosphere and the photosphere
are compared; the observed spectral lines of Si II at 1817 A and Fe
I at 5576 A are found to differ in height of formation by about 1400
km. The results show that supergranular motions are able to penetrate
at least 11 density scale heights into the middle chromosphere, that
the patterns of motion correlate well with the cellular structure seen
in the photosphere, and that the motion increases from about 800 m/s in
the photosphere to at least 3000 m/s in the middle chromosphere. These
observations imply that supergranular velocities should be evident
in the transition region and that strong horizontal shear layers in
supergranulation should produce turbulence and internal gravity waves.
---------------------------------------------------------
Title: Convective Instability when the Temperature Gradient and
Rotation Vector are Oblique to Gravity. I. Fluids without Diffusion
Authors: Hathaway, D. H.; Toomre, J.; Gilman, P. A.
1979GApFD..13..289H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Compressible Convection in the Outer Envelope of A-type Stars
Authors: Toomre, J.; Latour, J.; Zahn, J. -P.
1978BAAS...10..677T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Variation with Height of Supergranular Velocity Fields
Authors: Gebbie, K. B.; November, L. J.; Toomre, J.; Simon, G. W.
1978BAAS...10Q.672G Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Vertical and Horizontal Components of Supergranulation Velocity
Fields Observed with OSO-8
Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W.
1977BAAS....9..337N Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Anelastic Stellar Convection Theory Applied to A-type Stars.
Authors: Toomre, J.; Latour, J.; Zahn, J. -P.
1977BAAS....9..337T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Violent Tides Between Galaxies
Authors: Toomre, Alar; Toomre, Juri
1977nass.book..271T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Numerical solutions of single-mode convection equations
Authors: Toomre, J.; Gough, D. O.; Spiegel, E. A.
1977JFM....79....1T Altcode:
In the Boussinesq approximation, single-mode equations describing
thermal convection are constructed by expanding the fluctuating velocity
and temperature fields in a complete set of functions (or planforms)
of the horizontal coordinates and retaining just one term. Numerical
solutions of the single-mode equations are investigated, chief
consideration being given to hexagonal planforms. Extensive surveys of
steady solutions are presented for various Rayleigh numbers, Prandtl
numbers, and horizontal wavenumbers. The dependences on Rayleigh number
and Prandtl number at very large Rayleigh number are in satisfactory
agreement with the results of asymptotic expansions.
---------------------------------------------------------
Title: Stellar convection theory. II. Single-mode study of the second
convection zone in an A-type star.
Authors: Toomre, J.; Zahn, J. -P.; Latour, J.; Spiegel, E. A.
1976ApJ...207..545T Altcode:
The anelastic modal equations presented in Paper I are considered
in their simplest version: only one mode is retained in the
representation of the fluctuating dynamic and thermodynamic variables
of convection theory. These single-mode equations are used to examine
the structure of the second convection zone of an A-type star. Two-
and three-dimensional numerical solutions are obtained for a range of
parameters in the theory, and a simple analysis is provided for their
interpretation. The principal results are for three-dimensional motions,
since these are most likely to be relevant to stellar convection. Such
motions produce a convective heat flux several orders of magnitude
greater than predicted by standard mixing-length theory for the same
situation; we find that convection carries up to 6 percent of the
total flux. The most significant astrophysical implication of our
results is that they suggest strong overshooting into the adjacent
radiative zones. We anticipate that mixing will extend to the overlying
hydrogen convection zone. This would rule out some interpretations of
metallic-line stars which invoke diffusive element separation between
the two convection zones. Subject headings: convection - stars:
interiors - stars: metallic-line
---------------------------------------------------------
Title: Stellar convection theory. I. The anelastic modal equations.
Authors: Latour, J.; Spiegel, E. A.; Toomre, J.; Zahn, J. -P.
1976ApJ...207..233L Altcode:
Methods are developed for dealing with the various dynamical
problems that arise because of convective zones in stars. A system
of equations for stellar convection is derived from the full
equations of compressible fluid dynamics with the aid of two major
approximations. The first of these is the anelastic approximation,
which involves both the filtering out of acoustic waves and a suitable
linearization of the fluctuating thermodynamic variables. The second
one approximates the horizontal structure of convection by expanding
the motion in a set of horizontal cellular platforms and severely
truncating the expansion. The resulting system of partial differential
equations, referred to as the anelastic modal equations, is outlined
along with suggested boundary conditions and techniques for solving
the equations. Ways of assessing the overall validity of the present
treatment are discussed.
---------------------------------------------------------
Title: Supergranulation Velocity Fields Observed in the Solar
Transition Region with OSO-8
Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W.;
Bruner, E. C., Jr.; Chipman, E. G.; Lites, B. W.; Shine, R. A.;
Orrall, F. Q.; Athay, R. G.; White, O. R.
1976BAAS....8..311N Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Second Convection Zone in an A-type Star
Authors: Latour, J.; Spiegel, E. A.; Toomre, J.; Zahn, J. P.
1975BAAS....7..526L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Modal equations for cellular convection
Authors: Gough, D. O.; Spiegel, E. A.; Toomre, J.
1975JFM....68..695G Altcode:
We expand the fluctuating flow variables of Boussinesq convection in
the planform functions of linear theory. Our proposal is to consider a
drastic truncation of this expansion as a possible useful approximation
scheme for studying cellular convection. With just one term included,
we obtain a fairly simple set of equations which reproduces some of the
qualitative properties of cellular convection and whose steady-state
form has already been derived by Roberts (1966). This set of 'modal
equations' is analyzed at slightly supercritical and at very high
Rayleigh numbers. In the latter regime the Nusselt number varies
with Rayleigh number just as in the mean-field approximation with one
horizontal scale when the boundaries are rigid. However, the Nusselt
number now depends also on the Prandtl number in a way that seems
compatible with experiment. The chief difficulty with the approach is
the absence of a deductive scheme for deciding which planforms should
be retained in the truncated expansion.
---------------------------------------------------------
Title: What Velocities are Consistent with the Interpretation of
Supergranulation as Penetrative Convection?
Authors: Gebbie, K. B.; Toomre, J.
1975BAAS....7Q.363G Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Highly stretched meshes as functionals of solutions
Authors: Gough, D. O.; Spiegel, E. A.; Toomre, J.
1975LNP....35..191G Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Violent tides between galaxies.
Authors: Toomre, A.; Toomre, J.
1973SciAm.229f..38T Altcode: 1973SciAm.229...38T
No abstract at ADS
---------------------------------------------------------
Title: Violent Tides between Galaxies
Authors: Alar; Toomre, Juri
1973SciAm.229f..38A Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Radial Velocities in the Tail of NGC 4676A
Authors: Theys, J. C.; Spiegel, E. A.; Toomre, Juri
1972PASP...84..851T Altcode:
A spectrum of ffie long tail of NGC 4676A shows [011] x3727 in
emission. The radial velocity measured from one plate varies by about
400 km sec-1 along the length of the tail. Key words: peculiar galaxy -
radial velocities
---------------------------------------------------------
Title: Galactic Bridges and Tails
Authors: Toomre, Alar; Toomre, Juri
1972ApJ...178..623T Altcode:
This paper argues that the bridges and tails seen in some multiple
galaxies are just tidal relics of close encounters. These consequences
of the brief but violent tidal forces are here studied in a deliberately
simple-minded fashion: Each encounter is considered to involve only two
galaxies and to be roughly parabolic; each galaxy is idealized as just
a disk of noninteracting test particles which initially orbit a central
mass point. As shown here, the two-sided distortions provoked by gravity
alone in such circumstances can indeed evolve kinematically into some
remarkably narrow and elongated features: (i) After a relatively direct
passage of a small companion, the outer portions of the primary disk
often deform both into a near-side spiral arm or "bridge" extending
toward this satellite, and into a far-side "counterarm." (ii) A similar
encounter with an equal or more massive partner results typically in
a long and curving "tail" of escaping debris from the far side of the
victim disk, and in an avalanche of near-side particles, most of which
are captured by the satellite. Besides extensive pictorial surveys of
such tidal damage, this paper offers reconstructions of the orbits
and outer shapes of four specific interacting pairs: Arp 295, M51 +
NOC 5195, NGC 4676, and NOC 4038/9. Those models can be found in the
fairly self-explanatory figures 19, 21, 22, and 23. Also discussed are
some closely related issues of eccentric bound orbits, orbital decay,
accretion, and forced spiral waves.
---------------------------------------------------------
Title: Spectra of Extragalactic Rings.
Authors: Theys, J. C.; Spiegel, E. A.; Toomre, J.
1972BAAS....4..213T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Model of the Encounter Between NGC 5194 and 5195.
Authors: Toomre, A.; Toomre, J.
1972BAAS....4..214T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Theorectical Model of NGC 4038/39.
Authors: Toomre, Alar; Toomre, Juri
1971BAAS....3..390T Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On Intergalactic Bridges.
Authors: Toomre, Alar; Toomre, Juri
1970BAAS....2R.350T Altcode:
No abstract at ADS
