kapyla

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Author name code: kapyla
ADS astronomy entries on 2022-09-14
author:"Kapyla, Petri J."

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Title: Transition from anti-solar to solar-like differential rotation:
Dependence on Prandtl number
Authors: Käpylä, Petri J.
2022arXiv220700302K Altcode:
(abridged) Context: Late-type stars such as the Sun rotate
differentially due to the interaction of turbulent convection and
rotation. Aims: The aim of the study is to investigate the effects
of the thermal Prandtl number on the transition from anti-solar
(slow equator, fast poles) to solar-like (fast equator, slow poles)
differential rotation. Methods: Three-dimensional hydrodynamic and
magnetohydrodynamic simulations in semi-global spherical wedge geometry
are used to model convection zones of solar-like stars. Results:
The overall convective velocity amplitude increases as the Prandtl
number decreases in accordance with earlier studies. The transition
from anti-solar to solar-like differential rotation is insensitive
to the Prandtl number for Prandtl numbers below unity but for Prandtl
numbers greater than unity, solar-like differential rotation becomes
significantly harder to excite. Magnetic fields and more turbulent
regimes with higher fluid and magnetic Reynolds numbers help in
achieving solar-like differential rotation in near-transition
cases. Solar-like differential rotation occurs only in cases with
radially outward angular momentum transport at the equator. The
dominant contribution to such outward transport near the equator
is due to prograde propagating thermal Rossby waves. Conclusions:
The differential rotation is sensitive to the Prandtl number only for
large Prandtl numbers in the parameter regime explored in the current
study. Magnetic fields have a greater effect on the differential
rotation, although the inferred presence of a small-scale dynamo does
not lead to drastically different results in the present study. The
dominance of the thermal Rossby waves in the simulations is puzzling
given the non-detection in the Sun. The current simulations are shown
to be incompatible with the currently prevailing mean-field theory of
differential rotation.

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Title: Simulations of fully convective M dwarfs: dynamo action with
varying magnetic Prandtl numbers
Authors: Ortiz-Rodríguez, C. A.; Schleicher, D. R. G.; Käpylä,
P. J.; Navarrete, F. H.
2022BAAA...63...62O Altcode: 2022arXiv220614123O
M dwarfs are low-mass main-sequence stars, the most numerous type of
stars in the solar neighbourhood, which are known to have significant
magnetic activity. The aim of this work is to explore the dynamo
solutions and magnetic fields of fully convective M dwarfs with
varying magnetic Prandtl numbers PrM, and a rotation period
(Prot) of 43 days. PrM is known to play an
important role in the dynamo action; dynamos for low-PrM
and large-PrM have very different properties. We performed
three-dimensional magnetohydrodynamical (MHD) numerical simulations
with the “star-in-a- box” model using stellar parameters for an M5
dwarf with 0.21 M⊙. We found that the dynamo solutions
are sensitive to Pr_. The simulations at this rotation period present
periodic cycles of the large-scale magnetic field up to PrM
≤ 2; for higher values the cycles disappear and irregular solutions
to arise. Our results are consistent with previous studies and suggest
that the dynamos operating in fully convective stars behave similarly
as those in partially convective stars.

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Title: Origin of eclipsing time variations: Contributions of different
modes of the dynamo-generated magnetic field
Authors: Navarrete, Felipe H.; Käpylä, Petri J.; Schleicher,
Dominik R. G.; Ortiz, Carolina A.; Banerjee, Robi
2022A&A...663A..90N Altcode: 2021arXiv210211110N
Context. The possibility to detect circumbinary planets and to
study stellar magnetic fields through eclipsing time variations
(ETVs) in binary stars has sparked an increase of interest in this
area of research. Aims: We revisit the connection between
stellar magnetic fields and the gravitational quadrupole moment
Qxx and compare different dynamo-generated ETV models with
our simulations. Methods: We present magnetohydrodynamical
simulations of solar mass stars with rotation periods of 8.3, 1.2, and
0.8 days and perform a detailed analysis of the magnetic and quadrupole
moment using spherical harmonic decomposition. Results: The
extrema of Qxx are associated with changes in the magnetic
field structure. This is evident in the simulation with a rotation
period of 1.2 days. Its magnetic field has a more complex behavior
than in the other models, as the large-scale nonaxisymmetric field
dominates throughout the simulation and the axisymmetric component is
predominantly hemispheric. This triggers variations in the density field
that follow the magnetic field asymmetry with respect to the equator,
affecting the zz component of the inertia tensor, and thus modulating
Qxx. The magnetic fields of the two other runs are less
variable in time and more symmetric with respect to the equator,
such that the variations in the density are weaker, and therefore
only small variations in Qxx are seen. Conclusions:
If interpreted via the classical Applegate mechanism (tidal locking),
the quadrupole moment variations obtained in the current simulations are
about two orders of magnitude below those deduced from observations of
post-common-envelope binaries. However, if no tidal locking is assumed,
our results are compatible with the observed ETVs.

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Title: Turbulent Prandtl number from isotropically forced turbulence
Authors: Käpylä, Petri J.; Singh, Nishant K.
2022arXiv220710335K Altcode:
Turbulent motions enhance the diffusion of large-scale flows and
temperature gradients. Such diffusion is often parameterized by
coefficients of turbulent viscosity ($\nu_{\rm t}$) and turbulent
thermal diffusivity ($\chi_{\rm t}$) that are analogous to
their microscopic counterparts. We compute the turbulent diffusion
coefficients by imposing large-scale velocity and temperature gradients
on a turbulent flow and measuring the response of the system. We also
confirm our results using experiments where the imposed gradients
are allowed to decay. To achieve this, we use weakly compressible
three-dimensional hydrodynamic simulations of isotropically forced
homogeneous turbulence. We find that the turbulent viscosity and thermal
diffusion, as well as their ratio the turbulent Prandtl number, ${\rm
Pr}_{\rm t} = \nu_{\rm t}/\chi_{\rm t}$, approach asymptotic values at
sufficiently high Reynolds and Peclét numbers. We also do not find a
significant dependence of ${\rm Pr}_{\rm t}$ on the microscopic Prandtl
number ${\rm Pr} = \nu/\chi$. These findings are in stark contrast
to results from the $k-\epsilon$ model which suggests that ${\rm
Pr}_{\rm t}$ increases monotonically with decreasing ${\rm Pr}$. The
current results are relevant for the ongoing debate of, for example,
the nature of the turbulent flows in the very low ${\rm Pr}$ regimes
of stellar convection zones.

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Title: Magnetism, rotation, and nonthermal emission in cool
stars. Average magnetic field measurements in 292 M dwarfs
Authors: Reiners, A.; Shulyak, D.; Käpylä, P. J.; Ribas, I.; Nagel,
E.; Zechmeister, M.; Caballero, J. A.; Shan, Y.; Fuhrmeister, B.;
Quirrenbach, A.; Amado, P. J.; Montes, D.; Jeffers, S. V.; Azzaro,
M.; Béjar, V. J. S.; Chaturvedi, P.; Henning, Th.; Kürster, M.;
Pallé, E.
2022A&A...662A..41R Altcode: 2022arXiv220400342R
Stellar dynamos generate magnetic fields that are of fundamental
importance to the variability and evolution of Sun-like and low-mass
stars, and for the development of their planetary systems. As a
key to understanding stellar dynamos, empirical relations between
stellar parameters and magnetic fields are required for comparison to
ab initio predictions from dynamo models. We report measurements of
surface-average magnetic fields in 292 M dwarfs from a comparison with
radiative transfer calculations; for 260 of them, this is the first
measurement of this kind. Our data were obtained from more than 15 000
high-resolution spectra taken during the CARMENES project. They reveal
a relation between average field strength, ⟨B⟩, and Rossby number,
Ro, resembling the well-studied rotation-activity relation. Among the
slowly rotating stars, we find that magnetic flux, ΦB,
is proportional to rotation period, P, and among the rapidly rotating
stars that average surface fields do not grow significantly beyond the
level set by the available kinetic energy. Furthermore, we find close
relations between nonthermal coronal X-ray emission, chromospheric
Hα and Ca H&amp;K emission, and magnetic flux. Taken together,
these relations demonstrate empirically that the rotation-activity
relation can be traced back to a dependence of the magnetic dynamo on
rotation. We advocate the picture that the magnetic dynamo generates
magnetic flux on the stellar surface proportional to rotation rate with
a saturation limit set by the available kinetic energy, and we provide
relations for average field strengths and nonthermal emission that
are independent of the choice of the convective turnover time. We also
find that Ca H&amp;K emission saturates at average field strengths of
⟨B⟩≈800 G while Hα and X-ray emission grow further with stronger
fields in the more rapidly rotating stars. This is in conflict with the
coronal stripping scenario predicting that in the most rapidly rotating
stars coronal plasma would be cooled to chromospheric temperatures. Table B.1 is only available at the CDS via anonymous ftp to <A
href="http://cdsarc.u-strasbg.fr/">cdsarc.u-strasbg.fr</A>
(ftp://130.79.128.5) or via <A
href="http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/662/A41">http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/662/A41</A>

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Title: Solar-like Dynamos and Rotational Scaling of Cycles from
Star-in-a-box Simulations
Authors: Käpylä, Petri J.
2022ApJ...931L..17K Altcode: 2022arXiv220204329K
Magnetohydrodynamic star-in-a-box simulations of convection and dynamos
in a solar-like star with different rotation rates are presented. These
simulations produce solar-like differential rotation with a fast equator
and slow poles and magnetic activity that resembles that of the Sun with
equatorward migrating activity at the surface. Furthermore, the ratio
of rotation to cycle period is almost constant, as the rotation period
decreases in the limited sample considered here. This is reminiscent
of the suggested inactive branch of stars from observations and differs
from most earlier simulation results from spherical shell models. While
the exact excitation mechanism of the dynamos in the current simulations
is not yet clear, it is shown that it is plausible that the greater
freedom that the magnetic field has due to the inclusion of the
radiative core and regions exterior to the star are important in
shaping the dynamo.

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Title: Origin of eclipsing time variations in Post-Common-Envelope
binaries: role of the centrifugal force
Authors: Navarrete, Felipe H.; Schleicher, Dominik R. G.; Käpylä,
Petri J.; Ortiz, Carolina; Banerjee, Robi
2022arXiv220503163N Altcode:
The eclipsing time variations in post-common-envelope binaries were
proposed to be due to the time-varying component of the stellar
quadrupole moment. This is suggested to be produced by changes
in the stellar structure due to an internal redistribution of
the angular momentum and the effect of the centrifugal force. We
examine this hypothesis presenting 3D simulations of compressible
magneto-hydrodynamics (MHD) performed with the Pencil Code, modeling
the stellar dynamo for a solar mass star with angular velocities
of 20 and 30 times solar. We include and vary the strength of the
centrifugal force, comparing with reference simulations without
the centrifugal force and including a simulation where its effect
is enhanced. The centrifugal force is causing perturbations in the
evolution of the stars, so that the outcome in the details becomes
different as a result of non-linear evolution. While the average
density profile is unaffected by the centrifugal force, a relative
change in density difference between high altitudes and the equator of
order $\sim 10^{-4}$ is found. The power spectrum of the convective
velocity is found to be more sensitive to the angular velocity than
the strength of the centrifugal force. The quadrupole moment of the
stars includes a fluctuating and a time-independent component which
varies with the rotation rate. As very similar behavior is produced
in the absence of the centrifugal force, we conclude that it is not
the main ingredient for producing the time-averaged quadrupole moment
of the star. In a real physical system, we thus expect contributions
from both components, that is, due to the time-dependent gravitational
force from the variation in the quadrupole term and due to spin-orbit
coupling due to the persistent part of the quadrupole.

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Title: VizieR Online Data Catalog: Magnetic fields in 292 M
dwarfs. (Reiners+, 2022)
Authors: Reiners, A.; Shulyak, D.; Kaepylae, P. J.; Ribas, I.; Nagel,
E.; Zechmeister, M.; Caballero, J. A.; Shan, Y.; Fuhrmeister, B.;
Quirrenbach, A.; Amado, P. J.; Montes, D.; Jeffers, S. V.; Azzaro, M.;
Bejar, V. J. S.; Chaturvedi, P.; Henning, T.; Kuerster, M.; Palle, E.
2022yCat..36620041R Altcode:
The sample of stars used for our analysis, the number of spectra
co-added for each star, and the approximate S/N around λ=8700Å are
provided in Table B.1. (1 data file).

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Title: On Strengthening of the Solar f-mode Prior to Active Region
Emergence Using the Fourier-Hankel Analysis
Authors: Waidele, Matthias; Roth, Markus; Singh, Nishant; Käpylä,
Petri
2022arXiv220211236W Altcode:
Recent results of Singh et al. (2016) show that the emergence of an
active region (AR) can be seen in a strengthening of the f-mode power
up to two days prior of the region's formation. In the original work,
ring diagram analysis was used to estimate the power evolution. In this
study, we make use of the Fourier-Hankel method, essentially testing
the aforementioned results with an independent method. The data is
acquired from SDO/HMI, studying the ARs 11158, 11072, 11105, 11130,
11242 and 11768. Investigating the total power as a function of time,
we find a similar behavior to the original work, which is an enhancement
of f-mode power about one to three days prior to AR emergence. Analysis
of the absorption coefficient $\alpha$, yielded by a Fourier-Hankel
analysis, shows neither absorption ($\alpha &gt; 0$) nor emission
($\alpha &lt; 0$) of power during the enhancement. Finding no changes
of the absorption coefficient (i.e. $\alpha = 0$) is an important
result, as it narrows down the possible physical interpretation of
the original f-mode power enhancement, showing that no directional
dependence (in the sense of inward and outward moving waves) is present.

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Title: Generation of mean flows in rotating anisotropic turbulence:
The case of solar near-surface shear layer
Authors: Barekat, A.; Käpylä, M. J.; Käpylä, P. J.; Gilson, E. P.;
Ji, H.
2021A&A...655A..79B Altcode: 2020arXiv201206343B
Context. Results from helioseismology indicate that the radial gradient
of the rotation rate in the near-surface shear layer (NSSL) of the Sun
is independent of latitude and radius. Theoretical models using the
mean-field approach have been successful in explaining this property
of the NSSL, while global direct or large-eddy magnetoconvection
models have so far been unable to reproduce this. Aims:
We investigate the reason for this discrepancy by measuring the
mean flows, Reynolds stress, and turbulent transport coefficients
under conditions mimicking those in the solar NSSL. Methods:
Simulations with as few ingredients as possible to generate mean flows
were studied. These ingredients are inhomogeneity due to boundaries,
anisotropic turbulence, and rotation. The parameters of the simulations
were chosen such that they matched the weakly rotationally constrained
NSSL. The simulations probe locally Cartesian patches of the star
at a given depth and latitude. The depth of the patch was varied by
changing the rotation rate such that the resulting Coriolis numbers
covered the same range as in the NSSL. We measured the turbulent
transport coefficient relevant for the nondiffusive (Λ-effect)
and diffusive (turbulent viscosity) parts of the Reynolds stress and
compared them with predictions of current mean-field theories. 
Results: A negative radial gradient of the mean flow is generated only
at the equator where meridional flows are absent. At other latitudes,
the meridional flow is comparable to the mean flow corresponding to
differential rotation. We also find that the meridional components
of the Reynolds stress cannot be ignored. Additionally, we find that
the turbulent viscosity is quenched by rotation by about 50% from
the surface to the bottom of the NSSL. Conclusions: Our local
simulations do not validate the explanation for the generation of the
NSSL from mean-field theory where meridional flows and stresses are
neglected. However, the rotational dependence of the turbulent viscosity
in our simulations agrees well with theoretical predictions. Moreover,
our results agree qualitatively with global convection simulations in
that an NSSL can only be obtained near the equator.

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Title: Prandtl number dependence of stellar convection: Flow
statistics and convective energy transport
Authors: Käpylä, P. J.
2021A&A...655A..78K Altcode: 2021arXiv210508453K
Context. The ratio of kinematic viscosity to thermal diffusivity,
the Prandtl number, is much smaller than unity in stellar convection
zones. Aims: The main goal of this work is to study the
statistics of convective flows and energy transport as functions
of the Prandtl number. Methods: Three-dimensional numerical
simulations of compressible non-rotating hydrodynamic convection in
Cartesian geometry are used. The convection zone (CZ) is embedded
between two stably stratified layers. The dominant contribution
to the diffusion of entropy fluctuations comes in most cases from
a subgrid-scale diffusivity whereas the mean radiative energy flux
is mediated by a diffusive flux employing Kramers opacity law. Here,
we study the statistics and transport properties of up- and downflows
separately. Results: The volume-averaged rms velocity increases
with decreasing Prandtl number. At the same time, the filling factor
of downflows decreases and leads to, on average, stronger downflows
at lower Prandtl numbers. This results in a strong dependence
of convective overshooting on the Prandtl number. Velocity power
spectra do not show marked changes as a function of Prandtl number
except near the base of the convective layer where the dominance
of vertical flows is more pronounced. At the highest Reynolds
numbers, the velocity power spectra are more compatible with the
Bolgiano-Obukhov k−11/5 than the Kolmogorov-Obukhov
k−5/3 scaling. The horizontally averaged convected
energy flux (F̅conv), which is the sum of the enthalpy
(F̅enth) and kinetic energy fluxes (F̅kin),
is independent of the Prandtl number within the CZ. However,
the absolute values of F̅enth and F̅kin
increase monotonically with decreasing Prandtl number. Furthermore,
F̅enth and F̅kin have opposite signs for
downflows and their sum F̅↓conv diminishes
with Prandtl number. Thus, the upflows (downflows) are the dominant
contribution to the convected flux at low (high) Prandtl numbers. These
results are similar to those from Rayleigh-Benárd convection in the
low Prandtl number regime where convection is vigorously turbulent but
inefficient at transporting energy. Conclusions: The current
results indicate a strong dependence of convective overshooting
and energy flux on the Prandtl number. Numerical simulations of
astrophysical convection often use a Prandtl number of unity because it
is numerically convenient. The current results suggest that this can
lead to misleading results and that the astrophysically relevant low
Prandtl number regime is qualitatively different from the parameter
regimes explored in typical contemporary simulations.

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Title: Star-in-a-box simulations of fully convective stars
Authors: Käpylä, P. J.
2021A&A...651A..66K Altcode: 2020arXiv201201259K
Context. Main-sequence late-type stars with masses of less than 0.35
M⊙ are fully convective. Aims: The goal is to
study convection, differential rotation, and dynamos as functions of
rotation in fully convective stars. Methods: Three-dimensional
hydrodynamic and magnetohydrodynamic numerical simulations with a
star-in-a-box model, in which a spherical star is immersed inside
of a Cartesian cube, are used. The model corresponds to a 0.2
M⊙ main-sequence M5 dwarf. A range of rotation periods
(Prot) between 4.3 and 430 d is explored. Results:
The slowly rotating model with Prot = 430 days produces
anti-solar differential rotation with a slow equator and fast poles,
along with predominantly axisymmetric quasi-steady large-scale magnetic
fields. For intermediate rotation (Prot = 144 and 43 days)
the differential rotation is solar-like (fast equator, slow poles),
and the large-scale magnetic fields are mostly axisymmetric and either
quasi-stationary or cyclic. The latter occurs in a similar parameter
regime as in other numerical studies in spherical shells, and the cycle
period is similar to observed cycles in fully convective stars with
rotation periods of roughly 100 days. In the rapid rotation regime
the differential rotation is weak and the large-scale magnetic fields
are increasingly non-axisymmetric with a dominating m = 1 mode. This
large-scale non-axisymmetric field also exhibits azimuthal dynamo
waves. Conclusions: The results of the star-in-a-box models agree
with simulations of partially convective late-type stars in spherical
shells in that the transitions in differential rotation and dynamo
regimes occur at similar rotational regimes in terms of the Coriolis
(inverse Rossby) number. This similarity between partially and fully
convective stars suggests that the processes generating differential
rotation and large-scale magnetism are insensitive to the geometry of
the star.

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Title: Erratum: Magnetohydrodynamical origin of eclipsing time
variations in post-common-envelope binaries for solar mass secondaries
Authors: Navarrete, Felipe H.; Schleicher, Dominik R. G.; Käpylä,
Petri J.; Schober, Jennifer; Völschow, Marcel; Mennickent, Ronald E.
2021MNRAS.504.1676N Altcode:
No abstract at ADS

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Title: Common dynamo scaling in late-type main sequence and evolved
stars
Authors: Lehtinen, Jyri; Spada, Federico; Käpylä, Maarit; Olspert,
Nigul; Käpylä, Petri
2021csss.confE.193L Altcode:
Both the magnetic activity and magnetic field strengths of late-type
stars are observed to scale up with stellar rotation up to a certain
saturation level. We show strong evidence from chromospheric Ca II
H&amp;K line emission observations that the same rotation-activity
relation is shared by both main sequence stars and evolved giants. This
indicates that the dynamos of both young and evolved stars follow
the same underlying principles, irrespective of the stellar internal
structure. The common scaling relation can only be found in relation to
the Rossby number, i.e. the ratio of rotation period to the convective
turnover time, meaning that this shared dynamo must be governed by
turbulent convection. A more detailed analysis of the shape of the
rotation-activity relation reveals a localised break in its slope
at mid-activity levels. This knee point lies close to the threshold
where large scale non-axisymmetric activity appears on fast rotating
stars. It may thus be connected to a transition between axisymmetric
and non-axisymmetric dynamo modes in slow and fast rotating stars.

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Title: Reynolds number dependence of Lyapunov exponents of turbulence
and fluid particles
Authors: Fouxon, Itzhak; Feinberg, Joshua; Käpylä, Petri; Mond,
Michael
2021PhRvE.103c3110F Altcode: 2021arXiv210401235F
The Navier-Stokes equations generate an infinite set of generalized
Lyapunov exponents defined by different ways of measuring the
distance between exponentially diverging perturbed and unperturbed
solutions. This set is demonstrated to be similar, yet different, from
the generalized Lyapunov exponent that provides moments of distance
between two fluid particles below the Kolmogorov scale. We derive
rigorous upper bounds on dimensionless Lyapunov exponent of the fluid
particles that demonstrate the exponent's decay with Reynolds number
Re in accord with previous studies. In contrast, terms of cumulant
series for exponents of the moments have power-law growth with Re. We
demonstrate as an application that the growth of small fluctuations of
magnetic field in ideal conducting turbulence is hyperintermittent,
being exponential in both time and Reynolds number. We resolve
the existing contradiction between the theory, that predicts slow
decrease of dimensionless Lyapunov exponent of turbulence with Re,
and observations exhibiting quite fast growth. We demonstrate that
it is highly plausible that a pointwise limit for the growth of small
perturbations of the Navier-Stokes equations exists.

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Title: The Pencil Code, a modular MPI code for partial differential
equations and particles: multipurpose and multiuser-maintained
Authors: Pencil Code Collaboration; Brandenburg, Axel; Johansen,
Anders; Bourdin, Philippe; Dobler, Wolfgang; Lyra, Wladimir;
Rheinhardt, Matthias; Bingert, Sven; Haugen, Nils; Mee, Antony; Gent,
Frederick; Babkovskaia, Natalia; Yang, Chao-Chin; Heinemann, Tobias;
Dintrans, Boris; Mitra, Dhrubaditya; Candelaresi, Simon; Warnecke,
Jörn; Käpylä, Petri; Schreiber, Andreas; Chatterjee, Piyali;
Käpylä, Maarit; Li, Xiang-Yu; Krüger, Jonas; Aarnes, Jørgen;
Sarson, Graeme; Oishi, Jeffrey; Schober, Jennifer; Plasson, Raphaël;
Sandin, Christer; Karchniwy, Ewa; Rodrigues, Luiz; Hubbard, Alexander;
Guerrero, Gustavo; Snodin, Andrew; Losada, Illa; Pekkilä, Johannes;
Qian, Chengeng
2021JOSS....6.2807P Altcode: 2021JOSS....6.2807C; 2020arXiv200908231B
The Pencil Code is a highly modular physics-oriented simulation code
that can be adapted to a wide range of applications. It is primarily
designed to solve partial differential equations (PDEs) of compressible
hydrodynamics and has lots of add-ons ranging from astrophysical
magnetohydrodynamics (MHD) to meteorological cloud microphysics and
engineering applications in combustion. Nevertheless, the framework
is general and can also be applied to situations not related to
hydrodynamics or even PDEs, for example when just the message passing
interface or input/output strategies of the code are to be used. The
code can also evolve Lagrangian (inertial and noninertial) particles,
their coagulation and condensation, as well as their interaction with
the fluid.

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Title: Electrodynamics of turbulent fluids with fluctuating electric
conductivity
Authors: Rüdiger, G.; Küker, M.; Käpylä, P. J.
2020JPlPh..86c9018R Altcode: 2019arXiv191106611R
Consequences of fluctuating microscopic conductivity in mean-field
electrodynamics of turbulent fluids are formulated and discussed. If
the conductivity fluctuations are assumed to be uncorrelated with the
velocity fluctuations then only the turbulence-originated magnetic
diffusivity of the fluid is reduced and the decay time of a large-scale
magnetic field or the cycle times of oscillating turbulent dynamo models
are increased. If, however, the fluctuations of conductivity and flow
in a certain well-defined direction are correlated, an additional
diamagnetic pumping effect results, transporting the magnetic field
in the opposite direction to the diffusivity flux vector $\langle
\unicode[STIX]{x1D702}^' }\boldsymbol{u}^' }\rangle$. In the presence
of global rotation, even for homogeneous turbulence fields, an alpha
effect appears. If the characteristic values of the outer core of the
Earth or the solar convection zone are applied, the dynamo number of
the new alpha effect does not reach supercritical values to operate
as an $\unicode[STIX]{x1D6FC}2$-dynamo but oscillating
$\unicode[STIX]{x1D6FC}\unicode[STIX]{x1D6FA}$-dynamos with differential
rotation are not excluded.

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Title: Turbulent viscosity and magnetic Prandtl number from
simulations of isotropically forced turbulence
Authors: Käpylä, P. J.; Rheinhardt, M.; Brandenburg, A.; Käpylä,
M. J.
2020A&A...636A..93K Altcode: 2019arXiv190100787K
Context. Turbulent diffusion of large-scale flows and magnetic fields
plays a major role in many astrophysical systems, such as stellar
convection zones and accretion discs. Aims: Our goal is to
compute turbulent viscosity and magnetic diffusivity which are relevant
for diffusing large-scale flows and magnetic fields, respectively. We
also aim to compute their ratio, which is the turbulent magnetic
Prandtl number, Pmt, for isotropically forced homogeneous
turbulence. Methods: We used simulations of forced turbulence
in fully periodic cubes composed of isothermal gas with an imposed
large-scale sinusoidal shear flow. Turbulent viscosity was computed
either from the resulting Reynolds stress or from the decay rate of the
large-scale flow. Turbulent magnetic diffusivity was computed using
the test-field method for a microphysical magnetic Prandtl number of
unity. The scale dependence of the coefficients was studied by varying
the wavenumber of the imposed sinusoidal shear and test fields. 
Results: We find that turbulent viscosity and magnetic diffusivity are
in general of the same order of magnitude. Furthermore, the turbulent
viscosity depends on the fluid Reynolds number (Re) and scale separation
ratio of turbulence. The scale dependence of the turbulent viscosity is
found to be well approximated by a Lorentzian. These results are similar
to those obtained earlier for the turbulent magnetic diffusivity. The
results for the turbulent transport coefficients appear to converge at
sufficiently high values of Re and the scale separation ratio. However,
a weak trend is found even at the largest values of Re, suggesting that
the turbulence is not in the fully developed regime. The turbulent
magnetic Prandtl number converges to a value that is slightly below
unity for large Re. For small Re we find values between 0.5 and 0.6 but
the data are insufficient to draw conclusions regarding asymptotics. We
demonstrate that our results are independent of the correlation
time of the forcing function. Conclusions: The turbulent
magnetic diffusivity is, in general, consistently higher than the
turbulent viscosity, which is in qualitative agreement with analytic
theories. However, the actual value of Pmt found from the
simulations (≈0.9-0.95) at large Re and large scale separation ratio
is higher than any of the analytic predictions (0.4-0.8).

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Title: Common dynamo scaling in slowly rotating young and evolved
stars
Authors: Lehtinen, Jyri J.; Spada, Federico; Käpylä, Maarit J.;
Olspert, Nigul; Käpylä, Petri J.
2020NatAs...4..658L Altcode: 2020NatAs.tmp...46L; 2020arXiv200308997L
One interpretation of the activity and magnetism of late-type stars
is that these both intensify with decreasing Rossby number up to a
saturation level1-3, suggesting that stellar dynamos depend
on both rotation and convective turbulence4. Some studies
have claimed, however, that rotation alone suffices to parametrize
this scaling adequately5,6. Here, we tackle the question of
the relevance of turbulence to stellar dynamos by including evolved,
post-main-sequence stars in the analysis of the rotation-activity
relation. These stars rotate very slowly compared with main-sequence
stars, but exhibit similar activity levels7. We show that the
two evolutionary stages fall together in the rotation-activity diagram
and form a single sequence in the unsaturated regime in relation only
to Rossby numbers derived from stellar models, confirming earlier
preliminary results that relied on a more simplistic parametrization
of the convective turn-over time8,9. This mirrors recent
results of fully convective M dwarfs, which likewise fall on the
same rotation-activity sequence as partially convective solar-type
stars10,11. Our results demonstrate that turbulence plays
a crucial role in driving stellar dynamos and suggest that there is
a common turbulence-related dynamo mechanism explaining the magnetic
activity of all late-type stars.

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Title: Sensitivity to luminosity, centrifugal force, and boundary
conditions in spherical shell convection
Authors: Käpylä, P. J.; Gent, F. A.; Olspert, N.; Käpylä, M. J.;
Brandenburg, A.
2020GApFD.114....8K Altcode: 2018arXiv180709309K
We test the sensitivity of hydrodynamic and magnetohydrodynamic
turbulent convection simulations with respect to Mach number, thermal
and magnetic boundary conditions, and the centrifugal force. We find
that varying the luminosity, which also controls the Mach number, has
only a minor effect on the large-scale dynamics. A similar conclusion
can also be drawn from the comparison of two formulations of the lower
magnetic boundary condition with either vanishing electric field or
current density. The centrifugal force has an effect on the solutions,
but only if its magnitude with respect to acceleration due to gravity
is by two orders of magnitude greater than in the Sun. Finally, we find
that the parameterisation of the photospheric physics, either by an
explicit cooling term or enhanced radiative diffusion, is more important
than the thermal boundary condition. In particular, runs with cooling
tend to lead to more anisotropic convection and stronger deviations
from the Taylor-Proudman state. In summary, the fully compressible
approach taken here with the Pencil Code is found to be valid, while
still allowing the disparate timescales to be taken into account.

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Title: f-mode strengthening from a localised bipolar subsurface
magnetic field
Authors: Singh, Nishant K.; Raichur, Harsha; Käpylä, Maarit J.;
Rheinhardt, Matthias; Brandenburg, Axel; Käpylä, Petri J.
2020GApFD.114..196S Altcode:
Recent numerical work in helioseismology has shown that a periodically
varying subsurface magnetic field leads to a fanning of the f-mode,
which emerges from a density jump at the surface. In an attempt to model
a more realistic situation, we now modulate this periodic variation with
an envelope, giving thus more emphasis on localised bipolar magnetic
structures in the middle of the domain. Some notable findings are: (i)
compared to the purely hydrodynamic case, the strength of the f-mode is
significantly larger at high horizontal wavenumbers k, but the fanning
is weaker for the localised subsurface magnetic field concentrations
investigated here than the periodic ones studied earlier; (ii) when
the strength of the magnetic field is enhanced at a fixed depth below
the surface, the fanning of the f-mode in the ? diagram increases
proportionally in such a way that the normalised f-mode strengths remain
nearly the same in different such cases; (iii) the unstable Bloch modes
reported previously in case of harmonically varying magnetic fields
are now completely absent when more realistic localised magnetic field
concentrations are imposed beneath the surface, thus suggesting that
the Bloch modes are unlikely to be supported during most phases of the
solar cycle; (iv) the f-mode strength appears to depend also on the
depth of magnetic field concentrations such that it shows a relative
decrement when the maximum of the magnetic field is moved to a deeper
layer. We argue that detections of f-mode perturbations such as those
being explored here could be effective tracers of solar magnetic fields
below the photosphere before these are directly detectable as visible
manifestations in terms of active regions or sunspots.

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Title: VizieR Online Data Catalog: Rotation and activity across HR
diagram (Lehtinen+, 2020)
Authors: Lehtinen, J. J.; Spada, F.; Kapyla, M. J.; Olspert, N.;
Kapyla, P. J.
2020yCatp061000401L Altcode:
Derived values for the chromospheric activity, rotational and convective
characteristics, and the evolutionary stage, as well as literature
data used for deriving these, are presented for 224 stars observed
over four or more observing seasons in the Mount Wilson Observatory
HK Project. Data for five additional stars with photometrically
derived rotation periods (Lehtinen et al., 2016A&amp;A...588A..38L)
are presented in separate tables to supplement the short rotation
period end of the sample. Moreover, for the stars with newly derived
rotation periods, we present a comparison with period estimates found
from the literature. (5 data files).

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Title: Magnetohydrodynamical origin of eclipsing time variations in
post-common-envelope binaries for solar mass secondaries
Authors: Navarrete, Felipe H.; Schleicher, Dominik R. G.; Käpylä,
Petri J.; Schober, Jennifer; Völschow, Marcel; Mennickent, Ronald E.
2020MNRAS.491.1043N Altcode: 2019MNRAS.tmp.2642N; 2019arXiv190606787N
Eclipsing time variations have been observed for a wide range of binary
systems, including post-common-envelope binaries. A frequently proposed
explanation, apart from the possibility of having a third body, is the
effect of magnetic activity, which may alter the internal structure of
the secondary star, particularly its quadrupole moment, and thereby
cause quasi-periodic oscillations. Here, we present two compressible
non-ideal magnetohydrodynamical simulations of the magnetic dynamo in
a solar mass star, one of them with three times the solar rotation
rate ('slow rotator'), and the other one with 20 times the solar
rotation rate ('rapid rotator'), to account for the high rotational
velocities in close binary systems. For the slow rotator, we find that
both the magnetic field and the stellar quadrupole moment change in
a quasi-periodic manner, leading to O - C (observed minus corrected
times of the eclipse) variations of ∼0.025 s. For the rapid rotator,
the behaviour of the magnetic field as well as the quadrupole moment
changes becomes considerably more complex, due to the less coherent
dynamo solution. The resulting O - C variations are of the order of
0.13 s. The observed system V471 Tau shows two modes of eclipsing time
variations, with amplitudes of 151 and 20 s, respectively. However,
the current simulations may not capture all relevant effects due to
the neglect of the centrifugal force and self-gravity. Considering the
model limitations and that the rotation of V471 Tau is still a factor
of 2.5 faster than our rapid rotator, it may be conceivable to reach
the observed magnitudes.

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Title: Overshooting in simulations of compressible convection
Authors: Käpylä, P. J.
2019A&A...631A.122K Altcode: 2018arXiv181207916K
Context. Convective motions that overshoot into regions that are
formally convectively stable cause extended mixing. Aims: We aim
to determine the scaling of the overshooting depth (dos) at
the base of the convection zone as a function of imposed energy flux
(ℱn) and to estimate the extent of overshooting at the
base of the solar convection zone. Methods: Three-dimensional
Cartesian simulations of hydrodynamic compressible non-rotating
convection with unstable and stable layers were used. The simulations
used either a fixed heat conduction profile or a temperature- and
density-dependent formulation based on Kramers opacity law. The
simulations covered a range of almost four orders of magnitude in
the imposed flux, and the sub-grid scale diffusivities were varied
so as to maintain approximately constant supercriticality at each
flux. Results: A smooth heat conduction profile (either fixed
or through Kramers opacity law) leads to a relatively shallow power
law with dos ∝ ℱn0.08 for low
ℱn. A fixed step-profile of the heat conductivity at the
bottom of the convection zone leads to a somewhat steeper dependency
on dos ∝ ℱn0.12 in the same
regime. Experiments with and without subgrid-scale entropy diffusion
revealed a strong dependence on the effective Prandtl number, which is
likely to explain the steep power laws as a function of ℱn
reported in the literature. Furthermore, changing the heat conductivity
artificially in the radiative and overshoot layers to speed up thermal
saturation is shown to lead to a substantial underestimation of the
overshooting depth. Conclusions: Extrapolating from the results
obtained with smooth heat conductivity profiles, which are the most
realistic set-up we considered, suggest that the overshooting depth
for the solar energy flux is about 20% of the pressure scale height at
the base of the convection zone. This is two to four times higher than
the estimates from helioseismology. However, the current simulations
do not include rotation or magnetic fields, which are known to reduce
convective overshooting.

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Title: Stellar Dynamos in the Transition Regime: Multiple Dynamo
Modes and Antisolar Differential Rotation
Authors: Viviani, M.; Käpylä, M. J.; Warnecke, J.; Käpylä, P. J.;
Rheinhardt, M.
2019ApJ...886...21V Altcode: 2019arXiv190204019V
Global and semi-global convective dynamo simulations of solar-like
stars are known to show a transition from an antisolar (fast poles, slow
equator) to solar-like (fast equator, slow poles) differential rotation
(DR) for increasing rotation rate. The dynamo solutions in the latter
regime can exhibit regular cyclic modes, whereas in the former one,
only stationary or temporally irregular solutions have been obtained so
far. In this paper we present a semi-global dynamo simulation in the
transition region, exhibiting two coexisting dynamo modes, a cyclic
and a stationary one, both being dynamically significant. We seek to
understand how such a dynamo is driven by analyzing the large-scale flow
properties (DR and meridional circulation) together with the turbulent
transport coefficients obtained with the test-field method. Neither
an αΩ dynamo wave nor an advection-dominated dynamo are able to
explain the cycle period and the propagation direction of the mean
magnetic field. Furthermore, we find that the α effect is comparable
or even larger than the Ω effect in generating the toroidal magnetic
field, and therefore, the dynamo seems to be of α 2Ω or
α 2 type. We further find that the effective large-scale
flows are significantly altered by turbulent pumping.

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Title: Effects of small-scale dynamo and compressibility on the
Λ effect
Authors: Käpylä, Petri J.
2019AN....340..744K Altcode: 2019arXiv190304363K
The Λ effect describes a rotation-induced nondiffusive contribution to
the Reynolds stress. It is commonly held responsible for maintaining
the observed differential rotation of the Sun and other late-type
stars. Here, the sensitivity of the Λ effect to small-scale magnetic
fields and compressibility is studied by means of forced turbulence
simulations either with anisotropic forcing in fully periodic cubes
or in density-stratified domains with isotropic forcing. Effects of
small-scale magnetic fields are studied in cases where the magnetic
fields are self-consistently generated by a small-scale dynamo. The
results show that small-scale magnetic fields lead to a quenching of
the Λ effect which is milder than in cases where also a large-scale
field is present. The effect of compressibility on the Λ effect is
negligible in the range of Mach numbers from 0.015 to 0.8. Density
stratification induces a marked anisotropy in the turbulence and a
vertical Λ effect if the forcing scale is roughly two times larger
than the density scale height.

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Title: Antisolar differential rotation of slowly rotating cool stars
Authors: Rüdiger, G.; Küker, M.; Käpylä, P. J.; Strassmeier, K. G.
2019A&A...630A.109R Altcode: 2019arXiv190204172R
Rotating stellar convection transports angular momentum towards
the equator, generating the characteristic equatorial acceleration
of the solar rotation while the radial flux of angular momentum is
always inwards. New numerical box simulations for the meridional
cross-correlation ⟨uθuϕ⟩, however, reveal
the angular momentum transport towards the poles for slow rotation
and towards the equator for fast rotation. The explanation is that for
slow rotation a negative radial gradient of the angular velocity always
appears, which in combination with a so-far neglected rotation-induced
off-diagonal eddy viscosity term ν⊥ provides
"antisolar rotation" laws with a decelerated equator. Similarly,
the simulations provided positive values for the rotation-induced
correlation ⟨uruθ⟩, which is relevant for
the resulting latitudinal temperature profiles (cool or warm poles)
for slow rotation and negative values for fast rotation. Observations
of the differential rotation of slowly rotating stars will therefore
lead to a better understanding of the actual stress-strain relation,
the heat transport, and the underlying model of the rotating convection.

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Title: Effects of a subadiabatic layer on convection and dynamos in
spherical wedge simulations
Authors: Käpylä, P. J.; Viviani, M.; Käpylä, M. J.; Brandenburg,
A.; Spada, F.
2019GApFD.113..149K Altcode: 2018arXiv180305898K
We consider the effect of a subadiabatic layer at the base of the
convection zone on convection itself and the associated large-scale
dynamos in spherical wedge geometry. We use a heat conduction
prescription based on the Kramers opacity law which allows the depth
of the convection zone to dynamically adapt to changes in the physical
characteristics such as rotation rate and magnetic fields. We find
that the convective heat transport is strongly concentrated towards
the equatorial and polar regions in the cases without a substantial
radiative layer below the convection zone. The presence of a stable
layer below the convection zone significantly reduces the anisotropy
of radial enthalpy transport. Furthermore, the dynamo solutions are
sensitive to subtle changes in the convection zone structure. We find
that the kinetic helicity changes sign in the deeper parts of the
convection zone at high latitudes in all runs. This region expands
progressively towards the equator in runs with a thicker stably
stratified layer.

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Title: Magnetic and rotational quenching of the Λ effect
Authors: Käpylä, P. J.
2019A&A...622A.195K Altcode: 2017arXiv171208045K
Context. Differential rotation in stars is driven by the turbulent
transport of angular momentum. Aims: Our aim is to measure
and parameterize the non-diffusive contribution to the total
(Reynolds plus Maxwell) turbulent stress, known as the Λ effect,
and its quenching as a function of rotation and magnetic field. 
Methods: Simulations of homogeneous, anisotropically forced turbulence
in fully periodic cubes are used to extract their associated turbulent
Reynolds and Maxwell stresses. The forcing is set up such that the
vertical velocity component dominates over the horizontal ones, as in
turbulent stellar convection. This choice of the forcing defines the
vertical direction. Additional preferred directions are introduced
by the imposed rotation and magnetic field vectors. The angle between
the rotation vector and the vertical direction is varied such that the
latitude range from the north pole to the equator is covered. Magnetic
fields are introduced by imposing a uniform large-scale field on the
system. Turbulent transport coefficients pertaining to the Λ effect
are obtained by fitting. The results are compared with analytic
studies. Results: The numerical and analytic results agree
qualitatively at slow rotation and low Reynolds numbers. This means
that vertical (horizontal) transport is downward (equatorward). At
rapid rotation the latitude dependence of the stress is more complex
than predicted by theory. The existence of a significant meridional
Λ effect is confirmed. Large-scale vorticity generation is found at
rapid rotation when the Reynolds number exceeds a threshold value. The
Λ effect is severely quenched by large-scale magnetic fields due
to the tendency of the Reynolds and Maxwell stresses to cancel each
other. Rotational (magnetic) quenching of Λ occurs at more rapid
rotation (at lower field strength) in the simulations than in the
analytic studies. Conclusions: The current results largely
confirm the earlier theoretical results, and also offer new insights:
the non-negligible meridional Λ effect possibly plays a role in the
maintenance of meridional circulation in stars, and the appearance
of large-scale vortices raises the question of their effect on the
angular momentum transport in rapidly rotating stellar convective
envelopes. The results regarding magnetic quenching are consistent
with the strong decrease in differential rotation in recent semi-global
simulations and highlight the importance of including magnetic effects
in differential rotation models.

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Title: $f$-mode strengthening from a localized bipolar subsurface
magnetic field
Authors: Singh, Nishant K.; Raichur, Harsha; Käpylä, Maarit J.;
Rheinhardt, Matthias; Brandenburg, Axel; Käpylä, Petri J.
2018arXiv180808904S Altcode:
Recent numerical work in helioseismology has shown that a periodically
varying subsurface magnetic field leads to a fanning of the $f$-mode,
which emerges from the density jump at the surface. In an attempt
to model a more realistic situation, we now modulate this periodic
variation with an envelope, giving thus more emphasis on localized
bipolar magnetic structures in the middle of the domain. Some notable
findings are: (i) compared to the purely hydrodynamic case, the strength
of the $f$-mode is significantly larger at high horizontal wavenumbers
$k$, but the fanning is weaker for the localized subsurface magnetic
field concentrations investigated here than the periodic ones studied
earlier; (ii) when the strength of the magnetic field is enhanced at
a fixed depth below the surface, the fanning of the $f$-mode in the
$k\omega$ diagram increases proportionally in such a way that the
normalized $f$-mode strengths remain nearly the same in different
such cases; (iii) the unstable Bloch modes reported previously in
case of harmonically varying magnetic fields are now completely
absent when more realistic localized magnetic field concentrations
are imposed beneath the surface, thus suggesting that the Bloch modes
are unlikely to be supported during most phases of the solar cycle;
(iv) the $f$-mode strength appears to depend also on the depth of
magnetic field concentrations such that it shows a relative decrement
when the maximum of the magnetic field is moved to a deeper layer. We
argue that detections of $f$-mode perturbations such as those being
explored here could be effective tracers of solar magnetic fields
below the photosphere before these are directly detectable as visible
manifestations in terms of active regions or sunspots.

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Title: Transition from axi- to nonaxisymmetric dynamo modes in
spherical convection models of solar-like stars
Authors: Viviani, M.; Warnecke, J.; Käpylä, M. J.; Käpylä, P. J.;
Olspert, N.; Cole-Kodikara, E. M.; Lehtinen, J. J.; Brandenburg, A.
2018A&A...616A.160V Altcode: 2017arXiv171010222V
Context. Both dynamo theory and observations of stellar large-scale
magnetic fields suggest a change from nearly axisymmetric configurations
at solar rotation rates to nonaxisymmetric configurations for rapid
rotation. Aims: We seek to understand this transition using
numerical simulations. Methods: We use three-dimensional
simulations of turbulent magnetohydrodynamic convection in spherical
shell wedges and considered rotation rates between 1 and 31 times
the solar value. Results: We find a transition from axi-
to nonaxisymmetric solutions at around 1.8 times the solar rotation
rate. This transition coincides with a change in the rotation profile
from antisolar- to solar-like differential rotation with a faster
equator and slow poles. In the solar-like rotation regime, the
field configuration consists of an axisymmetric oscillatory field
accompanied by an m = 1 azimuthal mode (two active longitudes),
which also shows temporal variability. At slow (rapid) rotation,
the axisymmetric (nonaxisymmetric) mode dominates. The axisymmetric
mode produces latitudinal dynamo waves with polarity reversals, while
the nonaxisymmetric mode often exhibits a slow drift in the rotating
reference frame and the strength of the active longitudes changes
cyclically over time between the different hemispheres. In the majority
of cases we find retrograde waves, while prograde waves are more often
found from observations. Most of the obtained dynamo solutions exhibit
cyclic variability either caused by latitudinal or azimuthal dynamo
waves. In an activity-period diagram, the cycle lengths normalized
by the rotation period form two different populations as a function
of rotation rate or magnetic activity level. The slowly rotating
axisymmetric population lies close to what in observations is called
the inactive branch, where the stars are believed to have solar-like
differential rotation, while the rapidly rotating models are close to
the superactive branch with a declining cycle to rotation frequency
ratio and an increasing rotation rate. Conclusions: We can
successfully reproduce the transition from axi- to nonaxisymmetric
dynamo solutions for high rotation rates, but high-resolution
simulations are required to limit the effect of rotational quenching
of convection at rotation rates above 20 times the solar value.

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Title: Bihelical Spectrum of Solar Magnetic Helicity and Its Evolution
Authors: Singh, Nishant K.; Käpylä, Maarit J.; Brandenburg, Axel;
Käpylä, Petri J.; Lagg, Andreas; Virtanen, Ilpo
2018ApJ...863..182S Altcode: 2018arXiv180404994S
Using a recently developed two-scale formalism to determine the
magnetic helicity spectrum, we analyze synoptic vector magnetograms
built with data from the Vector Spectromagnetograph instrument on the
Synoptic Optical Long-term Investigations of the Sun telescope during
2010 January-2016 July. In contrast to an earlier study using only
three Carrington rotations (CRs), our analysis includes 74 synoptic
CR maps. We recover here bihelical spectra at different phases of
solar cycle 24, where the net magnetic helicity in the majority of the
data is consistent with a large-scale dynamo with helical turbulence
operating in the Sun. More than 20% of the analyzed maps, however,
show violations of the expected sign rule.

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Title: Large-scale dynamos in rapidly rotating plane layer convection
Authors: Bushby, P. J.; Käpylä, P. J.; Masada, Y.; Brandenburg,
A.; Favier, B.; Guervilly, C.; Käpylä, M. J.
2018A&A...612A..97B Altcode: 2017arXiv171003174B
Context. Convectively driven flows play a crucial role in the dynamo
processes that are responsible for producing magnetic activity in stars
and planets. It is still not fully understood why many astrophysical
magnetic fields have a significant large-scale component. 
Aims: Our aim is to investigate the dynamo properties of compressible
convection in a rapidly rotating Cartesian domain, focusing upon a
parameter regime in which the underlying hydrodynamic flow is known to
be unstable to a large-scale vortex instability. Methods: The
governing equations of three-dimensional non-linear magnetohydrodynamics
(MHD) are solved numerically. Different numerical schemes are compared
and we propose a possible benchmark case for other similar codes. Results: In keeping with previous related studies, we find that
convection in this parameter regime can drive a large-scale dynamo. The
components of the mean horizontal magnetic field oscillate, leading to
a continuous overall rotation of the mean field. Whilst the large-scale
vortex instability dominates the early evolution of the system, the
large-scale vortex is suppressed by the magnetic field and makes
a negligible contribution to the mean electromotive force that is
responsible for driving the large-scale dynamo. The cycle period of
the dynamo is comparable to the ohmic decay time, with longer cycles
for dynamos in convective systems that are closer to onset. In these
particular simulations, large-scale dynamo action is found only when
vertical magnetic field boundary conditions are adopted at the upper
and lower boundaries. Strongly modulated large-scale dynamos are
found at higher Rayleigh numbers, with periods of reduced activity
(grand minima-like events) occurring during transient phases in which
the large-scale vortex temporarily re-establishes itself, before being
suppressed again by the magnetic field.

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Title: Small-scale dynamos in simulations of stratified turbulent
convection
Authors: Käpylä, P. J.; Käpylä, M. J.; Brandenburg, A.
2018AN....339..127K Altcode: 2018arXiv180209607K
Small-scale dynamo action is often held responsible for the
generation of quiet Sun magnetic fields. We aim to determine the
excitation conditions and saturation level of small-scale dynamos in
nonrotating turbulent convection at low magnetic Prandtl numbers. We
use high-resolution direct numerical simulations of weakly stratified
turbulent convection. We find that the critical magnetic Reynolds
number for dynamo excitation increases as the magnetic Prandtl number
is decreased, which might suggest that small-scale dynamo action is not
automatically evident in bodies with small magnetic Prandtl numbers,
such as the Sun. As a function of the magnetic Reynolds number (Rm),
the growth rate of the dynamo is consistent with an Rm1/2
scaling. No evidence for a logarithmic increase of the growth rate
with Rm is found.

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Title: Turbulent transport coefficients in spherical wedge dynamo
simulations of solar-like stars
Authors: Warnecke, J.; Rheinhardt, M.; Tuomisto, S.; Käpylä, P. J.;
Käpylä, M. J.; Brandenburg, A.
2018A&A...609A..51W Altcode: 2016arXiv160103730W
 Aims: We investigate dynamo action in global compressible
solar-like convective dynamos in the framework of mean-field
theory. Methods: We simulate a solar-type star in a wedge-shaped
spherical shell, where the interplay between convection and rotation
self-consistently drives a large-scale dynamo. To analyze the dynamo
mechanism we apply the test-field method for azimuthally (φ) averaged
fields to determine the 27 turbulent transport coefficients of the
electromotive force, of which six are related to the α tensor. This
method has previously been used either in simulations in Cartesian
coordinates or in the geodynamo context and is applied here for the
first time to fully compressible simulations of solar-like dynamos. Results: We find that the φφ-component of the α tensor does
not follow the profile expected from that of kinetic helicity. The
turbulent pumping velocities significantly alter the effective mean
flows acting on the magnetic field and therefore challenge the flux
transport dynamo concept. All coefficients are significantly affected by
dynamically important magnetic fields. Quenching as well as enhancement
are being observed. This leads to a modulation of the coefficients with
the activity cycle. The temporal variations are found to be comparable
to the time-averaged values and seem to be responsible for a nonlinear
feedback on the magnetic field generation. Furthermore, we quantify the
validity of the Parker-Yoshimura rule for the equatorward propagation
of the mean magnetic field in the present case.

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Title: Extended Subadiabatic Layer in Simulations of Overshooting
Convection
Authors: Käpylä, Petri J.; Rheinhardt, Matthias; Brandenburg, Axel;
Arlt, Rainer; Käpylä, Maarit J.; Lagg, Andreas; Olspert, Nigul;
Warnecke, Jörn
2017ApJ...845L..23K Altcode: 2017arXiv170306845K
We present numerical simulations of hydrodynamic overshooting convection
in local Cartesian domains. We find that a substantial fraction
of the lower part of the convection zone (CZ) is stably stratified
according to the Schwarzschild criterion while the enthalpy flux is
outward directed. This occurs when the heat conduction profile at the
bottom of the CZ is smoothly varying, based either on a Kramers-like
opacity prescription as a function of temperature and density or a
static profile of a similar shape. We show that the subadiabatic layer
arises due to nonlocal energy transport by buoyantly driven downflows
in the upper parts of the CZ. Analysis of the force balance of the
upflows and downflows confirms that convection is driven by cooling
at the surface. We find that the commonly used prescription for the
convective enthalpy flux being proportional to the negative entropy
gradient does not hold in the stably stratified layers where the flux is
positive. We demonstrate the existence of a non-gradient contribution
to the enthalpy flux, which is estimated to be important throughout
the convective layer. A quantitative analysis of downflows indicates
a transition from a tree-like structure where smaller downdrafts merge
into larger ones in the upper parts to a structure in the deeper parts
where a height-independent number of strong downdrafts persist. This
change of flow topology occurs when a substantial subadiabatic layer
is present in the lower part of the CZ.

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Title: Methods for compressible fluid simulation on GPUs using
high-order finite differences
Authors: Pekkilä, Johannes; Väisälä, Miikka S.; Käpylä, Maarit
J.; Käpylä, Petri J.; Anjum, Omer
2017CoPhC.217...11P Altcode: 2017arXiv170708900P
We focus on implementing and optimizing a sixth-order finite-difference
solver for simulating compressible fluids on a GPU using third-order
Runge-Kutta integration. Since graphics processing units perform well
in data-parallel tasks, this makes them an attractive platform for fluid
simulation. However, high-order stencil computation is memory-intensive
with respect to both main memory and the caches of the GPU. We present
two approaches for simulating compressible fluids using 55-point and
19-point stencils. We seek to reduce the requirements for memory
bandwidth and cache size in our methods by using cache blocking
and decomposing a latency-bound kernel into several bandwidth-bound
kernels. Our fastest implementation is bandwidth-bound and integrates
343 million grid points per second on a Tesla K40t GPU, achieving a 3
. 6 × speedup over a comparable hydrodynamics solver benchmarked on two
Intel Xeon E5-2690v3 processors. Our alternative GPU implementation is
latency-bound and achieves the rate of 168 million updates per second.

---------------------------------------------------------
Title: Convection-driven spherical shell dynamos at varying Prandtl
numbers
Authors: Käpylä, P. J.; Käpylä, M. J.; Olspert, N.; Warnecke,
J.; Brandenburg, A.
2017A&A...599A...4K Altcode: 2016arXiv160505885K
Context. Stellar convection zones are characterized by vigorous
high-Reynolds number turbulence at low Prandtl numbers. Aims:
We study the dynamo and differential rotation regimes at varying
levels of viscous, thermal, and magnetic diffusion. Methods: We
perform three-dimensional simulations of stratified fully compressible
magnetohydrodynamic convection in rotating spherical wedges at various
thermal and magnetic Prandtl numbers (from 0.25 to 2 and from 0.25
to 5, respectively). Differential rotation and large-scale magnetic
fields are produced self-consistently. Results: We find that for
high thermal diffusivity, the rotation profiles show a monotonically
increasing angular velocity from the bottom of the convection zone to
the top and from the poles toward the equator. For sufficiently rapid
rotation, a region of negative radial shear develops at mid-latitudes
as the thermal diffusivity is decreased, corresponding to an increase
of the Prandtl number. This coincides with and results in a change of
the dynamo mode from poleward propagating activity belts to equatorward
propagating ones. Furthermore, the clearly cyclic solutions disappear
at the highest magnetic Reynolds numbers and give way to irregular sign
changes or quasi-stationary states. The total (mean and fluctuating)
magnetic energy increases as a function of the magnetic Reynolds
number in the range studied here (5-151), but the energies of the
mean magnetic fields level off at high magnetic Reynolds numbers. The
differential rotation is strongly affected by the magnetic fields and
almost vanishes at the highest magnetic Reynolds numbers. In some
of our most turbulent cases, however, we find that two regimes are
possible, where either differential rotation is strong and mean magnetic
fields are relatively weak, or vice versa. Conclusions: Our
simulations indicate a strong nonlinear feedback of magnetic fields on
differential rotation, leading to qualitative changes in the behaviors
of large-scale dynamos at high magnetic Reynolds numbers. Furthermore,
we do not find indications of the simulations approaching an asymptotic
regime where the results would be independent of diffusion coefficients
in the parameter range studied here.

---------------------------------------------------------
Title: Influence of a coronal envelope as a free boundary to global
convective dynamo simulations
Authors: Warnecke, J.; Käpylä, P. J.; Käpylä, M. J.; Brandenburg,
A.
2016A&A...596A.115W Altcode: 2015arXiv150305251W
 Aims: We explore the effects of an outer stably stratified
coronal envelope on rotating turbulent convection, differential
rotation, and large-scale dynamo action in spherical wedge models of
the Sun. Methods: We solve the compressible magnetohydrodynamic
equations in a two-layer model with unstable stratification below the
surface, representing the convection zone, and a stably stratified
coronal envelope above. The interface represents a free surface. We
compare our model to models that have no coronal envelope. 
Results: The presence of a coronal envelope is found to modify
the Reynolds stress and the Λ effect resulting in a weaker and
non-cylindrical differential rotation. This is related to the reduced
latitudinal temperature variations that are caused by and dependent
on the angular velocity. Some simulations develop a near-surface
shear layer that we can relate to a sign change in the meridional
Reynolds stress term in the thermal wind balance equation. Furthermore,
the presence of a free surface changes the magnetic field evolution
since the toroidal field is concentrated closer to the surface. In all
simulations, however, the migration direction of the mean magnetic field
can be explained by the Parker-Yoshimura rule, which is consistent
with earlier findings. Conclusions: A realistic treatment of
the upper boundary in spherical dynamo simulations is crucial for the
dynamics of the flow and magnetic field evolution.

---------------------------------------------------------
Title: Robustness of oscillatory α2 dynamos in spherical
wedges
Authors: Cole, E.; Brandenburg, A.; Käpylä, P. J.; Käpylä, M. J.
2016A&A...593A.134C Altcode: 2016arXiv160105246C
Context. Large-scale dynamo simulations are sometimes confined to
spherical wedge geometries by imposing artificial boundary conditions
at high latitudes. This may lead to spatio-temporal behaviours that
are not representative of those in full spherical shells. Aims:
We study the connection between spherical wedge and full spherical
shell geometries using simple mean-field dynamos. Methods: We
solve the equations for one-dimensional time-dependent α2
and α2Ω mean-field dynamos with only latitudinal extent to
examine the effects of varying the polar angle θ0 between
the latitudinal boundaries and the poles in spherical coordinates. Results: In the case of constant α and ηt profiles,
we find oscillatory solutions only with the commonly used perfect
conductor boundary condition in a wedge geometry, while for full spheres
all boundary conditions produce stationary solutions, indicating that
perfect conductor conditions lead to unphysical solutions in such a
wedge setup. To search for configurations in which this problem can be
alleviated we choose a profile of the turbulent magnetic diffusivity
that decreases toward the poles, corresponding to high conductivity
there. Oscillatory solutions are now achieved with models extending to
the poles, but the magnetic field is strongly concentrated near the
poles and the oscillation period is very long. By changing both the
turbulent magnetic diffusivity and α profiles so that both effects are
more concentrated toward the equator, we see oscillatory dynamos with
equatorward drift, shorter cycles, and magnetic fields distributed over
a wider range of latitudes. Those profiles thus remove the sensitive and
unphysical dependence on θ0. When introducing radial shear,
we again see oscillatory dynamos, and the direction of drift follows
the Parker-Yoshimura rule. Conclusions: A reduced α effect near
the poles with a turbulent diffusivity concentrated toward the equator
yields oscillatory dynamos with equatorward migration and reproduces
best the solutions in spherical wedges. For weak shear, oscillatory
solutions are obtained only for perfect conductor field conditions and
negative shear. Oscillatory solutions become preferred at sufficiently
strong shear. Recent three-dimensional dynamo simulations producing
solar-like magnetic activity are expected to lie in this range.

---------------------------------------------------------
Title: Multiple dynamo modes as a mechanism for long-term solar
activity variations
Authors: Käpylä, M. J.; Käpylä, P. J.; Olspert, N.; Brandenburg,
A.; Warnecke, J.; Karak, B. B.; Pelt, J.
2016A&A...589A..56K Altcode: 2015arXiv150705417K
Context. Solar magnetic activity shows both smooth secular changes,
such as the modern Grand Maximum, and quite abrupt drops that
are denoted as grand minima, such as the Maunder Minimum. Direct
numerical simulations (DNS) of convection-driven dynamos offer one
way of examining the mechanisms behind these events. Aims:
In this work, we analyze a solution of a solar-like DNS that was
evolved for roughly 80 magnetic cycles of 4.9 years and where epochs
of irregular behavior are detected. The emphasis of our analysis is
to find physical causes for such behavior. Methods: The DNS
employed is a semi-global (wedge-shaped) magnetoconvection model. For
the data analysis tasks we use Ensemble Empirical Mode Decomposition
and phase dispersion methods, as they are well suited for analyzing
cyclic (non-periodic) signals. Results: A special property
of the DNS is the existence of multiple dynamo modes at different
depths and latitudes. The dominant mode is solar-like (equatorward
migration at low latitudes and poleward at high latitudes). This mode
is accompanied by a higher frequency mode near the surface and at low
latitudes, showing poleward migration, and a low-frequency mode at the
bottom of the convection zone. The low-frequency mode is almost purely
antisymmetric with respect to the equator, while the dominant mode has
strongly fluctuating mixed parity. The overall behavior of the dynamo
solution is extremely complex, exhibiting variable cycle lengths, epochs
of disturbed and even ceased surface activity, and strong short-term
hemispherical asymmetries. Surprisingly, the most prominent suppressed
surface activity epoch is actually a global magnetic energy maximum;
during this epoch the bottom toroidal magnetic field obtains a maximum,
demonstrating that the interpretation of grand minima-type events
is non-trivial. The hemispherical asymmetries are seen only in the
magnetic field, while the velocity field exhibits considerably weaker
asymmetry. Conclusions: We interpret the overall irregular
behavior as being due to the interplay of the different dynamo modes
showing different equatorial symmetries, especially the smoother part
of the irregular variations being related to the variations of the
mode strengths, evolving with different and variable cycle lengths. The
abrupt low-activity epoch in the dominant dynamo mode near the surface
is related to a strong maximum of the bottom toroidal field strength,
which causes abrupt disturbances especially in the differential rotation
profile via the suppression of the Reynolds stresses.

---------------------------------------------------------
Title: Magnetic flux concentrations from turbulent stratified
convection
Authors: Käpylä, P. J.; Brandenburg, A.; Kleeorin, N.; Käpylä,
M. J.; Rogachevskii, I.
2016A&A...588A.150K Altcode: 2015arXiv151103718K
Context. The formation of magnetic flux concentrations within the solar
convection zone leading to sunspot formation is unexplained. Aims: We study the self-organization of initially uniform
sub-equipartition magnetic fields by highly stratified turbulent
convection. Methods: We perform simulations of magnetoconvection
in Cartesian domains representing the uppermost 8.5-24 Mm of the solar
convection zone with the horizontal size of the domain varying between
34 and 96 Mm. The density contrast in the 24 Mm deep models is more than
3 × 103 or eight density scale heights, corresponding to a
little over 12 pressure scale heights. We impose either a vertical or
a horizontal uniform magnetic field in a convection-driven turbulent
flow in set-ups where no small-scale dynamos are present. In the most
highly stratified cases we employ the reduced sound speed method to
relax the time step constraint arising from the high sound speed in
the deep layers. We model radiation via the diffusion approximation
and neglect detailed radiative transfer in order to concentrate on
purely magnetohydrodynamic effects. Results: We find that
super-equipartition magnetic flux concentrations are formed near
the surface in cases with moderate and high density stratification,
corresponding to domain depths of 12.5 and 24 Mm. The size of the
concentrations increases as the box size increases and the largest
structures (20 Mm horizontally near the surface) are obtained in the
models that are 24 Mm deep. The field strength in the concentrations
is in the range of 3-5 kG, almost independent of the magnitude of the
imposed field. The amplitude of the concentrations grows approximately
linearly in time. The effective magnetic pressure measured in the
simulations is positive near the surface and negative in the bulk of the
convection zone. Its derivative with respect to the mean magnetic field,
however, is positive in most of the domain, which is unfavourable for
the operation of the negative effective magnetic pressure instability
(NEMPI). Simulations in which a passive vector field is evolved do not
show a noticeable difference from magnetohydrodynamic runs in terms
of the growth of the structures. Furthermore, we find that magnetic
flux is concentrated in regions of converging flow corresponding to
large-scale supergranulation convection pattern. Conclusions:
The linear growth of large-scale flux concentrations implies that
their dominant formation process is a tangling of the large-scale
field rather than an instability. One plausible mechanism that
can explain both the linear growth and the concentration of the
flux in the regions of converging flow pattern is flux expulsion. A
possible reason for the absence of NEMPI is that the derivative of the
effective magnetic pressure with respect to the mean magnetic field
has an unfavourable sign. Furthermore, there may not be sufficient
scale separation, which is required for NEMPI to work. Movies
associated to Figs. 4 and 5 are available in electronic form at <A
href="http://www.aanda.org/10.1051/0004-6361/201527731/olm">http://www.aanda.org</A>

---------------------------------------------------------
Title: Magnetically controlled stellar differential rotation near
the transition from solar to anti-solar profiles
Authors: Karak, B. B.; Käpylä, P. J.; Käpylä, M. J.; Brandenburg,
A.; Olspert, N.; Pelt, J.
2015A&A...576A..26K Altcode: 2014arXiv1407.0984K
Context. Late-type stars rotate differentially owing to anisotropic
turbulence in their outer convection zones. The rotation is called
solar-like (SL) when the equator rotates fastest and anti-solar (AS)
otherwise. Hydrodynamic simulations show a transition from SL to AS
rotation as the influence of rotation on convection is reduced, but
the opposite transition occurs at a different point in the parameter
space. The system is bistable, i.e., SL and AS rotation profiles can
both be stable. Aims: We study the effect of a dynamo-generated
magnetic field on the large-scale flows, particularly on the possibility
of bistable behaviour of differential rotation. Methods: We
solve the hydromagnetic equations numerically in a rotating spherical
shell that typically covers ± 75° latitude (wedge geometry) for a
set of different radiative conductivities controlling the relative
importance of convection. We analyse the resulting differential
rotation, meridional circulation, and magnetic field and compare the
corresponding modifications of the Reynolds and Maxwell stresses. Results: In agreement with earlier findings, our models display SL
rotation profiles when the rotational influence on convection is strong
and a transition to AS when the rotational influence decreases. We find
that dynamo-generated magnetic fields help to produce SL differential
rotation compared to the hydrodynamic simulations. We do not observe
any bistable states of differential rotation. In the AS cases we find
coherent single-cell meridional circulation, whereas in SL cases
we find multi-cellular patterns. In both cases, we obtain poleward
circulation near the surface with a magnitude close to that observed
in the Sun. In the slowly rotating cases, we find activity cycles,
but no clear polarity reversals, whereas in the more rapidly rotating
cases irregular variations are obtained. Moreover, both differential
rotation and meridional circulation have significant temporal variations
that are similar in strength to those of the Sun. Conclusions:
Purely hydrodynamic simulations of differential rotation and meridional
circulation are shown to be of limited relevance as magnetic fields,
self-consistently generated by dynamo action, significantly affect
the flows.

---------------------------------------------------------
Title: Testing turbulent closure models with convection simulations
Authors: Snellman, J. E.; Käpylä, P. J.; Käpylä, M. J.; Rheinhardt,
M., Dintrans, B.
2015AN....336...32S Altcode:
We compare simple analytical closure models of homogeneous turbulent
Boussinesq convection for stellar applications with three-dimensional
simulations. We use turbulent closure models to compute the Reynolds
stresses and the turbulent heat flux as functions of rotation rate
measured by the Taylor number. We also investigate cases with varying
angles between the angular velocity and gravity vectors, corresponding
to locating the computational domain at different latitudes ranging
from the pole to the equator of the star. We perform three-dimensional
numerical simulations in the same parameter regimes for comparison. The
free parameters appearing in the closure models are calibrated by
two fitting methods using simulation data. A unique determination
of the closure parameters is possible only in the non-rotating case
or when the system is placed at the pole. In the other cases the fit
procedures yield somewhat differing results. The quality of the closure
is tested by substituting the resulting coefficients back into the
closure model and comparing with the simulation results. To eliminate
the possibilities that the results obtained depend on the aspect ratio
of the simulation domain or suffer from too small Rayleigh numbers we
performed runs varying these parameters. The simulation data for the
Reynolds stress and heat fluxes broadly agree with previous compressible
simulations. The closure works fairly well with slow and fast rotation
but its quality degrades for intermediate rotation rates. We find that
the closure parameters depend not only on rotation rate but also on
latitude. The weak dependence on Rayleigh number and on the aspect
ratio of the domain indicates that our results are generally valid.

---------------------------------------------------------
Title: Quenching and Anisotropy of Hydromagnetic Turbulent Transport
Authors: Karak, Bidya Binay; Rheinhardt, Matthias; Brandenburg, Axel;
Käpylä, Petri J.; Käpylä, Maarit J.
2014ApJ...795...16K Altcode: 2014arXiv1406.4521K
Hydromagnetic turbulence affects the evolution of large-scale magnetic
fields through mean-field effects like turbulent diffusion and the α
effect. For stronger fields, these effects are usually suppressed
or quenched, and additional anisotropies are introduced. Using
different variants of the test-field method, we determine the
quenching of the turbulent transport coefficients for the forced
Roberts flow, isotropically forced non-helical turbulence, and
rotating thermal convection. We see significant quenching only when
the mean magnetic field is larger than the equipartition value of the
turbulence. Expressing the magnetic field in terms of the equipartition
value of the quenched flows, we obtain for the quenching exponents of
the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts
flow, forced turbulence, and convection, respectively. However, when
the magnetic field is expressed in terms of the equipartition value
of the unquenched flows, these quenching exponents become about 4,
1.5, and 2.3, respectively. For the α effect, the exponent is about
1.3 for the Roberts flow and 2 for convection in the first case, but
4 and 3, respectively, in the second. In convection, the quenching of
turbulent pumping follows the same power law as turbulent diffusion,
while for the coefficient describing the {\boldsymbolΩ} × \boldsymbol
{{J}} effect nearly the same quenching exponent is obtained as for
α. For forced turbulence, turbulent diffusion proportional to the
second derivative along the mean magnetic field is quenched much less,
especially for larger values of the magnetic Reynolds number. However,
we find that in corresponding axisymmetric mean-field dynamos with
dominant toroidal field the quenched diffusion coefficients are the
same for the poloidal and toroidal field constituents.

---------------------------------------------------------
Title: On The Cause of Solar-like Equatorward Migration in Global
Convective Dynamo Simulations
Authors: Warnecke, Jörn; Käpylä, Petri J.; Käpylä, Maarit J.;
Brandenburg, Axel
2014ApJ...796L..12W Altcode: 2014arXiv1409.3213W
We present results from four convectively driven stellar dynamo
simulations in spherical wedge geometry. All of these simulations
produce cyclic and migrating mean magnetic fields. Through detailed
comparisons, we show that the migration direction can be explained by
an αΩ dynamo wave following the Parker-Yoshimura rule. We conclude
that the equatorward migration in this and previous work is due to a
positive (negative) α effect in the northern (southern) hemisphere and
a negative radial gradient of Ω outside the inner tangent cylinder of
these models. This idea is supported by a strong correlation between
negative radial shear and toroidal field strength in the region of
equatorward propagation.

---------------------------------------------------------
Title: Confirmation of bistable stellar differential rotation profiles
Authors: Käpylä, P. J.; Käpylä, M. J.; Brandenburg, A.
2014A&A...570A..43K Altcode: 2014arXiv1401.2981K
Context. Solar-like differential rotation is characterized by a rapidly
rotating equator and slower poles. However, theoretical models and
numerical simulations can also result in a slower equator and faster
poles when the overall rotation is slow. Aims: We study the
critical rotational influence under which differential rotation flips
from solar-like (fast equator, slow poles) to an anti-solar one (slow
equator, fast poles). We also estimate the non-diffusive (Λ effect)
and diffusive (turbulent viscosity) contributions to the Reynolds
stress. Methods: We present the results of three-dimensional
numerical simulations of mildly turbulent convection in spherical wedge
geometry. Here we apply a fully compressible setup which would suffer
from a prohibitive time step constraint if the real solar luminosity was
used. To avoid this problem while still representing the same rotational
influence on the flow as in the Sun, we increase the luminosity by a
factor of roughly 106 and the rotation rate by a factor of
102. We regulate the convective velocities by varying the
amount of heat transported by thermal conduction, turbulent diffusion,
and resolved convection. Results: Increasing the efficiency of
resolved convection leads to a reduction of the rotational influence
on the flow and a sharp transition from solar-like to anti-solar
differential rotation for Coriolis numbers around 1.3. We confirm
the recent finding of a large-scale flow bistability: contrasted
with running the models from an initial condition with unprescribed
differential rotation, the initialization of the model with certain
kind of rotation profile sustains the solution over a wider parameter
range. The anti-solar profiles are found to be more stable against
perturbations in the level of convective turbulent velocity than
the solar-type solutions. Conclusions: Our results may have
implications for real stars that start their lives as rapid rotators
implying solar-like rotation in the early main-sequence evolution. As
they slow down, they might be able to retain solar-like rotation for
lower Coriolis numbers, and thus longer in time, before switching
to anti-solar rotation. This could partially explain the puzzling
findings of anti-solar rotation profiles for models in the solar
parameter regime.

---------------------------------------------------------
Title: Quantifying the effect of turbulent magnetic diffusion on
the growth rate of the magneto-rotational instability
Authors: Väisälä, M. S.; Brandenburg, A.; Mitra, D.; Käpylä,
P. J.; Mantere, M. J.
2014A&A...567A.139V Altcode: 2013arXiv1310.3157V
Context. In astrophysics, turbulent diffusion is often used in place of
microphysical diffusion to avoid resolving the small scales. However,
we expect this approach to break down when time and length scales of the
turbulence become comparable with other relevant time and length scales
in the system. Turbulent diffusion has previously been applied to the
magneto-rotational instability (MRI), but no quantitative comparison of
growth rates at different turbulent intensities has been performed. Aims: We investigate to what extent turbulent diffusion can be
used to model the effects of small-scale turbulence on the kinematic
growth rates of the MRI, and how this depends on angular velocity
and magnetic field strength. Methods: We use direct numerical
simulations in three-dimensional shearing boxes with periodic boundary
conditions in the spanwise direction and additional random plane-wave
volume forcing to drive a turbulent flow at a given length scale. We
estimate the turbulent diffusivity using a mixing length formula and
compare with results obtained with the test-field method. 
Results: It turns out that the concept of turbulent diffusion is
remarkably accurate in describing the effect of turbulence on the
growth rate of the MRI. No noticeable breakdown of turbulent diffusion
has been found, even when time and length scales of the turbulence
become comparable with those imposed by the MRI itself. On the other
hand, quenching of turbulent magnetic diffusivity by the magnetic
field is found to be absent. Conclusions: Turbulence reduces
the growth rate of the MRI in the same way as microphysical magnetic
diffusion does. Appendix A is available in electronic form at <A
href="http://www.aanda.org/10.1051/0004-6361/201322837/olm">http://www.aanda.org</A>

---------------------------------------------------------
Title: An Azimuthal Dynamo Wave in Spherical Shell Convection
Authors: Cole, Elizabeth; Käpylä, Petri J.; Mantere, Maarit J.;
Brandenburg, Axel
2014ApJ...780L..22C Altcode: 2013arXiv1309.6802C
We report the discovery of an azimuthal dynamo wave of a low-order (m =
1) mode in direct numerical simulations (DNS) of turbulent convection in
spherical shells. Such waves are predicted by mean-field dynamo theory
and have been obtained previously in mean-field models. An azimuthal
dynamo wave has been proposed as a possible explanation for the
persistent drifts of spots observed on several rapidly rotating stars,
as revealed through photometry and Doppler imaging. However, this has
been judged unlikely because evidence for such waves from DNS has been
lacking. Here we present DNS of large-scale magnetic fields showing
a retrograde m = 1 mode. Its pattern speed is nearly independent of
latitude and does not reflect the speed of the differential rotation at
any depth. The extrema of magnetic m = 1 structures coincide reasonably
well with the maxima of m = 2 structures of the temperature. These
results provide direct support for the observed drifts being due to
an azimuthal dynamo wave.

---------------------------------------------------------
Title: Spoke-like Differential Rotation in a Convective Dynamo with
a Coronal Envelope
Authors: Warnecke, Jörn; Käpylä, Petri J.; Mantere, Maarit J.;
Brandenburg, Axel
2013ApJ...778..141W Altcode: 2013arXiv1301.2248W
We report on the results of four convective dynamo simulations with
an outer coronal layer. The magnetic field is self-consistently
generated by the convective motions beneath the surface. Above the
convection zone, we include a polytropic layer that extends to 1.6
solar radii. The temperature increases in this region to ≈8 times the
value at the surface, corresponding to ≈1.2 times the value at the
bottom of the spherical shell. We associate this region with the solar
corona. We find solar-like differential rotation with radial contours of
constant rotation rate, together with a near-surface shear layer. This
non-cylindrical rotation profile is caused by a non-zero latitudinal
entropy gradient that offsets the Taylor-Proudman balance through the
baroclinic term. The meridional circulation is multi-cellular with a
solar-like poleward flow near the surface at low latitudes. In most
of the cases, the mean magnetic field is oscillatory with equatorward
migration in two cases. In other cases, the equatorward migration is
overlaid by stationary or even poleward migrating mean fields.

---------------------------------------------------------
Title: Effects of Enhanced Stratification on Equatorward Dynamo
Wave Propagation
Authors: Käpylä, Petri J.; Mantere, Maarit J.; Cole, Elizabeth;
Warnecke, Jörn; Brandenburg, Axel
2013ApJ...778...41K Altcode: 2013arXiv1301.2595K
We present results from simulations of rotating magnetized turbulent
convection in spherical wedge geometry representing parts of the
latitudinal and longitudinal extents of a star. Here we consider a
set of runs for which the density stratification is varied, keeping
the Reynolds and Coriolis numbers at similar values. In the case
of weak stratification, we find quasi-steady dynamo solutions for
moderate rotation and oscillatory ones with poleward migration of
activity belts for more rapid rotation. For stronger stratification,
the growth rate tends to become smaller. Furthermore, a transition
from quasi-steady to oscillatory dynamos is found as the Coriolis
number is increased, but now there is an equatorward migrating branch
near the equator. The breakpoint where this happens corresponds to a
rotation rate that is about three to seven times the solar value. The
phase relation of the magnetic field is such that the toroidal field
lags behind the radial field by about π/2, which can be explained by
an oscillatory α2 dynamo caused by the sign change of the
α-effect about the equator. We test the domain size dependence of our
results for a rapidly rotating run with equatorward migration by varying
the longitudinal extent of our wedge. The energy of the axisymmetric
mean magnetic field decreases as the domain size increases and we
find that an m = 1 mode is excited for a full 2π azimuthal extent,
reminiscent of the field configurations deduced from observations of
rapidly rotating late-type stars.

---------------------------------------------------------
Title: Solar-like differential rotation and equatorward migration
in a convective dynamo with a coronal envelope
Authors: Warnecke, J.; Käpylä, P. J.; Mantere, M. J.; Brandenburg, A.
2013IAUS..294..307W Altcode: 2012arXiv1211.0452W
We present results of convective turbulent dynamo simulations including
a coronal layer in a spherical wedge. We find an equatorward migration
of the radial and azimuthal fields similar to the behavior of sunspots
during the solar cycle. The migration of the field coexist with a
spoke-like differential rotation and anti-solar (clockwise) meridional
circulation. Even though the migration extends over the whole convection
zone, the mechanism causing this is not yet fully understood.

---------------------------------------------------------
Title: Role of longitudinal activity complexes for solar and stellar
dynamos
Authors: Mantere, Maarit J.; Käpylä, Petri J.; Pelt, Jaan
2013IAUS..294..175M Altcode: 2012arXiv1211.2990M
In this paper we first discuss observational evidence of longitudinal
concentrations of magnetic activity in the Sun and rapidly rotating
late-type stars with outer convective envelopes. Scenarios arising from
the idea of rotationally influenced anisotropic convective turbulence
being the key physical process generating these structures are then
presented and discussed - such effects include the turbulent dynamo
mechanism, negative effective magnetic pressure instability (NEMPI) and
hydrodynamical vortex instability. Finally, we discuss non-axisymmetric
stellar mean-field dynamo models, the results obtained with them,
and compare those with the observational information gathered up so
far. We also present results from a pure α2 mean-field
dynamo model, which show that time-dependent behavior of the dynamo
solutions can occur both in the form of an azimuthal dynamo wave and/or
oscillatory behavior related to the alternating energy levels of the
active longitudes.

---------------------------------------------------------
Title: Flux concentrations in turbulent convection
Authors: Käpylä, Petri J.; Brandenburg, Axel; Kleeorin, Nathan;
Mantere, Maarit J.; Rogachevskii, Igor
2013IAUS..294..283K Altcode: 2012arXiv1211.2962K
We present preliminary results from high resolution magneto-convection
simulations where we find the formation of flux concentrations from
an initially uniform magnetic field. The structures appear in roughly
ten convective turnover times and live close to a turbulent diffusion
time. The time scales are compatible with the negative effective
magnetic pressure instability (NEMPI), although structure formation
is not restricted to regions where the effective magnetic pressure
is negative.

---------------------------------------------------------
Title: Oscillatory large-scale dynamos from Cartesian convection
simulations
Authors: Käpylä, P. J.; Mantere, M. J.; Brandenburg, A.
2013GApFD.107..244K Altcode: 2011arXiv1111.6894K
We present results from compressible Cartesian convection simulations
with and without imposed shear. In the former case the dynamo
is expected to be of α2 Ω type, which is generally
expected to be relevant for the Sun, whereas the latter case refers
to α2 dynamos that are more likely to occur in more
rapidly rotating stars whose differential rotation is small. We
perform a parameter study where the shear flow and the rotational
influence are varied to probe the relative importance of both types of
dynamos. Oscillatory solutions are preferred both in the kinematic and
saturated regimes when the negative ratio of shear to rotation rates,
q ≡ -S/Ω, is between 1.5 and 2, i.e. when shear and rotation are
of comparable strengths. Other regions of oscillatory solutions are
found with small values of q, i.e. when shear is weak in comparison to
rotation, and in the regime of large negative qs, when shear is very
strong in comparison to rotation. However, exceptions to these rules
also appear so that for a given ratio of shear to rotation, solutions
are non-oscillatory for small and large shear, but oscillatory in the
intermediate range. Changing the boundary conditions from vertical field
to perfect conductor ones changes the dynamo mode from oscillatory to
quasi-steady. Furthermore, in many cases an oscillatory solution exists
only in the kinematic regime whereas in the nonlinear stage the mean
fields are stationary. However, the cases with rotation and no shear
are always oscillatory in the parameter range studied here and the
dynamo mode does not depend on the magnetic boundary conditions. The
strengths of total and large-scale components of the magnetic field
in the saturated state, however, are sensitive to the chosen boundary
conditions.

---------------------------------------------------------
Title: New Scaling for the Alpha Effect in Slowly Rotating Turbulence
Authors: Brandenburg, A.; Gressel, O.; Käpylä, P. J.; Kleeorin,
N.; Mantere, M. J.; Rogachevskii, I.
2013ApJ...762..127B Altcode: 2012arXiv1208.5004B
Using simulations of slowly rotating stratified turbulence, we show that
the α effect responsible for the generation of astrophysical magnetic
fields is proportional to the logarithmic gradient of kinetic energy
density rather than that of momentum, as was previously thought. This
result is in agreement with a new analytic theory developed in
this paper for large Reynolds numbers and slow rotation. Thus, the
contribution of density stratification is less important than that
of turbulent velocity. The α effect and other turbulent transport
coefficients are determined by means of the test-field method. In
addition to forced turbulence, we also investigate supernova-driven
turbulence and stellar convection. In some cases (intermediate rotation
rate for forced turbulence, convection with intermediate temperature
stratification, and supernova-driven turbulence), we find that the
contribution of density stratification might be even less important
than suggested by the analytic theory.

---------------------------------------------------------
Title: Coronal ejections driven by convective dynamo action underneath
the surface
Authors: Warnecke, J.; Käpylä, P. J.; Mantere, M. J.; Brandeburg, A.
2012AGUFMSH51A2193W Altcode:
Observations show that the Sun sheds mass through twisted magnetic flux
configurations, like Coronal Mass Ejections (CMEs). Conventionally,
CMEs are modeled by adopting a given distribution of magnetic flux at
the solar surface and letting it evolve by shearing and twisting the
magnetic field at its footpoints at the surface. Of course, ultimately
such velocity and magnetic field patterns must come from a realistic
simulation of the Sun's convection zone, where the field is generated
by dynamo action. Therefore a unified treatment of convection zone and
CMEs is needed. We combine a convectively driven dynamo in a spherical
shell with a temperature and density stratification in the exterior
that mimics a solar corona to study the emergence and ejections of
magnetic field structures. This approach is an extension of earlier
models where we use an isothermal corona (Warnecke et al. 2011) or even
forced turbulence simulations to generate magnetic fields (Warnecke
&amp; Brandenburg 2010, Warnecke et al. 2011). A spherical wedge is
used which consists of a convection zone and a corona up to 1.5 of
the radius of the Sun. The wedge contains a quarter of the azimuthal
extent of the sphere and 150o in latitude. The magnetic
field is self-consistently generated by the turbulent motions due to
convection underneath the surface. An oscillatory large-scale dynamo
with equatorward migration in the lower layer can be found operating in
the convection zone. In the Figure we show the equatorward migration
of the radial magnetic field Br and the azimutal field
Bφ as a function of time and latitude at the height of
0.97 solar radii. Magnetic fields are found to emerge at the surface
and are ejected to the coronal part of the domain. These ejections
occur in irregular intervals. We associate these events with coronal
mass ejections on the Sun.; Variation of /line{Bφ } and
/line{Br} in the convection zone at r=0.97R. Dark blue
shades represent negative and light yellow positive values. The dotted
horizontal lines show the location of the equator at θ =π /2. The
magnetic field is normalized by the equipartition value.

---------------------------------------------------------
Title: Ejections of Magnetic Structures Above a Spherical Wedge
Driven by a Convective Dynamo with Differential Rotation
Authors: Warnecke, Jörn; Käpylä, Petri J.; Mantere, Maarit J.;
Brandenburg, Axel
2012SoPh..280..299W Altcode: 2012SoPh..tmp..214W; 2011arXiv1112.0505W
We combine a convectively driven dynamo in a spherical shell with a
nearly isothermal density-stratified cooling layer that mimics some
aspects of a stellar corona to study the emergence and ejections
of magnetic field structures. This approach is an extension of
earlier models, where forced turbulence simulations were employed to
generate magnetic fields. A spherical wedge is used which consists of
a convection zone and an extended coronal region to ≈ 1.5 times the
radius of the sphere. The wedge contains a quarter of the azimuthal
extent of the sphere and 150∘ in latitude. The magnetic
field is self-consistently generated by the turbulent motions due to
convection beneath the surface. Magnetic fields are found to emerge at
the surface and are ejected to the coronal part of the domain. These
ejections occur at irregular intervals and are weaker than in earlier
work. We tentatively associate these events with coronal mass ejections
on the Sun, even though our model of the solar atmosphere is rather
simplistic.

---------------------------------------------------------
Title: Testing turbulent closure models with convection simulations
Authors: Snellman, J. E.; Käpylä, P. J.; Käpylä, M. J.; Rheinhardt,
M.; Dintrans, B.
2012arXiv1209.4923S Altcode:
We compare simple analytical closure models of homogeneous turbulent
Boussinesq convection for stellar applications with three-dimensional
simulations. We use simple analytical closure models to compute the
fluxes of angular momentum and heat as a function of rotation rate
measured by the Taylor number. We also investigate cases with varying
angles between the angular velocity and gravity vectors, corresponding
to locating the computational domain at different latitudes ranging
from the pole to the equator of the star. We perform three-dimensional
numerical simulations in the same parameter regimes for comparison. The
free parameters appearing in the closure models are calibrated by
two fitting methods using simulation data. Unique determination of
the closure parameters is possible only in the non-rotating case
or when the system is placed at the pole. In the other cases the fit
procedures yield somewhat differing results. The quality of the closure
is tested by substituting the resulting coefficients back into the
closure model and comparing with the simulation results. To eliminate
the possibilities that the results obtained depend on the aspect ratio
of the simulation domain or suffer from too small Rayleigh numbers we
performed runs varying these parameters. The simulation data for the
Reynolds stress and heat fluxes broadly agree with previous compressible
simulations. The closure works fairly well with slow and fast rotation
but its quality degrades for intermediate rotation rates. We find that
the closure parameters depend not only on rotation rate but also on
latitude. The weak dependence on Rayleigh number and the aspect ratio
of the domain indicates that our results are generally valid

---------------------------------------------------------
Title: Cyclic Magnetic Activity due to Turbulent Convection in
Spherical Wedge Geometry
Authors: Käpylä, Petri J.; Mantere, Maarit J.; Brandenburg, Axel
2012ApJ...755L..22K Altcode: 2012arXiv1205.4719K
We report on simulations of turbulent, rotating, stratified,
magnetohydrodynamic convection in spherical wedge geometry. An initially
small-scale, random, weak-amplitude magnetic field is amplified by
several orders of magnitude in the course of the simulation to form
oscillatory large-scale fields in the saturated state of the dynamo. The
differential rotation is solar-like (fast equator), but neither coherent
meridional poleward circulation nor near-surface shear layer develop in
these runs. In addition to a poleward branch of magnetic activity beyond
50° latitude, we find for the first time a pronounced equatorward
branch at around 20° latitude, reminiscent of the solar cycle.

---------------------------------------------------------
Title: Coronal ejections from convective spherical shell dynamos
Authors: Warnecke, J.; Käpylä, P. J.; Mantere, M. J.; Brandenburg, A.
2012IAUS..286..154W Altcode: 2011arXiv1111.1763W
We present a three-dimensional model of rotating convection combined
with a simplified model of a corona in spherical coordinates. The
motions in the convection zone generate a large-scale magnetic
field which is sporadically ejected into the outer layers above. Our
model corona is approximately isothermal, but it includes density
stratification due to gravity.

---------------------------------------------------------
Title: Mean-field closure parameters for passive scalar turbulence
Authors: Snellman, J. E.; Rheinhardt, M.; Käpylä, P. J.; Mantere,
M. J.; Brandenburg, A.
2012PhyS...86a8406S Altcode: 2011arXiv1112.4777S
Direct numerical simulations (DNSs) of isotropically forced
homogeneous stationary turbulence with an imposed passive scalar
concentration gradient are compared with an analytical closure model
which provides evolution equations for the mean passive scalar flux
and variance. Triple correlations of fluctuations appearing in these
equations are described in terms of relaxation terms proportional to
the quadratic correlations. Three methods are used to extract the
relaxation timescales τi from DNSs. Firstly, we insert
the closure ansatz into our equations, assume stationarity and solve
for τi. Secondly, we use only the closure ansatz itself
and obtain τi from the ratio of quadratic and triple
correlations. Thirdly, we remove the imposed passive scalar gradient and
fit an exponential law to the decaying solution. We vary the Reynolds
(Re) and Péclet numbers (while fixing their ratio at unity) and the
degree of scale separation and find for large Re a fair correspondence
between the different methods. The ratio of the turbulent relaxation
time of the passive scalar flux to the turnover time of the turbulent
eddies is of the order of 3, which is in remarkable agreement with
earlier work. Finally, we make an effort to extract the relaxation
timescales relevant for the viscous and diffusive effects. We find two
regimes that are valid for small and large Re, respectively, but the
dependence of the parameters on scale separation suggests that they
are not universal.

---------------------------------------------------------
Title: Negative effective magnetic pressure in turbulent convection
Authors: Käpylä, P. J.; Brandenburg, A.; Kleeorin, N.; Mantere,
M. J.; Rogachevskii, I.
2012MNRAS.422.2465K Altcode: 2011arXiv1104.4541K
We investigate the effects of weakly and strongly stratified turbulent
convection on the mean effective Lorentz force, and especially on the
mean effective magnetic pressure. Earlier studies with isotropically
forced non-stratified and stratified turbulence have shown that
the contribution of the turbulence to the mean magnetic pressure is
negative for mean horizontal magnetic fields that are smaller than the
equipartition strength, so that the effective mean magnetic pressure
that takes into account the turbulence effects can be negative. Compared
with earlier cases of forced turbulence with an isothermal equation of
state, we find that the turbulence effect is similar to or even stronger
in the present case of turbulent convection. This is argued to be due
to the anisotropy of turbulence in the vertical direction. Another
important difference compared with earlier studies is the presence of
an evolution equation for the specific entropy. Mean-field modelling
with entropy evolution indicates that the negative effective magnetic
pressure can still lead to a large-scale instability which forms
local flux concentrations, even though the specific entropy evolution
tends to have a stabilizing effect when applied to a stably stratified
(e.g. isothermal) layer. It is argued that this large-scale instability
could be important for the formation of solar large-scale magnetic
structures such as active regions.

---------------------------------------------------------
Title: Verification of Reynolds stress parameterizations from
simulations
Authors: Snellman, J. E.; Brandenburg, A.; Käpylä, P. J.; Mantere,
M. J.
2012AN....333...78S Altcode: 2011arXiv1109.4857S
We determine the timescales associated with turbulent decay }and
isotropization in closure models using anisotropically forced and
freely decaying turbulence simulations and study the applicability
of these models. We compare the results from anisotropically forced
three-dimensional numerical simulations with the predictions of the
closure models and obtain the turbulent timescales mentioned above
as functions of the Reynolds number. In a second set of simulations,
turning the forcing off enables us to study the validity of the
closures in freely decaying turbulence. Both types of experiments
suggest that the timescale of turbulent decay converges to a constant
value at higher Reynolds numbers. Furthermore, the relative importance
of isotropization is found to be about 2.5 times larger at higher
Reynolds numbers than in the more viscous regime.

---------------------------------------------------------
Title: Dependence of the large-scale vortex instability on latitude,
stratification, and domain size
Authors: Mantere, M. J.; Käpylä, P. J.; Hackman, T.
2011AN....332..876M Altcode: 2011arXiv1109.4317M
In an earlier study, we reported on the excitation of large-scale
vortices in Cartesian hydrodynamical convection models subject to
rapid enough rotation. In that study, the conditions for the onset
of the instability were investigated in terms of the Reynolds (Re)
and Coriolis (Co) numbers in models located at the stellar North
pole. In this study, we extend our investigation to varying domain
sizes, increasing stratification, and place the box at different
latitudes. The effect of the increasing box size is to increase
the sizes of the generated structures, so that the principal vortex
always fills roughly half of the computational domain. The instability
becomes stronger in the sense that the temperature anomaly and change
in the radial velocity are observed to be enhanced. The model with
the smallest box size is found to be stable against the instability,
suggesting that a sufficient scale separation between the convective
eddies and the scale of the domain is required for the instability to
work. The instability can be seen upto the colatitude of 30 degrees,
above which value the flow becomes dominated by other types of
mean flows. The instability can also be seen in a model with larger
stratification. Unlike the weakly stratified cases, the temperature
anomaly caused by the vortex structures is seen to depend on depth.

---------------------------------------------------------
Title: Effects of stratification in spherical shell convection
Authors: Käpylä, P. J.; Mantere, M. J.; Brandenburg, A.
2011AN....332..883K Altcode: 2011arXiv1109.4625K
We report on simulations of mildly turbulent convection in spherical
wedge geometry with varying density stratification. We vary the density
contrast within the convection zone by a factor of 20 and study the
influence of rotation on the solutions. We demonstrate that the size of
convective cells decreases and the anisotropy of turbulence increases
as the stratification is increased. Differential rotation is found to
change from anti-solar (slow equator) to solar-like (fast equator) at
roughly the same Coriolis number for all stratifications. The largest
stratification runs, however, are sensitive to changes of the Reynolds
number. Evidence for a near-surface shear layer is found in runs with
strong stratification and large Reynolds numbers.

---------------------------------------------------------
Title: Pumping velocity in homogeneous helical turbulence with shear
Authors: Rogachevskii, Igor; Kleeorin, Nathan; Käpylä, Petri J.;
Brandenburg, Axel
2011PhRvE..84e6314R Altcode: 2011arXiv1105.5785R
Using different analytical methods (the quasilinear approach, the
path-integral technique, and the tau-relaxation approximation) we
develop a comprehensive mean-field theory for a pumping effect of the
mean magnetic field in homogeneous nonrotating helical turbulence
with imposed large-scale shear. The effective pumping velocity is
proportional to the product of α effect and large-scale vorticity
associated with the shear, and causes a separation of the toroidal and
poloidal components of the mean magnetic field along the direction of
the mean vorticity. We also perform direct numerical simulations of
sheared turbulence in different ranges of hydrodynamic and magnetic
Reynolds numbers and use a kinematic test-field method to determine the
effective pumping velocity. The results of the numerical simulations
are in agreement with the theoretical predictions.

---------------------------------------------------------
Title: Starspots due to Large-scale Vortices in Rotating Turbulent
Convection
Authors: Käpylä, Petri J.; Mantere, Maarit J.; Hackman, Thomas
2011ApJ...742...34K Altcode: 2011arXiv1106.6029K
We study the generation of large-scale vortices in rotating turbulent
convection by means of Cartesian direct numerical simulations. We
find that for sufficiently rapid rotation, cyclonic structures on a
scale large in comparison to that of the convective eddies emerge,
provided that the fluid Reynolds number exceeds a critical value. For
slower rotation, cool cyclonic vortices are preferred, whereas for
rapid rotation, warm anti-cyclonic vortices are favored. In some
runs in the intermediate regime both types of cyclones coexist for
thousands of convective turnover times. The temperature contrast
between the vortices and the surrounding atmosphere is of the order
of 5%. We relate the simulation results to observations of rapidly
rotating late-type stars that are known to exhibit large high-latitude
spots from Doppler imaging. In many cases, cool spots are accompanied
with spotted regions with temperatures higher than the average. In
this paper, we investigate a scenario according to which of the spots
observed in the temperature maps could have a non-magnetic origin due
to large-scale vortices in the convection zones of the stars.

---------------------------------------------------------
Title: Dynamo action and magnetic buoyancy in convection simulations
with vertical shear
Authors: Guerrero, G.; Käpylä, P.
2011sdmi.confE..62G Altcode:
A hypothesis for sunspot formation is the buoyant emergence of magnetic
flux tubes created by the strong radial shear at the tachocline. In this
scenario, the magnetic field has to exceed a threshold value before
it becomes buoyant and emerges through the whole convection zone. In
this work we present the results of direct numerical simulations
of compressible turbulent convection that include a vertical shear
layer. Like the solar tachocline, the shear is located at the interface
between convective and stable layers. We follow the evolution of a
random seed magnetic field with the aim of study under what conditions
it is possible to excite the dynamo instability and whether the dynamo
generated magnetic field becomes buoyantly unstable and emerges to
the surface as expected in the flux-tube context. We find that shear
and convection are able to amplify the initial magnetic field and
form large-scale elongated magnetic structures. The magnetic field
strength depends on several parameters such as the shear amplitude,
the thickness and location of the shear layer, and the magnetic
Reynolds number (Rm). Models with deeper and thicker shear layers allow
longer storage and are more favorable for generating a mean magnetic
field. Models with higher Rm grow faster but saturate at slightly
lower levels. Whenever the toroidal magnetic field reaches amplitudes
greater a threshold value which is close to the equipartition value,
it becomes buoyant and rises into the convection zone where it expands
and forms mushroom shape structures. Some events of emergence, i.e.,
those with the largest amplitudes of the amplified field, are able to
reach the very uppermost layers of the domain. These episodes are able
to modify the convective pattern forming either broader convection cells
or convective eddies elongated in the direction of the field. However,
in none of these events the field preserves its initial structure. The
back-reaction of the magnetic field on the fluid is also observed
in lower values of the turbulent velocity and in perturbations of
approximately three per cent on the shear profile.

---------------------------------------------------------
Title: Dynamo action and magnetic buoyancy in convection simulations
with vertical shear
Authors: Guerrero, G.; Käpylä, P. J.
2011A&A...533A..40G Altcode: 2011arXiv1102.3598G
Context. A hypothesis for sunspot formation is the buoyant emergence
of magnetic flux tubes created by the strong radial shear at the
tachocline. In this scenario, the magnetic field has to exceed a
threshold value before it becomes buoyant and emerges through the whole
convection zone. Aims: We follow the evolution of a random
seed magnetic field with the aim of study under what conditions it
is possible to excite the dynamo instability and whether the dynamo
generated magnetic field becomes buoyantly unstable and emerges to
the surface as expected in the flux-tube context. Methods: We
perform numerical simulations of compressible turbulent convection that
include a vertical shear layer. Like the solar tachocline, the shear
is located at the interface between convective and stable layers. Results: We find that shear and convection are able to amplify
the initial magnetic field and form large-scale elongated magnetic
structures. The magnetic field strength depends on several parameters
such as the shear amplitude, the thickness and location of the shear
layer, and the magnetic Reynolds number (Rm). Models with deeper and
thicker tachoclines allow longer storage and are more favorable for
generating a mean magnetic field. Models with higher Rm grow faster
but saturate at slightly lower levels. Whenever the toroidal magnetic
field reaches amplitudes greater a threshold value which is close to the
equipartition value, it becomes buoyant and rises into the convection
zone where it expands and forms mushroom shape structures. Some
events of emergence, i.e. those with the largest amplitudes of the
initial field, are able to reach the very uppermost layers of the
domain. These episodes are able to modify the convective pattern forming
either broader convection cells or convective eddies elongated in the
direction of the field. However, in none of these events the field
preserves its initial structure. The back-reaction of the magnetic
field on the fluid is also observed in lower values of the turbulent
velocity and in perturbations of approximately three per cent on the
shear profile. Conclusions: The results indicate that buoyancy
is a common phenomena when the magnetic field is amplified through
dynamo action in a narrow layer. It is, however, very hard for the
field to rise up to the surface without losing its initial coherence.

---------------------------------------------------------
Title: From convective to stellar dynamos
Authors: Brandenburg, Axel; Käpylä, Petri J.; Korpi, Maarit J.
2011IAUS..271..279B Altcode: 2011arXiv1103.5475B
Convectively driven dynamos with rotation generating magnetic fields
on scales large compared with the scale of the turbulent eddies are
being reviewed. It is argued that such fields can be understood as
the result of an α effect. Simulations in Cartesian domains show that
such large-scale magnetic fields saturate on a time scale compatible
with the resistive one, suggesting that the magnitude of the α
effect is here still constrained by approximate magnetic helicity
conservation. It is argued that, in the absence of shear and/or any
other known large-scale dynamo effects, these simulations prove the
existence of turbulent α2-type dynamos. Finally, recent
results are discussed in the context of solar and stellar dynamos.

---------------------------------------------------------
Title: Turbulence and magnetic spots at the surface of hot massive
stars
Authors: Cantiello, Matteo; Braithwaite, Jonathan; Brandenburg, Axel;
Del Sordo, Fabio; Käpylä, Petri; Langer, Norbert
2011IAUS..273..200C Altcode: 2010arXiv1010.2498C
Hot luminous stars show a variety of phenomena in their photospheres
and in their winds which still lack clear physical explanations at
this time. Among these phenomena are non-thermal line broadening, line
profile variability (LPVs), discrete absorption components (DACs), wind
clumping and stochastically excited pulsations. Cantiello et al. (2009)
argued that a convection zone close to the surface of hot, massive
stars, could be responsible for some of these phenomena. This convective
zone is caused by a peak in the opacity due to iron recombination
and for this reason is referred to as the “iron convection zone”
(FeCZ). 3D MHD simulations are used to explore the possible effects of
such subsurface convection on the surface properties of hot, massive
stars. We argue that turbulence and localized magnetic spots at the
surface are the likely consequence of subsurface convection in early
type stars.

---------------------------------------------------------
Title: 3D MHD simulations of subsurface convection in OB stars
Authors: Cantiello, Matteo; Braithwaite, Jonathan; Brandenburg, Axel;
Del Sordo, Fabio; Käpylä, Petri; Langer, Norbert
2011IAUS..272...32C Altcode: 2010arXiv1009.4462C
During their main sequence evolution, massive stars can develop
convective regions very close to their surface. These regions are
caused by an opacity peak associated with iron ionization. Cantiello
et al. (2009) found a possible connection between the presence
of sub-photospheric convective motions and small scale stochastic
velocities in the photosphere of early-type stars. This supports
a physical mechanism where microturbulence is caused by waves that
are triggered by subsurface convection zones. They further suggest
that clumping in the inner parts of the winds of OB stars could be
related to subsurface convection, and that the convective layers
may also be responsible for stochastic excitation of non-radial
pulsations. Furthermore, magnetic fields produced in the iron convection
zone could appear at the surface of such massive stars. Therefore
subsurface convection could be responsible for the occurrence of
observable phenomena such as line profile variability and discrete
absorption components. These phenomena have been observed for decades,
but still evade a clear theoretical explanation. Here we present
preliminary results from 3D MHD simulations of such subsurface
convection.

---------------------------------------------------------
Title: Reynolds stress and heat flux in spherical shell convection
Authors: Käpylä, P. J.; Mantere, M. J.; Guerrero, G.; Brandenburg,
A.; Chatterjee, P.
2011A&A...531A.162K Altcode: 2010arXiv1010.1250K
Context. Turbulent fluxes of angular momentum and enthalpy or heat due
to rotationally affected convection play a key role in determining
differential rotation of stars. Their dependence on latitude and
depth has been determined in the past from convection simulations
in Cartesian or spherical simulations. Here we perform a systematic
comparison between the two geometries as a function of the rotation
rate. Aims: Here we want to extend the earlier studies by
using spherical wedges to obtain turbulent angular momentum and
heat transport as functions of the rotation rate from stratified
convection. We compare results from spherical and Cartesian models
in the same parameter regime in order to study whether restricted
geometry introduces artefacts into the results. In particular,
we want to clarify whether the sharp equatorial profile of the
horizontal Reynolds stress found in earlier Cartesian models is
also reproduced in spherical geometry. Methods: We employ
direct numerical simulations of turbulent convection in spherical
and Cartesian geometries. In order to alleviate the computational
cost in the spherical runs, and to reach as high spatial resolution
as possible, we model only parts of the latitude and longitude. The
rotational influence, measured by the Coriolis number or inverse Rossby
number, is varied from zero to roughly seven, which is the regime
that is likely to be realised in the solar convection zone. Cartesian
simulations are performed in overlapping parameter regimes. 
Results: For slow rotation we find that the radial and latitudinal
turbulent angular momentum fluxes are directed inward and equatorward,
respectively. In the rapid rotation regime the radial flux changes sign
in accordance with earlier numerical results, but in contradiction with
theory. The latitudinal flux remains mostly equatorward and develops
a maximum close to the equator. In Cartesian simulations this peak
can be explained by the strong "banana cells". Their effect in the
spherical case does not appear to be as large. The latitudinal heat
flux is mostly equatorward for slow rotation but changes sign for
rapid rotation. Longitudinal heat flux is always in the retrograde
direction. The rotation profiles vary from anti-solar (slow equator) for
slow and intermediate rotation to solar-like (fast equator) for rapid
rotation. The solar-like profiles are dominated by the Taylor-Proudman
balance. Movies and Appendix A are available in electronic form
at <A href="http://www.aanda.org">http://www.aanda.org</A>

---------------------------------------------------------
Title: Magnetorotational instability driven dynamos at low magnetic
Prandtl numbers
Authors: Käpylä, P. J.; Korpi, M. J.
2011MNRAS.413..901K Altcode: 2010arXiv1004.2417K; 2011MNRAS.tmp..144K
Numerical simulations of the magnetorotational instability (MRI) with
zero initial net flux in a non-stratified isothermal cubic domain are
used to demonstrate the importance of magnetic boundary conditions. In
fully periodic systems, the level of turbulence generated by the MRI
strongly decreases as the magnetic Prandtl number (Pm), which is the
ratio of kinematic viscosity and magnetic diffusion, is decreased. No
MRI or dynamo action below Pm = 1 is found, agreeing with earlier
investigations. Using vertical field conditions, which allow the
generation of a net toroidal flux and magnetic helicity fluxes out of
the system, the MRI is found to be excited in the range 0.1 ≤ Pm ≤
10, and the saturation level is independent of Pm. In the vertical field
runs, strong mean-field dynamo develops and helps to sustain the MRI.

---------------------------------------------------------
Title: On global solar dynamo simulations
Authors: Käpylä, P. J.
2011AN....332...43K Altcode: 2010arXiv1010.1249K
Global dynamo simulations solving the equations of magnetohydrodynamics
(MHD) have been a tool of astrophysicists who try to understand the
magnetism of the Sun for several decades now. During recent years
many fundamental issues in dynamo theory have been studied in detail
by means of local numerical simulations that simplify the problem and
allow the study of physical effects in isolation. Global simulations,
however, continue to suffer from the age-old problem of too low spatial
resolution, leading to much lower Reynolds numbers and scale separation
than in the Sun. Reproducing the internal rotation of the Sun, which
plays a crucial role in the dynamo process, has also turned out to be
a very difficult problem. In the present paper the current status of
global dynamo simulations of the Sun is reviewed. Emphasis is put on
efforts to understand how the large-scale magnetic fields, i.e. whose
length scale is greater than the scale of turbulence, are generated
in the Sun. Some lessons from mean-field theory and local simulations
are reviewed and their possible implications to the global models are
discussed. Possible remedies to some current issues of solar simulations
are put forward.

---------------------------------------------------------
Title: Turbulent transport in hydromagnetic flows
Authors: Brandenburg, A.; Chatterjee, P.; Del Sordo, F.; Hubbard,
A.; Käpylä, P. J.; Rheinhardt, M.
2010PhST..142a4028B Altcode: 2010arXiv1004.5380B
The predictive power of mean-field theory is emphasized by comparing
theory with simulations under controlled conditions. The recently
developed test-field method is used to extract turbulent transport
coefficients both in the kinematic and the nonlinear or quasi-kinematic
cases. A striking example of the quasi-kinematic method is provided by
magnetic buoyancy-driven flows that produce an α effect and turbulent
diffusion.

---------------------------------------------------------
Title: Oscillatory Migrating Magnetic Fields in Helical Turbulence
in Spherical Domains
Authors: Mitra, Dhrubaditya; Tavakol, Reza; Käpylä, Petri J.;
Brandenburg, Axel
2010ApJ...719L...1M Altcode: 2009arXiv0901.2364M
We present direct numerical simulations of the equations of compressible
magnetohydrodynamics in a wedge-shaped spherical shell, without
shear, but with random helical forcing which has negative (positive)
helicity in the northern (southern) hemisphere. We find a large-scale
magnetic field that is nearly uniform in the azimuthal direction
and approximately antisymmetric about the equator. Furthermore,
the large-scale field in each hemisphere oscillates on nearly
dynamical timescales with reversals of polarity and equatorward
migration. Corresponding mean-field models also show similar migratory
oscillations with a frequency that is nearly independent of the magnetic
Reynolds number. This mechanism may be relevant for understanding
equatorward migration seen in the solar dynamo.

---------------------------------------------------------
Title: Angular Momentum Transport in Convectively Unstable Shear Flows
Authors: Käpylä, Petri J.; Brandenburg, Axel; Korpi, Maarit J.;
Snellman, Jan E.; Narayan, Ramesh
2010ApJ...719...67K Altcode: 2010arXiv1003.0900K
Angular momentum transport due to hydrodynamic turbulent convection
is studied using local three-dimensional numerical simulations
employing the shearing box approximation. We determine the turbulent
viscosity from non-rotating runs over a range of values of the shear
parameter and use a simple analytical model in order to extract the
non-diffusive contribution (Λ-effect) to the stress in runs where
rotation is included. Our results suggest that the turbulent viscosity
is on the order of the mixing length estimate and weakly affected by
rotation. The Λ-effect is non-zero and a factor of 2-4 smaller than
the turbulent viscosity in the slow rotation regime. We demonstrate that
for Keplerian shear, the angular momentum transport can change sign and
be outward when the rotation period is greater than the turnover time,
i.e., when the Coriolis number is below unity. This result seems to
be relatively independent of the value of the Rayleigh number.

---------------------------------------------------------
Title: Open and closed boundaries in large-scale convective dynamos
Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A.
2010A&A...518A..22K Altcode: 2009arXiv0911.4120K
Context. Earlier work has suggested that large-scale dynamos can reach
and maintain equipartition field strengths on a dynamical time scale
only if magnetic helicity of the fluctuating field can be shed from
the domain through open boundaries. Aims: Our aim is to test
this scenario in convection-driven dynamos by comparing results for
open and closed boundary conditions. Methods: Three-dimensional
numerical simulations of turbulent compressible convection with shear
and rotation are used to study the effects of boundary conditions on the
excitation and saturation of large-scale dynamos. Open (vertical-field)
and closed (perfect- conductor) boundary conditions are used for
the magnetic field. The shear flow is such that the contours of
shear are vertical, crossing the outer surface, and are thus ideally
suited for driving a shear-induced magnetic helicity flux. 
Results: We find that for given shear and rotation rate, the growth
rate of the magnetic field is larger if open boundary conditions are
used. The growth rate first increases for small magnetic Reynolds
number, Rm, but then levels off at an approximately constant value for
intermediate values of Rm. For large enough Rm, a small-scale dynamo
is excited and the growth rate of the field in this regime increases
as Rm1/2. Regarding the nonlinear regime, the saturation
level of the energy of the total magnetic field is independent of
Rm when open boundaries are used. In the case of perfect-conductor
boundaries, the saturation level first increases as a function of Rm,
but then decreases proportional to Rm-1 for Rm ⪆ 30,
indicative of catastrophic quenching. These results suggest that
the shear-induced magnetic helicity flux is efficient in alleviating
catastrophic quenching when open boundaries are used. The horizontally
averaged mean field is still weakly decreasing as a function of Rm
even for open boundaries.

---------------------------------------------------------
Title: The α effect in rotating convection with sinusoidal shear
Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A.
2010MNRAS.402.1458K Altcode: 2009arXiv0908.2423K; 2009MNRAS.tmp.1866K
Using three-dimensional convection simulations, it is shown that a
sinusoidal variation of horizontal shear leads to a kinematic α effect
with a similar sinusoidal variation. The effect exists even for weak
stratification and arises owing to the inhomogeneity of turbulence and
the presence of impenetrable vertical boundaries. This system produces
large-scale magnetic fields that also show a sinusoidal variation in
the cross-stream direction. It is argued that earlier investigations
overlooked these phenomena partly because of the use of horizontal
averaging and also because measurements of α using an imposed
field combined with long time averages give erroneous results. It
is demonstrated that in such cases the actual horizontally averaged
mean field becomes non-uniform. The turbulent magnetic diffusion term
resulting from such non-uniform fields can then no longer be neglected
and begins to balance the α effect.

---------------------------------------------------------
Title: Oscillatory migratory large-scale fields in mean-field and
direct simulations
Authors: Mitra, Dhrubaditya; Tavakol, Reza; Brandenburg, Axel;
Käpylä, Petri J.
2010IAUS..264..197M Altcode:
We summarise recent results form direct numerical simulations of
both non-rotating helically forced and rotating convection driven
MHD equations in spherical wedge-shape domains. In the former, using
perfect-conductor boundary conditions along the latitudinal boundaries
we observe oscillations, polarity reversals and equatorward migration
of the large-scale magnetic fields. In the latter we obtain angular
velocity with cylindrical contours and large-scale magnetic field which
shows oscillations, polarity reversals but poleward migration. The
occurrence of these behviours in direct numerical simulations is
clearly of interest. However the present models as they stand are
not directly applicable to the solar dynamo problem. Nevertheless,
they provide general insights into the operation of turbulent dynamos.

---------------------------------------------------------
Title: Influence of Ohmic diffusion on the excitation and dynamics
of MRI
Authors: Korpi, M. J.; Käpylä, P. J.; Väisälä, M. S.
2010AN....331...34K Altcode: 2009arXiv0909.1724K
In this paper we make an effort to understand the interaction of
turbulence generated by the magnetorotational instability (MRI) with
turbulence from other sources, such as supernova explosions (SNe) in
galactic disks. First we perform a linear stability analysis (LSA) of
non-ideal MRI to derive the limiting value of Ohmic diffusion that is
needed to inhibit the growth of the instability for different types of
rotation laws. With the help of a simple analytical expression derived
under first-order smoothing approximation (FOSA), an estimate of the
limiting turbulence level and hence the turbulent diffusion needed to
damp the MRI is derived. Secondly, we perform numerical simulations
in local cubes of isothermal nonstratified gas with external forcing
of varying strength to see whether the linear result holds for more
complex systems. Purely hydrodynamic calculations with forcing, rotation
and shear are made for reference purposes, and as expected, non-zero
Reynolds stresses are found. In the magnetohydrodynamic calculations,
therefore, the total stresses generated are a sum of the forcing and MRI
contributions. To separate these contributions, we perform reference
runs with MRI-stable shear profiles (angular velocity increasing
outwards), which suggest that the MRI-generated stresses indeed become
strongly suppressed as function of the forcing. The Maxwell to Reynolds
stress ratio is observed to decrease by an order of magnitude as the
turbulence level due to external forcing exceeds the predicted limiting
value, which we interpret as a sign of MRI suppression. Finally, we
apply these results to estimate the limiting radius inside of which
the SN activity can suppress the MRI, arriving at a value of 14 kpc.

---------------------------------------------------------
Title: Convective dynamos in spherical wedge geometry
Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A.; Mitra, D.;
Tavakol, R.
2010AN....331...73K Altcode: 2009arXiv0909.1330K
Self-consistent convective dynamo simulations in wedge-shaped
spherical shells are presented. Differential rotation is generated
by the interaction of convection with rotation. Equatorward
acceleration and dynamo action are obtained only for sufficiently
rapid rotation. The angular velocity tends to be constant along
cylinders. Oscillatory large-scale fields are found to migrate in
the poleward direction. Comparison with earlier simulations in full
spherical shells and Cartesian domains is made.

---------------------------------------------------------
Title: Stellar magnetic fields: observations and nonlinear modeling
Authors: Lindborg, M.; Korpi, M.; Tuominen, I.; Hackman, T.; Ilyin,
I.; Käpylä, P.
2009AGUFMSH13A1506L Altcode:
Magnetic fields on a global scale are observed in a wide variety of
astrophysical objects, spanning from planets, stars, and accretion
disks to galaxies. These magnetic fields are anything but passive,
taking part in the dynamics of their hosts, resulting for example in
the familiar activity phenomena of the Sun, which also affect life
here on the Earth. We have a long time series of temperature mapping
and photometry of an active late-type star II Peg. II Peg is known as
one of the most active RS Cvn stars representing the Sun at a younger
age. We are trying to establish the link between the Sun and the more
active rapidly rotating stars and compare the results to the dynamo
models of the Sun. Preliminary results show some resemblance to the
dynamo solutions.

---------------------------------------------------------
Title: The α effect with imposed and dynamo-generated magnetic fields
Authors: Hubbard, A.; Del Sordo, F.; Käpylä, P. J.; Brandenburg, A.
2009MNRAS.398.1891H Altcode: 2009MNRAS.tmp.1219H; 2009arXiv0904.2773H
Estimates for the non-linear α effect in helical turbulence
with an applied magnetic field are presented using two different
approaches: the imposed-field method where the electromotive force
owing to the applied field is used, and the test-field method where
separate evolution equations are solved for a set of different test
fields. Both approaches agree for stronger fields, but there are
apparent discrepancies for weaker fields that can be explained by
the influence of dynamo-generated magnetic fields on the scale of the
domain that are referred to as meso-scale magnetic fields. Examples are
discussed where these meso-scale fields can lead to both drastically
overestimated and underestimated values of α compared with the
kinematic case. It is demonstrated that the kinematic value can be
recovered by resetting the fluctuating magnetic field to zero in
regular time intervals. It is concluded that this is the preferred
technique both for the imposed-field and the test-field methods.

---------------------------------------------------------
Title: Reynolds stresses from hydrodynamic turbulence with shear
and rotation
Authors: Snellman, J. E.; Käpylä, P. J.; Korpi, M. J.; Liljeström,
A. J.
2009A&A...505..955S Altcode: 2009arXiv0906.1200S
Aims: We study the Reynolds stresses which describe turbulent
momentum transport from turbulence affected by large-scale shear and
rotation. Methods: Three-dimensional numerical simulations are
used to study turbulent transport under the influences of large-scale
shear and rotation in homogeneous, isotropically forced turbulence. We
study three cases: one with only shear, and two others where in addition
to shear, rotation is present. These cases differ by the angle (0 or
90°) the rotation vector makes with respect to the z-direction. Two
subsets of runs are performed with both values of θ where either
rotation or shear is kept constant. When only shear is present, the
off-diagonal stress can be described by turbulent viscosity whereas
if the system also rotates, nondiffusive contributions (Λ-effect) to
the stress can arise. Comparison of the direct simulations are made
with analytical results from a simple closure model. Results:
We find that the turbulent viscosity is of the order of the first
order smoothing result in the parameter regime studied and that for
sufficiently large Reynolds numbers the Strouhal number, describing
the ratio of correlation to turnover times, is roughly 1.5. This is
consistent with the closure model based on the minimal tau-approximation
which produces a reasonable fit to the simulation data for similar
Strouhal numbers. In the cases where rotation is present, separating
the diffusive and nondiffusive components of the stress turns out to
be challenging but taking the results at face value, we can obtain
nondiffusive contributions of the order of 0.1 times the turbulent
viscosity. We also find that the simple closure model is able to
reproduce most of the qualitative features of the numerical results
provided that the Strouhal number is of the order of unity. Tables
B1-B3 are only available in electronic form at http://www.aanda.org

---------------------------------------------------------
Title: Turbulent Dynamos with Shear and Fractional Helicity
Authors: Käpylä, Petri J.; Brandenburg, Axel
2009ApJ...699.1059K Altcode: 2008arXiv0810.2298K
Dynamo action owing to helically forced turbulence and large-scale shear
is studied using direct numerical simulations. The resulting magnetic
field displays propagating wave-like behavior. This behavior can be
modeled in terms of an αΩ dynamo. In most cases super-equipartition
fields are generated. By varying the fraction of helicity of the
turbulence the regeneration of poloidal fields via the helicity effect
(corresponding to the α-effect) is regulated. The saturation level of
the magnetic field in the numerical models is consistent with a linear
dependence on the ratio of the fractional helicities of the small
and large-scale fields, as predicted by a simple nonlinear mean-field
model. As the magnetic Reynolds number (Re M ) based on the
wavenumber of the energy-carrying eddies is increased from 1 to 180,
the cycle frequency of the large-scale field is found to decrease by a
factor of about 6 in cases where the turbulence is fully helical. This
is interpreted in terms of the turbulent magnetic diffusivity, which
is found to be only weakly dependent on the Re M .

---------------------------------------------------------
Title: Large-scale Dynamos in Rigidly Rotating Turbulent Convection
Authors: Käpylä, Petri J.; Korpi, Maarit J.; Brandenburg, Axel
2009ApJ...697.1153K Altcode: 2008arXiv0812.3958K
The existence of large-scale dynamos in rigidly rotating turbulent
convection without shear is studied using three-dimensional numerical
simulations of penetrative rotating compressible convection. We
demonstrate that rotating convection in a Cartesian domain can drive a
large-scale dynamo even in the absence of shear. The large-scale field
contains a significant fraction of the total field in the saturated
state. The simulation results are compared with one-dimensional
mean-field dynamo models where turbulent transport coefficients,
as determined using the test field method, are used. The reason for
the absence of large-scale dynamo action in earlier studies is shown
to be due to the rotation being too slow: whereas the α-effect can
change sign, its magnitude stays approximately constant as a function
of rotation, and the turbulent diffusivity decreases monotonically with
increasing rotation. Only when rotation is rapid enough a large-scale
dynamo can be excited. The one-dimensional mean-field model with dynamo
coefficients from the test-field results predicts reasonably well
the dynamo excitation in the direct simulations. This result further
validates the test field procedure and reinforces the interpretation
that the observed dynamo is driven by a turbulent α-effect. This result
demonstrates the existence of an α-effect and an α2-dynamo
with natural forcing.

---------------------------------------------------------
Title: Alpha effect and turbulent diffusion from convection
Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A.
2009A&A...500..633K Altcode: 2008arXiv0812.1792K
Aims: We study turbulent transport coefficients that describe the
evolution of large-scale magnetic fields in turbulent convection. Methods: We use the test field method, together with three-dimensional
numerical simulations of turbulent convection with shear and rotation,
to compute turbulent transport coefficients describing the evolution
of large-scale magnetic fields in mean-field theory in the kinematic
regime. We employ one-dimensional mean-field models with the derived
turbulent transport coefficients to examine whether they give results
that are compatible with direct simulations. Results: The results
for the α-effect as a function of rotation rate are consistent with
earlier numerical studies, i.e. increasing magnitude as rotation
increases and approximately cos θ latitude profile for moderate
rotation. Turbulent diffusivity, η_t, is proportional to the square of
the turbulent vertical velocity in all cases. Whereas ηt
decreases approximately inversely proportional to the wavenumber of
the field, the α-effect and turbulent pumping show a more complex
behaviour with partial or full sign changes and the magnitude staying
roughly constant. In the presence of shear and no rotation, a weak
α-effect is induced which does not seem to show any consistent trend
as a function of shear rate. Provided that the shear is large enough,
this small α-effect is able to excite a dynamo in the mean-field
model. The coefficient responsible for driving the shear-current
effect shows several sign changes as a function of depth but is also
able to contribute to dynamo action in the mean-field model. The
growth rates in these cases are, however, well below those in direct
simulations, suggesting that an incoherent α-shear dynamo may also
act in the simulations. If both rotation and shear are present, the
α-effect is more pronounced. At the same time, the combination of the
shear-current and Ω×{ J}-effects is also stronger than in the case
of shear alone, but subdominant to the α-shear dynamo. The results
of direct simulations are consistent with mean-field models where all
of these effects are taken into account without the need to invoke
incoherent effects.

---------------------------------------------------------
Title: Stellar nonlinear dynamos: observations and modelling
Authors: Tuominen, Ilkka; Korpi, Maarit J.; Käpylä, Petri J.;
Lindborg, Marjaana; Ilyin, Ilya
2009IAUS..259..417T Altcode:
Recent numerical modelling of mean-field stellar dynamos with induction
and Reynolds' equations show that, with increasing rotation, field
symmetry changes from an axisymmetric solar type to a nonaxymmetric one,
where the so-called active longitudes in the same stellar hemisphere
are predicted to be of opposite polarities. It was originally named
Active star Hale rule in Tuominen et al. (2002), being an analogue
to the famous bipolar sunspot polarity rule but different in scale
and being a global phenomenon. In addition to long timeseries of
temperature mapping and photometry, during the last few years we have
been able to measure accurately polarization spectra of an active
late-type star II Peg with the upgraded spectropolarimetric option of
the high-resolution spectrograph SOFIN at the Nordic Optical Telescope,
La Palma. The magnetic inversions (Carroll et al., Kochukhov et al.) can
be compared to the dynamo models and the preliminary results show some
resemblance to the dynamo solutions.

---------------------------------------------------------
Title: Alpha effect and diffusivity in helical turbulence with shear
Authors: Mitra, D.; Käpylä, P. J.; Tavakol, R.; Brandenburg, A.
2009A&A...495....1M Altcode: 2008arXiv0806.1608M
Aims: We study the dependence of turbulent transport coefficients, such
as the components of the α tensor (αij) and the turbulent
magnetic diffusivity tensor (ηij), on shear and magnetic
Reynolds number in the presence of helical forcing. Methods:
We use three-dimensional direct numerical simulations with periodic
boundary conditions and measure the turbulent transport coefficients
using the kinematic test field method. In all cases the magnetic Prandtl
number is taken as unity. Results: We find that with increasing
shear the diagonal components of αij quench, whereas those
of ηij increase. The antisymmetric parts of both tensors
increase with increasing shear. We also propose a simple expression for
the turbulent pumping velocity (or γ effect). This pumping velocity is
proportional to the kinetic helicity of the turbulence and the vorticity
of the mean flow. For negative helicity, i.e. for a positive trace of
αij, it points in the direction of the mean vorticity,
i.e. perpendicular to the plane of the shear flow. Our simulations
support this expression for low shear and magnetic Reynolds number. The
transport coefficients depend on the wavenumber of the mean flow in
a Lorentzian fashion, just as for non-shearing turbulence.

---------------------------------------------------------
Title: Turbulent stresses as a function of shear rate in a local
disk model
Authors: Liljeström, A. J.; Korpi, M. J.; Käpylä, P. J.;
Brandenburg, A.; Lyra, W.
2009AN....330...92L Altcode: 2008arXiv0811.2341L
We present local numerical models of accretion disk turbulence driven
by the magnetorotational instability with varying shear rate. The
resulting turbulent stresses are compared with predictions of a closure
model in which triple correlations are modelled in terms of quadratic
correlations. This local model uses five nondimensional parameters to
describe the properties of the flow. We attempt to determine these
closure parameters for our simulations and find that the model does
produce qualitatively correct behaviour. In addition, we present results
concerning the shear rate dependency of the magnetic to kinetic energy
ratio. We find both the turbulent stress ratio and the total stress
to be strongly dependent on the shear rate.

---------------------------------------------------------
Title: Numerical study of large-scale vorticity generation in
shear-flow turbulence
Authors: Käpylä, Petri J.; Mitra, Dhrubaditya; Brandenburg, Axel
2009PhRvE..79a6302K Altcode: 2008arXiv0810.0833K
Simulations of stochastically forced shear-flow turbulence in a
shearing-periodic domain are used to study the spontaneous generation of
large-scale flow patterns in the direction perpendicular to the plane of
the shear. Based on an analysis of the resulting large-scale velocity
correlations it is argued that the mechanism behind this phenomenon
could be the mean-vorticity dynamo effect pioneered by Elperin,
Kleeorin, and Rogachevskii [Phys. Rev. E 68, 016311 (2003)]. This
effect is based on the anisotropy of the eddy viscosity tensor. One
of its components may be able to replenish cross-stream mean flows by
acting upon the streamwise component of the mean flow. Shear, in turn,
closes the loop by acting upon the cross-stream mean flow to produce
stronger streamwise mean flows. The diagonal component of the eddy
viscosity is found to be of the order of the rms turbulent velocity
divided by the wave number of the energy-carrying eddies.

---------------------------------------------------------
Title: Large-scale dynamos in turbulent convection with shear
Authors: Käpylä, P. J.; Korpi, M. J.; Brandenburg, A.
2008A&A...491..353K Altcode: 2008arXiv0806.0375K
Aims: To study the existence of large-scale convective dynamos under
the influence of shear and rotation. Methods: Three-dimensional
numerical simulations of penetrative compressible convection with
uniform horizontal shear are used to study dynamo action and the
generation of large-scale magnetic fields. We consider cases where the
magnetic Reynolds number is either marginal or moderately supercritical
with respect to small-scale dynamo action in the absence of shear and
rotation. Our magnetic Reynolds number is based on the wavenumber of
the depth of the convectively unstable layer. The effects of magnetic
helicity fluxes are studied by comparing results for the magnetic
field with open and closed boundaries. Results: Without shear
no large-scale dynamos are found even if the ingredients necessary
for the α-effect (rotation and stratification) are present in the
system. When uniform horizontal shear is added, a large-scale magnetic
field develops, provided the boundaries are open. In this case the mean
magnetic field contains a significant fraction of the total field. For
those runs where the magnetic Reynolds number is between 60 and 250, an
additional small-scale dynamo is expected to be excited, but the field
distribution is found to be similar to cases with smaller magnetic
Reynolds number where the small-scale dynamo is not excited. In the
case of closed (perfectly conducting) boundaries, magnetic helicity
fluxes are suppressed and no large-scale fields are found. Similarly,
poor large-scale field development is seen when vertical shear is used
in combination with periodic boundary conditions in the horizontal
directions. If, however, open (normal-field) boundary conditions are
used in the x-direction, a large-scale field develops. These results
support the notion that shear not only helps to generate the field,
but it also plays a crucial role in driving magnetic helicity fluxes
out of the system along the isocontours of shear, thereby allowing
efficient dynamo action.

---------------------------------------------------------
Title: Lambda effect from forced turbulence simulations
Authors: Käpylä, P. J.; Brandenburg, A.
2008A&A...488....9K Altcode: 2008arXiv0806.3751K
Aims: We determine the components of the Λ-effect tensor that
quantifies the contributions to the turbulent momentum transport even
for uniform rotation. Methods: Three-dimensional numerical
simulations are used to study turbulent transport in triply
periodic cubes under the influence of rotation and anisotropic
forcing. Comparison is made with analytical results obtained via
the so-called minimal tau-approximation. Results: In the case
where the turbulence intensity in the vertical direction dominates,
the vertical stress is always negative. This situation is expected
to occur in stellar convection zones. The horizontal component of the
stress is weaker and exhibits a maximum at latitude 30° - regardless
of how rapid the rotation is. The minimal tau-approximation captures
many of the qualitative features of the numerical results, provided the
relaxation time tau is close to the turnover time, i.e. the Strouhal
number is of order unity. Tables [see full textsee full textsee
full text]-[see full textsee full textsee full text] are only available
in electronic form at http.//www.aanda.org

---------------------------------------------------------
Title: A solar mean field dynamo benchmark
Authors: Jouve, L.; Brun, A. S.; Arlt, R.; Brandenburg, A.; Dikpati,
M.; Bonanno, A.; Käpylä, P. J.; Moss, D.; Rempel, M.; Gilman, P.;
Korpi, M. J.; Kosovichev, A. G.
2008A&A...483..949J Altcode:
Context: The solar magnetic activity and cycle are linked to an
internal dynamo. Numerical simulations are an efficient and accurate
tool to investigate such intricate dynamical processes. Aims:
We present the results of an international numerical benchmark
study based on two-dimensional axisymmetric mean field solar dynamo
models in spherical geometry. The purpose of this work is to provide
reference cases that can be analyzed in detail and that can help in
further development and validation of numerical codes that solve such
kinematic problems. Methods: The results of eight numerical
codes solving the induction equation in the framework of mean field
theory are compared for three increasingly computationally intensive
models of the solar dynamo: an αΩ dynamo with constant magnetic
diffusivity, an αΩ dynamo with magnetic diffusivity sharply varying
with depth and an example of a flux-transport Babcock-Leighton dynamo
which includes a non-local source term and one large single cell of
meridional circulation per hemisphere. All cases include a realistic
profile of differential rotation and thus a sharp tachocline. Results: The most important finding of this study is that all codes
agree quantitatively to within less than a percent for the αΩ dynamo
cases and within a few percent for the flux-transport case. Both
the critical dynamo numbers for the onset of dynamo action and the
corresponding cycle periods are reasonably well recovered by all
codes. Detailed comparisons of butterfly diagrams and specific cuts of
both toroidal and poloidal fields at given latitude and radius confirm
the good quantitative agreement. Conclusions: We believe that
such a benchmark study will be a very useful tool since it provides
detailed standard cases for comparison and reference.

---------------------------------------------------------
Title: Magnetic Diffusivity Tensor and Dynamo Effects in Rotating
and Shearing Turbulence
Authors: Brandenburg, A.; Rädler, K. -H.; Rheinhardt, M.; Käpylä,
P. J.
2008ApJ...676..740B Altcode: 2007arXiv0710.4059B
The turbulent magnetic diffusivity tensor is determined in the presence
of rotation or shear. The question is addressed whether dynamo action
from the shear-current effect can explain large-scale magnetic field
generation found in simulations with shear. For this purpose a set
of evolution equations for the response to imposed test fields is
solved with turbulent and mean motions calculated from the momentum and
continuity equations. The corresponding results for the electromotive
force are used to calculate turbulent transport coefficients. The
diagonal components of the turbulent magnetic diffusivity tensor are
found to be very close together, but their values increase slightly
with increasing shear and decrease with increasing rotation rate. In
the presence of shear, the sign of the two off-diagonal components
of the turbulent magnetic diffusion tensor is the same and opposite
to the sign of the shear. This implies that dynamo action from the
shear-current effect is impossible, except perhaps for high magnetic
Reynolds numbers. However, even though there is no alpha effect on the
average, the components of the α tensor display Gaussian fluctuations
around zero. These fluctuations are strong enough to drive an incoherent
alpha-shear dynamo. The incoherent shear-current effect, on the other
hand, is found to be subdominant.

---------------------------------------------------------
Title: The helicity constraint in spherical shell dynamos
Authors: Brandenburg, A.; Käpylä, P. J.; Mitra, D.; Moss, D.;
Tavakol, R.
2007AN....328.1118B Altcode: 2007arXiv0711.3616B
The motivation for considering distributed large scale dynamos
in the solar context is reviewed in connection with the magnetic
helicity constraint. Preliminary accounts of 3-dimensional direct
numerical simulations (in spherical shell segments) and simulations
of 2-dimensional mean field models (in spherical shells) are
presented. Interesting similarities as well as some differences
are noted.

---------------------------------------------------------
Title: Turbulent viscosity and Λ-effect from numerical turbulence
models
Authors: Käpylä, P. J.; Brandenburg, A.
2007AN....328.1006K Altcode: 2007arXiv0710.5632K
Homogeneous anisotropic turbulence simulations are used to determine
off-diagonal components of the Reynolds stress tensor and its
parameterization in terms of turbulent viscosity and Λ-effect. The
turbulence is forced in an anisotropic fashion by enhancing the strength
of the forcing in the vertical direction. The Coriolis force is included
with a rotation axis inclined relative to the vertical direction. The
system studied here is significantly simpler than that of turbulent
stratified convection which has often been used to study Reynolds
stresses. Certain puzzling features of the results for convection,
such as sign changes or highly concentrated latitude distributions,
are not present in the simpler system considered here.

---------------------------------------------------------
Title: Magnetic helicity effects in astrophysical and laboratory
dynamos
Authors: Brandenburg, A.; Käpylä, P. J.
2007NJPh....9..305B Altcode: 2007arXiv0705.3507B
Magnetic helicity effects are discussed in laboratory and astro-physical
settings. Firstly, dynamo action in Taylor Green flows is discussed
for different boundary conditions. However, because of the lack of
scale separation with respect to the container, no large-scale field
is being produced and there is no resistively slow saturation phase as
otherwise expected. Secondly, the build-up of a large-scale field is
demonstrated in a simulation where a localized magnetic eddy produces
field on a larger scale if the eddy possesses a swirl. Such a set-up
might be realizable experimentally through coils. Finally, new emerging
issues regarding the connection between magnetic helicity and the solar
dynamo are discussed. It is demonstrated that dynamos with a nonlocal
(Babcock Leighton type) α effect can also be catastrophically quenched,
unless there are magnetic helicity fluxes.

---------------------------------------------------------
Title: Effects of rotation and input energy flux on convective
overshooting
Authors: Käpylä, Petri J.; Korpi, M. J.; Stix, M.; Tuominen, I.
2007IAUS..239..437K Altcode: 2006astro.ph..9350K
We study convective overshooting by means of local 3D convection
calculations. Using a mixing length model of the solar convection
zone (CZ) as a guide, we determine the Coriolis number (Co), which
is the inverse of the Rossby number, to be of the order of ten or
larger at the base of the solar CZ. Therefore we perform convection
calculations in the range Co = 0...10 and interpret the value of Co
realised in the calculation to represent a depth in the solar CZ. In
order to study the dependence on rotation, we compute the mixing length
parameters alpha_T and alpha_u relating the temperature and velocity
fluctuations, respectively, to the mean thermal stratification. We
find that the mixing length parameters for the rapid rotation case,
corresponding to the base of the solar CZ, are 3-5 times smaller than
in the nonrotating case. Introducing such depth-dependent alpha into
a solar structure model employing a non-local mixing length formalism
results in overshooting which is approximately proportional to alpha
at the base of the CZ. Although overshooting is reduced due to the
reduced alpha, a discrepancy with helioseismology remains due to the
steep transition to the radiative temperature gradient. In comparison
to the mixing length models the transition at the base of the CZ is
much gentler in the 3D models. It was suggested recently (Rempel 2004)
that this discrepancy is due to the significantly larger (up to seven
orders of magnitude) input energy flux in the 3D models in comparison
to the Sun and solar models, and that the 3D calculations should be
able to approach the mixing length regime if the input energy flux is
decreased by a moderate amount. We present results from local convection
calculations which support this conjecture.

---------------------------------------------------------
Title: Reynolds stresses and meridional circulation from rotating
cylinder simulations
Authors: Hupfer, C.; Käpylä, P. J.; Stix, M.
2006A&A...459..935H Altcode:
Aims.The latitude and depth dependences of Reynolds stresses are
obtained from numerical simulations of a solar-type convection zone
where the star is assumed to rotate with a uniform angular velocity. Methods: .A two-dimensional model, using a cylindrical annulus
with axis perpendicular to the axis of rotation, is introduced as an
approximation of a spherical section along the meridional plane. We
solve the fully compressible Navier-Stokes equations numerically and use
Cartesian and cylindrical geometries to simulate convection under the
influence of rotation. Results: .For moderate Coriolis numbers
both models yield strong extrema of the Reynolds stress component
Qθϕ at low latitudes near the equator, and a meridional
cell pattern is found in the cylindrical model. For Coriolis numbers
larger than about 10 the flow becomes aligned with the direction of
the rotation axis.

---------------------------------------------------------
Title: Solar dynamo models with α-effect and turbulent pumping from
local 3D convection calculations
Authors: Käpylä, P. J.; Korpi, M. J.; Tuominen, I.
2006AN....327..884K Altcode: 2006astro.ph..6089K
Results from kinematic solar dynamo models employing α-effect
and turbulent pumping from local convection calculations are
presented. We estimate the magnitude of these effects to be around 2-3
m s-1, having scaled the local quantities with the convective
velocity at the bottom of the convection zone from a solar mixing-length
model. Rotation profile of the Sun as obtained from helioseismology
is applied in the models; we also investigate the effects of the
observed surface shear layer on the dynamo solutions. With these
choices of the small- and large-scale velocity fields, we obtain
estimate of the ratio of the two induction effects, C_α/C_Ω ≈
10-3, which we keep fixed in all models. We also include a
one-cell meridional circulation pattern having a magnitude of 10-20 m
s-1 near the surface and 1-2 m s-1 at the bottom
of the convection zone. The model essentially represents a distributed
turbulent dynamo, as the α-effect is nonzero throughout the convection
zone, although it concentrates near the bottom of the convection zone
obtaining a maximum around 30° of latitude. Turbulent pumping of the
mean fields is predominantly down- and equatorward. The anisotropies
in the turbulent diffusivity are neglected apart from the fact that
the diffusivity is significantly reduced in the overshoot region. We
find that, when all these effects are included in the model, it is
possible to correctly reproduce many features of the solar activity
cycle, namely the correct equatorward migration at low latitudes and
the polar branch at high latitudes, and the observed negative sign of
B_r Bφ. Although the activity clearly shifts towards the
equator in comparison to previous models due to the combined action
of the α-effect peaking at midlatitudes, meridional circulation and
latitudinal pumping, most of the activity still occurs at too high
latitudes (between 5° ... 60°). Other problems include the relatively
narrow parameter space within which the preferred solution is dipolar
(A0), and the somewhat too short cycle lengths of the solar-type
solutions. The role of the surface shear layer is found to be important
only in the case where the α-effect has an appreciable magnitude near
the surface.

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Title: Magnetoconvection and dynamo coefficients. III. α-effect
and magnetic pumping in the rapid rotation regime
Authors: Käpylä, P. J.; Korpi, M. J.; Ossendrijver, M.; Stix, M.
2006A&A...455..401K Altcode: 2006astro.ph..2111K
Aims.The α- and γ-effects, which are responsible for the generation
and turbulent pumping of large scale magnetic fields, respectively,
due to passive advection by convection are determined in the rapid
rotation regime corresponding to the deep layers of the solar convection
zone. Methods.A 3D rectangular local model is used for solving the
full set of MHD equations in order to compute the electromotive force
(emf), E = overline {u × b}, generated by the interaction of imposed
weak gradient-free magnetic fields and turbulent convection with varying
rotational influence and latitude. By expanding the emf in terms of the
mean magnetic field, Ei = aij overline B_j, all
nine components of aij are computed. The diagonal elements
of aij describe the α-effect, whereas the off-diagonals
represent magnetic pumping. The latter is essentially the advection
of magnetic fields by means other than the underlying large-scale
velocity field. Comparisons are made to analytical expressions of the
coefficients derived under the first-order smoothing approximation
(FOSA). Results.In the rapid rotation regime the latitudinal
dependence of the α-components responsible for the generation of the
azimuthal and radial fields does not exhibit a peak at the poles, as
is the case for slow rotation, but at a latitude of about 30°. The
magnetic pumping is predominantly radially down- and latitudinally
equatorward as in earlier studies. The numerical results compare
surprisingly well with analytical expressions derived under first-order
smoothing, although the present calculations are expected to lie near
the limits of the validity range of FOSA.

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Title: Alpha-Effect and Turbulent Pumping In The Rapid Rotation
Regime - Implications For Solar Dynamo Models
Authors: Käpylä, P. J.; Korpi, M. J.; Ossendrijver, M.; Stix, M.;
Tuominen, I.
2006IAUJD...8E..46K Altcode:
We use local 3D convection calculations to compute the alpha-effect and
turbulent pumping of mean magnetic fields in the rapid rotation regime
corresponding to the deep layers of the solar convection zone. We find
that in this regime the alpha-effect responsible for generating the
poloidal field out of the toroidal one peaks at around latitude 30
degrees, in contrast to the slow rotation case and the often adopted
prescription in mean-field models of the solar dynamo, where the
maximum values are found at the poles. Furthermore, the turbulent
pumping of mean fields is predominantly down- and equatorward. We
find that the downward pumping is decreased near the equator for rapid
rotation and can be upward for the toroidal field component. In order
to investigate the implications of the obtained local results for the
problems in mean-field dynamo theory arising from the helioseismically
determined solar rotation profile, namely the poleward migration of
activity belts at low latitudes and the activity being concentrated at
too high latitudes, we introduce the alpha-effect and turbulent pumping
as they were found in the local calculations into a kinematic mean-field
model of the solar dynamo. We also investigate the effect of a one-cell
counter-clockwise meridional flow pattern on the dynamo solutions. We
find that using the alpha-effect and turbulent pumping adapted from
the results of the local calculations, the migration of the activity
belts is equatorward also at low latitudes. When the meridional flow is
added, the activity belts are shifted further closer to the equator,
and a poleward migration belt appears at high latitudes. With all the
effects included, the activity still appears at too high latitudes
(5...60 degrees). Other remaining problems include the somewhat too
short cycle periods for the solar-like dipole solutions.

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Title: Local models of stellar convection. III. The Strouhal number
Authors: Käpylä, P. J.; Korpi, M. J.; Ossendrijver, M.; Tuominen, I.
2006A&A...448..433K Altcode: 2004astro.ph.10586K
Aims.The Strouhal number (St), which is a nondimensional measure of the
correlation time, is determined from numerical models of convection. The
Strouhal number arises in the mean-field theories of angular momentum
transport and magnetic field generation, where its value determines
the validity of certain widely used approximations, such as the first
order smoothing (hereafter FOSA). More specifically, the relevant
transport coefficients can be calculated by means of a cumulative
series expansion if St &lt; Stcrit ≈ 1.Methods.We define
the Strouhal number as the ratio of the correlation and turnover times,
which we determine separately, the former from the autocorrelation of
velocity, and the latter by following test particles embedded in the
flow.Results.We find that the Strouhal numbers are, generally, of the
order of 0.1 to 0.4 which is close to the critical value above which
deviations from FOSA become significant. Increasing the rotational
influence tends to shorten both timescales in such a manner that St
decreases. However, we do not find a clear trend as a function of the
Rayleigh number for the parameter range explored in the present study.

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Title: Local numerical modelling of magnetoconvection and turbulence -
implications for mean-field theories
Authors: Käpylä, Petri J.
2006PhDT.......275K Altcode:
No abstract at ADS

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Title: Transport coefficients for solar and stellar dynamos
Authors: Ossendrijver, M.; Käpylä, P. J.
2006IAUS..233....3O Altcode:
The large-scale magnetic field of the Sun and solar-type stars is
probably generated near the interface of the radiative core and the
convection zone. One of the well-known difficulties of interface-type
and other dynamo models is to explain the latitudinal distribution
of magnetic fields as observed on the Sun. In this contribution new
results of numerical MHD simulations of transport coefficients of
magnetic fields in the rapid rotation regime, relevant for the base
of the solar convection zone, are presented that may contribute to
explaining the latitudinal distribution of magnetic fields observed on
the Sun. A brief outlook on further numerical simulations of transport
coefficients and their relevance for mean-field dynamo theory is given.

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Title: Connection between active longitudes and magnetic helicity
Authors: Brandenburg, A.; Käpylä, P. J.
2005astro.ph.12639B Altcode:
A two-dimensional mean field dynamo model is solved where magnetic
helicity conservation is fully included. The model has a negative
radial velocity gradient giving rise to equatorward migration of
magnetic activity patterns. In addition the model develops longitudinal
variability with activity patches travelling in longitude. These
patches may be associated with active longitudes.

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Title: Local models of stellar convection. II. Rotation dependence
of the mixing length relations
Authors: Käpylä, P. J.; Korpi, M. J.; Stix, M.; Tuominen, I.
2005A&A...438..403K Altcode: 2004astro.ph.10584K
We study the mixing length concept in comparison to three-dimensional
numerical calculations of convection with rotation. In a limited range,
the velocity and temperature fluctuations are linearly proportional
to the superadiabaticity, as predicted by the mixing length concept
and in accordance with published results. The effects of rotation
are investigated by varying the Coriolis number, Co = 2 Ω τ,
from zero to roughly ten, and by calculating models at different
latitudes. We find that α decreases monotonically as a function of
the Coriolis number. This can be explained by the decreased spatial
scale of convection and the diminished efficiency of the convective
energy transport, the latter of which leads to a large increase of the
superadibaticity, δ = nabla - nabla_ad as function of Co. Applying a
decreased mixing length parameter in a solar model yields very small
differences in comparison to the standard model within the convection
zone. The main difference is the reduction of the overshooting depth,
and thus the depth of the convection zone, when a non-local version
of the mixing length concept is used. Reduction of α by a factor of
roughly 2.5 is sufficient to reconcile the difference between the model
and helioseismic results. The numerical results indicate reduction of
α by this order of magnitude.

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Title: Reynolds stresses - dependence on latitude
Authors: Hupfer, C.; Käpylä, P.; Stix, M.
2005AN....326..223H Altcode:
We present some results of three-dimensional hydrodynamic simulations of
a compressible flow under the influence of rotation. The code implements
a three-layer (stably-unstably-stably stratified) rectangular box placed
at various latitudes in a convection zone of a star. We focus on the
Reynolds stresses Qij = &lt; u'i u'j
&gt; which in mean-field models have a crucial influence on angular
momentum transport and differential rotation. Especially we examine
the occurrence of a strong peak of Qθφ at low latitude
very close to the equator, which may have implications to the theory
of the angular velocity profile observed on the Sun.

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Title: Estimates of the Strouhal number from numerical models of
convection
Authors: Käpylä, P. J.; Korpi, M. J.; Ossendrijver, M.; Tuominen, I.
2005AN....326..186K Altcode: 2004astro.ph.10587K
We determine the Strouhal number (hereafter St), which is essentially
a nondimensional measure of the correlation time, from numerical
calculations of convection. We use two independent methods to estimate
St. Firstly, we apply the minimal tau-approximation (MTA) on the
equation of the time derivative of the Reynolds stress. A relaxation
time is obtained from which St can be estimated by normalising with
a typical turnover time. Secondly, we calculate the correlation and
turnover times separately, the former from the autocorrelation of
velocity and the latter by following test particles embedded in the
flow. We find that the Strouhal number is in general of the order of
0.1 to 1, i.e. rather large in comparison to the typical assumption
in the mean-field theories that St ≪ 1. However, there is a clear
decreasing trend as function of the Rayleigh number and increasing
rotation. Furthermore, for the present range of parameters the decrease
of St does not show signs of saturation, indicating that in stellar
convection zones, where the Rayleigh numbers are much larger, the
Strouhal number may indeed be significantly smaller.

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Title: The problem of small and large scale fields in the solar dynamo
Authors: Brandenburg, A.; Haugen, N. E. L.; Käpylä, P. J.; Sandin, C.
2005AN....326..174B Altcode: 2004astro.ph.12364B
Three closely related stumbling blocks of solar mean field dynamo
theory are discussed: how dominant are the small scale fields,
how is the alpha effect quenched, and whether magnetic and current
helicity fluxes alleviate the quenching? It is shown that even at the
largest currently available resolution there is no clear evidence
of power law scaling of the magnetic and kinetic energy spectra in
turbulence. However, using subgrid scale modeling, some indications
of asymptotic equipartition can be found. The frequently used first
order smoothing approach to calculate the alpha effect and other
transport coefficients is contrasted with the superior minimal tau
approximation. The possibility of catastrophic alpha quenching is
discussed as a result of magnetic helicity conservation. Magnetic and
current helicity fluxes are shown to alleviate catastrophic quenching
in the presence of shear. Evidence for strong large scale dynamo action,
even in the absence of helicity in the forcing, is presented.

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Title: Local models of stellar convection:. Reynolds stresses and
turbulent heat transport
Authors: Käpylä, P. J.; Korpi, M. J.; Tuominen, I.
2004A&A...422..793K Altcode: 2003astro.ph.12376K
We study stellar convection using a local three-dimensional MHD model,
with which we investigate the influence of rotation and large-scale
magnetic fields on the turbulent momentum and heat transport and their
role in generating large-scale flows in stellar convection zones. The
former is studied by computing the turbulent velocity correlations,
known as Reynolds stresses, the latter by calculating the correlation of
velocity and temperature fluctuations, both as functions of rotation
and latitude. We find that the horizontal correlation, Qθ
φ, capable of generating horizontal differential rotation,
attains significant values and is mostly negative in the southern
hemisphere for Coriolis numbers exceeding unity, corresponding
to equatorward flux of angular momentum. This result is also in
accordance with solar observations. The radial component Qr
φ is negative for slow and intermediate rotation indicating
inward transport of angular momentum, while for rapid rotation, the
transport occurs outwards. Parametrisation in terms of the mean-field
Λ-effect shows qualitative agreement with the turbulence model of
Kichatinov &amp; Rüdiger (\cite{KiRu93}) for the horizontal part H ∝
(Qθ φ)/(cos θ), whereas for the vertical Λ-effect, V ∝
(Qr φ/(sin θ), agreement only for intermediate rotation
exists. The Λ-coefficients become suppressed in the limit of rapid
rotation, this rotational quenching being stronger and occurring
with slower rotation for the V component than for H. We have also
studied the behaviour of the Reynolds stresses under the influence of
a large-scale azimuthal magnetic field of varying strength. We find
that the stresses are enhanced by the presence of the magnetic field
for field strengths up to and above the equipartition value, without
significant quenching. Concerning the turbulent heat transport, our
calculations show that the transport in the radial direction is most
efficient at the equatorial regions, obtains a minimum at midlatitudes,
and shows a slight increase towards the poles. The latitudinal heat
transport does not show a systematic trend as a function of latitude
or rotation.

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Title: Non-Fickian diffusion and tau approximation from numerical
turbulence
Authors: Brandenburg, Axel; Käpylä, Petri J.; Mohammed, Amjed
2004PhFl...16.1020B Altcode: 2003astro.ph..6521B
Evidence for non-Fickian diffusion of a passive scalar is presented
using direct simulations of homogeneous isotropic turbulence. The
results compare favorably with an explicitly time-dependent closure
model based on the tau approximation. In the numerical experiments
three different cases are considered: (i) zero mean concentration
with finite initial concentration flux, (ii) an initial top hat
profile for the concentration, and (iii) an imposed background
concentration gradient. All cases agree in the resulting relaxation
time in the tau approximation relating the triple correlation to the
concentration flux. The first order smoothing approximation is shown
to be inapplicable.

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Title: Helical coronal ejections and their role in the solar cycle
Authors: Brandenburg, Axel; Sandin, Christer; Käpylä, Petri J.
2004IAUS..223...57B Altcode: 2005IAUS..223...57B; 2004astro.ph..7598B
The standard theory of the solar cycle in terms of an alpha-Omega dynamo
hinges on a proper understanding of the nonlinear alpha effect. Boundary
conditions play a surprisingly important role in determining the
magnitude of alpha. For closed boundaries, the total magnetic helicity
is conserved, and since the alpha effect produces magnetic helicity
of one sign in the large scale field, it must simultaneously produce
magnetic helicity of the opposite sign. It is this secondary magnetic
helicity that suppresses the dynamo in a potentially catastrophic
fashion. Open boundaries allow magnetic helicity to be lost. Simulations
are presented that allow an estimate of alpha in the presence of open
or closed boundaries, either with or without solar-like differential
rotation. In all cases the sign of the magnetic helicity agrees with
that observed at the solar surface (negative in the north, positive
in the south), where significant amounts of magnetic helicity can be
ejected via coronal mass ejections. It is shown that open boundaries
tend to alleviate catastrophic alpha quenching. The importance of
looking at current helicity instead of magnetic helicity is emphasized
and the conceptual advantages are discussed.

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Title: What can we learn from Local Convection Simulations in the
Context of mean Field Models of Stellar Rotation and Magnetism?
Authors: Käpylä, Petri J.; Korpi, Maarit J.; Ossendrijver, Mathieu;
Stix, Michael
2003ANS...324...63K Altcode: 2003ANS...324..I02K
No abstract at ADS

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Title: Numerical study of the magnetorotational instability in
weakly magnetised accretion disks: Resolution dependence of the
Shakura-Sunyaev alpha
Authors: Kapyla, P. J.; Korpi, M. J.
2001astro.ph.11554K Altcode:
In this letter, we present numerical calculations made to investigate
the possible resolution dependence of the Shakura &amp; Sunyaev (1973)
viscosity parameter alpha from local magnetohydrodynamic simulations
of the magnetorotational instability (MRI). We find that the values of
alpha do indeed depend significantly on the numerical resolution but
also that when the highest resolutions attainable by the computational
resources available are used, the growth of the alpha-parameter seems
to saturate. The values of alpha are at most of the order of 10^(-3),
which indicates that the sole presence of turbulence due to dynamo
generated magnetic field in the disk is not enough to reproduce alphas
of the order unity which could explain some observational results
(e.g. Cannizzo 1993).