Author name code: toomre ADS astronomy entries on 2022-09-14 author:"Toomre, Juri" ------------------------------------------------------------------------ Title: Confinement of the Solar Tachocline by Dynamo Action in the Radiative Interior Authors: Matilsky, Loren I.; Hindman, Bradley W.; Featherstone, Nicholas A.; Blume, Catherine C.; Toomre, Juri Bibcode: 2022arXiv220612920M Altcode: A major outstanding problem in solar physics is the confinement of the solar tachocline, the thin shear layer that separates nearly solid-body rotation in the radiative interior from strong differential rotation in the convection zone. Here, we present the first 3-D, global solar simulation in which a tachocline is confined by a self-excited dynamo. The non-axisymmetric magnetism is initially built in the convection zone and then diffusively imprints downward. Additionally, the field is locally amplified throughout the radiative interior by vigorous horizontal motions that arise from equatorial Rossby waves and possibly shear instabilities. Our work thus challenges the long-held notion that the Sun's dynamo magnetic field is amplified only as deep as the tachocline and stored in a quiescent radiative interior. Title: Longitudinally Modulated Dynamo Action in Simulated M-dwarf Stars Authors: Bice, Connor P.; Toomre, Juri Bibcode: 2022ApJ...928...51B Altcode: 2022arXiv220202869B M-dwarf stars are well known for the intense magnetic activity that many of them exhibit. In cool stars with near-surface convection zones, this magnetic activity is thought to be driven largely by the interplay of convection and the large-scale differential rotation and circulations it establishes. The highly nonlinear nature of these flows yields a fascinatingly sensitive and diverse parameter space, with a wide range of possible dynamics. We report here on a set of three global MHD simulations of rapidly rotating M2 (0.4 M ) stars. Each of these three models established nests of vigorous convection that were highly modulated in longitude at low latitudes. Slight differences in their magnetic parameters led each model to disparate dynamo states, but the effect of the convective nest was a unifying feature. In each case, the action of longitudinally modulated convection led to localized (and in one case, global) reversals of the toroidal magnetic field, as well as the formation of an active longitude, with enhanced poloidal field amplitudes and flux emergence. Title: Powering Stellar Magnetism: Energy Transfers in Cyclic Dynamos of Sun-like Stars Authors: Brun, Allan Sacha; Strugarek, Antoine; Noraz, Quentin; Perri, Barbara; Varela, Jacobo; Augustson, Kyle; Charbonneau, Paul; Toomre, Juri Bibcode: 2022ApJ...926...21B Altcode: 2022arXiv220113218B We use the anelastic spherical harmonic code to model the convective dynamo of solar-type stars. Based on a series of 15 3D MHD simulations spanning four bins in rotation and mass, we show what mechanisms are at work in these stellar dynamos with and without magnetic cycles and how global stellar parameters affect the outcome. We also derive scaling laws for the differential rotation and magnetic field based on these simulations. We find a weaker trend between differential rotation and stellar rotation rate, ( ${\rm{\Delta }}{\rm{\Omega }}\propto {(| {\rm{\Omega }}| /{{\rm{\Omega }}}_{\odot })}^{0.46}$ ) in the MHD solutions than in their HD counterpart ${\left(| {\rm{\Omega }}| /{{\rm{\Omega }}}_{\odot }\right)}^{0.66}$ ), yielding a better agreement with the observational trends based on power laws. We find that for a fluid Rossby number between 0.15 ≲ Ro f ≲ 0.65, the solutions possess long magnetic cycle, if Ro f ≲ 0.42 a short cycle and if Ro f ≳ 1 (antisolar-like differential rotation), a statistically steady state. We show that short-cycle dynamos follow the classical Parker-Yoshimura rule whereas the long-cycle period ones do not. We also find efficient energy transfer between reservoirs, leading to the conversion of several percent of the star's luminosity into magnetic energy that could provide enough free energy to sustain intense eruptive behavior at the star's surface. We further demonstrate that the Rossby number dependency of the large-scale surface magnetic field in the simulation ( ${B}_{{\rm{L}},\mathrm{surf}}\sim {{Ro}}_{{\rm{f}}}^{-1.26}$ ) agrees better with observations ( ${B}_{V}\sim {{Ro}}_{{\rm{s}}}^{-1.4\pm 0.1}$ ) and differs from dynamo scaling based on the global magnetic energy ( ${B}_{\mathrm{bulk}}\sim {{Ro}}_{{\rm{f}}}^{-0.5}$ ). Title: Global Confinement Of The Solar Tachocline By A Convective Dynamo Authors: Matilsky, L.; Hindman, B.; Toomre, J. Bibcode: 2021AAS...23830401M Altcode: After more than thirty years, the most striking feature of the internal rotation profile of the Sun as revealed by helioseismology­—the tachocline of shear at the base of the convection zone (CZ)—remains poorly understood. Here we present rotating, 3D, spherical-shell simulations of a CZ overlying a stable radiative zone (RZ) that confine the tachocline against inward diffusive spreading via a convective dynamo. In particular, the viscous imprinting of the differential rotation from the CZ onto the RZ is prevented by the non-axisymmetric Lorentz torque, producing a tachocline-like shear layer at all latitudes. The balance remains stable on centuries-long timescales and overall resembles a more complex (non-axisymmetric) version of Ferraro's Law of Isorotation, in which isorotation contours are forced to fall along poloidal magnetic field lines. These results add an unexpected path toward solving the tachocline confinement problem. Namely, a dynamo operating mostly in the CZ (and notably in the absence of a primordial magnetic field confined beneath the tachocline in the RZ, as suggested in Gough and McIntyre 1998) can by itself stop the inward burrowing of the differential rotation. Title: Neural network to analyze rising magnetic flux ropes in M-dwarf stellar convective dynamo simulations Authors: Bice, C. P.; Toomre, J. Bibcode: 2021AAS...23820805B Altcode: Despite the central role that rising magnetic flux ropes are thought to play in the formation of active regions on the surfaces of the Sun and other stars, global MHD simulations of stellar interiors have struggled to self-consistently capture their dynamics. By their nature, these structures tend to be short-lived or wholly absent in all but the most turbulent high-resolution convective dynamo simulations — environments which make their hand-identification and study prohibitively time-consuming. We present here an analysis of hundreds of self-consistent, rising flux ropes identified autonomously in global simulations of M-dwarf convective dynamos with the help of a novel machine-learning pipeline developed for the task. We report on the details of the neural network models employed, as well as the variation of flux rope formation rates, locations, and trajectories across differing stellar parameters. Title: Building and Maintaining a Solar Tachocline through Convective Dynamo Action Authors: Matilsky, Loren I.; Toomre, Juri Bibcode: 2021arXiv210505412M Altcode: For more than thirty years, the dynamical maintenance of the thin solar tachocline has remained one of the central outstanding problems of stellar astrophysics. Three main theories have been developed to explain the tachocline's thinness, but so far none of them has been shown to work convincingly in the extreme parameter regime of the solar interior. Here, we present a rotating, 3D, spherical-shell simulation of a combined solar-like convection zone and radiative zone that achieves a tachocline built and maintained by convective dynamo action. Because of numerical constraints, the dynamo prevents the viscous spread of the tachocline instead of the Eddington-Sweet-time-scale radiative spread believed to occur in the Sun. Nonetheless, our simulation supports the scenario of tachocline confinement via the cyclic solar dynamo, and is the first time one of the main confinement scenarios has been realized in a global, 3D, spherical-shell geometry including nonlinear fluid motions and a self-consistently generated dynamo. Title: Machine Learning analysis of self-consistent magnetic flux ropes realized in M-dwarf dynamo simulations Authors: Bice, Connor P.; Toomre, Juri Bibcode: 2021csss.confE.300B Altcode: The dynamical origins of the intense magnetic activity exhibited by most M-dwarf stars remains an unanswered question in stellar astrophysics. Despite the central role magnetic flux ropes are thought to play in the formation of sun and star spots, global MHD simulations of stellar interiors have historically struggled to self-consistently capture their dynamics. By their nature, these structures tend to be short-lived or wholly absent in all but the most turbulent high-resolution simulations -- environments which make their hand-identification and study prohibitively time-consuming. We present here a novel machine learning approach for the identification and dynamical analysis of the hundreds of self-consistent, rising flux ropes in our simulations of M-dwarf interiors. We report on the details of the models developed, as well as the prospects for their continued use with not only our own simulations, but those of the entire stellar convection community. Title: Machine Learning Analysis of Self-Consistent Magnetic Flux Ropes Realized In M-Dwarf Dynamo Simulations Authors: Bice, Connor; Toomre, Juri Bibcode: 2021csss.confE.327B Altcode: The dynamical origins of the intense magnetic activity exhibited by most M-dwarf stars must be tied to their internal convective dynamos, and yet there remain many unanswered questions concerning its details. Despite the central role magnetic flux ropes are thought to play in the formation of solar and stellar starspots, global MHD simulations of stellar interiors have historically struggled to self-consistently capture their dynamics. By their nature, these structures tend to be short-lived or wholly absent in all but the most turbulent high-resolution simulations -- environments which make their hand-identification and study prohibitively time-consuming. We present here a novel machine-learning pipeline for the autonomous identification and analysis of self-consistent, rising flux ropes found in our global 3D MHD simulations of M-dwarf convective interiors. We report on the details of the models developed, as well as early results from the project and its prospects moving forward. Title: Building and maintaining a solar tachocline through convective dynamo action Authors: Matilsky, Loren Isaac; Toomre, Juri Bibcode: 2021csss.confE.331M Altcode: For more than thirty years, the dynamical maintenance of the thin solar tachocline has remained one of the central outstanding problems of stellar astrophysics. Three main theories have been developed to explain the tachocline's thinness, but so far none of them has been shown to work convincingly in the extreme parameter regime of the solar interior. Here, we present a rotating, 3D, spherical-shell simulation of a combined solar-like convection zone and radiative zone that achieves a tachocline built and maintained by convective dynamo action. Because of numerical constraints, the dynamo prevents the viscous spread of the tachocline instead of the Eddington-Sweet-time-scale radiative spread believed to occur in the Sun. Nonetheless, our simulation supports the scenario of tachocline confinement via the cyclic solar dynamo, and is the first time one of the main confinement scenarios has been realized in a global, 3D, spherical-shell geometry including nonlinear fluid motions and a self-consistently generated dynamo. Title: Revisiting the Sun's Strong Differential Rotation along Radial Lines Authors: Matilsky, Loren I.; Hindman, Bradley W.; Toomre, Juri Bibcode: 2020ApJ...898..111M Altcode: 2020arXiv200400208M Current state-of-the-art models of the solar convection zone consist of solutions to the Navier-Stokes equations in rotating, 3D spherical shells. Such models are highly sensitive to the choice of boundary conditions. Here we present two suites of simulations differing only in their outer thermal boundary condition, which is either one of fixed entropy (FE) or fixed flux (FF; corresponding to a fixed gradient in the entropy). We find that the resulting differential rotation is markedly different between the two sets. The FF simulations have strong differential rotation contrast and isocontours tilted along radial lines (in good agreement with the Sun's interior rotation revealed by helioseismology), whereas the FE simulations have weaker contrast and contours tilted in the opposite sense. We examine in detail the force balances in our models and find that the poleward transport of heat by Busse columns drives a thermal wind responsible for the different rotation profiles. We conclude that the Sun's strong differential rotation along radial lines may result from the solar emissivity being invariant with latitude (which is similar to the FF condition in our models) and the poleward transport of heat by Busse columns. In future work on convection in the solar context, we strongly advise modelers to use an FF outer boundary condition. Title: Exploring Bistability in the Cycles of the Solar Dynamo through Global Simulations Authors: Matilsky, Loren I.; Toomre, Juri Bibcode: 2020ApJ...892..106M Altcode: 2019arXiv191208158M The calling card of solar magnetism is the sunspot cycle, during which sunspots regularly reverse their polarity sense every 11 yr. However, a number of more complicated time-dependent behaviors have also been identified. In particular, there are temporal modulations associated with active longitudes and hemispheric asymmetry, when sunspots appear at certain solar longitudes or else in one hemisphere preferentially. So far, a direct link between this asymmetric temporal behavior and the underlying solar dynamo has remained elusive. In this work, we present results from global 3D magnetohydrodynamic simulations, which display both behavior reminiscent of the sunspot cycle (regular polarity reversals and equatorward migration of internal magnetic field) and asymmetric, irregular behavior which we interpret as active longitudes and hemispheric asymmetry in the simulations. The simulations are thus bistable, in that the turbulent convection can stably support two distinct flavors of magnetism at different times, in superposition or with smooth transitions from one state to the other. We discuss this new family of dynamo models in the context of the extensive observations of the Sun's surface magnetic field with the Solar and Heliospheric Observatory and the Solar Dynamics Observatory, as well as earlier observations of sunspot number and synoptic maps. We suggest that the solar dynamo itself may be bistable in nature, exhibiting two types of temporal behavior in the magnetic field. Title: Probing the Influence of a Tachocline in Simulated M-dwarf Dynamos Authors: Bice, C. P.; Toomre, J. Bibcode: 2020ApJ...893..107B Altcode: 2020arXiv200105555B M-type stars are among the best candidates in searches for habitable Earth-like exoplanets, and yet many M-dwarfs exhibit extraordinary flaring that would bombard otherwise habitable planets with ionizing radiation. Observers have found that the fraction of M-stars demonstrating significant activity transitions from roughly 10% for main-sequence stars more massive than 0.35 M to nearly 90% for less massive stars. The latter are typically rotating quite rapidly, suggesting differing spin-down histories. It is also below 0.35 M when main-sequence stars become fully convective and may no longer contain a tachocline. We turn here to the more massive M-stars to study the impact such a layer may have on their internal dynamics. Using the global MHD code Rayleigh, we compare the properties of convective dynamos generated within rapidly rotating 0.4 M stars, with the computational domain either terminating at the base of the convection zone or permitting overshoot into the underlying stable region. We find that a tachocline is not necessary for the organization of strong toroidal wreaths of magnetism in these stars, though it can increase the coupling of mean field amplitudes to the stellar rotation rate. Additionally, we note that the presence of a tachocline tends to make magnetic cycles more regular than they would otherwise have been, and can permit alternative field configurations with much longer cycles. Finally, we find that the tachocline helps enhance the emergent fields and organize them into larger spatial scales, providing favorable conditions for more rapid spin-down via the stellar wind. Title: Dynamo States with Strikingly Different Symmetries Coexisting in Global Solar Simulations Authors: Matilsky, Loren I.; Toomre, Juri Bibcode: 2020ASSP...57..197M Altcode: We present new global 3D MHD simulations of the solar convection zone that exhibit two distinct states of the dynamo coexisting simultaneously. We discuss our results in terms of the solar active longitudes and hemispheric asymmetry. Title: Touching the Interior Structure and Dynamics of Our Nearest Star Authors: Toomre, Juri Bibcode: 2020ASSP...57...37T Altcode: Michael Thompson has had a pivotal and continuing role in developing and refining inversion techniques to be applied to the great blossoming of helioseismic data forthcoming from the GONG, MDI (on SOHO) and HMI (on SDO) observational projects. This has enabled major discoveries about the internal differential rotation of the Sun, revealing both a tachocline of shear at the base of its convection zone and a near-surface shear layer near its surface, and of its temporal variations. It has also guided efforts to map subsurface flows of many scales in the convection zone. In parallel with his abiding interests in helioseismology, Michael was very enthusiastic about recent efforts in solar convection and dynamo theory to address what he saw as the outstanding questions about the dynamics proceeding deep within our nearest star, and thus we touch briefly upon some of these here. Title: Exploring the Origins of Intense Magnetism in Early M-Dwarf Stars Authors: Bice, Connor; Toomre, Juri Bibcode: 2020ASSP...57..285B Altcode: We present the results of new global 3D MHD simulations of early M-Dwarf stars, exploring the influence that a tachocline of shear has on their instantaneous and long-term magnetic activity. Title: Probing the Origins of Intense Magnetism in Early M-Dwarf Stars Authors: Bice, Connor; Toomre, Juri Bibcode: 2019AAS...23412203B Altcode: M-type stars are quickly stepping into the forefront as some of the best candidates in searches for habitable Earth-like exoplanets, and yet many M-dwarfs exhibit extraordinary flaring events which would bombard otherwise habitable planets with ionizing radiation. In recent years, observers have found that the fraction of M-stars demonstrating significant magnetic activity transitions sharply from roughly 10% for main-sequence stars earlier (more massive) than spectral type M3.5 (0.35 M) to nearly 90% for stars later than M3.5. Stellar dynamos are are driven primarily by fluid motions in the convection zone, the base of which migrates inward with decreasing stellar mass. Suggestively, it is also later than M3.5 at which main-sequence stars become fully convective, and may no longer contain a tachocline. This layer of rotational shear separating the convection and radiative zones is thought to play a significant role in solar magnetism, and so we here investigate its influence on M-dwarf dynamos. Using the spherical 3D MHD simulation code Rayleigh, we compare the convective flows, magnetic field configurations and generation, and time dependencies of dynamos operating within quickly rotating M2 (0.4 M) stars spanning a range of rotation rates and diffusivities, with the computational domain either terminating at the base of the convection zone or permitting overshoot into the underlying stable region. We find that a tachocline is not necessary for the organization of strong (10-20 kG) toroidal wreaths of magnetism in these stars, though its presence can increase the coupling of mean field amplitudes to the stellar rotation rate and in some cases drastically alter the character of the fields produced. Additionally, in stars that undergo periodic magnetic cycles, we find that the presence of a tachocline makes these cycles both longer and more regular than they would have otherwise been. Finally, we find that the tachocline helps to enhance the surface poloidal fields and organize them into larger spatial scales, both of which provide favorable conditions for more rapid angular momentum loss through a magnetized stellar wind. Title: The Relationship Between Differential Rotation and Constant Effective Temperature in the Sun Authors: Matilsky, Loren; Hindman, Bradley W.; Toomre, Juri Bibcode: 2019AAS...23431806M Altcode: Helioseismology has shown that the rotation rate of the solar interior is constant along radial lines (conical rotation contours) and has a mostly uniform gradient from equator to pole, facts which are still not completely understood. Conical rotation contours and uniform rotation gradients have been reproduced in previous global, 3D, hydrodynamic simulations of the solar convective envelope by imposing a small temperature gradient at the base of the convective layer, consistent with thermal wind balance in the tachocline. Here we show that similar results can be obtained in global simulations by demanding that the conductive flux through the outer boundary of the convective layer (corresponding physically to the solar effective temperature) be constant with latitude. For the Sun, this is in line with observations that show no significant dependence of the effective temperature with latitude. By contrast, if instead the entropy at the outer boundary is fixed (keeping all other simulation parameters constant), the outward conductive flux is allowed to vary with latitude and a markedly different rotation profile emerges, namely one that has cylindrical contours and strong rotation gradients confined mainly to low latitudes. We discuss in detail how the outer boundary condition on the entropy (fixed flux vs. fixed entropy) affects the dynamics responsible for the differential rotation achieved in our simulations. Title: Exploring the Coexistence of Two Distinct Dynamo States in the Sun through Global Simulations Authors: Matilsky, Loren; Toomre, Juri Bibcode: 2019AAS...23431803M Altcode: The origin of the Sun's magnetism remains one of the most pressing outstanding problems in solar physics. The number of sunspots (eruptions of magnetic flux through the photosphere) rises and falls over a regular 11-year cycle. Within each cycle, the sunspots emerge at mid-latitudes near solar maximum and then closer to the equator as the cycle progresses. Furthermore, the polarity sense of sunspot pairs is opposite in the Northern hemisphere compared to the Southern hemisphere, and this polarity sense flips from one 11-year cycle to the next. Recently, 3D, global, MHD dynamo simulations have made substantial contact with observations, yielding regular cycling, polarity reversals, and in a few cases, equatorward propagation of interior magnetic field. Here we present a new class of 3D, global simulations of a solar convection zone that remarkably achieve two distinct states of the dynamo coexisting simultaneously. One state consists of two opposite-polarity reservoirs of magnetism in each hemisphere that cycle, flip polarity, and exhibit equatorward propagation, in remarkable agreement with the observed solar cycle. Superimposed is another state, asymmetric about the equator, that consists of one reservoir of strong toroidal field in a single hemisphere that flips polarity and migrates poleward with the cycle, in agreement with many other dynamo simulations. We describe theoretically how our simulated dynamos might be achieved and whether such processes could be at work in the solar dynamo. We also investigate the possible observable signatures of two distinct dynamo states if they were present in the solar interior. Title: Some travels in the land of nonlinear convection and magnetism Authors: Toomre, J. Bibcode: 2019EAS....82..273T Altcode: Rotating stars with convection zones are the great builders of magnetism in our universe. Seeking to understand how turbulent convection actually operates, and so too the dynamo action that it can achieve, has advanced through distinctive stages in which Jean-Paul Zahn was often a central player, or joined by his former students. Some of the opening steps in dealing with the basic nonlinearity in such dynamics involved modal equations (with specified horizontal structure) to study convective amplitudes and heat transports achieved as solutions equilibrated by feeding back on the mean stratification. These dealt in turn with laboratory convection, with penetrative convection in Boussinesq settings, then with compressible penetration via anelastic equations in simple geometries, and finally with stellar penetrative convection in A-type stars that coupled two convection zones. Advances in computation power allowed 2-D fully compressible simulations, and then 3-D modeling including rotation, to revisit some of these convection and penetration settings within planar layers. With externally imposed magnetic fields threading the 2-D layers, magnetoconvection could then be studied to see how the flows concentrated the fields into complex sheets, or how new classes of traveling waves could result. The era of considering turbulent convection in rotating spherical shells had also arrived, using 3-D MHD codes such as ASH to evaluate how the solar differential rotation is achieved and maintained. Similarly the manner in which global magnetic fields could be built by dynamo action within the solar convection zone took center stage, finding that coherent wreaths of strong magnetism could be built, and also cycling solutions with field reversals. The coupling of convection and magnetism continues as a vibrant research subject. It is also clear that stars like the Sun do not give up their dynamical mysteries readily when highly turbulent systems are at play. Title: Rossby and Magnetic Prandtl Number Scaling of Stellar Dynamos Authors: Augustson, K. C.; Brun, A. S.; Toomre, J. Bibcode: 2019ApJ...876...83A Altcode: Rotational scaling relationships are examined for the degree of equipartition between magnetic and kinetic energies in stellar convection zones. These scaling relationships are approached from two paradigms, with first a glance at scaling relationship built on an energy-balance argument and second a look at a force-based scaling. The latter implies a transition between a nearly constant inertial scaling when in the asymptotic limit of minimal diffusion and magnetostrophy, whereas the former implies a weaker scaling with convective Rossby number. Both scaling relationships are then compared to a suite of 3D convective dynamo simulations with a wide variety of domain geometries, stratifications, and range of convective Rossby numbers. Title: Rossby and Magnetic Prandtl Number Scaling of Stellar Dynamos Authors: ~C. Augustson, K.; ~S. Brun, A.; Toomre, J. Bibcode: 2019arXiv190400225C Altcode: Rotational scaling relationships are examined for the degree of equipartition between magnetic and kinetic energies in stellar convection zones. These scaling relationships are approached from two paradigms, with first a glance at scaling relationship built upon an energy-balance argument and second a look at a force-based scaling. The latter implies a transition between a nearly-constant inertial scaling when in the asymptotic limit of minimal diffusion and magnetostrophy, whereas the former implies a weaker scaling with convective Rossby number. Both scaling relationships are then compared to a suite of 3D convective dynamo simulations with a wide variety of domain geometries, stratifications, and range of convective Rossby numbers. Title: The Role of Downflows in Establishing Solar Near-surface Shear Authors: Matilsky, Loren I.; Hindman, Bradley W.; Toomre, Juri Bibcode: 2019ApJ...871..217M Altcode: 2018arXiv181000115M The dynamical origins of the Sun’s tachocline and near-surface shear layer (NSSL) are still not well understood. We have attempted to self-consistently reproduce an NSSL in numerical simulations of a solar-like convection zone by increasing the density contrast across rotating 3D spherical shells. We explore the hypothesis that high density contrast leads to near-surface shear by creating a rotationally unconstrained layer of fast flows near the outer surface. Although our high-contrast models do have near-surface shear, it is confined primarily to low latitudes (between ±15°). Two distinct types of flow structures maintain the shear dynamically: rotationally constrained Busse columns aligned with the rotation axis and fast, rotationally unconstrained downflow plumes that deplete angular momentum from the outer fluid layers. The plumes form at all latitudes and, in fact, are more efficient at transporting angular momentum inward at high latitudes. The presence of Busse columns at low latitudes thus appears essential to creating near-surface shear in our models. We conclude that a solar-like NSSL is unobtainable from a rotationally unconstrained outer fluid layer alone. In numerical models, the shear is eliminated through the advection of angular momentum by the meridional circulation. Therefore, a detailed understanding of how the solar meridional circulation is dynamically achieved will be necessary to elucidate the origin of the Sun’s NSSL. Title: Exploring the Role of a Tachocline in M-Dwarf Magnetism Authors: Bice, Connor; Toomre, Juri Bibcode: 2018csss.confE..27B Altcode: 2018arXiv180902238B M-type stars are quickly stepping into the forefront as some of the best candidates in searches for habitable Earth-like exoplanets, and yet many M-dwarfs exhibit extraordinary flaring events which would bombard otherwise habitable planets with ionizing radiation. In recent years, observers have found that the fraction of M-stars demonstrating significant magnetic activity transitions sharply from roughly 10% for main-sequence stars earlier (more massive) than spectral type M3.5 (0.35 M_⊙) to nearly 90% for stars later than M3.5. Suggestively, it is also later than M3.5 at which main-sequence stars become fully convective, and may no longer contain a tachocline. Using the spherical 3D MHD simulation code Rayleigh, we compare the peak field strengths, topologies, and time dependencies of convective dynamos generated within a quickly rotating (2 Omega_⊙) M2 (0.4 M_⊙) star, with the computational domain either terminating at the base of the convection zone or including the tachocline. We find that while both models generate strong (∼10kG), wreathlike toroidal fields exhibiting polarity reversals, the tachocline model provided a further reservoir for the toroidal field, which slowed the average reversal period from 100 rotations to more than 220 rotations and increased the spectral power of the low-order modes of the near-surface radial field by a factor of 4. Title: Exploring the Influence of Density Contrast on Solar Near-Surface Shear Authors: Matilsky, Loren I.; Hindman, Bradley W.; Toomre, Juri Bibcode: 2018csss.confE..49M Altcode: 2018arXiv181100665M The advent of helioseismology has determined in detail the average rotation rate of the Sun as a function of radius and latitude. These data immediately reveal two striking boundary layers of shear in the solar convection zone (CZ): a tachocline at the base, where the differential rotation of the CZ transitions to solid-body rotation in the radiative zone, and a 35-Mm-thick near-surface shear layer (NSSL) at the top, where the rotation rate slows by about 5% with increasing radius. Though asteroseismology cannot probe the differential rotation of distant stars to the same level of detail that helioseismology can achieve for the Sun, it is possible that many cool stars with outer convective envelopes possess similar differential rotation characteristics, including both a tachocline and a NSSL. Here we present the results of 3D global hydrodynamic simulations of spherical-shell convection for a Sun-like star at different levels of density contrast across the shell. The simulations with high stratification possess characteristics of near-surface shear, especially at low latitudes. We discuss in detail the dynamical balance of torques giving rise to the NSSL in our models and interpret what these balances imply for the real Sun. We further discuss the dynamical causes that may serve to wipe out near-surface shear at high latitudes, and conclude by offering some theories as to how this problem might be tackled in future work. Title: Driving Solar Giant Cells through the Self-organization of Near-surface Plumes Authors: Nelson, Nicholas J.; Featherstone, Nicholas A.; Miesch, Mark S.; Toomre, Juri Bibcode: 2018ApJ...859..117N Altcode: 2018arXiv180401166N Global 3D simulations of solar giant-cell convection have provided significant insight into the processes which yield the Sun’s observed differential rotation and cyclic dynamo action. However, as we move to higher-resolution simulations a variety of codes have encountered what has been termed the convection conundrum. As these simulations increase in resolution and hence the level of turbulence achieved, they tend to produce weak or even anti-solar differential rotation patterns associated with a weak rotational influence (high Rossby number) due to large convective velocities. One potential culprit for this convection conundrum is the upper boundary condition applied in most simulations, which is generally impenetrable. Here we present an alternative stochastic plume boundary condition which imposes small-scale convective plumes designed to mimic near-surface convective downflows, thus allowing convection to carry the majority of the outward solar energy flux up to and through our simulated upper boundary. The use of a plume boundary condition leads to significant changes in the convective driving realized in the simulated domain and thus to the convective energy transport, the dominant scale of the convective enthalpy flux, and the relative strength of the strongest downflows, the downflow network, and the convective upflows. These changes are present even far from the upper boundary layer. Additionally, we demonstrate that, in spite of significant changes, giant cell morphology in the convective patterns is still achieved with self-organization of the imposed boundary plumes into downflow lanes, cellular patterns, and even rotationally aligned banana cells in equatorial regions. This plume boundary presents an alternative pathway for 3D global convection simulations where driving is non-local and may provide a new approach toward addressing the convection conundrum. Title: The Role of Rotation in Convective Heat Transport: an Application to Low-Mass Stars Authors: Matilsky, Loren; Hindman, Bradley W.; Toomre, Juri; Featherstone, Nicholas Bibcode: 2018AAS...23230603M Altcode: It is often supposed that the convection zones (CZs) of low-mass stars are purely adiabatically stratified. This is thought to be because convective motions are extremely efficient at homogenizing entropy within the CZ. For a purely adiabatic fluid layer, only very small temperature variations are required to drive convection, making the amplitude and overall character of the convection highly sensitive to the degree of adiabaticity established in the CZ. The presence of rotation, however, fundamentally changes the dynamics of the CZ; the strong downflow plumes that are required to homogenize entropy are unable to penetrate through the entire fluid layer if they are deflected too soon by the Coriolis force. This talk discusses 3D global models of spherical-shell convection subject to different rotation rates. The simulation results emphasize the possibility that for stars with a high enough rotation rate, large fractions of their CZs are not in fact adiabatically stratified; rather, there is a finite superadiabatic gradient that varies in magnitude with radius, being at a minimum in the CZ’s middle layers. Two consequences of the varying superadiabatic gradient are that the convective amplitudes at the largest length scales are effectively suppressed and that there is a strong latitudinal temperature gradient from a cold equator to a hot pole, which self-consistently drives a thermal wind. A connection is naturally drawn to the Sun’s CZ, which has supergranulation as an upper limit to its convective length scales and isorotational contours along radial lines, which can be explained by the presence of a thermal wind. Title: Dynamo Scaling Relationships Authors: Augustson, Kyle; Mathis, Stéphane; Brun, Sacha; Toomre, Juri Bibcode: 2017IAUS..329..233A Altcode: 2017arXiv170204227A This paper provides a brief look at dynamo scaling relationships for the degree of equipartition between magnetic and kinetic energies. Two simple models are examined, where one that assumes magnetostrophy and another that includes the effects of inertia. These models are then compared to a suite of convective dynamo simulations of the convective core of a main-sequence B-type star and applied to its later evolutionary stages. Title: On Differential Rotation and Overshooting in Solar-like Stars Authors: Brun, Allan Sacha; Strugarek, Antoine; Varela, Jacobo; Matt, Sean P.; Augustson, Kyle C.; Emeriau, Constance; DoCao, Olivier Long; Brown, Benjamin; Toomre, Juri Bibcode: 2017ApJ...836..192B Altcode: 2017arXiv170206598B We seek to characterize how the change of global rotation rate influences the overall dynamics and large-scale flows arising in the convective envelopes of stars covering stellar spectral types from early G to late K. We do so through numerical simulations with the ASH code, where we consider stellar convective envelopes coupled to a radiative interior with various global properties. As solar-like stars spin down over the course of their main sequence evolution, such a change must have a direct impact on their dynamics and rotation state. We indeed find that three main states of rotation may exist for a given star: anti-solar-like (fast poles, slow equator), solar-like (fast equator, slow poles), or a cylindrical rotation profile. Under increasingly strict rotational constraints, the last profile can further evolve into a Jupiter-like profile, with alternating prograde and retrograde zonal jets. We have further assessed how far the convection and meridional flows overshoot into the radiative zone and investigated the morphology of the established tachocline. Using simple mixing length arguments, we are able to construct a scaling of the fluid Rossby number {R}{of}=\tilde{ω }/2{{{Ω }}}* ∼ \tilde{v}/2{{{Ω }}}* {R}* , which we calibrate based on our 3D ASH simulations. We can use this scaling to map the behavior of differential rotation versus the global parameters of stellar mass and rotation rate. Finally, we isolate a region on this map (R of ≳ 1.5-2) where we posit that stars with an anti-solar differential rotation may exist in order to encourage observers to hunt for such targets. Title: Prospects and Challenges for Helioseismology Authors: Toomre, J.; Thompson, M. J. Bibcode: 2017hdsi.book....7T Altcode: No abstract at ADS Title: The Magnetic Furnace: Intense Core Dynamos in B Stars Authors: Augustson, Kyle C.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2016ApJ...829...92A Altcode: 2016arXiv160303659A The dynamo action achieved in the convective cores of main-sequence massive stars is explored here through three-dimensional (3D) global simulations of convective core dynamos operating within a young 10 {M} B-type star, using the anelastic spherical harmonic code. These simulations capture the inner 65% of this star by radius, encompassing the convective nuclear-burning core (about 23% by radius) and a portion of the overlying radiative envelope. Eight rotation rates are considered, ranging from 0.05% to 16% of the surface breakup velocity, thereby capturing both convection that barely senses the effects of rotation and other situations in which the Coriolis forces are prominent. The vigorous dynamo action realized within all of these turbulent convective cores builds magnetic fields with peak strengths exceeding a megagauss, with the overall magnetic energy (ME) in the faster rotators reaching super-equipartition levels compared to the convective kinetic energy (KE). The core convection typically involves turbulent columnar velocity structures roughly aligned with the rotation axis, with magnetic fields threading through these rolls and possessing complex linkages throughout the core. The very strong fields are able to coexist with the flows without quenching them through Lorentz forces. The velocity and magnetic fields achieve such a state by being nearly co-aligned, and with peak magnetic islands being somewhat displaced from the fastest flows as the intricate evolution proceeds. As the rotation rate is increased, the primary force balance shifts from nonlinear advection balancing Lorentz forces to a magnetostrophic balance between Coriolis and Lorentz forces. Title: Magnetoconvection Authors: Toomre, Juri Bibcode: 2016GApFD.110..458T Altcode: No abstract at ADS Title: The Magnetic Furnace: Examining Fully Convective Dynamos And The Influence Of Rotation Authors: Augustson, Kyle; Mathis, S.; Brun, A. S.; Toomre, J. Bibcode: 2016csss.confE..29A Altcode: The dynamo action likely present within fully convective regions is explored through global-scale 3-D simulations. These simulations provide a contextual analog for the convective dynamos that are likely operating deep within the interiors of fully convective low mass stars. A logarithmic range of rotation rates is considered, thereby capturing both convection barely sensing the effects of rotation to others in which the Coriolis forces are prominent. The vigorous dynamo action realized within all of these turbulent convective cores builds magnetic fields with peak strengths exceeding a megagauss, with the overall magnetic energy (ME) in the faster rotators reaching super-equipartition levels compared to the convective kinetic energy (KE). Such strong fields are able to coexist with the flows without quenching them through Lorentz forces. This state is achieved due to the velocity and magnetic fields being nearly co-aligned, and with peak magnetic islands being somewhat displaced from the fastest flows as the intricate evolution of these MHD structures proceeds. As the rotation rate is increased, the primary force balance shifts from nonlinear advection balancing Lorentz forces to a magnetostrophic balance between Coriolis and Lorentz forces. Title: Helioseismic Imaging of Supergranulation throughout the Sun’s Near-Surface Shear Layer Authors: Greer, Benjamin J.; Hindman, Bradley W.; Toomre, Juri Bibcode: 2016ApJ...824..128G Altcode: We present measurements of the Sun’s sub-surface convective flows and provide evidence that the pattern of supergranulation is driven at the surface. The pattern subsequently descends slowly throughout the near-surface shear layer in a manner that is inconsistent with a 3D cellular structure. The flow measurements are obtained through the application of a new helioseismic technique based on traditional ring analysis. We measure the flow field over the course of eleven days and perform a correlation analysis between all possible pairs of depths and temporal separations. In congruence with previous studies, we find that the supergranulation pattern remains coherent at the surface for slightly less than two days and the instantaneous surface pattern is imprinted to a depth of 7 Mm. However, these correlation times and depths are deceptive. When we admit a potential time lag in the correlation, we find that peak correlation in the convective flows descends at a rate of 10-40 m s-1 (or equivalently 1-3 Mm per day). Furthermore, the correlation extends throughout all depths of the near-surface shear layer. This pattern-propagation rate is well matched by estimates of the speed of downflows obtained through the anelastic approximation. Direct integration of the measured speed indicates that the supergranulation pattern that first appears at the surface eventually reaches the bottom of the near-surface shear layer a month later. Thus, the downflows have a Rossby radius of deformation equal to the depth of the shear layer and we suggest that this equality may not be coincidental. Title: Helioseismic Measurements of the Rossby Number in the Sun's Near-surface Shear Layer Authors: Greer, Benjamin J.; Hindman, Bradley W.; Toomre, Juri Bibcode: 2016ApJ...824....4G Altcode: Through helioseismic measurement of the Sun’s subsurface flows, we assess the Rossby number associated with the convective motions. The helioseismic procedure is a new form of the ring-analysis technique that is capable of resolving supergranulation. The extremely fine spatial resolution is achieved by deconvolving the set of p-mode Doppler shifts measured separately within a multitude of densely overlapping analysis regions. We find that just below the photosphere, the Rossby number is large ({Ro}≈ 5) and the convective flows are only weakly influenced by rotation. Below a depth of 10 {Mm}, the flows become rotationally constrained and the concomitant Rossby number is small ({Ro}≈ 0.2). These results support the supposition that the near-surface shear layer is a transition region for the degree of rotational impact on convective motions. Title: Global Solar Convective Dynamo with Cycles, Equatorward Propagation and Grand Minima Authors: Toomre, Juri; Augustson, Kyle C.; Brun, Allan Sacha; Miesch, Mark S. Bibcode: 2016SPD....47.1013T Altcode: The 3-D MHD Anelastic Spherical Harmonic (ASH) code, using slope-limited diffusion, is used to study the interaction of turbulent convection, rotation and magnetism in a full spherical shell comparable to the solar convection zone. Here a star of one solar mass, with a solar luminosity, is considered that is rotating at three times the solar rate. The dynamo generated magnetic field forms large-scale toroidal wreaths, whose formation is tied to the low Rossby number of the convection in this simulation which we have labeled K3S. This case displays prominent polarity cycles with regular reversals occurring roughly every 6.2 years. These reversals are linked to the weakened differential rotation and a resistive collapse of the large-scale magnetic field. Distinctive equatorial migration of the strong magnetic wreaths is seen, arising from modulation of the differential rotation rather than a dynamo wave. As the wreaths approach the equator, cross-equatorial magnetic flux is achieved that permits the low-latitude convection to generate poloidal magnetic field with opposite polarity. Poleward migration of such magnetic flux from the equator eventually leads to the reversal of the polarity of the high-latitude magnetic field. This K3S simulation also enters an interval with reduced magnetic energy at low latitudes lasting roughly 16 years (about 2.5 polarity cycles), during which the polarity cycles are disrupted and after which the dynamo recovers its regular polarity cycles. An analysis of this striking grand minimum reveals that it likely arises through the interplay of symmetric and antisymmetric dynamo families. Title: Helioseismic Imaging of Supergranulation throughout the Sun's Near-Surface Shear Layer Authors: Hindman, Bradley; Greer, Benjamin; Toomre, Juri Bibcode: 2016SPD....4720304H Altcode: We present measurements of the Sun's sub-surface convective flows and provide evidence that the pattern of supergranulation is driven at the surface. The pattern subsequently descends slowly throughout the near-surface shear layer in a manner that is inconsistent with a 3-D cellular structure. The flow measurements are obtained through the application of a new helioseismic technique based on traditional ring analysis. We measure the flow field over the course of eleven days and perform a correlation analysis between all possible pairs of depths and temporal separations. In congruence with previous studies, we find that the supergranulation pattern remains coherent at the surface for slightly less than two days and the instantaneous surface pattern is imprinted to a depth of 7 Mm. However, these correlation times and depths are deceptive. When we admit a potential time lag in the correlation, we find that peak correlation in the convective flows descends at a rate of 10 - 30 m s-1 (or equivalently 1 - 3 Mm per day). Furthermore, the correlation extends throughout all depths of the near-surface shear layer. This pattern-propagation rate is well matched by estimates of the speed of down flows obtained through the anelastic approximation. Direct integration of the measured speed indicates that the supergranulation pattern that first appears at the surface eventually reaches the bottom of the near-surface shear layer a month later. Thus, the transit time is roughly equal to a solar rotation period and we suggest this equality may not be coincidental. Title: Tiny Stars, Strong Fields: Exploring the Origin of Intense Magnetism in M Stars Authors: Toomre, Juri Bibcode: 2016atp..prop...15T Altcode: The M-type stars are becoming dominant targets in searches for Earth-like planets that could occupy their habitable zones. The low masses and luminosities of M-dwarf central stars make them very attractive for such exoplanetary hunts. The habitable zone of M dwarfs is close to the star due to their low luminosity. Thus possibly habitable planets will have short orbital periods, making their detection feasible both with the transit method (used by Kepler, K2 and soon with TESS) and with the radial velocity approaches. Yet habitability on a planet likely requires both solid surfaces and atmospheres, but also a favorable radiation environment. It is here that the M-dwarf central stars raise major theoretical puzzles, for many of them exhibit remarkably intense and frequent flaring, despite their modest intrinsic luminosities. The super-flares release their energy both in white light and in X-rays, and can be thousands of times brighter than the strongest solar flares. Such striking events must have magnetic origins, likely from fields built by convective dynamos operating in their interiors. Further, recent observations suggest that the surface of some M stars is carpeted with magnetic fields of 3 kG or more. Such field strengths are reminiscent of a sunspot, but here instead cover much of the stellar surface. With M stars now taking center stage in the search for Earthlike planets, it is crucial to begin to understand how convective dynamos may be able to build intense magnetic fields involved with super-flares and vast star spots, and how they depend upon the mass and rotation rate of these stars. We propose to use major 3-D MHD simulations with our Anelastic Spherical Harmonic (ASH) code to study the coupling of turbulent convection, rotation, and magnetism within full spherical domains such as the interior of an M dwarf. This permits the exploration of the magnetic dynamos that must be responsible for the evolving magnetism and intense activity of many M dwarfs. We bring to this our prior experience with studying dynamo processes in the outer convective envelopes of G- (the Sun) and Ftype stars, briefly of M dwarfs, and in full convective cores within more massive A- and B-type stars. Our previous work suggests that M dwarfs could display a broad range of dynamo behavior, from cyclic reversals to more chaotic variations, and further to both weak and strong dynamo states. We will focus on the latter, exploring how superequipartition magnetic fields could be achieved by dynamo action in M dwarfs, as are likely needed to energize super-flares and huge active regions, and what limits the peak field strengths. M-type stars are distinctive in becoming fully convective with decreasing mass at about M3.5 in spectral type (or about 0.35 solar masses). At this transition, a steep rise in the fraction of magnetically active stars is observed that is accompanied by an increasing rotational velocity. Clearly how mass-loss and spin-down can lead to this is of interest in itself. However, here we propose to study the manner in which dynamos operating in fully convective M dwarf interiors beyond the transition may be able to achieve very strong magnetic fields, and how field strengths and apparent magnetic activity increases with rotation rate as suggested by observations. We believe that global connectivity of flows and fields across the core center will admit new classes of strong behavior, as revealed by our B star core dynamos, not realized when a convective envelope is bounded below by a tachocline. These ideas need to be tested in a self-consistent manner with global ASH simulations to gain theoretical insights into what is the origin of the fierce magnetic activity in some of M dwarfs that may be potential hosts to Earth-like planets. Such 3-D MHD simulations, though challenging, are now feasible and would complement the intensive observational searches under way. Title: Prospects and Challenges for Helioseismology Authors: Toomre, J.; Thompson, M. J. Bibcode: 2015SSRv..196....1T Altcode: 2015SSRv..tmp...22T Helioseismology has advanced considerably our knowledge of the interior of the Sun over the past three decades. Our understanding of the Sun's internal structure, its dynamics, rotation, convection and magnetism, have all been advanced. Yet there are challenges, areas where the results from helioseismology are tantalizing but inconclusive, and aspects where the interpretation of the data has still to be put on a firm footing. In this paper we shall focus on a number of those challenges and give our assessment of where progress needs to be made in the next decade. Title: Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics Authors: Miesch, Mark; Matthaeus, William; Brandenburg, Axel; Petrosyan, Arakel; Pouquet, Annick; Cambon, Claude; Jenko, Frank; Uzdensky, Dmitri; Stone, James; Tobias, Steve; Toomre, Juri; Velli, Marco Bibcode: 2015SSRv..194...97M Altcode: 2015arXiv150501808M; 2015SSRv..tmp...83M We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) flows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several specific applications in heliophysics and astrophysics, assessing triumphs, challenges, and future directions. Title: Grand Minima and Equatorward Propagation in a Cycling Stellar Convective Dynamo Authors: Augustson, Kyle; Brun, Allan Sacha; Miesch, Mark; Toomre, Juri Bibcode: 2015ApJ...809..149A Altcode: 2014arXiv1410.6547A The 3D MHD Anelastic Spherical Harmonic code, using slope-limited diffusion, is employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate. The dynamo-generated magnetic fields possesses many timescales, with a prominent polarity cycle occurring roughly every 6.2 years. The magnetic field forms large-scale toroidal wreaths, whose formation is tied to the low Rossby number of the convection in this simulation. The polarity reversals are linked to the weakened differential rotation and a resistive collapse of the large-scale magnetic field. An equatorial migration of the magnetic field is seen, which is due to the strong modulation of the differential rotation rather than a dynamo wave. A poleward migration of magnetic flux from the equator eventually leads to the reversal of the polarity of the high-latitude magnetic field. This simulation also enters an interval with reduced magnetic energy at low latitudes lasting roughly 16 years (about 2.5 polarity cycles), during which the polarity cycles are disrupted and after which the dynamo recovers its regular polarity cycles. An analysis of this grand minimum reveals that it likely arises through the interplay of symmetric and antisymmetric dynamo families. This intermittent dynamo state potentially results from the simulation’s relatively low magnetic Prandtl number. A mean-field-based analysis of this dynamo simulation demonstrates that it is of the α-Ω type. The timescales that appear to be relevant to the magnetic polarity reversal are also identified. Title: Super-equipartition Convective Dynamo Action in the Cores of B-Type Stars Authors: Augustson, Kyle C.; Brown, Benjamin P.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2015IAUGA..2258137A Altcode: Observations have revealed the presence and topology of magnetic fields on the surfaces of some main sequence massive stars. These stars possess a convective core that supports strong dynamo action. This core is linked to the dynamics of the rest of the star through overshooting convection and magnetic fields and may influence the surface magnetism. Such effects are captured through 3-D MHD simulations of a 10 M B-type star, using the anelastic spherical harmonic (ASH) code. These simulations capture the inner 65% of the star by radius, encompassing the convective core and an extensive portion of the radiative exterior. Vigorous dynamo action is achieved in the convective core with self-consistent super-equipartition (SE) states sustained over a range of rotation rates. Indeed, the ratio of magnetic to convective kinetic energy shows a distinct scaling with Elsasser and Coriolis number. The impact of this dynamo action upon the differential rotation of the core is assessed by contrasting hydrodynamic and magnetohydrodynamic simulations. The processes that permit the maintenance of such SE states are examined. We further study how the magnetic field generated during main-sequence dynamo action may carry over into later evolutionary stages. Title: Super-equipartition Convective Dynamo Action in the Cores of B-Type Stars Authors: Augustson, Kyle C.; Brown, Benjamin P.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2015IAUGA..2257925A Altcode: Observations have revealed the presence and topology of magnetic fields on the surfaces of some main sequence massive stars. These stars possess a convective core that supports strong dynamo action. This core is linked to the dynamics of the rest of the star through overshooting convection and magnetic fields and may influence the surface magnetism. Such effects are captured through 3-D MHD simulations of a 10 M B-type star, using the anelastic spherical harmonic (ASH) code. These simulations capture the inner 65% of the star by radius, encompassing the convective core and an extensive portion of the radiative exterior. Vigorous dynamo action is achieved in the convective core with self-consistent super-equipartition (SE) states sustained over a range of rotation rates. Indeed, the ratio of magnetic to convective kinetic energy shows a distinct scaling with Elsasser and Coriolis number. The impact of this dynamo action upon the differential rotation of the core is assessed by contrasting hydrodynamic and magnetohydrodynamic simulations. The processes that permit the maintenance of such SE states are examined. We further study how the magnetic field generated during main-sequence dynamo action may carry over into later evolutionary stages. Title: Grand Minima and Equatorward Propagation in a Cycling Stellar Convective Dynamo Authors: Augustson, Kyle C.; Brun, Allan Sacha; Miesch, Mark; Toomre, Juri Bibcode: 2015IAUGA..2257912A Altcode: The 3-D magnetohydrodynamic (MHD) Anelastic Spherical Harmonic (ASH) code, using slope-limited diffusion, is employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate. The dynamo generated magnetic fields possesses many time scales, with a prominent polarity cycle occurring roughly every 6.2 years. The magnetic field forms large-scale toroidal wreaths, whose formation is tied to the low Rossby number of the convection in this simulation. The polarity reversals are linked to the weakened differential rotation and a resistive collapse of the large-scale magnetic field. An equatorial migration of the magnetic field is seen, which is due to the strong modulation of the differential rotation rather than a dynamo wave. A poleward migration of magnetic flux from the equator eventually leads to the reversal of the polarity of the high-latitude magnetic field. This simulation also enters an interval with reduced magnetic energy at low latitudes lasting roughly 16 years (about 2.5 polarity cycles), during which the polarity cycles are disrupted and after which the dynamo recovers its regular polarity cycles. An analysis of this grand minimum reveals that it likely arises through the interplay of symmetric and antisymmetric dynamo families. This intermittent dynamo state potentially results from the simulations relatively low magnetic Prandtl number. A mean-field-based analysis of this dynamo simulation demonstrates that it is of the α-Ω type. The time scales that appear to be relevant to the magnetic polarity reversal are also identified. Title: Grand Minima and Equatorward Propagation in a Cycling Stellar Convective Dynamo Authors: Augustson, Kyle C.; Brun, Allan Sacha; Miesch, Mark; Toomre, Juri Bibcode: 2015IAUGA..2258283A Altcode: The 3-D magnetohydrodynamic (MHD) Anelastic Spherical Harmonic (ASH) code, using slope-limited diffusion, is employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate. The dynamo generated magnetic fields possesses many time scales, with a prominent polarity cycle occurring roughly every 6.2 years. The magnetic field forms large-scale toroidal wreaths, whose formation is tied to the low Rossby number of the convection in this simulation. The polarity reversals are linked to the weakened differential rotation and a resistive collapse of the large-scale magnetic field. An equatorial migration of the magnetic field is seen, which is due to the strong modulation of the differential rotation rather than a dynamo wave. A poleward migration of magnetic flux from the equator eventually leads to the reversal of the polarity of the high-latitude magnetic field. This simulation also enters an interval with reduced magnetic energy at low latitudes lasting roughly 16 years (about 2.5 polarity cycles), during which the polarity cycles are disrupted and after which the dynamo recovers its regular polarity cycles. An analysis of this grand minimum reveals that it likely arises through the interplay of symmetric and antisymmetric dynamo families. This intermittent dynamo state potentially results from the simulations relatively low magnetic Prandtl number. A mean-field-based analysis of this dynamo simulation demonstrates that it is of the α-Ω type. The time scales that appear to be relevant to the magnetic polarity reversal are also identified. Title: Helioseismic Imaging of Fast Convective Flows throughout the Near-surface Shear Layer Authors: Greer, Benjamin J.; Hindman, Bradley W.; Featherstone, Nicholas A.; Toomre, Juri Bibcode: 2015ApJ...803L..17G Altcode: 2015arXiv150400699G Using a new implementation of ring-diagram helioseismology, we ascertain the strength and spatial scale of convective flows throughout the near-surface shear layer. Our ring-diagram technique employs highly overlapped analysis regions and an efficient method of three-dimensional inversion to measure convective motions with a resolution that ranges from 3 Mm at the surface to 80 Mm at the base of the layer. We find the rms horizontal flow speed to peak at 427 m s-1 at the photosphere and fall to a minimum of 124 m s-1 between 20 and 30 Mm. From the velocity amplitude and the dominant horizontal scales seen at each depth, we infer the level of rotational influence on convection to be low near the surface, but transition to a significant level at the base of the near-surface shear layer with a Rossby number varying between 2.2 to as low as 0.1. Title: Convective Dynamo Simulation with a Grand Minimum Authors: Augustson, Kyle C.; Brun, A. S.; Miesch, Mark; Toomre, Juri Bibcode: 2015csss...18..451A Altcode: 2015arXiv150304225A The global-scale dynamo action achieved in a simulation of a Sun-like star rotating at thrice the solar rate is assessed. The 3-D MHD Anelastic Spherical Harmonic (ASH) code, augmented with a viscosity minimization scheme, is employed to capture convection and dynamo processes in this G-type star. The simulation is carried out in a spherical shell that encompasses 3.8 density scale heights of the solar convection zone. It is found that dynamo action with a high degree of time variation occurs, with many periodic polarity reversals occurring roughly every 6.2 years. The magnetic energy also rises and falls with a regular period. The magnetic energy cycles arise from a Lorentz-force feedback on the differential rotation, whereas the processes leading to polarity reversals are more complex, appearing to arise from the interaction of convection with the mean toroidal fields. Moreover, an equatorial migration of toroidal field is found, which is linked to the changing differential rotation, and potentially to a nonlinear dynamo wave. This simulation also enters a grand minimum lasting roughly 20 years, after which the dynamo recovers its regular polarity cycles. Title: Measuring the Solar Meridional Circulation Using Local Helioseismology Authors: Greer, B.; Hindman, B.; Toomre, J. Bibcode: 2014AGUFMSH41B4143G Altcode: The solar meridional circulation plays an important role in the transport of angular momentum and magnetic field throughout the convection zone and is a key component in setting the time-scale for the solar cycle in flux-transport dynamo models. The meridional flow is detectable with a variety of methods, including ring-diagram helioseismology. Many of these methods are plagued with systematic errors that have only recently been analyzed in detail. For ring-diagram analysis, the systematic errors introduce a signal that is easily confused with that of the meridional flow and is often of significant amplitude. Accurately determining the character of the solar meridional circulation requires careful attention to these errors. I use observations from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) to measure both the meridional flow and the associated systematics. I will present recent measurements of the solar meridional circulation with all known systematics accounted for. Title: Multi-Ridge Fitting for Ring-Diagram Helioseismology Authors: Greer, Benjamin J.; Hindman, Bradley W.; Toomre, Juri Bibcode: 2014SoPh..289.2823G Altcode: 2014arXiv1402.5166G; 2014SoPh..tmp...46G Inferences of subsurface flow velocities using local domain ring-diagram helioseismology depend on measuring the frequency shifts of oscillation modes seen in acoustic power spectra. Current methods for making these measurements use maximum-likelihood fitting techniques to match a model of modal power to the spectra. The model typically describes a single oscillation mode, and each mode in a given power spectrum is fit independently. We present a new method that produces measurements with higher reliability and accuracy by fitting multiple modes simultaneously. We demonstrate that this method permits measuring sub-surface flows deeper into the Sun while providing higher uniformity in data coverage and velocity response closer to the limb of the solar disk. While the previous fitting method performs better for some measurements of low phase-speed modes, we find this new method to be particularly useful for high phase-speed modes and small spatial areas. Title: Towards a Unified Simulation of Convective Dynamo Action and Flux Emergence in the Sun Authors: Nelson, Nicholas J.; Brown, Benjamin; Miesch, Mark S.; Toomre, Juri Bibcode: 2014AAS...22421104N Altcode: Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Our recent simulations have achieved sufficiently high levels of turbulence to permit portions of these wreaths to become magnetically buoyant and rise through the simulated convective layer through a combination of magnetic buoyancy and advection by convective giant cells. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much higher values than is possible through laminar processes. Examining many such loops over a simulated magnetic activity cycle, we measure statistical trends in the polarity, twist, and tilt of these loops that mimic Hale’s Law, Joy’s Law, and the hemispheric helicity rule observed in sunspots. We further show that these magnetic structures are primarily generated by non-axisymmetric turbulent amplification on timescales of about 15 days and not by the Ω-effect which primarily generates the large-scale wreaths. Title: Buoyant Magnetic Loops Generated by Global Convective Dynamo Action Authors: Nelson, Nicholas J.; Brown, Benjamin P.; Sacha Brun, A.; Miesch, Mark S.; Toomre, Juri Bibcode: 2014SoPh..289..441N Altcode: 2012arXiv1212.5612N Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions in a simulation with solar stratification but rotating at three times the current solar rate. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much higher values than is possible through laminar processes. These amplified portions can rise through the convective layer by a combination of magnetic buoyancy and advection by convective giant cells, forming buoyant loops. We measure statistical trends in the polarity, twist, and tilt of these loops. Loops are shown to preferentially arise in longitudinal patches somewhat reminiscent of active longitudes in the Sun, although broader in extent. We show that the strength of the axisymmetric toroidal field is not a good predictor of the production rate for buoyant loops or the amount of magnetic flux in the loops that are produced. Title: Center-to-Limb Velocity Systematic in Ring-Diagram Analysis Authors: Greer, B.; Hindman, B.; Toomre, J. Bibcode: 2013ASPC..478..199G Altcode: We use HMI ring-diagram pipeline data to measure a center-to-limb systematic effect seen in velocities. To separate this signal from persistent flow patterns of physical origin, we perform a least-squares fit to the data for each wave mode. We fit a model that includes both the radially symmetric systematic as well as global zonal and meridional flow components. The resulting measurements of the systematic error reveal a smooth trend as a function of both mode frequency and phase speed. The systematic error at 45° from disk center ranges from 20 m/s radially inward to 50 m/s radially outward. The implications for determining global scale meridional flow is discussed. Title: Dynamo Action and Magnetic Cycles in F-type Stars Authors: Augustson, Kyle C.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2013ApJ...777..153A Altcode: Magnetic activity and differential rotation are commonly observed features on main-sequence F-type stars. We seek to make contact with such observations and to provide a self-consistent picture of how differential rotation and magnetic fields arise in the interiors of these stars. The three-dimensional magnetohydrodynamic anelastic spherical harmonic code is employed to simulate global-scale convection and dynamo processes in a 1.2 M F-type star at two rotation rates. The simulations are carried out in spherical shells that encompass most of the convection zone and a portion of the stably stratified radiative zone below it, allowing us to explore the effects a stable zone has upon the morphology of the global-scale magnetic fields. We find that dynamo action with a high degree of time variation occurs in the star rotating more rapidly at 20 Ω, with the polarity of the mean field reversing on a timescale of about 1600 days. Between reversals, the magnetic energy rises and falls with a fairly regular period, with three magnetic energy cycles required to complete a reversal. The magnetic energy cycles and polarity reversals arise due to a linking of the polar-slip instability in the stable region and dynamo action present in the convection zone. For the more slowly rotating case (10 Ω), persistent wreaths of magnetism are established and maintained by dynamo action. Compared to their hydrodynamic progenitors, the dynamo states here involve a marked reduction in the exhibited latitudinal differential rotation, which also vary during the course of a cycle. Title: Cycling Dynamo in a Young Sun: Grand Minima and Equatorward Propagation Authors: Augustson, Kyle; Brun, Allan Sacha; Miesch, Mark Steven; Toomre, Juri Bibcode: 2013arXiv1310.8417A Altcode: We assess the global-scale dynamo action achieved in a simulation of a sun-like star rotating at three times the solar rate. The 3-D MHD Anelastic Spherical Harmonic code, using slope-limited diffusion, is employed to capture convection and dynamo processes in such a young sun. The simulation is carried out in a spherical shell that encompasses 3.8 density scale heights of the solar convection zone. We find that dynamo action with a high degree of time variation occurs, with many periodic polarity reversals every 6.2 years. The magnetic energy also rises and falls with a regular period, with two magnetic energy cycles required to complete a polarity cycle. These magnetic energy cycles arise from a Lorentz-force feedback on the differential rotation, whereas the polarity reversals are present due to the spatial separation of the equatorial and polar dynamos. Moreover, an equatorial migration of toroidal field is found, which is linked to the changing differential rotation and to a near-surface shear layer. This simulation also enters a grand minimum lasting roughly 20 years, after which the dynamo recovers its regular polarity cycles. Title: Magnetic Wreaths and Cycles in Convective Dynamos Authors: Nelson, Nicholas J.; Brown, Benjamin P.; Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri Bibcode: 2013ApJ...762...73N Altcode: 2012arXiv1211.3129N Solar-type stars exhibit a rich variety of magnetic activity. Seeking to explore the convective origins of this activity, we have carried out a series of global three-dimensional magnetohydrodynamic simulations with the anelastic spherical harmonic code. Here we report on the dynamo mechanisms achieved as the effects of artificial diffusion are systematically decreased. The simulations are carried out at a nominal rotation rate of three times the solar value (3 Ω), but similar dynamics may also apply to the Sun. Our previous simulations demonstrated that convective dynamos can build persistent toroidal flux structures (magnetic wreaths) in the midst of a turbulent convection zone and that high rotation rates promote the cyclic reversal of these wreaths. Here we demonstrate that magnetic cycles can also be achieved by reducing the diffusion, thus increasing the Reynolds and magnetic Reynolds numbers. In these more turbulent models, diffusive processes no longer play a significant role in the key dynamical balances that establish and maintain the differential rotation and magnetic wreaths. Magnetic reversals are attributed to an imbalance in the poloidal magnetic induction by convective motions that is stabilized at higher diffusion levels. Additionally, the enhanced levels of turbulence lead to greater intermittency in the toroidal magnetic wreaths, promoting the generation of buoyant magnetic loops that rise from the deep interior to the upper regions of our simulated domain. The implications of such turbulence-induced magnetic buoyancy for solar and stellar flux emergence are also discussed. Title: New Era in 3-D Modeling of Convection and Magnetic Dynamos in Stellar Envelopes and Cores Authors: Toomre, J.; Augustson, K. C.; Brown, B. P.; Browning, M. K.; Brun, A. S.; Featherstone, N. A.; Miesch, M. S. Bibcode: 2012ASPC..462..331T Altcode: The recent advances in asteroseismology and spectropolarimetry are beginning to provide estimates of differential rotation and magnetic structures for a range of F and G-type stars possessing convective envelopes, and in A-type stars with convective cores. It is essential to complement such observational work with theoretical studies based on 3-D simulations of highly turbulent convection coupled to rotation, shear and magnetic fields in full spherical geometries. We have so employed the anelastic spherical harmonic (ASH) code, which deals with compressible magnetohydrodynamics (MHD) in spherical shells, to examine the manner in which the global-scale convection can establish differential rotation and meridional circulations under current solar rotation rates, and these make good contact with helioseismic findings. For younger G stars rotating 3 to 5 times faster than the current Sun, the convection establishes ever stronger angular velocity contrasts between their fast equators and slow poles, and these are accompanied by prominent latitudinal temperature contrasts as well. Turning to MHD simulation of magnetic dynamo action within these younger G stars, the resulting magnetism involves wreaths of strong toroidal magnetic fields (up to 50 to 100 kG strengths) in the bulk of the convection zone, typically of opposite polarity in the northern and southern hemispheres. These fields can persist for long intervals despite being pummeled by the fast convective downflows, but they can also exhibit field reversals and cycles. Turning to shallower convective envelopes in the more luminous F-type stars that range in mass from 1.2 to 1.4 solar masses and for various rotation rates, we find that the convection can again establish solar-like differential rotation profiles with a fast equator and slow poles, but the opposite is achieved at the slower rotation rates. The F stars are also capable of building strong magnetic fields, often as wreaths, through dynamo action. We also consider dynamo action within the cores of rotating A-type stars, finding that striking super-equipartition magnetic fields can be built there. These families of 3-D simulations are showing that a new era of detailed stellar modeling is becoming feasible through rapid advances in supercomputing, and these have the potential to help interpret and possibly even guide some of the observational efforts now under way. Title: Convection and Differential Rotation in F-type Stars Authors: Augustson, Kyle C.; Brown, Benjamin P.; Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri Bibcode: 2012ApJ...756..169A Altcode: Differential rotation is a common feature of main-sequence spectral F-type stars. In seeking to make contact with observations and to provide a self-consistent picture of how differential rotation is achieved in the interiors of these stars, we use the three-dimensional anelastic spherical harmonic (ASH) code to simulate global-scale turbulent flows in 1.2 and 1.3 M F-type stars at varying rotation rates. The simulations are carried out in spherical shells that encompass most of the convection zone and a portion of the stably stratified radiative zone below it, allowing us to explore the effects of overshooting convection. We examine the scaling of the mean flows and thermal state with rotation rate and mass and link these scalings to fundamental parameters of the simulations. Indeed, we find that the differential rotation becomes much stronger with more rapid rotation and larger mass, scaling as ΔΩvpropM 3.9Ω0.6 0. Accompanying the growing differential rotation is a significant latitudinal temperature contrast, with amplitudes of 1000 K or higher in the most rapidly rotating cases. This contrast in turn scales with mass and rotation rate as ΔTvpropM 6.4Ω1.6 0. On the other hand, the meridional circulations become much weaker with more rapid rotation and with higher mass, with their kinetic energy decreasing as KEMCvpropM -1.2Ω-0.8 0. Additionally, three of our simulations exhibit a global-scale shear instability within their stable regions that persists for the duration of the simulations. The flow structures associated with the instabilities have a direct coupling to and impact on the flows within the convection zone. Title: Effects of Granulation upon Larger-Scale Convection Authors: Hurlburt, N. E.; DeRosa, M. L.; Augustson, K. C.; Toomre, J. Bibcode: 2012ASPC..454...13H Altcode: 2012arXiv1201.4809H We examine the role of small-scale granulation in helping to drive supergranulation and even larger scales of convection. The granulation is modeled as localized cooling events introduced at the upper boundary of a 3-D simulation of compressible convection in a rotating spherical shell segment. With a sufficient number of stochastic cooling events compared to uniform cooling, we find that supergranular scales are realized, along with a differential rotation that becomes increasingly solar-like. Title: Modeling the Dynamical Coupling of Solar Convection with the Radiative Interior Authors: Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri Bibcode: 2011ApJ...742...79B Altcode: The global dynamics of a rotating star like the Sun involves the coupling of a highly turbulent convective envelope overlying a seemingly benign radiative interior. We use the anelastic spherical harmonic code to develop a new class of three-dimensional models that nonlinearly couple the convective envelope to a deep stable radiative interior. The numerical simulation assumes a realistic solar stratification from r = 0.07 up to 0.97R (with R the solar radius), thus encompassing part of the nuclear core up through most of the convection zone. We find that a tachocline naturally establishes itself between the differentially rotating convective envelope and the solid body rotation of the interior, with a slow spreading that is here diffusively controlled. The rapid angular momentum redistribution in the convective envelope leads to a fast equator and slow poles, with a conical differential rotation achieved at mid-latitudes, much as has been deduced by helioseismology. The convective motions are able to overshoot downward about 0.04R into the radiative interior. However, the convective meridional circulation there is confined to a smaller penetration depth and is directed mostly equatorward at the base of the convection zone. Thermal wind balance is established in the lower convection zone and tachocline but departures are evident in the upper convection zone. Internal gravity waves are excited by the convective overshooting, yielding a complex wave field throughout the radiative interior. Title: Global-scale Magnetism (and Cycles) in Dynamo Simulations of Stellar Convection Zones Authors: Brown, B. P.; Browning, M. K.; Brun, A. S.; Miesch, M. S.; Toomre, J. Bibcode: 2011ASPC..448..277B Altcode: 2011arXiv1101.0171B; 2011csss...16..277B Young solar-type stars rotate rapidly and are very magnetically active. The magnetic fields at their surfaces likely originate in their convective envelopes where convection and rotation can drive strong dynamo action. Here we explore simulations of global-scale stellar convection in rapidly rotating suns using the 3-D MHD anelastic spherical harmonic (ASH) code. The magnetic fields built in these dynamos are organized on global-scales into wreath-like structures that span the convection zone. We explore one case rotates five times faster than the Sun in detail. This dynamo simulation, called case D5, has repeated quasi-cyclic reversals of global-scale polarity. We compare this case D5 to the broader family of simulations we have been able to explore and discuss how future simulations and observations can advance our understanding of stellar dynamos and magnetism. Title: The 3D Nature of Convective Dynamos Authors: Miesch, M.; Brown, B.; Nelson, N.; Browning, M.; Brun, A. S.; Toomre, J. Bibcode: 2011AGUFMSH23D..01M Altcode: Solar observations throughout the extended minimum between cyles 23 and 24 have highlighted the intrinsically three-dimensional (3D) nature of the solar magnetic field. These include prominent multipolar components and low-latitude coronal holes observed with STEREO, asymmetric surface flux distributions in photospheric magnetograms, ond global, multi-scale magnetic linkages revealed by SDO. Axisymmetric mean-field dynamo models cannot capture this complexity, which ultimately arises from turbulent convection. The solar dynamo is a convective dynamo; convection is clearly responsible for the diversity of solar magnetic activity we observe, generating and organizing magnetic fields both directly by turbulent induction and indirectly via mean flows and MHD instabilities. Simulations of convective dynamos reveal the 3D nature of how large-scale magnetic fields are generated and provide insight into the intricate topology of the solar magnetic field, apparent even during solar minimum. I will describe recent work on the role of helicity and shear in magnetic self-organization and promising first steps toward linking convective dynamos with flux emergence. Title: Exploring the Deep Convection and Magnetism of A-type stars Authors: Featherstone, Nicholas; Browning, Matthew; Brun, Allan Sacha; Toomre, Juri Bibcode: 2011APS..DPPN10003F Altcode: A-type stars have both a near-surface layer of fast convection that can excite acoustic modes and a deep zone of core convection whose properties may be probed with asteroseismology. Many A-type stars also exhibit large magnetic spots that are often attributed to surviving primordial fields of global scale in the intervening radiative zone. We have explored the potential for core convection in rotating A-type stars to build strong magnetic fields through dynamo action. Using the ASH code, we model the inner 30% by radius of a two solar mass A-type star, rotating at four times the solar rate and capturing the convective core and a portion of the overlying radiative envelope. Convection in these stars drives a strong retrograde differential rotation and yields a core that is prolate in shape. When dynamo action is admitted, the convection generates strong magnetic fields largely in equipartition with the dynamics. Remarkably, introducing a modest but large-scale external field threading the radiative envelope (which may be of primordial origin) can substantially alter the turbulent dynamics of the convective interior. The resulting convection establishes a complex assembly of helical rolls that link distant portions of the core and yield magnetic fields of super-equipartition strength. Title: Buoyant Magnetic Loops in a Global Dynamo Simulation of a Young Sun Authors: Nelson, Nicholas J.; Brown, Benjamin P.; Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri Bibcode: 2011ApJ...739L..38N Altcode: 2011arXiv1108.4697N The current dynamo paradigm for the Sun and Sun-like stars places the generation site for strong toroidal magnetic structures deep in the solar interior. Sunspots and starspots on Sun-like stars are believed to arise when sections of these magnetic structures become buoyantly unstable and rise from the deep interior to the photosphere. Here, we present the first three-dimensional global magnetohydrodynamic (MHD) simulation in which turbulent convection, stratification, and rotation combine to yield a dynamo that self-consistently generates buoyant magnetic loops. We simulate stellar convection and dynamo action in a spherical shell with solar stratification, but rotating three times faster than the current solar rate. Strong wreaths of toroidal magnetic field are realized by dynamo action in the convection zone. By turning to a dynamic Smagorinsky model for subgrid-scale turbulence, we here attain considerably reduced diffusion in our simulation. This permits the regions of strongest magnetic field in these wreaths to rise toward the top of the convection zone via a combination of magnetic buoyancy instabilities and advection by convective giant cells. Such a global simulation yielding buoyant loops represents a significant step forward in combining numerical models of dynamo action and flux emergence. Title: Convection and dynamo action in B stars Authors: Augustson, Kyle C.; Brun, Allan S.; Toomre, Juri Bibcode: 2011IAUS..271..361A Altcode: 2010arXiv1011.1016A Main-sequence massive stars possess convective cores that likely harbor strong dynamo action. To assess the role of core convection in building magnetic fields within these stars, we employ the 3-D anelastic spherical harmonic (ASH) code to model turbulent dynamics within a 10 Msolar main-sequence (MS) B-type star rotating at 4 Ωsolar. We find that strong (900 kG) magnetic fields arise within the turbulence of the core and penetrate into the stably stratified radiative zone. These fields exhibit complex, time-dependent behavior including reversals in magnetic polarity and shifts between which hemisphere dominates the total magnetic energy. Title: Onward from solar convection to dynamos in cores of massive stars Authors: Toomre, Juri Bibcode: 2011IAUS..271..347T Altcode: We reflect upon a few of the research challenges in stellar convection and dynamo theory that are likely to be addressed in the next five or so years. These deal firstly with the Sun and continuing study of the two boundary layers at the top and bottom of its convection zone, namely the tachocline and the near-surface shear layer, both of which are likely to have significant roles in how the solar dynamo may be operating. Another direction concerns studying core convection and dynamo action within the central regions of more massive A, B and O-type stars, for the magnetism may have a key role in controlling the winds from these stars, thus influencing their ultimate fate. Such studies of the interior dynamics of massive stars are becoming tractable with recent advances in codes and supercomputers, and should also be pursued with some vigor. Title: Global-scale wreath-building dynamos in stellar convection zones Authors: Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri Bibcode: 2011IAUS..271...78B Altcode: 2010arXiv1011.0445B When stars like our Sun are young they rotate rapidly and are very magnetically active. We explore dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code. The magnetic fields built in these dynamos are organized on global-scales into wreath-like structures that span the convection zone. Wreath-building dynamos can undergo quasi-cyclic reversals of polarity and such behavior is common in the parameter space we have been able to explore. These dynamos do not appear to require tachoclines to achieve their spatial or temporal organization. Wreath-building dynamos are present to some degree at all rotation rates, but are most evident in the more rapidly rotating simulations. Title: Global magnetic cycles in rapidly rotating younger suns Authors: Nelson, Nicholas J.; Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri Bibcode: 2011IAUS..273..272N Altcode: 2010arXiv1010.6073N Observations of sun-like stars rotating faster than our current sun tend to exhibit increased magnetic activity as well as magnetic cycles spanning multiple years. Using global simulations in spherical shells to study the coupling of large-scale convection, rotation, and magnetism in a younger sun, we have probed effects of rotation on stellar dynamos and the nature of magnetic cycles. Major 3-D MHD simulations carried out at three times the current solar rotation rate reveal hydromagnetic dynamo action that yields wreaths of strong toroidal magnetic field at low latitudes, often with opposite polarity in the two hemispheres. Our recent simulations have explored behavior in systems with considerably lower diffusivities, achieved with sub-grid scale models including a dynamic Smagorinsky treatment of unresolved turbulence. The lower diffusion promotes the generation of magnetic wreaths that undergo prominent temporal variations in field strength, exhibiting global magnetic cycles that involve polarity reversals. In our least diffusive simulation, we find that magnetic buoyancy coupled with advection by convective giant cells can lead to the rise of coherent loops of magnetic field toward the top of the simulated domain. Title: Magnetic Cycles and Meridional Circulation in Global Models of Solar Convection Authors: Miesch, Mark S.; Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2011IAUS..271..261M Altcode: 2010arXiv1009.6184M We review recent insights into the dynamics of the solar convection zone obtained from global numerical simulations, focusing on two recent developments in particular. The first is quasi-cyclic magnetic activity in a long-duration dynamo simulation. Although mean fields comprise only a few percent of the total magnetic energy they exhibit remarkable order, with multiple polarity reversals and systematic variability on time scales of 6-15 years. The second development concerns the maintenance of the meridional circulation. Recent high-resolution simulations have captured the subtle nonlinear dynamical balances with more fidelity than previous, more laminar models, yielding more coherent circulation patterns. These patterns are dominated by a single cell in each hemisphere, with poleward and equatorward flow in the upper and lower convection zone respectively. We briefly address the implications of and future of these modeling efforts. Title: Exploring the deep convection and magnetism of A-type stars Authors: Featherstone, Nicholas A.; Browning, Matthew K.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2011IAUS..273..111F Altcode: A-type stars have both a near-surface layer of fast convection that can excite acoustic modes and a deep zone of core convection whose properties may be probed with asteroseismology. Many A-type stars also exhibit large magnetic spots that are often attributed to surviving primordial fields of global scale in the intervening radiative zone. We have explored the potential for core convection in rotating A-type stars to build strong magnetic fields through dynamo action. These 3-D simulations using the ASH code provide guidance on the nature of differential rotation and magnetic fields that may be present in the deep interiors of these stars, thus informing the asteroseismic deductions now becoming feasible. Our models encompass the inner 30% by radius of a two solar mass A-type star, rotating at four times the solar rate and capturing the convective core and a portion of the overlying radiative envelope. Convection in these stars drives a strong retrograde differential rotation and yields a core that is prolate in shape. When dynamo action is admitted, the convection generates strong magnetic fields largely in equipartition with the dynamics. Remarkably, introducing a modest but large-scale external field threading the radiative envelope (which may be of primordial origin) can substantially alter the turbulent dynamics of the convective interior. The resulting convection involves a complex assembly of helical rolls that link distant portions of the core and stretch and advect magnetic field, ultimately yielding magnetic fields of super-equipartition strength. Title: Probing Subsurface Flows Around Sunspots with 3-Dimensional Ring Inversions Authors: Featherstone, Nicholas Andrew; Hindman, Bradley W.; Thompson, Michael J.; Toomre, Juri Bibcode: 2011shin.confE...7F Altcode: We examine convective flows around sunspots as inferred through ring-analysis helioseismology of MDI Dopplergrams. These flow measurements were obtained using a novel 3-D inversion procedure termed Adaptively Resolved Ring-Diagram Inversions, or ARRDI, which uses sensitivity kernels based on the Born approximation. The ARRDI algorithm is multi-scale in nature, folding together information from tiles located at different positions on the solar surface and from tiles of different sizes, thus enabling fine control of the horizontal resolution and the probing depth. When we apply ARRDI to sunspots, we measure outflows persisting to depths of at least 7 Mm. In many instances, the surface outflow diminishes within the upper 3 Mm of the convection zone. Beyond 3 Mm, such outflows strengthen and attain peak amplitudes of 200 m/s at depths of 5-7 Mm. We discuss the implications of such a two-component outflow for understanding the magneto-hydrodynamic behavior and evolution of sunspots. Title: Magnetic Cycles in a Convective Dynamo Simulation of a Young Solar-type Star Authors: Brown, Benjamin P.; Miesch, Mark S.; Browning, Matthew K.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2011ApJ...731...69B Altcode: 2011arXiv1102.1993B Young solar-type stars rotate rapidly and many are magnetically active. Some appear to undergo magnetic cycles similar to the 22 yr solar activity cycle. We conduct simulations of dynamo action in rapidly rotating suns with the three-dimensional magnetohydrodynamic anelastic spherical harmonic (ASH) code to explore dynamo action achieved in the convective envelope of a solar-type star rotating at five times the current solar rotation rate. We find that dynamo action builds substantial organized global-scale magnetic fields in the midst of the convection zone. Striking magnetic wreaths span the convection zone and coexist with the turbulent convection. A surprising feature of this wreath-building dynamo is its rich time dependence. The dynamo exhibits cyclic activity and undergoes quasi-periodic polarity reversals where both the global-scale poloidal and toroidal fields change in sense on a roughly 1500 day timescale. These magnetic activity patterns emerge spontaneously from the turbulent flow and are more organized temporally and spatially than those realized in our previous simulations of the solar dynamo. We assess in detail the competing processes of magnetic field creation and destruction within our simulations that contribute to the global-scale reversals. We find that the mean toroidal fields are built primarily through an Ω-effect, while the mean poloidal fields are built by turbulent correlations which are not well represented by a simple α-effect. During a reversal the magnetic wreaths propagate toward the polar regions, and this appears to arise from a poleward propagating dynamo wave. As the magnetic fields wax and wane in strength and flip in polarity, the primary response in the convective flows involves the axisymmetric differential rotation which varies on similar timescales. Bands of relatively fast and slow fluid propagate toward the poles on timescales of roughly 500 days and are associated with the magnetic structures that propagate in the same fashion. In the Sun, similar patterns are observed in the poleward branch of the torsional oscillations, and these may represent poleward propagating magnetic fields deep below the solar surface. Title: Magnetic Cycles in a Wreath-Building Dynamo Simulation of a Young Solar-type Star Authors: Brown, Benjamin; Miesch, M. S.; Browning, M. K.; Brun, A. S.; Nelson, N. J.; Toomre, J. Bibcode: 2011AAS...21724222B Altcode: 2011BAAS...4324222B Stars like the Sun build global-scale magnetic fields though dynamo processes in their convection zones. There, global-scale plasma motions couple with rotation and likely drive cycles of magnetic activity, though the exact processes at work in solar and stellar dynamos remain elusive. Observations of younger suns indicate that they rotate quite rapidly, have strong magnetic fields at their surfaces, and show signs of cyclic activity. Here we explore recent 3-D MHD simulations of younger, more rapidly rotating solar-type stars conducted with the anelastic spherical harmonic (ASH) code. These simulations of global-scale convection and dynamo action produce strikingly organized magnetic structures in the bulk of their convection zones. Wreaths of magnetic field fill the convection zone and can undergo regular cycles of polarity reversal. Indeed, we find that cyclic behavior is a common feature throughout the parameter space we have explored. Though these magnetic wreaths can coexist with tachoclines of penetration and shear, they do not rely on that internal boundary layer for their formation or persistence. Tachoclines may play a less critical role in the stellar dynamos of younger Suns than has been supposed in solar dynamo theory. Title: Modeling the Near-Surface Shear Layer: Diffusion Schemes Studied With CSS Authors: Augustson, Kyle; Rast, Mark; Trampedach, Regner; Toomre, Juri Bibcode: 2011JPhCS.271a2070A Altcode: 2010arXiv1012.4781A As we approach solar convection simulations that seek to model the interaction of small-scale granulation and supergranulation and even larger scales of convection within the near-surface shear layer (NSSL), the treatment of the boundary conditions and minimization of sub-grid scale diffusive processes become increasingly crucial. We here assess changes in the dynamics and the energy flux balance of the flows established in rotating spherical shell segments that capture much of the NSSL with the Curved Spherical Segment (CSS) code using two different diffusion schemes. The CSS code is a new massively parallel modeling tool capable of simulating 3-D compressible MHD convection with a realistic solar stratification in rotating spherical shell segments. Title: Magnetic Cycles and Buoyant Magnetic Structures in a Rapidly Rotating Sun Authors: Nelson, Nicholas J.; Brown, B. P.; Brun, S.; Miesch, M. S.; Toomre, J. Bibcode: 2011AAS...21715512N Altcode: 2011BAAS...4315512N Observations of sun-like stars rotating faster than our current sun show that they exhibit solar-like magnetic cycles and features, such as star spots. Using global 3-D simulations to study the coupling of large-scale convection, rotation, and magnetism in a younger sun, we have probed the effects of more rapid rotation on stellar dynamos and the nature of magnetic cycles. Our anelastic spherical harmonics (ASH) code allows study of the convective envelope, occupying the outer 30% by radius of a sun-like star. Major MHD simulations carried out at three times the current solar rotation rate reveal magnetic dynamo action that can produce wreaths of strong toroidal magnetic field at low latitudes, often with opposite polarity in the two hemispheres. The presence of the wreaths is quite surprising, for they arise as quite persistent global structures amidst the vigorous and turbulent convection. We have recently explored behavior in systems with considerably lower diffusivities, achieved with a dynamic Smagorinsky treatment of unresolved turbulence. The lower levels of diffusion create magnetic wreaths that undergo prominent variations in field strength, even exhibiting global magnetic cycles that involve polarity reversals. Additionally, during the cycle maximum, when magnetic energies and mean magnetic fields peak, the wreaths possess buoyant magnetic structures that rise coherently through much of the convective envelope via a combination of advection by convective upflows and magnetic buoyancy. We explore aspects of these rising magnetic structures and the evolving global dynamo action which produces them. Title: Assessing the Deep Interior Dynamics and Magnetism of A-type Stars Authors: Featherstone, Nicholas A.; Browning, Matthew K.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2011JPhCS.271a2068F Altcode: A-type stars have both a shallow near-surface zone of fast convection that can excite acoustic modes and a deep zone of core convection whose properties may be studied through asteroseismology. Many A stars also exhibit large magnetic spots as they rotate. We have explored the properties of core convection in rotating A-type stars and their ability to build strong magnetic fields. These 3-D simulations using the ASH code may serve to inform asteroseismic deductions of interior rotation and magnetism that are now becoming feasible. Our models encompass the inner 30% by radius of a 2 solar mass A-type star, capturing both the convective core and some of the overlying radiative envelope. Convection can drive a column of strong retrograde differential rotation and yield a core prolate in shape. When dynamo action is admitted, the convection is able to generate strong magnetic fields largely in equipartition with the dynamics. Introducing a modest external field (which may be of primordial origin) into the radiative envelope can substantially alter the turbulent dynamics of the convective core, yielding magnetic fields of remarkable super-equipartition strength. The turbulent convection involves a complex assembly of helical rolls that link distant portions of the core and stretch and advect magnetic field into broad swathes of strong toroidal field. These simulations reveal that supercomputing is providing a perspective of the deep dynamics that may become testable with asteroseismology for these stars. Title: Rotation-rate variations at the tachocline: An update Authors: Howe, R.; Komm, R.; Hill, F.; Christensen-Dalsgaard, J.; Larson, T. P.; Schou, J.; Thompson, M. J.; Toomre, J. Bibcode: 2011JPhCS.271a2075H Altcode: After 15 years of GONG and MDI observations of the solar interior rotation, we revisit the issue of variations in the rotation rate near the base of the convection zone. The 1.3-year period seen in the first few years of the observations disappeared after 2000 and has still not returned. On the other hand, the agreement between GONG and MDI observations suggests that variations seen in this region have some solar origin, whether a true rotation-rate change or possibly mere stochastic variation; we present a numerical experiment supporting this contention. Title: The Influence of Tracking Rate on Helioseismic Flow Inferences Authors: Routh, Swati; Haber, Deborah A.; Hindman, Bradley W.; Bogart, Richard S.; Toomre, Juri Bibcode: 2011JPhCS.271a2014R Altcode: Traditionally, most local helioseismic studies of subsurface flows have removed the large signal due to the Sun's rotation by tracking the analysis region across the solar surface. In order to work in a uniformly rotating reference frame, the ring-analysis pipeline of the recently launched Helioseismic and Magnetic Imager (HMI) will track all analysis regions at the solid-body Carrington rate. To test this tracking scheme, we compare flow determinations resulting from two different tracking schemes. In one scheme we use the HMI pipeline implementation which tracks at the Carrington rotation rate. In the other, the tiles are tracked at the local differential surface rotation rate as measured by Snodgrass (1984). We observe systematic differences between the flows obtained by the two schemes even after transforming them to a common frame (Snodgrass frame), with the zonal flows measured in the Carrington frame being faster by 5-20 m/s. Title: Developing Physics-Based Procedures for Local Helioseismic Probing of Sunspots and Magnetic Regions Authors: Birch, Aaron; Braun, D. C.; Crouch, A.; Rempel, M.; Fan, Y.; Centeno, R.; Toomre, J.; Haber, D.; Hindman, B.; Featherstone, N.; Duvall, T., Jr.; Jackiewicz, J.; Thompson, M.; Stein, R.; Gizon, L.; Cameron, R.; Saidi, Y.; Hanasoge, S.; Burston, R.; Schunker, H.; Moradi, H. Bibcode: 2010AAS...21630805B Altcode: We have initiated a project to test and improve the local helioseismic techniques of time-distance and ring-diagram analysis. Our goals are to develop and implement physics-based methods that will (1) enable the reliable determinations of subsurface flow, magnetic field, and thermal structure in regions of strong magnetic fields and (2) be quantitatively tested with realistic solar magnetoconvection simulations in the presence of sunspot-like magnetic fields. We are proceeding through a combination of improvements in local helioseismic measurements, forward modeling of the helioseismic wavefield, kernel computations, inversions, and validation through numerical simulations. As improvements over existing techniques are made they will be applied to the SDO/HMI observations. This work is funded through the the NASA Heliophysics Science Division through the Solar Dynamics Observatory (SDO) Science Center program. Title: Core Convection and Dynamos in Spectral Type O and B Stars Authors: Augustson, Kyle; Brun, A. S.; Toomre, J. Bibcode: 2010AAS...21642301A Altcode: 2010BAAS...41..835A Recent observations have revealed that about one-third of O and B type stars have strong magnetic fields at their surfaces. It is currently unclear where these fields originate. In order to address this question, we examine the effects of core convection and magnetic dynamo processes within massive O and B stars with simulations in rotating spherical shells using the 3-D Spherical Harmonic (ASH) magnetohydrodynamic code. Title: Modeling the Near-Surface Shear Layer Through Coupled Simulations of Surface and Deep Convection Authors: Augustson, Kyle; Hurlburt, N.; DeRosa, M.; Toomre, J. Bibcode: 2010AAS...21640008A Altcode: 2010BAAS...41..855A We examine the role of small-scale granulation in helping to drive supergranulation and even larger scales of convection. The granulation is modeled as localized plumes with statistics taken from surface convection simulations introduced at the upper boundary of a 3-D simulation of compressible convection in a rotating spherical shell segment. With a sufficient number of stochastic plume events compared to a uniform cooling, we find that supergranular scales are realized, along with a differential rotation that becomes increasingly solar-like. Title: Persistent Magnetic Wreaths in a Rapidly Rotating Sun Authors: Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri Bibcode: 2010ApJ...711..424B Altcode: 2010arXiv1011.2831B When our Sun was young it rotated much more rapidly than now. Observations of young, rapidly rotating stars indicate that many possess substantial magnetic activity and strong axisymmetric magnetic fields. We conduct simulations of dynamo action in rapidly rotating suns with the three-dimensional magnetohydrodynamic anelastic spherical harmonic (ASH) code to explore the complex coupling between rotation, convection, and magnetism. Here, we study dynamo action realized in the bulk of the convection zone for a system rotating at 3 times the current solar rotation rate. We find that substantial organized global-scale magnetic fields are achieved by dynamo action in this system. Striking wreaths of magnetism are built in the midst of the convection zone, coexisting with the turbulent convection. This is a surprise, for it has been widely believed that such magnetic structures should be disrupted by magnetic buoyancy or turbulent pumping. Thus, many solar dynamo theories have suggested that a tachocline of penetration and shear at the base of the convection zone is a crucial ingredient for organized dynamo action, whereas these simulations do not include such tachoclines. We examine how these persistent magnetic wreaths are maintained by dynamo processes and explore whether a classical mean-field α-effect explains the regeneration of poloidal field. We find that the global-scale toroidal magnetic fields are maintained by an Ω-effect arising from the differential rotation, while the global-scale poloidal fields arise from turbulent correlations between the convective flows and magnetic fields. These correlations are not well represented by an α-effect that is based on the kinetic and magnetic helicities. Title: Solar Convective Dynamo Action With A Tachocline Authors: Featherstone, Nicholas; Brun, A. S.; Miesch, M. S.; Brown, B. P.; Toomre, J. Bibcode: 2010AAS...21532202F Altcode: 2010BAAS...42..323F We present continuing simulations of solar-like convection penetrating into the tachocline at the base of the convection zone and examine the resulting dynamo action. Prior simulations using the 3-D anelastic spherical harmonic (ASH) code of convection in a full spherical shell admitting penetration into a tachocline have yielded differential rotation profiles whose latitudinal contrast is considerably smaller than in simulations without penetration. We believe that the relatively soft stabilizing entropy gradients in the overshooting regions may have resulted in unusually strong circulations that worked against the Reynolds stresses, thus diminishing the differential rotation. Here we turn to ASH simulations with more realistic stiffer entropy gradients and reduced diffusivities in the radiative zone. We report on the hydrodynamic balances achieved within the region of penetration that allows the convection zone to return to differential rotation profiles in closer accord with helioseismic deductions, including possessing a tachocline of shear. We then examine the possibilities for dynamo action in this system and find that weak wreathes of toroidal field, similar to those found in simulations of faster rotating suns, are realized in the convection zone. Convective pumping of these fields into the tachocline leads to the generation of strong axisymmetric toroidal fields there, with oppositely signed polarities about the equator. We examine the temporal variation of these magnetic fields as well as their effects on the angular momentum transport within the bulk of the convection zone. Title: Wreath-Building Dynamos in Rapidly Rotating Suns Authors: Brown, Benjamin; Browning, M. K.; Brun, A. S.; Miesch, M. S.; Toomre, J. Bibcode: 2010AAS...21542415B Altcode: 2010BAAS...42..332B When stars like our Sun are young, they rotate quite rapidly. Observations of these young suns indicate that they generally possess strong magnetic activity. Here we explore 3-D MHD simulations of dynamo action in rapidly rotating suns. Our simulations with the anelastic spherical harmonic (ASH) code extend from 0.72 to 0.97 solar radii and thus span the bulk of the stellar convection zone. We find that these stars achieve strong dynamo action, and naturally build remarkable global-scale magnetic structures in their convection zones. These wreaths of magnetism fill the convection zone and retain coherence over long epochs despite being embedded in the turbulent convection. This is in striking contrast to many theories of the global solar dynamo, which is thought to require a tachocline of shear and penetration at the base of the convection zone to achieve such structures. Wreath-building dynamos can undergo repeated cycles of magnetic polarity reversal, with the global-scale magnetic structures changing their sense on thousand day timescales. Title: Three-Dimensional Simulations of Solar and Stellar Dynamos: The Influence of a Tachocline Authors: Miesch, M. S.; Browning, M. K.; Brun, A. S.; Toomre, J.; Brown, B. P. Bibcode: 2009ASPC..416..443M Altcode: 2008arXiv0811.3032M We review recent advances in modeling global-scale convection and dynamo processes with the Anelastic Spherical Harmonic (ASH) code. In particular, we have recently achieved the first global-scale solar convection simulations that exhibit turbulent pumping of magnetic flux into a simulated tachocline and the subsequent organization and amplification of toroidal field structures by rotational shear. The presence of a tachocline not only promotes the generation of mean toroidal flux, but it also enhances and stabilizes the mean poloidal field throughout the convection zone, promoting dipolar structure with less frequent polarity reversals. The magnetic field generated by a convective dynamo with a tachocline and overshoot region is also more helical overall, with a sign reversal in the northern and southern hemispheres. Toroidal tachocline fields exhibit little indication of magnetic-buoyancy instabilities, but may be undergoing magneto-shear instabilities. Title: Dynamo Action and Wreaths of Magnetism in a Younger Sun Authors: Brown, B. P.; Browning, M. K.; Brun, A. S.; Miesch, M. S.; Toomre, J. Bibcode: 2009ASPC..416..369B Altcode: When our Sun was younger it rotated much more rapidly. Observations of many young stars indicate that magnetic activity and perhaps dynamo action are stronger in the rapidly rotating suns. Here we use the anelastic spherical harmonic (ASH) code to explore 3-D MHD simulations of the dynamo action that might occur in such younger suns. As a great surprise, we find that coherent global-scale structures of toroidal magnetic field are formed in the bulk of the convection zone. These wreaths of magnetism persist for long periods of time amidst the still turbulent convection. In contrast to previous solar dynamo simulations, the wreaths of magnetism formed in these more rapidly rotating suns do not require a tachocline of penetration and shear at the base of the convection zone for their creation or survival. Title: Effects of Fossil Magnetic Fields on Convective Core Dynamos in A-type Stars Authors: Featherstone, Nicholas A.; Browning, Matthew K.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2009ApJ...705.1000F Altcode: The vigorous magnetic dynamo action achieved within the convective cores of A-type stars may be influenced by fossil magnetic fields within their radiative envelopes. We study such effects through three-dimensional simulations that model the inner 30% by radius of a 2 M sun A-type star, capturing the convective core and a portion of the overlying radiative envelope within our computational domain. We employ the three-dimensional anelastic spherical harmonic code to model turbulent dynamics within a deep rotating spherical shell. The interaction between a fossil field and the core dynamo is examined by introducing a large-scale magnetic field into the radiative envelope of a mature A star dynamo simulation. We find that the inclusion of a twisted toroidal fossil field can lead to a remarkable transition in the core dynamo behavior. Namely, a super-equipartition state can be realized in which the magnetic energy built by dynamo action is 10-fold greater than the kinetic energy of the convection itself. Such strong-field states may suggest that the resulting Lorentz forces should seek to quench the flows, yet we have achieved super-equipartition dynamo action that persists for multiple diffusion times. This is achieved by the relative co-alignment of the flows and magnetic fields in much of the domain, along with some lateral displacements of the fastest flows from the strongest fields. Convection in the presence of such strong magnetic fields typically manifests as 4-6 cylindrical rolls aligned with the rotation axis, each possessing central axial flows that imbue the rolls with a helical nature. The roll system also possesses core-crossing flows that couple distant regions of the core. We find that the magnetic fields exhibit a comparable global topology with broad, continuous swathes of magnetic field linking opposite sides of the convective core. We have explored several poloidal and toroidal fossil field geometries, finding that a poloidal component is essential for a transition to super-equipartition to occur. Title: Subsurface Circulations Established by Active Regions Authors: Hindman, Bradley Wade; Haber, Deborah; Toomre, Juri Bibcode: 2009shin.confE..17H Altcode: Using the local helioseismic technique of ring analysis we deduce subsurface flows within and surrounding magnetic active regions. We apply this technique to data from MDI and analyze the resulting flow fields for durations of several months from each of three consecutive years. We compute the mean motion of magnetic plage, mean inflow rates into magnetic complexes and mean circulation speeds around active regions. We find that the plage within active regions rotates more rapidly than quiet sun by roughly 20 m/s, yet advects poleward at the same rate as quiet sun. We also find that almost all active regions possess a mean inflow (20-30 m/s) and a cyclonic circulation ( 5 m/s) at their peripheries; whereas their cores, where the sunspots are located, are zones of strong anticyclonic outflow ( 50 m/s). Title: Subsurface Circulations within Active Regions Authors: Hindman, Bradley W.; Haber, Deborah A.; Toomre, Juri Bibcode: 2009ApJ...698.1749H Altcode: 2009arXiv0904.1575H Using high-resolution ring analysis, we deduce subsurface flows within magnetic active regions and within the quiet Sun. With this procedure, we are capable of measuring flows with a horizontal spatial resolution of 2° in heliographic angle (or roughly 20 Mm). From the resulting flow fields we deduce mean inflow rates into active regions, mean circulation speeds around active regions, and probability density functions (PDFs) of properties of the flow field. These analyses indicate that active regions have a zonal velocity that exceeds that of the quiet Sun at the same latitude by 20 m s-1, yet active regions advect poleward at the same rate as the quiet Sun. We also find that almost all active regions possess a mean inflow (20-30 m s-1) and a cyclonic circulation (≈5 m s-1) at their peripheries, whereas their cores, where the sunspots are located, are zones of strong anticyclonic outflow (≈50 m s-1). From the PDFs, we find that active regions modify the structure of convection with a scale greater than that of supergranulation. Instead of possessing an asymmetry between inflows and outflows (with a larger percentage of the surface occupied by outflows), as is seen in the quiet Sun, active regions possess symmetric distributions. Title: Wreathes of Magnetism in Rapidly Rotating Suns Authors: Brown, Benjamin P.; Browning, Matthew K.; Miesch, Mark S.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2009arXiv0906.2407B Altcode: When our Sun was young it rotated much more rapidly than now. Observations of young, rapidly rotating stars indicate that many possess substantial magnetic activity and strong axisymmetric magnetic fields. We conduct simulations of dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code to explore the complex coupling between rotation, convection and magnetism. Here we study dynamo action realized in the bulk of the convection zone for two systems, rotating at three and five times the current solar rate. We find that substantial organized global-scale magnetic fields are achieved by dynamo action in these systems. Striking wreathes of magnetism are built in the midst of the convection zone, coexisting with the turbulent convection. This is a great surprise, for many solar dynamo theories have suggested that a tachocline of penetration and shear at the base of the convection zone is a crucial ingredient for organized dynamo action, whereas these simulations do not include such tachoclines. Some dynamos achieved in these rapidly rotating states build persistent global-scale fields which maintain amplitude and polarity for thousands of days. In the case at five times the solar rate, the dynamo can undergo cycles of activity, with fields varying in strength and even changing polarity. As the magnetic fields wax and wane in strength, the primary response in the convective flows involves the axisymmetric differential rotation, which begins to vary on similar time scales. Bands of relatively fast and slow fluid propagate toward the poles on time scales of roughly 500 days. In the Sun, similar patterns are observed in the poleward branch of the torsional oscillations, and these may represent a response to poleward propagating magnetic field deep below the solar surface. Title: Mean-Field Generation in Turbulent Convective Dynamos: The Role of a Tachocline Authors: Miesch, Mark S.; Browning, M. K.; Brun, A. S.; Brown, B. P.; Toomre, J. Bibcode: 2009SPD....40.0406M Altcode: Turbulent dynamos tend to generate turbulent magnetic fields. The Sun exhibits such disordered fields but it also exhibits large-scale magnetic activity patterns of striking order, including cyclically varying sunspot distributions and a reversing dipole moment. The challenge of global solar dynamo theory is to account for such order. Rotational shear almost certainly plays an essential role, placing the solar tachocline at center stage. Here we present global simulations of convective dynamos with and without a tachocline, focusing on how the presence of a tachocline alters mean field generation. The presence of a tachocline not only promotes the generation of mean toroidal flux, but it also enhances and stabilizes the mean poloidal field throughout the convection zone, promoting dipolar structure with less frequent polarity reversals. Magnetic fields generated in the presence of a tachocline are more helical overall, with opposite senses among hemispheres and among mean and fluctuating components. Toroidal tachocline fields exhibit little indication of magnetic buoyancy instabilities but may be undergoing magneto-shear instabilities. Title: Stochastic Effects of Granulation and Supergranulation Upon Deep Convection Authors: Augustson, Kyle; De Rosa, M. L.; Hurlburt, N. E.; Toomre, J. Bibcode: 2009SPD....40.0805A Altcode: Vigorous fluid motions associated with the observed patterns of supergranulation, mesogranulation, and granulation play a large role in the turbulent transport of heat to the solar surface. The downflows associated with these convective motions plunge from the surface into the near-surface layers of the Sun bringing cooler, low entropy material with them. These flow structures may provide some stochastic effects upon the dynamics of the giant cells of deep convection that extend into the near-surface regions. To investigate such dynamics, we have carried out several 3-D numerical simulations of fully compressible fluids within curved, spherical segments that, at this stage, approximate conditions near the top of the rotating solar convection zone. The upper boundary of the segment is stochastically driven with cool plumes that approximate the spatial and temporal scales of supergranular cell downflows, in essence creating a network of supergranular cells. The segment spans 30° in latitude and 30° in longitude, and has a radial extent of 15% of the solar radius. We explore the formation and evolution of the boundary layer resulting from such stochastic driving, and discuss these dynamics in the context of the near-surface shear layer of the solar convection zone. Title: Marching Toward More Realistic Penetration of Convection into a Tachocline Authors: Featherstone, Nicholas; Brun, A. S.; Miesch, M. S.; Toomre, J. Bibcode: 2009SPD....40.0803F Altcode: The solar convection zone has provided many challenges for the theoretical modeling of dynamics within our nearest star. The tachocline, a region of strong shear near the base of the convection zone, has received much attention due to its likely role in the generation of the global-scale magnetic fields. The establishment and maintenance of the solar tachocline has been variously attributed to angular momentum transport via gravity waves, magnetic torques and anisotropic mixing processes. Self consistently capturing the turbulent dynamics of the convection zone and underlying radiative zone through 3-D numerical modeling is difficult due to the wide range of scales involved. Prior simulations using the 3-D anelastic spherical harmonic (ASH) code of convection in a full spherical shell admitting penetration into a stable region below have yielded differential rotation profiles whose latitudinal contrast is considerably smaller than in simulations without penetration. We believe that the relatively soft stabilizing entropy gradients in the overshooting regions may have resulted in unusually strong circulations that worked against the Reynolds stresses, thus diminishing the differential rotation. Here we turn to ASH simulations with more realistic stiffer entropy gradients and reduced diffusivities in the radiative zone. We report on the balances achieved within the region of penetration that allows the convection zone to return to differential rotation profiles in closer accord with helioseismic deductions, including possessing a tachocline of shear. Title: Global Magnetic Reversal in a Rapidly Rotating Sun Authors: Nelson, Nicholas J.; Brown, B. P.; Toomre, J. Bibcode: 2009SPD....40.0804N Altcode: Global MHD simulations of the solar convection zone and a tachocline of shear at its base have demonstrated that strong bands of toroidal magnetic field can be built in the tachocline through stretching and organizing of small-scale fields that have been pumped downward into it. Recent 3-D simulations of more rapidly rotating suns have revealed that global-scale wreathes of toroidal magnetic field can even be achieved in the bulk of the convection zone itself, remarkably without a tachocline of shear present at its base. Continuing this work, we simulate a sun without a tachocline, rotating at three times the solar rate, and at a higher turbulence level than previous simulations. We find toroidal magnetic wreathes which have large temporal variations in field strength as they interact with turbulent convection and global differential rotation, yet rebuild themselves, persisting in the bulk of the convection zone for thousands of days. These magnetic structures can even undergo a reversal of global magnetic polarity, and may persist in this state for some time. We describe here the nature of such a reversal and the relative timing of changes in the poloidal and toroidal fields. Title: Turbulence, Magnetism, and Shear in Stellar Interiors Authors: Miesch, Mark S.; Toomre, Juri Bibcode: 2009AnRFM..41..317M Altcode: Stars can be fascinating settings in which to study intricate couplings among convection, rotation, magnetism, and shear, usually under distinctly nonlinear conditions that yield vigorous turbulence. The emerging flux and the rotation rates of stars can vary widely, yet there are common elements that must contribute to building and maintaining the vibrantly evolving magnetic activity they exhibit. Some of these elements, such as the rotational shear and meridional flows established by the coupling of convection with rotation, can now be studied in detail within our nearest star using helioseismology. Major three-dimensional numerical simulations help refine our intuitions about such interior dynamics, aided by rapid advances in supercomputing that are improving the fidelity of the modeling. These developments, combined with intense thrusts at new high resolution and continuous observations of solar magnetism and solar oscillations, herald a promising era for exploring such astrophysical fluid dynamics. Title: Rapidly Rotating Suns and Active Nests of Convection Authors: Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri Bibcode: 2008ApJ...689.1354B Altcode: 2008arXiv0808.1716B In the solar convection zone, rotation couples with intensely turbulent convection to drive a strong differential rotation and achieve complex magnetic dynamo action. Our Sun must have rotated more rapidly in its past, as is suggested by observations of many rapidly rotating young solar-type stars. Here we explore the effects of more rapid rotation on the global-scale patterns of convection in such stars and the flows of differential rotation and meridional circulation, which are self-consistently established. The convection in these systems is richly time-dependent, and in our most rapidly rotating suns a striking pattern of localized convection emerges. Convection near the equator in these systems is dominated by one or two nests in longitude of locally enhanced convection, with quiescent streaming flow in between them at the highest rotation rates. These active nests of convection maintain a strong differential rotation despite their small size. The structure of differential rotation is similar in all of our more rapidly rotating suns, with fast equators and slower poles. We find that the total shear in differential rotation Δ Ω grows with more rapid rotation, while the relative shear Δ Ω/Ω0 decreases. In contrast, at more rapid rotation, the meridional circulations decrease in energy and peak velocities and break into multiple cells of circulation in both radius and latitude. Title: Structure and Evolution of Giant Cells in Global Models of Solar Convection Authors: Miesch, Mark S.; Brun, Allan Sacha; DeRosa, Marc L.; Toomre, Juri Bibcode: 2008ApJ...673..557M Altcode: 2007arXiv0707.1460M The global scales of solar convection are studied through three-dimensional simulations of compressible convection carried out in spherical shells of rotating fluid that extend from the base of the convection zone to within 15 Mm of the photosphere. Such modeling at the highest spatial resolution to date allows study of distinctly turbulent convection, revealing that coherent downflow structures associated with giant cells continue to play a significant role in maintaining the differential rotation that is achieved. These giant cells at lower latitudes exhibit prograde propagation relative to the mean zonal flow, or differential rotation, that they establish, and retrograde propagation of more isotropic structures with vortical character at mid and high latitudes. The interstices of the downflow networks often possess strong and compact cyclonic flows. The evolving giant-cell downflow systems can be partly masked by the intense smaller scales of convection driven closer to the surface, yet they are likely to be detectable with the helioseismic probing that is now becoming available. Indeed, the meandering streams and varying cellular subsurface flows revealed by helioseismology must be sampling contributions from the giant cells, yet it is difficult to separate out these signals from those attributed to the faster horizontal flows of supergranulation. To aid in such detection, we use our simulations to describe how the properties of giant cells may be expected to vary with depth and how their patterns evolve in time. Title: Rapid rotation, active nests of convection and global-scale flows in solar-like stars Authors: Brown, B. P.; Browning, M. K.; Brun, A. S.; Miesch, M. S.; Toomre, J. Bibcode: 2007AN....328.1002B Altcode: 2008arXiv0801.1672B In the solar convection zone, rotation couples with intensely turbulent convection to build global-scale flows of differential rotation and meridional circulation. Our sun must have rotated more rapidly in its past, as is suggested by observations of many rapidly rotating young solar-type stars. Here we explore the effects of more rapid rotation on the patterns of convection in such stars and the global-scale flows which are self-consistently established. The convection in these systems is richly time dependent and in our most rapidly rotating suns a striking pattern of spatially localized convection emerges. Convection near the equator in these systems is dominated by one or two patches of locally enhanced convection, with nearly quiescent streaming flow in between at the highest rotation rates. These active nests of convection maintain a strong differential rotation despite their small size. The structure of differential rotation is similar in all of our more rapidly rotating suns, with fast equators and slower poles. We find that the total shear in differential rotation, as measured by latitudinal angular velocity contrast, \Delta \Omega, increases with more rapid rotation while the relative shear, \Delta \Omega/ \Omega, decreases. In contrast, at more rapid rotation the meridional circulations decrease in both energy and peak velocities and break into multiple cells of circulation in both radius and latitude. Title: Dynamo action in simulations of penetrative solar convection with an imposed tachocline Authors: Browning, M. K.; Brun, A. S.; Miesch, M. S.; Toomre, J. Bibcode: 2007AN....328.1100B Altcode: We summarize new and continuing three-dimensional spherical shell simulations of dynamo action by convection allowed to penetrate downward into a tachocline of rotational shear. The inclusion of an imposed tachocline allows us to examine several processes believed to be essential in the operation of the global solar dynamo, including differential rotation, magnetic pumping, and the stretching and organization of fields within the tachocline. In the stably stratified core, our simulations reveal that strong axisymmetric magnetic fields (of ∼ 3000 G strength) can be built, and that those fields generally exhibit a striking antisymmetric parity, with fields in the northern hemisphere largely of opposite polarity to those in the southern hemisphere. In the convection zone above, fluctuating fields dominate over weaker mean fields. New calculations indicate that the tendency toward toroidal fields of antisymmetric parity is relatively insensitive to initial magnetic field configurations; they also reveal that on decade-long timescales, the magnetic fields can briefly enter (and subsequently emerge from) states of symmetric parity. We have not yet observed any overall reversals of the field polarity, nor systematic latitudinal propagation. Title: Dynamo action in the presence of an imposed magnetic field Authors: Featherstone, N. A.; Browning, M. K.; Brun, A. S.; Toomre, J. Bibcode: 2007AN....328.1126F Altcode: Dynamo action within the cores of Ap stars may offer intriguing possibilities for understanding the persistent magnetic fields observed on the surfaces of these stars. Deep within the cores of Ap stars, the coupling of convection with rotation likely yields magnetic dynamo action, generating strong magnetic fields. However, the surface fields of the magnetic Ap stars are generally thought to be of primordial origin. Recent numerical models suggest that a primordial field in the radiative envelope may possess a highly twisted toroidal shape. We have used detailed 3-D simulations to study the interaction of such a twisted magnetic field in the radiative envelope with the core-dynamo operating in the interior of a 2 solar mass A-type star. The resulting dynamo action is much more vigorous than in the absence of such a fossil field, yielding magnetic field strengths (of order 100 kG) much higher than their equipartition values relative to the convective velocities. We examine the generation of these fields, as well as the growth of large-scale magnetic structure that results from imposing a fossil magnetic field. Title: Strong Dynamo Action in Rapidly Rotating Suns Authors: Brown, Benjamin P.; Browning, Matthew K.; Brun, Allan Sacha; Miesch, Mark S.; Nelson, Nicholas J.; Toomre, Juri Bibcode: 2007AIPC..948..271B Altcode: 2008arXiv0801.1684B Stellar dynamos are driven by complex couplings between rotation and turbulent convection, which drive global-scale flows and build and rebuild stellar magnetic fields. When stars like our sun are young, they rotate much more rapidly than the current solar rate. Observations generally indicate that more rapid rotation is correlated with stronger magnetic activity and perhaps more effective dynamo action. Here we examine the effects of more rapid rotation on dynamo action in a star like our sun. We find that vigorous dynamo action is realized, with magnetic field generated throughout the bulk of the convection zone. These simulations do not possess a penetrative tachocline of shear where global-scale fields are thought to be organized in our sun, but despite this we find strikingly ordered fields, much like sea-snakes of toroidal field, which are organized on global scales. We believe this to be a novel finding. Title: Convective Core Dynamos of A-type Stars in the Presence of Fossil Magnetic Fields Authors: Featherstone, N. A.; Browning, M. K.; Brun, A. S.; Toomre, J. Bibcode: 2007AIPC..948..279F Altcode: The persistent magnetic fields of Ap stars are generally thought to be of primordial origin, but dynamo generation of magnetic fields may offer alternative possibilities. Deep within the interiors of such stars, vigorous core convection likely couples with rotation to yield magnetic dynamo action, generating strong magnetic fields. Recent numerical models suggest that a primordial field remaining from the star's formation may possess a highly twisted toroidal shape in the radiative interior. We have used detailed 3-D simulations to study the interaction of such a magnetic field with a dynamo generated within the core of a 2 solar mass A-type star. Dynamo action realized under these circumstances is much more vigorous than in the absence of a fossil field in the radiative envelope, yielding magnetic field strengths (of order 100 kG) much higher than their equipartition values relative to the convective velocities. We examine the generation of these fields, as well as their effect on the complex dynamics of the convective core. Title: Global Models of Solar Convection Authors: Miesch, Mark S.; Browning, Matthew K.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2007AIPC..948..149M Altcode: Convection is fundamental and enigmatic enough to rank high on any pundit's list of unsolved problems in stellar physics. It is responsible in large part for why stars shine since most stellar interiors are at least partially convective. Furthermore, convection plays an essential role in how stars build magnetic fields. Magnetism in turn accounts for most short-term solar and stellar variability. Despite its ubiquity, stellar convection is challenging to model theoretically or numerically. In this paper we provide an overview of some recent insights into solar and stellar convection obtained from high-resolution numerical simulations. Thanks to continuing advances in high performance computing technology, such simulations continue to achieve unprecedented parameter regimes revealing turbulent dynamics inaccessible to previous models. Here we focus in particular on the subtle and profound influence of the complex boundary layers which exist near the top and bottom of the solar convection zone. Title: Challenges of magnetism in the turbulent Sun Authors: Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri Bibcode: 2007IAUS..239..488B Altcode: No abstract at ADS Title: Simulations of solar magnetic dynamo action in the convection zone and tachocline Authors: Browning, Matthew K.; Miesch, Mark S.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2007IAUS..239..510B Altcode: No abstract at ADS Title: Magnetic Dynamo Action In The Convective Cores Of A-type Stars In The Presence Of Fossil Fields Authors: Featherstone, Nicholas; Browning, M. K.; Brun, A. S.; Toomre, J. Bibcode: 2007AAS...210.1702F Altcode: 2007BAAS...39Q.117F The intense surface magnetism of Ap stars has attracted much scrutiny. The observed persistent fields are generally thought to be of primordial origin, but dynamo generation of magnetic fields may offer alternative possibilities. Deep within the interiors of such stars, vigorous core convection likely couples with rotation to yield magnetic dynamo action, generating strong magnetic fields. Recent numerical models suggest that a primordial field remaining from the star’s formation may possess a highly twisted toroidal shape in the radiative interior. We have used detailed 3-D simulations to study the interaction of such a magnetic field with a dynamo generated within the core of a 2 solar mass A-type star. Dynamo action realized under these circumstances is much more vigorous than in the absence of a fossil field in the radiative envelope, yielding magnetic field strengths (of order 100 kG) much higher than their equipartition values relative to the convective velocities. We examine the generation of these fields, as well as their effect on the complex dynamics of the convective core. Title: Structure and Evolution of Giant Cells in Global Models of Solar Convection Authors: Miesch, Mark S.; Brun, A. S.; De Rosa, M. L.; Toomre, J. Bibcode: 2007AAS...210.2217M Altcode: 2007BAAS...39..127M We present the highest-resolution simulations of global-scale solar convection so far achieved, dealing with turbulent compressible flows interacting with rotation in a full spherical shell. The three-dimensional simulation domain extends from 0.71R-0.98R, close enough to the photosphere to overlap with solar subsurface weather (SSW) maps inferred from local helioseismology. The convective patterns achieved are complex and continually evolving on a time scale of several days. However, embedded within the intricate downflow network near the surface are coherent downflow lanes associated with giant cells which persist for weeks to months and which extend through much of the convection zone. These coherent downflow lanes are generally confined to low latitudes and are oriented in a north-south direction. The low dissipation in these simulations permits a more realistic balance of forces which yields differential rotation and meridional circulation profiles in good agreement with those inferred from helioseismology. Title: Round table discussion of session G: MHD convection and dynamos Authors: Toomre, Juri Bibcode: 2007IAUS..239..494T Altcode: No abstract at ADS Title: Rapid Rotation And Nests Of Convection In Solar-like Stars Authors: Brown, Benjamin; Browning, M. K.; Brun, A. S.; Miesch, M. S.; Toomre, J. Bibcode: 2007AAS...210.1703B Altcode: 2007BAAS...39..117B Earlier in its life our Sun must have rotated considerably more rapidly, given that its magnetized wind slowly carries away angular momentum. Indeed many G-type stars are found to rotate rapidly, and their deep convective envelopes and the dynamos operating there must sense the effects of rotation. Here we use 3-D simulations to study the differential rotation and patterns of convection established in these more rapidly rotating stars. Our simulations with the anelastic spherical harmonic (ASH) code capture the deep solar convection zone with a solar-like radial stratification and within a spherical geometry, which admits global-scale flows. We explore a range of rotation rates from 1 to 10 times the solar rotation rate. Convection in the equatorial regions of these rapidly rotating stars shows strong longitudinal modulation. At the fastest rotation rates, convection is restricted to active nests spanning compact regions in longitude, with quiescent streaming flow filling the regions in between. These nests of convection persist for long periods and drive a strong differential rotation. Convection at high latitudes is more isotropic but couples to the equatorial regions through the meridional circulations present throughout the shell. Title: Dynamo Action, Magnetic Activity, And Rotation In F Stars Authors: Augustson, Kyle; Brown, B. P.; Brun, A. S.; Toomre, J. Bibcode: 2007AAS...210.1701A Altcode: 2007BAAS...39..117A The origin of stellar magnetic fields must rest with dynamo processes occurring deep within a star. Observations of F-type stars suggest unusual relations between their rotation rates and magnetic activity. Generally in cooler stars, magnetic activity increases with more rapid rotation, but, in F-type stars, there is observational evidence for a sharp transition from this behavior around spectral type F5. Stars hotter than F5 show an anti-correlation between magnetic activity and rotation: more rapidly rotating stars seem to possess weaker magnetic fields, possibly because they have less efficient dynamos. We have conducted 3-D simulations of compressible MHD convection with the anelastic spherical harmonic (ASH) code, in order to study F-type star convection zone dynamics in rotating spherical shells. Our initial radial stratification is based on stellar models of stars in the narrow mass range between 1.2 and 1.4 solar masses. We exhibit the resulting differential rotation profiles and rich convective behavior realized as the rotation rates of the stars are increased. We also discuss our preliminary foray into studying the magnetic dynamo achieved within several models, considering the effects of rotation rates. Title: Helioseismic Searches for the Elusive Giant Cells of Convection Authors: Featherstone, Nicholas; Hindman, B. W.; Haber, D. A.; Toomre, J. Bibcode: 2007AAS...210.2216F Altcode: 2007BAAS...39..127F The turbulent solar convection zone exhibits a range of scales of convection which are visible at the solar surface, ranging from granules ( 1 Mm) to supergranules ( 30 Mm). Numerical simulations of solar convection carried out in full-spherical shells consistently reveal even larger scales of convection, termed giant cells, which may span a few hundred Mm in the horizontal and extend throughout the depth of the convection zone. Recent correlation tracking of supergranular motions has revealed the tendency of supergranules to align themselves in the north-south direction. This alignment may be due to organization by larger-scale giant-cell motions and is generally weak, with the strongest alignment occurring at low latitudes. Using f-mode time-distance helioseismology, we have probed the flow signals associated with the presence of these giant cells and have found good agreement with the results from previous correlation tracking studies. Moreover, we find that the horizontal divergence of our measured flows exhibit particularly striking alignment at larger scales. Title: Strong Global Dynamo Action in a Younger Sun Authors: Brown, Benjamin; Brun, A. S.; Miesch, M. S.; Toomre, J. Bibcode: 2007AAS...210.2414B Altcode: 2007BAAS...39..130B Stellar dynamos are powered by the coupling of rotation, convection and the global scale flows which are established in these systems. Our Sun has lost angular momentum through its magnetized wind and once rotated more rapidly than it currently does. We explore the nature of dynamo action in a younger sun rotating five times its current rate. Our explorations employ 3-D simulations of compressible MHD convection within a spherical shell extending from 0.72 to 0.97 solar radii using the anelastic spherical harmonic (ASH) code on massively parallel supercomputers. The dynamo which naturally arises in this convective system is vigorous and builds organized magnetic structures which fill the bulk of the convection zone. This is in striking contrast to the global dynamo thought to operate in the current sun, which appears to require the pumping of magnetic field into a tachocline of shear at the base of the convection zone to generate similar magnetic structures. Particularly in the equatorial regions, we find strong toroidal fields ( 30 kG) coexisting with the turbulent convection. This dynamo system exhibits cyclic behavior, with the large-scale toroidal and poloidal fields switching their polarity. Title: Temporal variations in solar rotation at the bottom of the convection zone: The current status Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R.; Schou, J.; Thompson, M. J.; Toomre, J. Bibcode: 2007AdSpR..40..915H Altcode: We present the most recent results on the short-period variations in the solar rotation rate near the base of the convection zone. The 1.3-year period which was reported in the early years of solar cycle 23 appears not to persist after 2001, but there are hints of fluctuations at a different period during the declining phase of the cycle. Title: Helioseismically Determined Near-Surface Flows Underlying a Quiescent Filament Authors: Hindman, Bradley W.; Haber, Deborah A.; Toomre, Juri Bibcode: 2006ApJ...653..725H Altcode: The extended filaments seen in Hα images of the solar disk, and the corresponding prominences when viewed at the solar limb, are one of the great hallmarks of solar magnetism. Such arches of magnetic field and the coronal plasma structures they support are both beautiful and enigmatic. Many models of filament formation and maintenance invoke the existence of surface plasma flows, which are used to drive the magnetic reconnection needed to form twisted loops of flux held down by a coronal arcade. These flows are typically composed of a converging flow, which brings flux elements of opposite polarity together, combined with a tangential shear that stresses the coronal arcade. In this paper we present helioseismic measurements of near-surface flows underlying a single quiescent filament lying within a decayed active region. Newly devised high-resolution ring analyses (HRRA) with both 2° and 4° spatial resolution were applied to Doppler imaging data provided by the Michelson Doppler Imager (MDI) instrument on the SOHO spacecraft. A long-lived filament appearing in 2002 May and April was studied. We find that the filament channel is a region of vigorous subphotospheric convection. The largest observed scales of such convection span the region of weak magnetic field separating the active region's two polarities. Thus, the magnetic neutral line that forms the spine of the filament channel tends to lie along the centers of large convection cells. In temporal and spatial averages of the flow field, we do not find a systematic converging flow. However, we do detect a significant shearing flow parallel to the neutral line. This shear takes the form of two oppositely directed jets, one to either side of the neutral line and within 20 Mm of the line. The jets produce a net shear in the flow speed of 30 m s-1 occurring over a distance of 20 Mm. Title: Helioseismic probing of giant-cell convection Authors: Featherstone, N. A.; Haber, D. A.; Hindman, B. W.; Toomre, J. Bibcode: 2006ESASP.624E.133F Altcode: 2006soho...18E.133F No abstract at ADS Title: Subsurface convective flows within active regions Authors: Hindman, B. W.; Haber, D. A.; Toomre, J. Bibcode: 2006ESASP.624E..11H Altcode: 2006soho...18E..11H No abstract at ADS Title: Large-scale circulations using ring analysis Authors: Haber, D.; Hindman, B.; Toomre, J.; Bogart, R. S. Bibcode: 2006ESASP.624E..45H Altcode: 2006soho...18E..45H No abstract at ADS Title: Various dynamical puzzle pieces in the seismic Rubik's cube Authors: Toomre, J. Bibcode: 2006ESASP.624E...1T Altcode: 2006soho...18E...1T No abstract at ADS Title: Dynamo Action in the Solar Convection Zone and Tachocline: Pumping and Organization of Toroidal Fields Authors: Browning, Matthew K.; Miesch, Mark S.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2006ApJ...648L.157B Altcode: 2006astro.ph..9153B We present the first results from three-dimensional spherical shell simulations of magnetic dynamo action realized by turbulent convection penetrating downward into a tachocline of rotational shear. This permits us to assess several dynamical elements believed to be crucial to the operation of the solar global dynamo, variously involving differential rotation resulting from convection, magnetic pumping, and amplification of fields by stretching within the tachocline. The simulations reveal that strong axisymmetric toroidal magnetic fields (about 3000 G in strength) are realized within the lower stable layer, unlike in the convection zone where fluctuating fields are predominant. The toroidal fields in the stable layer possess a striking persistent antisymmetric parity, with fields in the northern hemisphere largely of opposite polarity to those in the southern hemisphere. The associated mean poloidal magnetic fields there have a clear dipolar geometry, but we have not yet observed any distinctive reversals or latitudinal propagation. The presence of these deep magnetic fields appears to stabilize the sense of mean fields produced by vigorous dynamo action in the bulk of the convection zone. Title: Introductory - Overview: Close interplay between global helioseismology and dynamical models Authors: Toomre, J. Bibcode: 2006IAUJD..17E...1T Altcode: The nearly continuous full-disk imaging of solar resonant oscillations with both the ground-based Global Oscillation Network Group (GONG) and the space-based Michelson Doppler Imager (MDI) on SOHO have yielded detailed inferences about differential rotation, meridional circulations, and large-scale streaming flows within the solar convection zone. Of particular interest has been the evolution of such dynamical structures, and their coupling to magnetism, variously in the tachocline of rotational shear at its base and in the near-surface shear layer. We review properties of such dynamics involving variations in rotation rates near the tachocline, of propagating banded features in the differential rotation in the upper reaches of the convection zone, and of evolving patterns in the circulations there. In addition, local helioseismic probing shows the presence of striking subsurface flows appearing variously as meandering jets and a wide range of structured and possibly cellular flows. These samplings of dynamics proceeding within the solar convection zone provides challenges and inspiration for three-dimensional simulations of turbulent convection, rotation and magnetism in spherical shells now enabled by massively-parallel supercomputers. We review the interplay between features emerging from such high-resolution simulations of the solar convection zone and the richness of dynamics being revealed by helioseismic probing. The simulations now make good contact with differential rotation profiles so deduced in the bulk of the convection zone. Yet all models possess complex downflow structures that extend over most of that zone. Such large-scale convection so evident in global simulations may now have been identified in the helioseismic data, with simulations guiding the manner in which the elusive giant cells may be detected amidst the intense flows of supergranulation. Title: Solar-Cycle Variations of Internal Structure, Rotation and Circulations Authors: Toomre, J. Bibcode: 2006IAUJD...8E..67T Altcode: Helioseismology is permitting detailed study of structure and dynamics in the solar interior as the magnetic cycle advances. Although many International helioseismic projects have contributed, the nearly continuous Doppler imaging provided for over ten years by the ground-based Global Oscillation Network Group (GONG) project and the Michelson Doppler Imager (MDI) on the SOHO spacecraft allow us to evaluate changes within the sun over a significant fraction of the 22-year activity cycle. Nearly 10 million resonant acoustic modes of oscillation observable in the solar atmosphere provide probes of flows and structures over a wide range of depths within the solar convection zone and the tachocline of rotational shear at its base. The global magnetic dynamo responsible for the activity cycles is believed to operate in a distributed manner throughout these regions, but the principal stretching to achieve strong toroidal magnetic fields (responsible for the eventual emergence of sunspot pairs) proceeds in the tachocline. We review the evidence for variations in the differential rotation observed near the tachocline, of propagating bands of zonal flow speedup observed in the near-surface shear layer, and of changes in the meridional circulations as the cycle advances. We also discuss the evolving patterns of streaming flows known as solar subsurface weather (SSW) and of their interactions with magnetic active regions, often exhibiting prominent inflows at shallow depths and strong outflows deeper down within that near-surface shear layer. Such a range of clues being provided by helioseismology about the complex dynamics proceeding with the convection zone are serving to guide efforts to build self-consistent models of the solar global dynamo. Title: Solar Filament Evolution in the Presence of Subsurface Flows Authors: Haber, Deborah A.; Hindman, B. W.; Toomre, J.; Bogart, R. S. Bibcode: 2006SPD....37.3202H Altcode: 2006BAAS...38..257H Many models of filament formation and evolution are driven by converging and shearing flows in the photosphere and upper convection zone, where the gas is dense enough to move the magnetic footpoints of a filament. With our recent development of High-Resolution Ring Analysis (HRRA) procedures, we are now able to measure flows below the surface with a horizontal resolution of 2 heliographic degrees (∼20 Mm). With this HRRA analysis of the flows underlying filaments and filament channels, we have found evidence of shearing flows along the neutral line in at least one instance and will be presenting the results from several more filaments. This research is funded in part by NASA grants NAG5-12491 and NNG05GM83G. Title: Helioseismic Probing of Giant-Cell Convection Authors: Featherstone, Nicholas; Haber, D. A.; Hindman, B. W.; Toomre, J. Bibcode: 2006SPD....37.3201F Altcode: 2006BAAS...38R.257F The turbulent solar convection zone exhibits a range of scales of convection which are visible at the solar surface, ranging from granules ( 1 Mm) to supergranules ( 30 Mm). Numerical simulations of solar convection carried out in full spherical shells consistently reveal even larger scales of convection, termed giant cells, which may span a few hundreds of Mm in the horizontal and extend over much of the convection zone. Recent correlation tracking of supergranular motions has revealed the tendency of supergranules to align themselves in the north-south direction. This alignment is possibly due to organization by larger-scale giant cell motions and is generally weak, with the strongest alignment occurring at the equator. Using f-mode time-distance and specialized averaging and tracking techniques, we probe for the possible flow signals associated with the presence of these giant cells near the solar equator. Title: Localized Nests of Convection in Rapidly Rotating Suns Authors: Brown, Benjamin; Browning, M.; Brun, A.; Toomre, J. Bibcode: 2006SPD....37.3205B Altcode: 2006BAAS...38..258B Many solar-like stars rotate more rapidly than the sun. Through their magnetized winds, these stars gradually lose angular momentum and spin down. By similar processes, our Sun must have rotated more rapidly in the past than it currently does. We explore the effects of more rapid rotation upon turbulent stellar convection, studying full spherical shells that admit global scale flows. We conduct 3-D simulations of compressible turbulent convection with the anelastic spherical harmonic (ASH) code on massively parallel supercomputers. For simplicity, we adopt the radial stratification of the present-day sun and examine global scale convection in a zone extending from 0.72 to 0.97 solar radii, and consider a range of rotation rates from 1 to 5 times the solar rotation rate. With increasing rotation we observe that convection at low latitudes becomes spatially modulated in strength, yielding localized nests of strong convection. These nests are persistent over very long periods and propagate in longitude at slower rates than individual convective structures within them. It is striking that a strong differential rotation is achieved by these modulated states. The convection at high latitudes is more isotropic but influenced by the meridional circulations present throughout the shell. Weak modulation can be recognized even at the solar rotation rate, with some implications for active magnetic longitudes in the Sun. Title: Solar Differential Rotation Influenced by Latitudinal Entropy Variations in the Tachocline Authors: Miesch, Mark S.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2006ApJ...641..618M Altcode: Three-dimensional simulations of solar convection in spherical shells are used to evaluate the differential rotation that results as thermal boundary conditions are varied. In some simulations a latitudinal entropy variation is imposed at the lower boundary in order to take into account the coupling between the convective envelope and the radiative interior through thermal wind balance in the tachocline. The issue is whether the baroclinic forcing arising from tachocline-induced entropy variations can break the tendency for numerical simulations of convection to yield cylindrical rotation profiles, unlike the conical profiles deduced from helioseismology. As the amplitude of the imposed variation is increased, cylindrical rotation profiles do give way to more conical profiles that exhibit nearly radial angular velocity contours at midlatitudes. Conical rotation profiles are maintained primarily by the resolved convective heat flux, which transmits entropy variations from the lower boundary into the convective envelope, giving rise to baroclinic forcing. The relative amplitude of the imposed entropy variations is of order 10-5, corresponding to a latitudinal temperature variation of about 10 K. The role of thermal wind balance and tachocline-induced entropy variations in maintaining the solar differential rotation is discussed. Title: Simulations of Core Convection in Rotating A-Type Stars: Magnetic Dynamo Action Authors: Brun, Allan Sacha; Browning, Matthew K.; Toomre, Juri Bibcode: 2005ApJ...629..461B Altcode: 2006astro.ph.10072B Core convection and dynamo activity deep within rotating A-type stars of 2 Msolar are studied with three-dimensional nonlinear simulations. Our modeling considers the inner 30% by radius of such stars, thus capturing within a spherical domain the convective core and a modest portion of the surrounding radiative envelope. The magnetohydrodynamic (MHD) equations are solved using the anelastic spherical harmonic (ASH) code to examine turbulent flows and magnetic fields, both of which exhibit intricate time dependence. By introducing small seed magnetic fields into our progenitor hydrodynamic models rotating at 1 and 4 times the solar rate, we assess here how the vigorous convection can amplify those fields and sustain them against ohmic decay. Dynamo action is indeed realized, ultimately yielding magnetic fields that possess energy densities comparable to that of the flows. Such magnetism reduces the differential rotation obtained in the progenitors, partly by Maxwell stresses that transport angular momentum poleward and oppose the Reynolds stresses in the latitudinal balance. In contrast, in the radial direction we find that the Maxwell and Reynolds stresses may act together to transport angular momentum. The central columns of slow rotation established in the progenitors are weakened, with the differential rotation waxing and waning in strength as the simulations evolve. We assess the morphology of the flows and magnetic fields, their complex temporal variations, and the manner in which dynamo action is sustained. Differential rotation and helical convection are both found to play roles in giving rise to the magnetic fields. The magnetism is dominated by strong fluctuating fields throughout the core, with the axisymmetric (mean) fields there relatively weak. The fluctuating magnetic fields decrease rapidly with radius in the region of overshooting, and the mean toroidal fields less so due to stretching by rotational shear. Title: Helioseismic Ring Analyses of Artificial Data Computed for Two-dimensional Shearing Flows Authors: Hindman, Bradley W.; Gough, Douglas; Thompson, Michael J.; Toomre, Juri Bibcode: 2005ApJ...621..512H Altcode: The local helioseismological technique of ring analysis has been crucial in the discovery of complex large-scale flows in the Sun's near-surface shear layer. However, current implementations of ring-analysis procedures assume that the flow field is horizontally homogeneous over the analysis region. This assumption is certainly incorrect, and in the present paper we assess the significance of this approximation by analyzing artificial data sets computed from models of horizontal shear flows. We consider the simple case of purely horizontal and unidirectional flow that varies solely in the horizontal direction orthogonal to the flow in a piecewise-constant manner. An ensemble of plane waves is incident on the flow, and the scattered wave field produced by the prescribed two-dimensional flow is computed to generate an artificial helioseismic power spectrum. The artificial spectrum is processed in a manner similar to standard ring analysis, and the flow field that is thereby inferred is compared with the known imposed flow. We find that the inferred flow velocity is essentially an average of the true flow velocity over the region of the analysis, weighted by the square of the spatial apodization function used in processing the oscillation signal. Furthermore, the shape of a p-mode line profile is determined by the distribution of speeds across the analysis region. Title: Simulations of core convection and resulting dynamo action in rotating A-type stars Authors: Browning, Matthew K.; Brun, Allan S.; Toomre, Juri Bibcode: 2004IAUS..224..149B Altcode: 2004astro.ph..9703B We present the results of 3-D nonlinear simulations of magnetic dynamo action by core convection within A-type stars of 2 M with a range of rotation rates. We consider the inner 30% by radius of such stars, with the spherical domain thereby encompassing the convective core and a portion of the surrounding radiative envelope. The compressible Navier-Stokes equations, subject to the anelastic approximation, are solved to examine highly nonlinear flows that span multiple scale heights, exhibit intricate time dependence, and admit magnetic dynamo action. Small initial seed magnetic fields are found to be amplified greatly by the convective and zonal flows. The central columns of strikingly slow rotation found in some of our progenitor hydrodynamic simulations continue to be realized in some simulations to a lesser degree, with such differential rotation arising from the redistribution of angular momentum by the nonlinear convection and magnetic fields. We assess the properties of the magnetic fields thus generated, the extent of the convective penetration, the magnitude of the differential rotation, and the excitation of gravity waves within the radiative envelope. Title: Evolution of Solar Supergranulation Authors: De Rosa, Marc L.; Toomre, Juri Bibcode: 2004ApJ...616.1242D Altcode: The structure and evolution of solar supergranulation is studied using horizontal velocity fields, deduced from applying local correlation tracking (LCT) techniques to full-disk, line-of-sight Doppler velocity data observed by the Michelson Doppler Imager on board the Solar and Heliospheric Observatory spacecraft. Two 45° square regions of photospheric plasma, one of the quiet Sun and one with increased magnetic activity, are tracked for as long as they remain visible on the disk of the Sun (about 6 days), enabling a determination of the complete life histories of over 3000 supergranules in each region. With this method, the horizontal outflows associated with the pattern of supergranulation are revealed with clarity, even for locations near disk center where little of the horizontal velocity field is projected into the line of sight. The LCT flow mappings are of sufficient temporal extent that they can be used to study the complex evolution of a broad spectrum of supergranules, revealing that merging and fragmentation events figure prominently in the life histories of more than half of the supergranules in each data set. Such dynamics lead to many short-lived supergranules (about 75% of the total population) having lifetimes of less than 24 hr, coexisting among numerous long-lived supergranules, many of which exist for several days. Average supergranular lifetimes lie in the 16-23 hr range, although about 7% of all are recognizable for time periods of 48 hr or more. The average supergranular cell diameter lies in the 12-20 Mm range, with smaller cells more prevalent in areas of greater magnetism. There exists a tendency for larger cells to preferentially have longer lifetimes when embedded in a region of increased magnetic flux. Title: Core Convection and Dynamo Action in Rotating A-type Stars Authors: Browning, M. K.; Brun, A. S.; Toomre, J. Bibcode: 2004AAS...205.3403B Altcode: 2004BAAS...36.1402B We have carried out 3-D simulations of core convection and dynamo activity within A-type stars of two solar masses at a range of rotation rates. Our models consider the inner 30% by radius of such stars, thus capturing the entire convective core and a portion of the surrounding radiative envelope within the spherical computational domain. Using the anelastic spherical harmonic (ASH) code on massively parallel supercomputers, we solve the compressible MHD equations to examine highly nonlinear and evolving flows and magnetic fields. Vigorous dynamo action is realized, with initial seed magnetic fields amplified by many orders of magnitude and sustained against ohmic decay. The resulting complex magnetism possesses energy densities comparable to that in the flows, is structured on many scales, and serves to modify the convective and zonal flows that gave rise to it. The differential rotation established in progenitor hydrodynamic simulations is weakened, and waxes and wanes in strength as the simulations evolve. We discuss the morphology and evolution of the flows and magnetic fields, the penetrative properties of the convection, and the nature of the dynamo process. Title: Simulations of Core Convection and Dynamo Activity in Rotating A-Type Stars Authors: Browning, M. K.; Brun, A. S.; Toomre, J. Bibcode: 2004ESASP.559..349B Altcode: 2004soho...14..349B No abstract at ADS Title: Subphotospheric Flows Near Active Region NOAA 10486 Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.; Thompson, M. J. Bibcode: 2004ESASP.559..148H Altcode: 2004soho...14..148H No abstract at ADS Title: Cause of Shrinking Sun Effect in Local Correlation Tracking and Impacts on the Mapping of Ssw Flows Authors: Lisle, J.; Toomre, J. Bibcode: 2004ESASP.559..556L Altcode: 2004soho...14..556L No abstract at ADS Title: Differential Rotation when the Sun Spun Faster Authors: Brown, B. P.; Browning, M. K.; Brun, A. S.; Toomre, J. Bibcode: 2004ESASP.559..341B Altcode: 2004soho...14..341B No abstract at ADS Title: Comparison of Solar Subsurface Flows Assessed by Ring and Time-Distance Analyses Authors: Hindman, Bradley W.; Gizon, Laurent; Duvall, Thomas L., Jr.; Haber, Deborah A.; Toomre, Juri Bibcode: 2004ApJ...613.1253H Altcode: The solar near-surface shear layer exhibits a rich medley of flows that are now being measured by a variety of local helioseismic techniques. We present comparisons of the horizontal flows obtained with two of these techniques, ring and time-distance analyses, applied to Michelson Doppler Imager (MDI) Dynamics Program data from the years 1998 and 1999. The ring analyses use the frequencies of both f and p modes in inversions to obtain flows within the near-surface shear layer as a function of depth. The f-mode time-distance analyses make velocity inferences just beneath the photosphere. After degrading the spatial resolution of the time-distance analyses to match the coarser resolution of the ring analyses, we find that the flows deduced with the two methods are remarkably similar, with common inflow and outflow sites as well as agreement in flow direction. The flows from ring and time-distance analyses are highly correlated with each other (correlation coefficients ~0.8) direct correspondence of features in the flows is largely realized in both the quiet-Sun and magnetic active regions. Title: Time-Distance Helioseismology: a Fourier Transform Method and Measurement of Reynolds Stresses Authors: Featherstone, N. A.; Hindman, B. W.; Haber, D. A.; Toomre, J. Bibcode: 2004ESASP.559..428F Altcode: 2004soho...14..428F No abstract at ADS Title: Comparison of Local Helioseismic Techniques Applied to MDI Doppler Data Authors: Hindman, B. W.; Featherstone, N. A.; Haber, D. A.; Musman, S.; Toomre, J. Bibcode: 2004ESASP.559..460H Altcode: 2004soho...14..460H No abstract at ADS Title: Global-Scale Turbulent Convection and Magnetic Dynamo Action in the Solar Envelope Authors: Brun, Allan Sacha; Miesch, Mark S.; Toomre, Juri Bibcode: 2004ApJ...614.1073B Altcode: 2006astro.ph.10073B The operation of the solar global dynamo appears to involve many dynamical elements, including the generation of fields by the intense turbulence of the deep convection zone, the transport of these fields into the tachocline region near the base of the convection zone, the storage and amplification of toroidal fields in the tachocline by differential rotation, and the destabilization and emergence of such fields due to magnetic buoyancy. Self-consistent magnetohydrodynamic (MHD) simulations that realistically incorporate all of these processes are not yet computationally feasible, although some elements can now be studied with reasonable fidelity. Here we consider the manner in which turbulent compressible convection within the bulk of the solar convection zone can generate large-scale magnetic fields through dynamo action. We accomplish this through a series of three-dimensional numerical simulations of MHD convection within rotating spherical shells using our anelastic spherical harmonic (ASH) code on massively parallel supercomputers. Since differential rotation is a key ingredient in all dynamo models, we also examine here the nature of the rotation profiles that can be sustained within the deep convection zone as strong magnetic fields are built and maintained. We find that the convection is able to maintain a solar-like angular velocity profile despite the influence of Maxwell stresses, which tend to oppose Reynolds stresses and thus reduce the latitudinal angular velocity contrast throughout the convection zone. The dynamo-generated magnetic fields exhibit a complex structure and evolution, with radial fields concentrated in downflow lanes and toroidal fields organized into twisted ribbons that are extended in longitude and achieve field strengths of up to 5000 G. The flows and fields exhibit substantial kinetic and magnetic helicity although systematic hemispherical patterns are only apparent in the former. Fluctuating fields dominate the magnetic energy and account for most of the back-reaction on the flow via Lorentz forces. Mean fields are relatively weak and do not exhibit systematic latitudinal propagation or periodic polarity reversals as in the Sun. This may be attributed to the absence of a tachocline, i.e., a penetrative boundary layer between the convection zone and the deeper radiative interior possessing strong rotational shear. The influence of such a layer will await subsequent studies. Title: Variations of Solar Subsurface Weather in the Vicinity of Active Regions Authors: Brown, B. P.; Haber, D. A.; Hindman, B. W.; Toomre, J. Bibcode: 2004ESASP.559..345B Altcode: 2004soho...14..345B No abstract at ADS Title: Solar Differential Revealed by Helioseismology and Simulations of Deep Shells of Turbulent Convection Authors: Toomre, J.; Brun, A. S. Bibcode: 2004IAUS..215..326T Altcode: No abstract at ADS Title: The Spectrum of the Solar Supergranulation: Multiple Nonwave Components Authors: Rast, Mark P.; Lisle, Jason P.; Toomre, Juri Bibcode: 2004ApJ...608.1156R Altcode: It has recently been suggested that the solar supergranulation undergoes oscillations, with a spectrum of superposed traveling waves of unknown origin showing excess prograde power to yield superrotation. We show here that the observed supergranular spectrum does not necessarily imply a wave origin but is instead consistent with two components of nonoscillatory bulk motions having differing rotation rates and somewhat asymmetrically distributed in space. The two components are identified with solar mesogranulation and supergranulation, and the spatial asymmetry is shown to be caused by a weak north-south alignment of the supergranular flows. The source of both the supergranular alignment and its enhanced rotation is likely underlying giant cell motions. Because no single rotation rate characterizes all components of a solar image, the spectral properties, including the Fourier dispersion relation, are extremely sensitive to the rate at which the solar disk is tracked when making up the time series. A spuriously wavelike spectrum is obtained when the image tracking rate falls between the actual mesogranular and supergranular rotation rates. Title: Looking Deep Within an A-type Star: Core Convection Under the Influence of Rotation Authors: Brun, A. S.; Browning, M.; Toomre, J. Bibcode: 2004IAUS..215..388B Altcode: 2003astro.ph..2598B The advent of massively parallel supercomputing has begun to permit explicit 3--D simulations of turbulent convection occurring within the cores of early-type main sequence stars. Such studies should complement the stellar structure and evolution efforts that have so far largely employed 1--D nonlocal mixing length descriptions for the transport, mixing and overshooting achieved by core convection. We have turned to A-type stars as representative of many of the dynamical challenges raised by core convection within rotating stars. The differential rotation and meridional circulations achieved deep within the star by the convection, the likelihood of sustained magnetic dynamo action there, and the bringing of fresh fuel into the core by overshooting motions, thereby influencing main sequence lifetimes, all constitute interesting dynamical questions that require detailed modelling of global-scale convection. Using our anelastic spherical harmonic (ASH) code tested on the solar differential rotation problem, we have conducted a series of 3--D spherical domain simulations that deal with a simplified description of the central regions of rotating A-type stars, i.e a convectively unstable core is surrounded by a stable radiative envelope. A sequence of 3--D simulations are used to assess the properties of the convection (its global patterns, differential rotation, meridional circulations, extent and latitudinal variation of the overshooting) as transitions are made between laminar and turbulent states by changing the effective diffusivities, rotation rates, and subadiabaticity of the radiative exterior. We report on the properties deduced from these models for both the extent of penetration and the profile of rotation sustained by the convection. Title: Simulations of Core Convection Dynamos in Rotating A-type Stars Authors: Browning, M.; Brun, A. S.; Toomre, J. Bibcode: 2004IAUS..215..376B Altcode: No abstract at ADS Title: Persistent North-South Alignment of the Solar Supergranulation Authors: Lisle, Jason P.; Rast, Mark P.; Toomre, Juri Bibcode: 2004ApJ...608.1167L Altcode: We have found evidence of an alignment of the solar supergranulation in the direction parallel to the Sun's rotation axis. Signatures of the alignment are apparent in both time-averaged images and in three-dimensional power spectra. The north-south organization is persistent in time, extending over many supergranular lifetimes. It occurs over a wide latitudinal extent, to +/-60°, and shows variation on a 10°-30° scale. These properties, as well as the rotation rate of the pattern, suggest a underlying larger scale dynamical cause. We examine a mechanism by which giant cell motions may contribute to such alignment. Title: Subphotospheric Flows Around Active Region NOAA 10486 Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.; Thompson, M. J.; LoHCo Team Bibcode: 2004AAS...204.0211H Altcode: 2004BAAS...36Q.669H We have used MDI Dynamics Program Doppler data taken between October 18th and November 15th 2003 to study the interaction of solar subsurface flows with NOAA 10486, one of the most dynamic active regions of the past solar cycle. Using the local helioseismic techniques of ring and time-distance analyses, we assess the horizontal flows that surrounded and permeated this region and how they varied with depth in the upper 14 Mm of the convection zone. We examine and identify structures in the flow field that may have been associated with the energetic flares that occurred during the period of observation. This research is in part supported by NASA through grants NAG5-11920, NAG5-10917, and NAG5-12491. Title: Simulations of Core Convection and Dynamo Activity in A-type Stars at a Range of Rotation Rates Authors: Browning, M. K.; Brun, A. S.; Toomre, J. Bibcode: 2004AAS...204.0707B Altcode: 2004BAAS...36..786B We present the results of nonlinear 3--D simulations of magnetic dynamo action by core convection within A-type stars of 2 solar masses, at a range of rotation rates. We consider the inner 30% by radius of such stars, with the spherical domain thereby encompassing the convective core and a portion of the surrounding radiative envelope. We solve the compressible Navier-Stokes equations in the anelastic approximation to examine highly nonlinear flows that span multiple scale heights, exhibit intricate time dependence, and admit magnetic dynamo action. Small initial seed magnetic fields are found to be amplified greatly by the convective and zonal flows. The central columns of strikingly slow rotation found in some of our progenitor hydrodynamic simulations continue to be realized in some simulations to a lesser degree, with such differential rotation arising from the redistribution of angular momentum by the nonlinear convection and magnetic fields. We assess the properties of the magnetic fields thus generated and the magnitude of the differential rotation sustained as the rotation rate in our simulations is varied. Title: Organized Subsurface Flows near Active Regions Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Thompson, M. J. Bibcode: 2004SoPh..220..371H Altcode: Local helioseismic techniques, such as ring analysis and time-distance helioseismology, have already shown that large-scale flows near the surface converge towards major active regions. Ring analysis has further demonstrated that at greater depths some active regions exhibit strong outflows. A critique leveled at the ring-analysis results is that the Regularized Least Squares (RLS) inversion kernels on which they are based have negative sidelobes near the surface. Such sidelobes could result in a surface inflow being misidentified as a diverging outflow at depth. In this paper we show that the Optimally Located Averages (OLA) inversion technique, which produces kernels without significant sidelobes, generates flows markedly similar to the RLS results. Active regions are universally zones of convergence near the surface, while large complexes evince strong outflows deeper down. Title: Simulations of Core Convection in Rotating A-Type Stars: Differential Rotation and Overshooting Authors: Browning, Matthew K.; Brun, Allan Sacha; Toomre, Juri Bibcode: 2004ApJ...601..512B Altcode: 2003astro.ph.10003B We present the results of three-dimensional simulations of core convection within A-type stars of 2 Msolar, at a range of rotation rates. We consider the inner 30% by radius of such stars, thereby encompassing the convective core and some of the surrounding radiative envelope. We utilize our anelastic spherical harmonic code, which solves the compressible Navier-Stokes equations in the anelastic approximation, to examine highly nonlinear flows that can span multiple scale heights. The cores of these stars are found to rotate differentially, with central cylindrical regions of strikingly slow rotation achieved in our simulations of stars whose convective Rossby number (Roc) is less than unity. Such differential rotation results from the redistribution of angular momentum by the nonlinear convection that strongly senses the overall rotation of the star. Penetrative convective motions extend into the overlying radiative zone, yielding a prolate shape (aligned with the rotation axis) to the central region in which nearly adiabatic stratification is achieved. This is further surrounded by a region of overshooting motions, the extent of which is greater at the equator than at the poles, yielding an overall spherical shape to the domain experiencing at least some convective mixing. We assess the overshooting achieved as the stability of the radiative exterior is varied and the weak circulations that result in that exterior. The convective plumes serve to excite gravity waves in the radiative envelope, ranging from localized ripples of many scales to some remarkable global resonances. Title: Simulations of core convection in rotating A-type stars: Magnetic dynamo action Authors: Browning, M. K.; Brun, A. S.; Toomre, J. Bibcode: 2003AAS...203.8502B Altcode: 2003BAAS...35.1342B We present the results of 3--D simulations of core convection dynamos within A-type stars of 2 solar masses, at a range of rotation rates. The inner 30% by radius of such stars are considered in our calculations, with the spherical domain thereby encompassing the convective core and some of the surrounding radiative envelope. We utilize our anelastic spherical harmonic (ASH) code to examine highly nonlinear flows that can admit magnetic dynamo action. Small initial seed magnetic fields are found to be amplified greatly by the convective and zonal flows. The resulting global fields possess structure on many scales, are strong enough to influence the convective flows themselves, and persist for as long as we have continued our calculations. The central columns of strikingly slow rotation found in some of our progenitor hydrodynamic simulations continue to be realized here to a lesser degree, with such differential rotation arising from the redistribution of angular momentum by the nonlinear convection and magnetic fields. We assess the properties of the magnetic fields, the extent of convective penetration, and the excitation of gravity waves within the radiative envelope. Title: The LoHCo Project. 1 -- Comparison of Ring-Diagram Local Helioseismology on GONG++, MDI and Mt. Wilson Data Sets Authors: Bogart, R. S.; Schou, J.; Basu, S.; Bolding, J.; Hill, F.; Howe, R.; Komm, R. W.; Leibacher, J. W.; Toner, C. G.; Corbard, T.; Haber, D. A.; Hindman, B. W.; Toomre, J.; Rhodes, E. J.; Rose, P. J.; LoHCo Project Team Bibcode: 2003SPD....34.0804B Altcode: 2003BAAS...35..822B Full deployment of the GONG+ enhanced observing network in October 2001 and implementation of ring-diagram helioseismology in the GONG++ analysis pipeline this year has enabled us to make a detailed intercomparison of results obtained through multiple paths, from observation through each of the analysis steps. Such comparisons can provide a certain degree of validation of the implementations of the analysis procedures, hints of systematic errors, and better characterization of the observations, possibly leading to improved calibrations. The Local Helioseismology Comparison (LoHCo) Project has been established to provide standards for intercomparison of results obtained with different local helioseismic analysis techniques applied to the available observational data sources. We present here a detailed comparison of ring-diagram determinations of localized sub-surface flows and frequency shifts obtained from both MDI and GONG in common observing intervals during Carrington Rotation 1988 (2002/3/30 -- 2002/4/26), using both the MDI and the GONG analysis pipelines. We also present preliminary results of similar analyses of data obtained by the Mt. Wilson MOF during the same times.

This work is partially supported by grants from NASA and NSF. Title: Comparison of Solar Subsurface Weather Obtained with Time-Distance Tomography and Ring Analysis Authors: Hindman, B. W.; Zhao, J.; Haber, D. A.; Kosovichev, A. G.; Toomre, J. Bibcode: 2003SPD....34.0806H Altcode: 2003BAAS...35R.822H The near-surface shear layer exhibits a rich medley of flows that vary in size from granular and supergranular flows to flows of global scale. The largest of these flows have been dubbed Solar Surface Weather (SSW), and have been detected with both time-distance tomography and ring analysis. We present comparisons of synoptic maps of SSW flows obtained with both techniques from SOI-MDI Dynamics Program data. Both techniques provide measurements of the flows as a function of depth through inversion. The time-distance method utilizes only p-mode oscillations, while the ring analysis uses f modes as well. We find that the flows obtained with the two helioseismic techniques are remarkably similar, with common inflow and outflow sites as well as agreement in the general flow direction. At a depth of roughly 1.5 Mm the Spearman rank correlation coefficient between maps is on the order of 0.80. As the depth increases the correlation become weaker. The reduction in the correlation coefficient with depth is due to the increasing difference between the vertical resolution kernel of the two seismic techniques. Title: Overview - where do we stand with helioseismology? Authors: Toomre, Juri Bibcode: 2003ESASP.517....3T Altcode: 2003soho...12....3T The advent of GONG+ and the selection of the Helioseismic and Magnetic Imager (HMI) for the Solar Dynamics Observatory (SDO) together promise a high-resoluton future for helioseismology in probing the internal dynamics and structure of the sun. We address some of the dynamical issues in the upper reaches of the solar convection zone that inspire these observational efforts which seek to understand the complex couplings between the highly turbulent convection and the intense magnetism exhibited by the sun. We examine findings to date about the evolving flows, called Solar Subsurface Weather (SSW), and their interaction with magnetism deduced from various local helioseismic approaches. We discuss the substantial efforts that appear to be required to make these procedures capable of subsurface flows with GONG+ and HMI over a wide range of depths for much of the visible solar disk. We shall also review some recent evidence for variability with advancing solar cycle both within the body of the convection zone and within its upper shear layer. Title: Comparison of near-surface flows assessed by ring-diagram and f-mode time-distance analyses Authors: Hindman, Bradley; Gizon, Laurent; Haber, Deborah; Duval, Thomas, Jr.; Toomre, Juri Bibcode: 2003ESASP.517..299H Altcode: 2003soho...12..299H The near-surface shear layer exhibits a rich medley of flows that are now being measured by time-distance and ring analysis techniques. We present comparisons of the flows obtained with the two techniques using SOI-MDI Dynamics Program data from the years 1998 and 1999. The time-distance analyses utilize f-mode data without depth inversion. The flows deduced with the two methods are remarkably similar, with common inflow and outflow sites as well as agreement in the general flow directions. The direct correspondence of features in the flows is realized in both quiet and active regions. Title: Transient oscillations near the solar tachocline Authors: Toomre, Juri; Christensen-Dalsgaard, Jorgen; Hill, Frank; Howe, Rachel; Komm, Rudolf W.; Schou, Jesper; Thompson, Michael J. Bibcode: 2003ESASP.517..409T Altcode: 2003soho...12..409T We report on further developments in the 1.3-yr quasi-periodic oscillations reported by Howe et al. (2000). These are small (6 to 8 nHz peak-to-peak) oscillations in the inferred rotation rate near the bottom of the convection zone and in the outer part of the radiative interior. The oscillations are strongest and most coherent at about a fractional radius of 0.72 in the equatorial region. Further monitoring of the oscillations near the equator shows that they continued for a period after the end of the data analyzed by Howe et al., but appear to have now diminished in amplitude. This is reminiscent of the transient behavior of similar (1.3 to 1.4 yr) periodicities in solar-wind and geomagnetic datasets previously reported. We speculate that the near tachocline oscillation is associated with the rising phase of the solar cycle. We discuss tests performed to eliminate various possible explanations of the oscillations due to systematic errors in the data and in their analyses. Title: Interaction of solar subsurface flows with major active regions Authors: Haber, Deborah A.; Hindman, Bradley W.; Toomre, Juri Bibcode: 2003ESASP.517..103H Altcode: 2003soho...12..103H Solar Subsurface Weather (SSW), which consists of complex and meandering large-scale horizontal flows below the solar surface, has been studied in detail with ring analyses of SOI-MDI data from SOHO. SSW flows are of particular significance since they appear to interact and influence the magnetic fields visible at the surface, with active regions appearing as zones of convergent flow and possible downflows. Such subsurface flows over a range of depths can mechanically twist and displace field lines, possibly leading to unstable magnetic configurations that may flare or erupt as coronal mass ejections. It is highly likely that such flows and magnetic fields are broadly linked in their evolution. We have studied in detail horizontal flow fields in the vicinity of several major active regions observed during 2001 and 2002, finding that at shallow depths there is general flow convergence toward these regions and noticeable flow deflections in the large-scale zonal and meridional circulations. We have detected strengthening of jet-like features in the converging flows occurring over the course of several days. These features are accompanied by prominent diverging outflows at greater depths. It appears that the large-scale flow fields surrounding active complexes have a distinct cellular structure that may contribute to both the overall cohesion of active regions as well as to the movement of magnetic flux within those regions that can lead to flares and other eruptive phenomena. Title: Solar Differential Rotation and Magnetism: a 3--D MHD View Authors: Brun, Allan Sacha; Toomre, Juri Bibcode: 2003IAUJD..12E...7B Altcode: We discuss recent progresses made in modelling the complex magnetohydrodynamics of the Sun using our anelastic spherical harmonics (ASH) code on massively parallel computers. We have conducted 3--D MHD simulations of compressible convection in spherical shells to study the coupling between convection rotation and magnetic field in seeking to understand how the solar differential rotation is established and maintained. The resulting convection within domains that capture a good fraction of the bulk of the solar convection zone is highly time dependent and intricate and is dominated by intermittent upflows and networks of strong downflows (i.e. plumes). These plumes play a significant role in yielding Reynolds stresses that serve to redistribute angular momentum leading to angular velocity profiles that make good contact with helioseismic deductions. Such complex convective flows are efficient in amplifying the magnetic energy near equipartition. The resulting magnetic fields are found to concentrate around the downflowing networks and to have significant north-south asymmetry and helicity. But these strong fields yield Maxwell stresses that seek to speed up the poles and destroy the agreement with helioseismic observations. So for a given angular velocity profile the level of magnetism that the Sun can sustain is likely to be limited Title: Bridges between helioseismology and models of convection zone dynamics Authors: Toomre, Juri Bibcode: 2003safd.book..299T Altcode: The sun is a magnetic star whose variable activity has a profound effect on our technological society. The high speed solar wind and its energetic particles, mass ejections and flares that affect the solar-terrestrial interaction all stem from the variability of the underlying solar magnetic fields. We are in an era of fundamental discovery about the overall dynamics of the solar interior and its ability to generate magnetic fields through dynamo action. This has come about partly through guidance and challenges to theory from helioseismology as we now observationally probe the interior of this star. It also rests on our increasing ability to conduct simulations of the crucial solar turbulent processes using the latest generation of supercomputers. Title: Solar Turbulence and Magnetism Studied Within a Rotating Convective Spherical Shell Authors: Brun, A. S.; Toomre, J. Bibcode: 2003ASPC..293..134B Altcode: 2003astro.ph..2593B; 2003tdse.conf..134B We discuss recent advances made in modelling the complex magnetohydrodynamics of the Sun using our anelastic spherical harmonics (ASH) code. We have conducted extensive 3--D simulations of compressible convection in rotating spherical shells with and without magnetic fields, to study the coupling between global-scale convection and rotation in seeking to understand how the solar differential rotation is established and maintained. Such simulations capable of studying fairly turbulent convection have been enabled by massively parallel supercomputers. The resulting convection within domains that capture a good fraction of the bulk of the convection zone is highly time dependent and intricate, and is dominated by intermittent upflows and networks of strong downflows. A high degree of coherent structures involving downflowing plumes can be embedded in otherwise chaotic flow fields. These vortical structures play a significant role in yielding Reynolds stresses that serve to redistribute angular momentum, leading to differential rotation profiles with pole-to-equator contrasts of about 30% in angular velocity, Omega, and some constancy along radial lines at mid latitudes, thereby making good contact with deductions from helioseismology. When a magnetic field is introduced, a dynamo regime can be found that does not destroy the strong differential rotation achieved in pure hydrodynamics cases. The magnetic fields are found to concentrate around the downflowing networks and to have significant north-south asymmetry and helicity. Title: The Internal Rotation of the Sun Authors: Thompson, Michael J.; Christensen-Dalsgaard, Jørgen; Miesch, Mark S.; Toomre, Juri Bibcode: 2003ARA&A..41..599T Altcode: Helioseismology has transformed our knowledge of the Sun's rotation. Earlier studies revealed the Sun's surface rotation, but now a detailed observational picture has been built up of the internal rotation of our nearest star. Unlike the predictions of stellar-evolution models, the radiative interior is found to rotate roughly uniformly. The rotation within the convection zone is also very different from prior expectations, which had been that the rotation rate would depend primarily on the distance from the rotation axis. Layers of rotational shear have been discovered at the base of the convection zone and in the subphotospheric layers. Studies of the time variation of rotation have uncovered zonal-flow bands, extending through a substantial fraction of the convection zone, which migrate over the course of the solar cycle, and there are hints of other temporal variations and of a jet-like structure. At the same time, building on earlier work with mean-field models, researchers have made great progress in supercomputer simulations of the intricate interplay between turbulent convection and rotation in the Sun's interior. Such studies are beginning to transform our understanding of how rotation organizes itself in a stellar interior. Title: Solar Multiscale Convection and Rotation Gradients Studied in Shallow Spherical Shells Authors: De Rosa, Marc L.; Gilman, Peter A.; Toomre, Juri Bibcode: 2002ApJ...581.1356D Altcode: 2002astro.ph..9054D The differential rotation of the Sun, as deduced from helioseismology, exhibits a prominent radial shear layer near the top of the convection zone wherein negative radial gradients of angular velocity are evident in the low- and midlatitude regions spanning the outer 5% of the solar radius. Supergranulation and related scales of turbulent convection are likely to play a significant role in the maintenance of such radial gradients and may influence dynamics on a global scale in ways that are not yet understood. To investigate such dynamics, we have constructed a series of three-dimensional numerical simulations of turbulent compressible convection within spherical shells, dealing with shallow domains to make such modeling computationally tractable. In all but one case, the lower boundary is forced to rotate differentially in order to approximate the influence that the differential rotation established within the bulk of the convection zone might have upon a near-surface shearing layer. These simulations are the first models of solar convection in a spherical geometry that can explicitly resolve both the largest dynamical scales of the system (of order the solar radius) as well as smaller scale convective overturning motions comparable in size to solar supergranulation (20-40 Mm). We find that convection within these simulations spans a large range of horizontal scales, especially near the top of each domain, where convection on supergranular scales is apparent. The smaller cells are advected laterally by the larger scales of convection within the simulations, which take the form of a connected network of narrow downflow lanes that horizontally divide the domain into regions measuring approximately 100-200 Mm across. We also find that the radial angular velocity gradient in these models is typically negative, especially in the low- and midlatitude regions. Analyses of the angular momentum transport indicate that such gradients are maintained by Reynolds stresses associated with the convection, transporting angular momentum inward to balance the outward transport achieved by viscous diffusion and large-scale flows in the meridional plane, a mechanism first proposed by Foukal & Jokipii and tested by Gilman & Foukal. We suggest that similar mechanisms associated with smaller scale convection in the Sun may contribute to the maintenance of the observed radial shear layer located immediately below the solar photosphere. Title: Solar Subsurface Weather and Possible Giant Cell Signatures Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.; Hill, F. Bibcode: 2002AAS...200.0414H Altcode: 2002BAAS...34Q.645H Helioseismic observations taken with SOI-MDI aboard SOHO have led to a new era of discovery about complex and evolving dynamics within the upper solar convection zone. The data now span nearly six years. Using the technique of ring-diagram analysis applied to MDI Dynamics Program Doppler data over a large number of regions on the solar disk, we have generated synoptic maps of horizontal flows at a variety of depths below the photosphere. These maps have been assembled for all of the years for which the SOI-MDI Dynamics Program data are available, with the latest data coming from March 2002. Flows associated with Solar Subsurface Weather (SSW) are observed to vary from month to month and year to year, with the largest flows occurring in and around regions of intense magnetic activity. Longitudinal averages of the flows reveal that the fast banded zonal flows seen in previous years have now merged at the equator while the multiple cell structure found in the meridional circulation within the northern hemisphere over the last four years is still present at a reduced level in 2002. When the average flows are removed, it is possible to see areas of cyclonic flow in regions of quiet sun as well as divergent cells on the order of 30 to 40 degrees in diameter that might be signatures of giant convection cells. This research was supported by NAG5-7996. Title: Turbulent Convection under the Influence of Rotation: Sustaining a Strong Differential Rotation Authors: Brun, Allan Sacha; Toomre, Juri Bibcode: 2002ApJ...570..865B Altcode: 2002astro.ph..6196B The intense turbulence present in the solar convection zone is a major challenge to both theory and simulation as one tries to understand the origins of the striking differential rotation profile with radius and latitude that has been revealed by helioseismology. The differential rotation must be an essential element in the operation of the solar magnetic dynamo and its cycles of activity, yet there are many aspects of the interplay between convection, rotation, and magnetic fields that are still unclear. We have here carried out a series of three-dimensional numerical simulations of turbulent convection within deep spherical shells using our anelastic spherical harmonic (ASH) code on massively parallel supercomputers. These studies of the global dynamics of the solar convection zone concentrate on how the differential rotation and meridional circulation are established. We have addressed two issues raised by previous simulations with ASH. First, can solutions be obtained that possess the apparent solar property that the angular velocity Ω continues to decrease significantly with latitude as the pole is approached? Prior simulations had most of their rotational slowing with latitude confined to the interval from the equator to about 45°. Second, can a strong latitudinal angular velocity contrast ΔΩ be sustained as the convection becomes increasingly more complex and turbulent? There was a tendency for ΔΩ to diminish in some of the turbulent solutions that also required the emerging energy flux to be invariant with latitude. In responding to these questions, five cases of increasingly turbulent convection coupled with rotation have been studied along two paths in parameter space. We have achieved in one case the slow pole behavior comparable to that deduced from helioseismology and have retained in our more turbulent simulations a consistently strong ΔΩ. We have analyzed the transport of angular momentum in establishing such differential rotation and clarified the roles played by Reynolds stresses and the meridional circulation in this process. We have found that the Reynolds stresses are crucial in transporting angular momentum toward the equator. The effects of baroclinicity (thermal wind) have been found to have a modest role in the resulting mean zonal flows. The simulations have produced differential rotation profiles within the bulk of the convection zone that make reasonable contact with ones inferred from helioseismic inversions, namely, possessing a fast equator, an angular velocity difference of about 30% from equator to pole, and some constancy along radial lines at midlatitudes. Future studies must address the implications of the tachocline at the base of the convection zone, and the near-surface shear layer, on that differential rotation. Title: Evolving Submerged Meridional Circulation Cells within the Upper Convection Zone Revealed by Ring-Diagram Analysis Authors: Haber, Deborah A.; Hindman, Bradley W.; Toomre, Juri; Bogart, Richard S.; Larsen, Rasmus M.; Hill, Frank Bibcode: 2002ApJ...570..855H Altcode: Using the local helioseismic technique of ring-diagram analysis applied to Michelson Doppler Imager (MDI) Dynamics Program data from the Solar and Heliospheric Observatory, we have discovered that the meridional flow within the upper convection zone can develop additional circulation cells whose boundaries wander in latitude and depth as the solar cycle progresses. We report on the large-scale meridional and zonal flows that we observe from 1996 to 2001. In particular, we discuss the appearance and evolution of a submerged meridional cell during the years 1998-2001, which arose in the northern hemisphere and disrupted the orderly poleward flow and symmetry about the equator that is typically observed. The meridional flows in the southern and northern hemispheres exhibit striking asymmetry during the past four years of the advancing solar cycle. Such asymmetry and additional circulation cells should have profound impact on the transport of angular momentum and magnetic field within the surface layers. These flows may have a significant role in the establishment and maintenance of the near-surface rotational shear layer. Title: Solar Subsurface Weather: Recent Measurements of Flows Using Ring-Diagram Analysis Authors: Hindman, B. W.; Haber, D. A.; Toomre, J.; Bogart, R. S. Bibcode: 2002AAS...200.7904H Altcode: 2002BAAS...34..780H Continuous helioseismic observations from SOI-MDI on SOHO have led to a new era of discovery about complex and evolving dynamics within the solar convection zone. Local probing of the Sun's acoustic wave field, using ring-diagram analysis, has revealed the presence of large-scale horizontal flows within the near-surface layers of the Sun. These remarkable weather-like flow patterns, called Solar Subsurface Weather (SSW), possess intricate patterns that change from one day to the next, accompanied by more gradually evolving patterns such as banded zonal flows and meridional circulation cells. Synoptic maps of these flow structures reveal that solar magnetism strongly modulates flow speeds and directions with an effect that varies with depth. I will present out latest measurements of the flows associated with SSW and briefly discuss the implications of these measurements on the redistribution of angular momentum and magnetic fields. This research has been supported by NASA and NSF. Title: Penetration and Overshooting in Turbulent Compressible Convection Authors: Brummell, Nicholas H.; Clune, Thomas L.; Toomre, Juri Bibcode: 2002ApJ...570..825B Altcode: We present the results of a series of high-resolution, three-dimensional numerical experiments that investigate the nature of turbulent compressible convective motions extending from a convection zone into a stable layer below. In such convection, converging flows in the near-surface cellular convecting network create strong downflowing plumes that can traverse the multiple scale heights of the convection zone. Such structures can continue their downward motions beyond the convecting region, piercing the stable layer, where they are decelerated by buoyancy braking. If these motions mix entropy to an adiabatic state below the convection zone, the process is known as penetration; otherwise it is termed overshooting. We find that in three-dimensional turbulent compressible convection at the parameters studied, motions generally overshoot a significant fraction of the local pressure scale height but do not establish an adiabatic penetrative region, even at the highest Péclet numbers considered. This is mainly due to the low filling factor of the turbulent plumes. The scaling of the overshooting depth with the relative stability S of the two layers is affected by this lack of true penetration. Only an S-1 dependence is exhibited, reflecting the existence of a thermal adjustment region without a nearly adiabatic penetration zone. Rotation about a vertical axis decreases the depth of overshooting, owing to horizontal mixing induced by the rotation. For rotation about an inclined axis, turbulent rotational alignment of the strong downflow structures decreases the overshooting further at mid-latitudes, but the laminar effects of cellular roll solutions take over at low latitudes. Turbulent penetrative convection is quite distinct from its laminar counterpart and from the equivalent motions in a domain confined by impenetrable horizontal boundaries. Although overshooting would not be so deep in the solar case, the lack of true penetration extending the adiabatic region may explain why helioseismic inferences show little evidence of the expected abrupt change between the convection zone and the radiative interior. These results may also provide insight into how overshooting motions can provide a coupling between the solar convection zone and the tachocline. Title: Eddies and vortices in ocean basin dynamics Authors: Siegel, A.; Weiss, Jeffrey B.; Toomre, Juri; McWilliams, James C.; Berloff, Pavel S.; Yavneh, Irad Bibcode: 2001GeoRL..28.3183S Altcode: A wind-driven, closed-basin quasi-geostrophic ocean model is computed at very high horizontal resolution to study the effect of increasing Reynolds number (Re) on eddy variability. Five numerical simulations are performed with identical configurations, varying only in horizontal resolution and viscosity coefficient (and therefore Re). Qualitative changes in the structure of eddy variability are evident in the dramatic increase of isolated vortex structures at the highest Re. While the time-mean kinetic energy is relatively independent of Re, the vortex emergence contributes to a continual increase with Re of eddy kinetic energy and meridional vorticity flux. The rate of increase slows somewhat at the highest Re, indicating the possibility of a regime where eddy variability becomes insensitive to further increases in Re. Title: Evolving Large-Scale Flows With Advancing Solar Cycle Using Helioseismic Dense-Pack Ring-Diagram Analyses Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.; Hill, F. Bibcode: 2001AGUSM..SP22A02H Altcode: We have recently completed the first local helioseismic ring-diagram analysis of the entire SOI-MDI Dynamics Program data. These data sets include up to three months of continuous Doppler velocity data from each of the years 1996 through 2000. A single ring-diagram analysis over a 15o region of the sun, followed by an inversion of the frequency shifts thus obtained, yields measurements of the horizontal velocity field as a function of depth within the upper 14 Mm of the convection zone beneath that region. By performing the analysis over a Dense-Pack mosaic of 189 overlapping tiles and repeating the procedure for each day of data, we have mapped the velocity field as a function of time over a substantial fraction of the solar disk for a number of full Carrington rotations. Our studies of the dynamics of the upper convection zone have revealed the presence of striking north-south asymmetries in both the zonal and meridional flows as a function of depth. For example, a small second meridional flow cell appeared at depths below 10 Mm at latitudes north of 45oN in 1998, expanded upwards to 3 Mm in depth at all latitudes above 22oN in 1999, and then receded again in 2000. Synoptic maps, formed from nearly 4500 ring-diagram analyses per Carrington rotation, show that active regions are sites of convergent flow and appear at the boundaries of the northern meridional cells in 1999. Even finer sampling grids show that there are steep gradients in the flows within active regions. Our work has also revealed a relationship between the fast zonal "torsional oscillation" bands that migrate towards the equator and the meridional flow as the solar cycle progresses. The dominantly poleward meridional flow reaches maxima in both hemispheres at the latitudes at which the zonal fast belts occur. As the zonal fast belts drift towards the equator, the latitudes of maximal meridional flow also drift equatorward. Title: Variations in Rotation Rate Within the Solar Convection Zone From GONG and MDI 1995-2000 Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.; Schou, J.; Thompson, M. J.; Toomre, J. Bibcode: 2001AGUSM..SP31A15H Altcode: Helioseismic measurements with the Michelson Doppler Imager (MDI) instrument aboard SOHO, and complementary measurements from the Global Oscillation Network Group (GONG) project, are revealing changes deep within the Sun as the solar cycle progresses. We will present the latest results based on recent data from both experiments, including flows in the upper part of the convection zone and variations in the rotation rate near its base. Title: Transport and Storage of Magnetic Field by Overshooting Turbulent Compressible Convection Authors: Tobias, Steven M.; Brummell, Nicholas H.; Clune, Thomas L.; Toomre, Juri Bibcode: 2001ApJ...549.1183T Altcode: We present the results of a series of numerical experiments that investigate the transport of magnetic fields by turbulent penetrative compressible convection. We find that magnetic flux is preferentially transported downward out of a turbulent convecting region and stored in a stably stratified region below. This pumping mechanism is believed to be a crucial component for the operation of a large-scale solar interface dynamo since it may be responsible for the transport of flux from the solar convection zone to the stable overshoot region. The high-resolution three-dimensional simulations show that efficient pumping occurs as a result of the action of strong coherent downflowing plumes. The properties of the transport are evaluated as a function of magnetic field strength, rotation rate, supercriticality, stiffness of the interface, and configuration. The turbulent pumping of magnetic flux is remarkably robust and more efficient than its laminar counterpart. The turbulent convection naturally amplifies magnetic energy from any existing mean field. The transport of flux from the convection zone removes the source for this local amplification there, and thus the peak magnetic energy also comes to reside in the stable region. This is important for an effective interface dynamo. Title: Fractional Frequency Shifts of Local Helioseismic Modes With Magnetic Activity Using Ring-Diagram Analysis Authors: Hindman, B.; Haber, D.; Toomre, J.; Bogart, R. S. Bibcode: 2001IAUS..203..215H Altcode: Using full-disk Doppler velocity data from SOI-MDI during the advancing solar cycle from 1996 through 1999, we have computed the local frequencies of high-degree p modes and f modes over a dense mosaic of localized regions of the sun using ring-diagram analysis. The motion of active regions as they rotate across the solar disk is well traced by changes in the frequencies. Active regions appear as locations of large positive frequency shifts. Depending on the radial order and wavenumber of the observed acoustic modes the frequency shifts can be as much as 10 to 30 microHz. Shifts of this amplitude are 20 to 60 times larger than the shifts in global acoustic oscillations. The magnitude and frequency dependence of the large frequency shifts are consistent with those measured in global modes provided the local frequency shifts are averaged over the solar disk and are scaled to the appropriate wavenumber regimes. The frequency dependence of the shifts indicates that the physical phenomena inducing them is largely confined to the surface layers of the sun, although there is some indication that there may be a deeper structural component as well. These local area samplings may help to understand the restructuring of the near-surface layers of the convection zone by magnetic fields. Title: Comparing local frequency shifts measured through ring-diagram analysis with global frequency shifts Authors: Hindman, Bradley W.; Haber, Deborah A.; Toomre, Juri; Bogart, Richard S. Bibcode: 2001ESASP.464..143H Altcode: 2001soho...10..143H Using ring-diagram mode fitting of a subset of the MDI Dynamics Program data called the dense-pack data set (Haber et al. 2000), we measure the frequencies of high-degree p modes and f modes as a function of position on the solar disk and of time. Daily maps of the resulting frequencies reveal that high-degree mode frequencies are spatially and temporally variable and are composed of the sum of two components. One component is stationary and is produced primarily by imperfections in the MDI optics, while the other component is spatially intermittent, rotates with the solar surface, and is associated with the presence of active regions. The frequency shifts within active regions can exceed 60 μHz for some wavelengths and mode orders. We remove the instrumentally dependent portion of the signal and average the resulting frequency shifts over the solar disk and over time producing a global average. The frequency and wavenumber dependence of these average frequency shifts indicates that the physical phenomena inducing the shifts is largely confined to the surface layers of the sun, although there is evidence that a small contribution from deeper layers exists. The average frequency shifts strongly resemble the solar cycle variations that are observed in the frequencies of global p-mode oscillations of low harmonic degree. Title: Comparing mode frequencies from MDI and GONG Authors: Howe, R.; Hill, F.; Basu, S.; Christensen-Dalsgaard, J.; Komm, R. W.; Munk Larsen, R.; Roth, M.; Schou, J.; Thompson, M. J.; Toomre, J. Bibcode: 2001ESASP.464..137H Altcode: 2001soho...10..137H We present results of analyses of MDI and GONG time series covering the same time intervals, and using both the MDI and GONG peakbagging algorithms. We discuss some of the likely causes of differences between the inferred frequencies and frequency splittings. In addition, we consider the effect of these differences on the results of inversions for the solar internal rotation and sound speed. Title: Daily variations of large-scale subsurface flows and global synoptic flow maps from dense-pack ring-diagram analyses Authors: Haber, Deborah A.; Hindman, Bradley W.; Toomre, Juri; Bogart, Richard S.; Hill, Frank Bibcode: 2001ESASP.464..209H Altcode: 2001soho...10..209H Ring-diagram analyses carried out daily on a mosaic of sites spanning much of the solar disk have allowed the mapping of large-scale flows in the upper portion of the solar convection zone. Inversion of frequency splittings from such local helioseismic analyses reveal large-scale flows, in addition to the mean zonal and meridional flows, that vary from day-to-day and with depth. We contrast such flow behavior in regions of active and quiet sun. We also provide synoptic maps based on dense-pack studies covering three full solar rotations in 1999. Title: Solar cycle changes in convection zone dynamics from MDI and GONG 1995 - 2000 Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.; Munk Larsen, R.; Schou, J.; Thompson, M. J.; Toomre, J. Bibcode: 2001ESASP.464...19H Altcode: 2001soho...10...19H The combined GONG and MDI medium-degree helioseismic data sets now cover just over 5 years and allow us to probe the changing dynamics of the convection zone in unprecedented detail. Here we present the latest results from both projects, showing the evolution of the migrating zonal flows close to the surface and also changes close to and below the base of the convection zone. Title: Comparison of phase inversion and time-distance analysis of one-dimensional artificial seismic data Authors: Gough, D. O.; Sekii, T.; Toomre, J. Bibcode: 2001ESASP.464..207G Altcode: 2001soho...10..207G We have studied the application of a phase inversion technique (Gough, Merryfield and Toomre 1991, 1993, 1998; Gough, Sekii and Toomre 1998, 2000) to stochastically excited damped oscillations in an inhomogeneous one-dimensional loop, using artificial seismic data (Gough, Sekii and Toomre 2000). It has been found that within a parameter range that might be relevant to the solar case, strong damping can significantly degrade inversions for the wave propagation speed. Here we analyse the same artificial data by a time-distance technique, to compare how the two techniques differ in their response to the presence of strong damping. Title: Development of multiple cells in meridional flows and evolution of mean zonal flows from ring-diagram analyses Authors: Haber, Deborah A.; Hindman, Bradley W.; Toomre, Juri; Bogart, Richard S.; Hill, Frank Bibcode: 2001ESASP.464..213H Altcode: 2001soho...10..213H Meridional flows within the solar convection zone have been observed with both direct Doppler measurements and with local helioseismic techniques based on ring-diagram analyses and time-distance methods. Typically these mean flows are poleward with speeds of roughly 20 m s-1. Using ring-diagram analyses on a subset of the MDI Dynamics Program data, called the dense-pack data set, we find that a deviation from this general behavior occurs in 1999. A second meridional cell appears below the surface in the northern hemisphere. At the same time, the mean zonal flows do not reveal any evidence of this cell. The zonal bands or "torsional oscillations" continue their steady migration toward the equator. Title: Numerical simulations of supergranular scales of convection in shallow spherical shells Authors: De Rosa, Marc L.; Toomre, Juri Bibcode: 2001ESASP.464..595D Altcode: 2001soho...10..595D The differential rotation of the sun, as deduced from helioseismology, exhibits a prominent radial shear layer near the top of the convection zone. Supergranulation and related scales of turbulent convection are likely to play a significant role in the maintenance of strong radial gradients in angular velocity which vary with latitude near the surface. We present results from 3-D numerical simulations of such turbulent convection in shallow spherical shells, using the anelastic spherical harmonic (ASH) code running on massively parallel computers to study the effects of rotation and compressibility on the resulting highly nonlinear convection. Convection of supergranular nature is driven by imposing the solar heat flux at the bottom of a shallow spherical shell located near the top of the convection zone which is rotating at the mean solar rate. The angular momentum balance in the shell is studied for cases where a solar-like differential rotation profile is imposed at the lower boundary. Convection spanning a large range of horizontal scales is driven within the shell, especially near the top of the domain. The resulting radial angular velocity gradient is negative for all latitudes, suggesting that fluid parcels partially conserve their angular momentum while moving radially. Title: Mean flows in rotating turbulent convective shells Authors: Brun, Allan Sacha; Toomre, Juri Bibcode: 2001ESASP.464..619B Altcode: 2001soho...10..619B We conduct numerical simulations of turbulent compressible convection within rotating spherical shells to model solar differential rotation and meridional circulation. These 3-D simulations are carried out on massively parallel computers using the Anelastic Spherical Harmonic (ASH) code. The evolution of such convection is studied in four cases which sample several paths in achieving highly turbulent flows that are able to drive a strong differential rotation from equator to pole. The resulting angular velocity Ω profiles make reasonable contact with many aspects of the solar rotation profiles inferred from helioseismic inversions of both MDI and GONG data. The substantial contrast in Ω of order 30% achieved in our simulations of turbulent convection is considerably greater than realized in previous studies. Title: Magnetic Pumping at the Base of the Solar Convection Zone Authors: Tobias, S. M.; Brummell, N. H.; Toomre, J. Bibcode: 2001IAUS..203..156T Altcode: We present the results of a series of numerical experiments that investigate the pumping of magnetic fields by turbulent penetrative convection. This pumping mechanism, which is responsible for the transport of flux from the solar convection zone to the stable overshoot region, is believed to be a crucial component for the operation of a large-scale solar interface dynamo. The high-resolution three dimensional simulations show that efficient pumping occurs due to the action of strong coherent downwards plumes. The pumping depth is then calculated as a function of magnetic field strength, rotation rate, supercriticality and stiffness of the interface. Title: Turbulent Convection and Subtleties of Differential Rotation Within the Sun Authors: Toomre, J.; Brun, A. Sacha; De Rosa, M.; Elliott, J. R.; Miesch, M. S. Bibcode: 2001IAUS..203..131T Altcode: Differential rotation and cycles of magnetic activity are intimately linked dynamical processes within the deep shell of highly turbulent convection occupying the outer 200 Mm below the solar surface. Helioseismology has shown that the angular velocity Ω within the solar convection zone involves strong shear layers both near the surface and especially at its base near the interface with the radiative interior. The tachocline of radial shear there that varies with latitude is thought to be the site of the global magnetic dynamo. Most recent continuous helioseismic probing with MDI on SOHO and from GONG have revealed systematic temporal changes in Ω with the advancing solar cycle. These include propagating bands of zonal flow speedup extending from the surface to a depth of about 70 Mm, distinctive out-of-phase vacillations in Ω above and below the tachocline with a period of about 1.3 years near the equator, a changing pattern of meridional circulation cells with broken symmetries in the two hemispheres, and complex speedups and slowdowns in the bulk of the convection zone. We review these helioseismic findings and their implications. We also describe current 3-D numerical simulations of anelastic rotating convection in full spherical shells used to study the differential rotation that can be established by such turbulence exhibiting coherent structures. These simulations enabled by massively parallel computers are making promising contact with aspects of the Ω profiles deduced from helioseismology, but challenges remain. Title: Interior Solar-Cycle Changes Detected by Helioseismology Authors: Howe, R.; Hill, F.; Komm, R. W.; Christensen-Dalsgaard, J.; Munk Larsen, R.; Schou, J.; Thompson, M. J.; Toomre, J. Bibcode: 2001IAUS..203...40H Altcode: Helioseismic measurements with the MDI instrument aboard SOHO, and complementary measurements from the GONG network, are revealing changes deep within the Sun as the solar cycle progresses. We will present results based on recent data from both experiments, including variations in the rotation rate deep inside the convection zone. Title: Subsurface Flows with Advancing Solar Cycle Using Dense-Pack Ring-Diagram Analyses Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.; Hill, F. Bibcode: 2001IAUS..203..211H Altcode: Large-scale horizontal flows within the upper convection zone of the sun are analyzed using the helioseismic technique of ring-diagram analysis applied to data from SOI-MDI. We map the velocity field over a substantial fraction of the solar disk by carrying out local inversion analyses over a Dense-Pack mosaic of many overlapping sites. There are substantial changes in subsurface flows at any given site from one day to the next that appear to be of solar origin. Such mosaics are processed almost daily for at least two solar rotations during each of the MDI Dynamics Campaigns from 1996 through 1999. We find that longitudinally-averaged zonal velocity possess bands of fast and slow flow. As the solar cycle progresses, the latitudes at which the fast bands occur migrate towards the equator and vary in their flow amplitudes. These bands are not symmetric about the solar equator, and their asymmetry changes with time. The average meridional flow for the years 1996 to 1998 is primarily poleward, reaching maxima in the two hemispheres at the latitudes at which the zonal fast belts occur. The latitudes of maximal meridional flow drift equatorward in time much as the zonal fast belts. However, in 1999, the meridional circulation in the northern hemisphere develops a two-celled structure with latitude, whereas in the southern hemisphere it remains single celled. Title: Solar Interior: Convection Zone Authors: Toomre, J. Bibcode: 2000eaa..bookE1995T Altcode: The Sun, like all main sequence stars of moderate mass, possesses a deep convective envelope just below its surface in which turbulent fluid motions serve to carry outward the energy flux that results from nuclear burning within its core. Observations of the Sun reveal complex flows and magnetic structures that are evidence of highly turbulent convection just below the surface of this rotating s... Title: New Approach to Study Extended Evolution of Supergranular Flows and Their Advection of Magnetic Elements Authors: Lisle, Jason; De Rosa, Marc; Toomre, Juri Bibcode: 2000SoPh..197...21L Altcode: Using velocity and magnetogram data extracted from the full-disk field of view of MDI during the 1999 Dynamics Program, we have studied the dynamics of small-scale magnetic elements (3-7 Mm in size) over time periods as long as six days while they are readily visible on the solar disk. By exploiting concurrent time series of magnetograms and Doppler images, we have compared the motion of magnetic flux elements with the supergranular velocity field inferred from the correlation tracking of mesogranular motions. Using this new method (which combines the results from correlation tracking of mesogranules with detailed analysis of simultaneous magnetograms), it is now possible to correlate the motions of the velocity field and magnetic flux for long periods of time and at high temporal resolution. This technique can be utilized to examine the long-term evolution of supergranulation and associated magnetic fields, for it can be applied to data that span far longer time durations than has been possible previously. As tests of its efficacy, we are able to use this method to verify many results of earlier investigations. We confirm that magnetic elements travel at approximately 350 m s −1 throughout the duration of their lifetime as they are transported by supergranular outflows. We also find that the positions of the magnetic flux elements coincide with the supergranular network boundaries and adjust as the supergranular network itself evolves over the six days of this data set. Thus we conclude that this new method permits us to study the extended evolution of the supergranular flow field and its advection of magnetic elements. Since small-scale magnetic elements are strongly advected by turbulent convection, their dynamics can give important insight into the properties of the subsurface convection. Title: Phase inversion of one-dimensional artificial seismic data Authors: Gough, D. O.; Sekii, T.; Toomre, J. Bibcode: 2000SoPh..195....1G Altcode: Oscillations of an inhomogeneous one-dimensional loop have been simulated for the purpose of examining the effect of excitation and damping on the sound-speed inversion based on phase analysis. It has been demonstrated that the procedure is robust against the realization noise arising from frequent, stochastic excitation of weakly damped waves, but that strong damping can spoil the inversion. Title: Turbulent Convection, Rotation, and the Solar Dynamo Authors: Tobias, Steve; Toomre, Juri; Weiss, Nigel Bibcode: 2000astu.progE..30T Altcode: No abstract at ADS Title: Global Models of Turbulent Convection Authors: Toomre, Juri Bibcode: 2000astu.confE..35T Altcode: No abstract at ADS Title: Local Fractional Frequency Shifts of Helioseismic Modes Associated With Magnetic Activity Using Ring-Diagram Analyses Authors: Hindman, B. W.; Haber, D. A.; Toomre, J.; Bogart, R. S. Bibcode: 2000SPD....31.0109H Altcode: 2000BAAS...32..802H Using full-disk velocity data from SOI-MDI during the advancing solar cycle from 1996 through 1999, we have computed the local frequencies of high-degree p modes and f modes over localized regions of the sun. The frequencies are obtained through ring-diagram mode fitting over Dense-Pack data sets consisting of mosaics of 189 overlapping tiles, each tracked separately at the surface rotation rate over 1664-minute time intervals during the MDI Dynamics Programs. Each tile is 16 degrees square, and the tile centers are separated by 7.5 degrees in latitude and longitude. For each observational day and for each tile, we have computed the frequency shift measured relative to the temporal and spatial average of the entire set of frequencies sampled over a full rotation. The magnetic field is computed for each of the 189 regions using the magnetograms supplied every 90 min by MDI. The motion of active regions as they rotate across the solar disk is vividly traced by changes in the frequencies. Active regions appear as locations of large positive frequency shifts. Depending on the radial order and wavenumber of the observed acoustic modes the frequency shifts can be as much as 10 to 30 microHz. The magnitude and frequency dependence of the large frequency shifts are consistent with the far smaller changes measured in global oscillation frequencies over the solar cycle, provided the local frequency shifts are averaged over the solar disk and are scaled to the appropriate wavenumber regimes. The frequency dependence of the shifts indicates that the physical phenomena inducing the shifts is largely confined to the surface layers of the sun, although there is some indication that there may be a deeper structural component as well. This research was supported by NASA through grants NAG 5-8133 and NAG 5-7996, and by NSF through grant ATM-9731676. Title: Solar-Cycle Changes in Convection-Zone Dynamics from SOI and GONG Data Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.; Larsen, R. M.; Schou, J.; Thompson, M. J.; Toomre, J. Bibcode: 2000SPD....31.0113H Altcode: 2000BAAS...32..803H The combined GONG and MDI medium-degree helioseismic data sets now cover more than 4.5 years and allow us to probe the changing dynamics of the convection zone in unprecedented detail. Here we present the latest results from both projects, showing the evolution of the migrating zonal flows close to the surface and also changes close to and below the base of the convection zone. This work utilizes data obtained by the Global Oscillation Network Group (GONG) project, managed by the National Solar Observatory, a Division of the National Optical Astronomy Observatories, which is operated by AURA, Inc. under a cooperative agreement with the National Science Foundation. SOHO is a joint project of ESA and NASA. Title: Evolving Dynamics of the Supergranular Flow Field Authors: De Rosa, M. L.; Lisle, J. P.; Toomre, J. Bibcode: 2000SPD....31.0106D Altcode: 2000BAAS...32..802D We study several large (45-degree square) fields of supergranules for as long as they remain visible on the solar disk (about 6 days) to characterize the dynamics of the supergranular flow field and its interaction with surrounding photospheric magnetic field elements. These flow fields are determined by applying correlation tracking methods to time series of mesogranules seen in full-disk SOI-MDI velocity images. We have shown previously that mesogranules observed in this way are systematically advected by the larger scale supergranular flow field in which they are embedded. Applying correlation tracking methods to such time series yields the positions of the supergranular outflows quite well, even for locations close to disk center. These long-duration datasets contain several instances where individual supergranules are recognizable for time scales as long as 50 hours, though most cells persist for about 25 hours that is often quoted as a supergranular lifetime. Many supergranule merging and splitting events are observed, as well as other evolving flow patterns such as lanes of converging and diverging fluid. By comparing the flow fields with the corresponding images of magnetic fields, we confirm the result that small-scale photospheric magnetic field elements are quickly advected to the intercellular lanes to form a network between the supergranular outflows. In addition, we characterize the influence of larger-scale regions of magnetic flux, such as active regions, on the flow fields. Furthermore, we have measured even larger-scale flows by following the motions of the supergranules, but these flow fields contain a high noise component and are somewhat difficult to interpret. This research was supported by NASA through grants NAG 5-8133 and NAG 5-7996, and by NSF through grant ATM-9731676. Title: Helioseismic Dense-Pack Ring Diagram Analyses to Study Evolution of Subsurface Flows With Advancing Solar Cycle Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.; Larsen, R. M.; Hill, F. Bibcode: 2000SPD....31.0103H Altcode: 2000BAAS...32..801H We analyze data obtained from the Michelson Doppler Imager (MDI) on SOHO in 1996-1999 using the helioseismic ring-diagram technique to infer large-scale horizontal flows within the upper solar convection zone. Each separate ring analysis deduces the average flow components below a 16 degree square region on the solar surface. We map the velocity field over a substantial fraction of the solar disk by repeating the analysis over a Dense-Pack mosaic of 189 overlapping tiles, with each sampling interval spanning 1664 minutes. We process such a mosaic on a nearly daily schedule and have analyzed two Carrington rotations (48 days) in 1996 and one or two rotations each in 1997, 1998, and 1999. There are substantial changes in subsurface flows at any given site from one day to the next that appear to be of solar origin. The mean zonal and meridional flows display gradual and systematic changes. We find that the longitudinally-averaged zonal velocity, after removing a smooth differential rotation component, possesses bands of fast and slow flow, much like `torsional oscillations' first reported from surface Doppler measurements and recently from global helioseismic assessments. As the solar cycle progresses, the latitudes at which the fast bands occur migrate towards the equator. The amplitudes of these banded zonal flows increase with magnetic activity. Our local-area analyses reveal that these belts of fast and slow flow are not symmetric about the solar equator, and their asymmetry changes with time. The average meridional flow (of typical amplitudes 10-20 m/s) deduced from our samplings for 1996, 1997 and 1998 is primarily poleward and reaches maxima in the two hemispheres at the latitudes at which the zonal fast belts occur. As these zonal fast belts drift towards the equator, the latitudes of maximal meridional flow also drift equatorward. We further find that in 1999 the meridional circulation in the northern hemisphere has developed a two-celled structure with latitude, whereas that in the southern hemisphere is still single celled. This research was supported by NASA through grants NAG 5-8133 and NAG 5-7996, and by NSF through grant ATM-9731676. Title: Deeply Penetrating Banded Zonal Flows in the Solar Convection Zone Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.; Larsen, R. M.; Schou, J.; Thompson, M. J.; Toomre, J. Bibcode: 2000ApJ...533L.163H Altcode: 2000astro.ph..3121H Helioseismic observations have detected small temporal variations of the rotation rate below the solar surface that correspond to the so-called ``torsional oscillations'' known from Doppler measurements of the surface. These appear as bands of slower- and faster-than-average rotation moving equatorward. Here we establish, using complementary helioseismic observations over 4 yr from the GONG network and from the MDI instrument on board SOHO, that the banded flows are not merely a near-surface phenomenon: rather, they extend downward at least 60 Mm (some 8% of the total solar radius) and thus are evident over a significant fraction of the nearly 200 Mm depth of the solar convection zone. Title: Turbulent Solar Convection and Its Coupling with Rotation: The Effect of Prandtl Number and Thermal Boundary Conditions on the Resulting Differential Rotation Authors: Elliott, J. R.; Miesch, M. S.; Toomre, J. Bibcode: 2000ApJ...533..546E Altcode: The dynamics of the vigorous convection in the outer envelope of the Sun must determine the transport of energy, angular momentum, and magnetic fields and must therefore be responsible for the observed surface activity and the angular velocity profile inferred helioseismically from SOI-MDI p-mode frequency splittings. Many different theoretical treatments have been applied to the problem, ranging from simple physical models such as mixing-length theory to sophisticated numerical simulations. Although mixing-length models provide a good first approximation to the structure of the convection zone, recent progress has mainly come from numerical simulations. Computational constraints have until now limited simulations in full spheres to essentially laminar convection. The angular velocity profiles have shown constancy on cylinders, in striking contrast to the approximately constant angular velocity on radial lines inferred for the Sun. In an effort to further our understanding of the dynamics of the solar convection zone, we have developed a new computer code that, by exploiting massively parallel architectures, enables us to study fully turbulent spherical shell convection. Here we present five fully evolved solutions. Motivated by the fact that a constant entropy upper boundary condition produces a latitudinal modulation of the emergent energy flux (of about 10%, i.e., far larger than is observed for the Sun), three of these solutions have a constant energy flux upper boundary condition. This leads to a latitudinal modulation of the specific entropy that breaks the constancy of the angular velocity on cylinders, making it more nearly constant on radial lines at midlatitudes. The effect of lowering the Prandtl number is also considered-highly time-dependent, vortical convective motions are revealed, and the Reynolds stresses are altered, leading to a reduced differential rotation. The differential rotation in all of our simulations shows a balance between driving by Reynolds stresses and damping by viscosity. This contrasts with the situation in the Sun, where the effect of viscosity on the mean differential rotation is almost negligible. Title: Near-Surface Flow Fields Deduced Using Correlation Tracking and Time-Distance Analyses Authors: De Rosa, Marc; Duvall, T. L., Jr.; Toomre, Juri Bibcode: 2000SoPh..192..351D Altcode: Near-photospheric flow fields on the Sun are deduced using two independent methods applied to the same time series of velocity images observed by SOI-MDI on SOHO. Differences in travel times between f modes entering and leaving each pixel measured using time-distance helioseismology are used to determine sites of supergranular outflows. Alternatively, correlation tracking analysis of mesogranular scales of motion applied to the same time series is used to deduce the near-surface flow field. These two approaches provide the means to assess the patterns and evolution of horizontal flows on supergranular scales even near disk center, which is not feasible with direct line-of-sight Doppler measurements. We find that the locations of the supergranular outflows seen in flow fields generated from correlation tracking coincide well with the locations of the outflows determined from the time-distance analysis, with a mean correlation coefficient after smoothing of s=0.890. Near-surface velocity field measurements can be used to study the evolution of the supergranular network, as merging and splitting events are observed to occur in these images. The data consist of one 2048-min time series of high-resolution (0.6'' pixels) line-of-sight velocity images taken by MDI on 1997 January 16 -18 at a cadence of one minute. Title: Solar shear flows deduced from helioseismic dense-pack samplings of ring diagrams Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.; Thompson, M. J.; Hill, F. Bibcode: 2000SoPh..192..335H Altcode: We report on large-scale horizontal flows in the solar convection zone and their variability in time and space using a local-helioseismology technique known as ring-diagram analysis. By performing this analysis on a dense mosaic of individual regions on the solar disk, i.e., a `Dense-Pack' sampling, and repeating the analysis periodically on several time scales, we are able to assess the variation of horizontal flows from day-to-day, week-to-week, and year-to-year. We find that although there are changes in the flows on all these time scales, there are also basic patterns that persist. On a daily time scale we observe that the flow is reduced in those areas which are occupied by large active regions. On somewhat longer time-scales we see bands of persistent fast and slow zonal flow that are identifiable as torsional oscillations. As we examine these bands during a series of years, we find that these bands migrate toward the equator as solar activity increases. Similarly, the latitudes at which the meridional flow reaches maximum follow these regions of fast zonal flow as they migrate equatorwards. These Dense-Pack samplings also reveal substantial differences in the zonal and meridional flow patterns in the northern and southern hemispheres. Title: Time Variability of Rotation in Solar Convection Zone From soi-mdi Authors: Toomre, J.; Christensen-Dalsgaard, J.; Howe, R.; Larsen, R. M.; Schou, J.; Thompson, M. J. Bibcode: 2000SoPh..192..437T Altcode: The variation of rotation in the convection zone over a period of two years from mid-1996 is studied using inversions of SOI-MDI data. We confirm the existence of near-surface banded zonal flows migrating towards the equator from higher latitudes, and reveal that these banded flows extend substantially beneath the surface, possibly to depths as great as 70 Mm (10% of the solar radius). Our results also reveal apparently significant temporal variations in the rotation rate at high latitudes and in the vicinity of the tachocline over the period of study. Title: Dynamic Variations at the Base of the Solar Convection Zone Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.; Larsen, R. M.; Schou, J.; Thompson, M. J.; Toomre, J. Bibcode: 2000Sci...287.2456H Altcode: We have detected changes in the rotation of the sun near the base of its convective envelope, including a prominent variation with a period of 1.3 years at low latitudes. Such helioseismic probing of the deep solar interior has been enabled by nearly continuous observation of its oscillation modes with two complementary experiments. Inversion of the global-mode frequency splittings reveals that the largest temporal changes in the angular velocity Ω are of the order of 6 nanohertz and occur above and below the tachocline that separates the sun's differentially rotating convection zone (outer 30% by radius) from the nearly uniformly rotating deeper radiative interior beneath. Such changes are most pronounced near the equator and at high latitudes and are a substantial fraction of the average 30-nanohertz difference in Ω with radius across the tachocline at the equator. The results indicate variations of rotation close to the presumed site of the solar dynamo, which may generate the 22-year cycles of magnetic activity. Title: Three-dimensional Spherical Simulations of Solar Convection. I. Differential Rotation and Pattern Evolution Achieved with Laminar and Turbulent States Authors: Miesch, Mark S.; Elliott, Julian R.; Toomre, Juri; Clune, Tom L.; Glatzmaier, Gary A.; Gilman, Peter A. Bibcode: 2000ApJ...532..593M Altcode: Rotationally constrained convection possesses velocity correlations that transport momentum and drive mean flows such as differential rotation. The nature of this transport can be very complex in turbulent flow regimes, where large-scale, coherent vorticity structures and mean flows can be established by smaller scale turbulence through inverse cascades. The dynamics of the highly turbulent solar convection zone therefore may be quite different than in early global-scale numerical models, which were limited by computational resources to nearly laminar flows. Recent progress in high-performance computing technology and ongoing helioseismic investigations of the dynamics of the solar interior have motivated us to develop more sophisticated numerical models of global-scale solar convection. Here we report three-dimensional simulations of compressible, penetrative convection in rotating spherical shells in both laminar and turbulent parameter regimes. The convective structure in the laminar case is dominated by ``banana cells,'' but the turbulent case is much more complex, with an intricate, rapidly evolving downflow network in the upper convection zone and an intermittent, plume-dominated structure in the lower convection zone and overshoot region. Convective patterns generally propagate prograde at low latitudes and retrograde at high latitudes relative to the local rotation. The differential rotation profiles show some similarity with helioseismic determinations of the solar rotation but still exhibit significantly more cylindrical alignment. Strong, intermittent, vortical downflow lanes and plumes play an important dynamical role in turbulent flow regimes and are responsible for significant differences relative to laminar flows with regard to momentum and energy transport and to the structure of the overshoot region at the base of the convection zone. Title: Local Fractional Frequency Shifts Used as Tracers of Magnetic Activity Authors: Hindman, Bradley; Haber, Deborah; Toomre, Juri; Bogart, Rick Bibcode: 2000SoPh..192..363H Altcode: Using data from SOI-MDI (Haber et al., 2000), we compute the local frequencies of high-degree p modes and f modes. The frequencies are obtained through ring-diagram mode fitting. The Dense-Pack data set consists of a mosaic of 189 overlapping tiles, each tracked separately at the surface rotation rate over 1664-min time intervals during the Dynamics Programs. Each tile is 16° square and the tile centers are separated by 7.5° in latitude and longitude. For each sampling day and for each tile, we have computed the frequency shift measured relative to the temporal and spatial average of the entire set of frequencies. The motion of active regions as they rotate across the solar disk is vividly traced by these measurements. Active regions appear as locations of large positive frequency shifts. If the shifts are averaged over the solar disk and are scaled down to the appropriate wave number regime, the magnitude and frequency dependence of the shifts are consistent with the measured changes in global oscillation frequencies that occur over the solar cycle. As with the frequency shifts of low-degree global oscillations, the frequency dependence of the shifts indicates that the physical phenomena inducing the shifts is confined to the surface layers of the Sun. Title: Helioseismic detection of temporal variations of solar rotation rate near the base of the convection zone Authors: Howe, R.; Christensen-Dalsgaard, J.; Hill, F.; Komm, R. W.; Larsen, R. M.; Schou, J.; Thompson, M. J.; Toomre, J. Bibcode: 1999AAS...19510702H Altcode: 1999BAAS...31R1530H The differential rotation of the Sun and its ability to generate large-scale magnetic fields through cyclic dynamo action appear to be intimately linked. It is now commonly thought that the global dynamo behavior responsible for the emergence of active regions is derived from strong organized toroidal magnetic fields generated by rotational shear in a thin region (the tachocline) at the base of the convection zone. The magnetic field could well have a feedback effect on the fluid motions in the region. We are thus motivated to use helioseismology to look for changes in rotation profiles near the tachocline as the Sun's magnetic cycle progresses. This approach has become possible using frequency-splitting data for p- and f-mode oscillations derived over four years (from May 1995 to Sept 1999) of full-disk Doppler observations from the ground-based Global Oscillation Network Group (GONG) project and from the Michelson Doppler Imager (MDI) experiment aboard the SOHO spacecraft. Inversions using two different methods of the splittings from these two independent data sets reveal systematic variations of the rotation rate close to the base of the convection zone, with different behavior at low and high latitudes. Notable are variations of order 6 nHz in rotation rates near the equator, to be compared with the radial angular velocity contrast across the tachocline of about 30 nHz. These exhibit several nearly repetitive changes with a period of about 1.2-1.4 years and appear to be real changes in the deep convection zone and tachocline rotation rates that need to be followed as the solar cycle progresses. The GONG project is managed by the National Solar Observatory, a Division of the National Optical Astronomy Observatories, which is operated by AURA, Inc. under a cooperative agreement with the National Science Foundation. SOHO is a joint project of ESA and NASA. Title: Evolution of Subsurface Zonal and Meridional Flows With Advancing Solar Cycle Using Helioseismic Dense-Pack Samplings of Ring Diagrams Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.; Larsen, R. M.; Hill, F. Bibcode: 1999AAS...19510701H Altcode: 1999BAAS...31Q1530H We report on the behavior of large-scale horizontal flows within the upper convection zone of the sun, using the helioseismic technique of ring-diagram analysis applied to data from the Michelson Doppler Imager (MDI) on the SOHO spacecraft. Horizontal flows yield displacements in the rings of power (at fixed frequency) associated with solar acoustic waves propagating in different directions below a localized area being studied. We pass these shifts through an inversion procedure and obtain measurements of the zonal and meridional flows as a function of depth to about 10 Mm below the surface. Each separate ring analysis deduces the average flow below a 16 degree square region on the solar surface. We map the velocity field over a substantial fraction of the solar disk by repeating the analysis over a densely packed mosaic of 189 overlapping tiles (called a Dense-Pack). We process such a mosaic on a nearly daily schedule and have fully analyzed two Carrington rotations (48 days) in 1996 and one rotation each in 1997, 1998, and 1999 during MDI Dynamics Campaigns. We find that the longitudinally-averaged zonal velocity, after removing a smooth differential rotation component, possesses bands of fast and slow flow, much like `torsional oscillations' first reported from surface Doppler measurements and recently from global helioseismic assessments. As the solar cycle progresses, the latitudes at which the fast bands occur migrate towards the equator. The amplitudes of these banded zonal flows increase with magnetic activity. Our local-area analyses reveal that these belts of fast and slow flow are not symmetric about the solar equator, and their asymmetry changes with time. The average meridional flow is primarily poleward and reaches maxima in the two hemispheres at the latitudes at which the zonal fast belts occur. As these zonal fast belts drift towards the equator, the latitudes of maximal meridional flow also drift equatorward. This research was supported by NASA grants NAG 5--8133, NAG 5--7996 and NAG 5--3077 and by NSF grant ATM-9731676. Title: Daily Variations and Average Structure of Solar Shear Flows Deduced from Helioseismic Dense-Pack Samplings of Ring Diagrams Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.; Schou, J.; Hill, F. Bibcode: 1999AAS...194.5611H Altcode: 1999BAAS...31..913H We report on the daily variations and average behavior of large-scale flows in the upper convection zone as determined by ring-diagram helioseismic analysis applied to SOI-MDI full-disk velocity data from the 1996 and 1998 Dynamics Campaigns. We have tracked many small regions of 15 degrees diameter whose centers are spaced 7.5 degrees apart in latitude and longitude, creating a mosaic of tiles that oversample the spatial domain. The tiles cover the solar disk out to a distance of 52.5 degrees from disk center. An individual dense-pack mosaic is prepared by tracking each of 189 regions for 1664 minutes (27.7 hrs). Successive mosaics are prepared every 15 degrees in Carrington longitude, roughly once every 1633 minutes. Such mosaics now cover more than two full Carrington rotations in 1996 and one rotation in 1998. This is the best spatial and temporal coverage of any ring-diagram study carried out to date. The longitudinally averaged meridional flow varies with latitude but remains relatively constant with depth below the upper shear layer at 2 Mm down to a depth of about 16 Mm. The averaged zonal flow increases with depth within this same layer and agrees well with the rotation rates found from global modes. However with the high-degree wave field data from this analysis we are better able to resolve that shear layer within the upper convection zone. We see bands of faster averaged zonal flow near 30 degrees latitude both in the northern and southern hemisphere that are present at all depths studied. We also present movies of the daily variations in the flows within this dense pack for given depths that show the evolution of the complex velocity field. This research was supported by NASA grants NAG5-3077 and NAG5-7996, and NSF grant AST-9417337. Title: Comparison Between Near-Surface Flow Fields Deduced from Correlation Tracking and Time-Distance Helioseismology Methods Authors: De Rosa, M. L.; Toomre, J.; Duvall, T. L., Jr. Bibcode: 1999AAS...194.5608D Altcode: 1999BAAS...31..913D Near-photospheric flow fields deduced using two independent methods applied to the same SOI-MDI time series of images from SOHO are compared. Differences in travel times between incoming and outgoing f modes measured using time-distance helioseismology are used to determine the sites of supergranule outflows. Alternatively, correlation tracking analysis is applied to granular and mesogranular structures seen in time series of Doppler and intensity images. We find that the locations of the supergranular outflows seen in flow fields generated from correlation tracking coincide well with the locations of the outflows determined from the time-distance analysis. The near-surface flow fields provide us with insight in understanding the dyanmics of the turbulent convection occurring below the photosphere. The data consist of four 512-minute time series of high-resolution (0.6'' pixels) Doppler images and continuum intensity images taken by MDI on 17--18 January 1997 at a cadence of one minute. Title: Time-Variability of the Inferred Rotation in the Upper Convection Zone Authors: Toomre, J.; Christensen-Dalsgaard, J.; Howe, R.; Larsen, R. M.; Schou, J.; Thompson, M. J. Bibcode: 1999soho....9E..87T Altcode: We present results of inverting for the rotation of the upper convection zone, using frequency splittings derived from successive 72-day time series of SOI-MDI observations. Schou (1999; also Schou et al. 1998) has studied the evolution of the pattern of small-scale zonal flows in the near-surface layers using f-mode splittings and has found that this flow pattern migrates equatorward in a manner similar to that seen in the so-called torsional oscillation observed in surface Doppler measurements. In the present work we look at the time variability of the rotation at greater depth, in the upper convection zone, by inverting both f- and p-mode splittings. The evolution of the flow is less regular than is seen at the surface, but we do observe apparently significant variations in the inferred flow pattern, on latitudinal scales similar to those seen at the surface. In particular, in the subsurface shear layer we see intriguing variations, with the first year's data showing apparent emergence of zonal flows of some 10-15 m/s amplitude at around 20 degrees latitude. Title: Large-Eddy Simulations of Turbulent Solar Convection and its Coupling with Rotation Authors: Elliott, J. R.; Miesch, M.; Toomre, J. Bibcode: 1999soho....9E..54E Altcode: Turbulent fluid motions in the sun's convection zone must play a large part in setting up the observed differential rotation. Studies of convection have either been based on the parametrizations of the effects of turbulent motions (for example the Reynolds stresses), or upon numerical simulations. Most of the recent progress has come from numerical simulations. In this poster we present results from anelastic convection simulations carried out in a spherical shell geometry, and calculated with a code specifically optimized for high performance on Massively Parallel machines. Whereas early simulations tended to show angular velocity approximately constant on cylinders aligned with the rotation axis (in disagreement with deductions from helioseismology), our latest simulations show a differential rotation in much closer agreement with helioseismic inversions. This results from several improvements over earlier models, including the use of a higher resolution coupled with longer integration times, and the implementation of the idea of large-eddy simulation. We hope to demonstrate convergence of our results as the resolution of the shell is increased. Title: Comparison Between Near-Surface Flow Fields Deduced from Correlation Tracking and Time-Distance Helioseismology Methods Authors: de Rosa, Marc; Toomre, Juri; Duvall, T. L., Jr. Bibcode: 1999soho....9E..51D Altcode: Near-photospheric flow fields deduced using two independent methods applied to the same SOI-MDI time series of images from SOHO are compared. Differences in travel times between incoming and outgoing f modes measured using time-distance helioseismology are used to determine the sites of supergranule outflows. Alternatively, correlation tracking analysis is applied to granular and mesogranular structures seen in time series of Doppler and intensity images. We find that the locations of the supergranular outflows seen in flow fields generated from correlation tracking coincide well with the locations of the outflows determined from the time-distance analysis. The near-surface flow fields provide us with insight in understanding the dynamics of the turbulent convection occurring below the photosphere. The data consist of four 512-minute time series of high-resolution (0.6 arc-second pixels) Doppler images and continuum intensity images taken by MDI on 17-18 January 1997 at a cadence of one minute. Title: Long-Term Dynamics of Small-Scale Magnetic Flux Elements Embedded in the Near-Surface Velocity Field Authors: Lisle, Jason; de Rosa, Marc; Toomre, Juri Bibcode: 1999soho....9E..72L Altcode: Using velocity and magnetogram data generated by SOI-MDI during the 1999 Dynamics Program, we have studied the dynamics of small-scale magnetic elements over time periods of several days. By exploiting concurrent time series of MDI magnetograms and velocity images, we have correlated the motions of the magnetic flux elements with the supergranular velocity field inferred from tracking of mesogranular motions. We confirm that these magnetic elements travel at approximately 200 m/s throughout the duration of their lifetime (10-20 hours) as they are transported by supergranular outflows. We also find that boundaries of supergranules traced by magnetic flux elements coincide with the boundaries determined from the tracking of mesogranules. In addition, we have studied the association between magnetic flux emergence and destruction events and the evolution of the supergranular network. The data consist of several tracked regions of corresponding magnetogram and photospheric velocity images extracted from full-disk SOI-MDI images taken during the 1999 Dynamics Program when the MDI instrument was at best focus. Time series were created by following these individual patches as they rotated across the solar disk. Individual magnetic elements were identified by thresholding the magnetograms, while the supergranular flow fields were determined by applying a correlation tracking algorithm to time series of mesogranules. The mesogranules were isolated by removing the signal due to solar rotation, p-mode oscillations, and supergranulation from the velocity data. Title: Phase Inversion of One-Dimensional Artificial Seismic Data Authors: Gough, D. O.; Sekii, T.; Toomre, J. Bibcode: 1999soho....9E..30G Altcode: It has been pointed out (Sekii 1997; Gough, Sekii & Toomre 1998, 1999) that the application of the phase inversion technique (Gough, Merryfield & Toomre 1991, 1993, 1998) to the solar high-degree sectoral data, for detecting the background inhomogeneity in the solar equatorial region, may be facing difficulty arising from the presence of excitation and damping. We have studied the implication of the effects of these, using a simple model of stochastically excited damped oscillations of a one-dimensional loop. The results of phase inversions for various cases will be presented and various strategies to overcome the difficulty will be discussed. Title: Simulation of Wave Fields to Assess the Sensitivity of Ring-Diagram Analyses to Shearing Flows Authors: Hindman, B. W.; Gough, D. O.; Haber, D. A.; Thompson, M. J.; Toomre, J. Bibcode: 1999soho....9E..64H Altcode: Ring-diagram analyses of acoustic-wave distortion by flows map horizontal motions within the solar convection beneath the localized regions where the observations are taken. To leading order, the flow field responsible for the advection of waves is taken to be horizontally uniform across the region. Current ring-diagram analyses are only carried out to this order, although in reality the flow is likely to vary across the local patch of the Sun. It is crucial for the interpretation of the results of ring-diagram analyses that the effects of shearing flows be assessed. Furthermore, the present analyses ignore any influence on the ring parameters of flows exterior to the region being studied. We present a progress report on the forward calculation of the modification of ring parameters produced by spatially varying flow fields. We examine effects of flow fields both inside and outside the region of observation. Additionally, we assess the influence of the non-uniform flow on the maps of the velocity field obtained by inverting the ring-parameter data. The effect of the inhomogeneous flow can be studied as a scattering problem. We have developed Green functions connecting an underlying inhomogeneous horizontal flow to the scattered wave field that results when an incident plane wave encounters the flow. By considering an ensemble of such incident waves, ring parameters can be inferred from the wave field. One application is to analyze artificial data sets, computed from models that contain horizontal shear flows. The scattered wave field produced by a prescribed 3-D shearing flow is computed, and the original and scattered wave fields are combined to generate an artificial helioseismic data set. The artificial data so produced should then be passed through a ring-diagram analysis and the deduced velocity field compared to the known imposed flow. Another application is to compute 3-D kernels relating the ring parameters to the underlying flow: these will in the future permit 3-D inversions for the flows within the solar convection zone, using mosaics of many ring-diagram samplings. Title: Changes in High-Degree Oscillation Frequencies from 1996 to 1999 Determined from Ring-Diagram Analysis Authors: Bogart, R. S.; Schou, J.; Haber, D. A.; Hindman, B. W.; Toomre, J.; Hill, F. Bibcode: 1999soho....9E..45B Altcode: Ring-diagram analysis has traditionally been used primarily as a diagnostic for large-scale flows in the upper convection zone. It also yields values for the unperturbed (rest) frequencies of the local high-degree p-mode oscillations. These frequencies, positioned predominantly in a regime where ridge-fitting of traditional global modes is difficult, possess information about the average near-surface temperature profile in the region being analyzed. As the solar magnetic activity level increased from 1996 through 1999, we might expect these frequencies to have changed correspondingly. We present spatially and temporally averaged rest frequencies determined from ring-diagram analysis of full-disk Doppler data for selected intervals from each of the four annual SOI Dynamics campaigns covering the rise in solar activity from 1996 through 1999. These analyses are performed on a `dense-pack' mosaic of tracked tiles that oversample the spatial domain with a resolution of 15 heliographic degrees (180 Mm). Tiles are individually tracked over time spans of 1664 minutes (27.7 hr), so a given physical region on the Sun is sampled from 7 to 15 times depending on its latitude as it rotates across the visible hemisphere. We discuss the frequency changes seen for comparable areas on the disc over the years analyzed. This research is supported by NASA grant NAG5-3077 at Stanford University. Title: Local p-Mode Frequency Shifts Used as Tracers of Solar Activity Authors: Hindman, B. W.; Haber, D. A.; Toomre, J. Bibcode: 1999soho....9E...5H Altcode: The Dense-Pack data set from SOI-MDI was originally devised for ring-diagram analyses. Each day of data consists of 189 separately tracked tiles on the solar surface. Each tile is 16 degrees square and the tile centers are separated by 7.5 degrees in latitude and longitude. The tiling extends out to roughly 52.5 degrees from disk center. I have computed the local frequency of low order p modes in each of the Dense-Pack tiles. The frequencies were calculated once a day for a period of roughly two months during the 1996 dynamics campaign and for a period of more than week during the 1998 dynamics campaign. For each day of data and for each latitude and longitude in the Dense-Pack grid, I have computed the fractional frequency shift by subtracting the spatial and temporal average of the entire set of frequencies. The motion of active regions as they rotate across the solar disk is vividly tracked by these measurement of the local fractional frequency shift. Active regions are locations with a positive frequency shift, indicating a region of higher wave propagation speed. To demonstrate this correspondence, I will present animations of the fractional frequency shift overlaid with contemporaneous magnetograms. Title: Solar Shear Flows Deduced From Helioseismic Dense-Pack Samplings of Ring Diagrams Authors: Haber, D. A.; Hindman, B. W.; Toomre, J.; Bogart, R. S.; Schou, J.; Hill, F. Bibcode: 1999soho....9E..62H Altcode: Large-scale flows in the upper convection zone can be inferred by ring-diagram helioseismic analysis, permitting the study of both their daily variations and their longer temporal means. We use selected full-disk SOI-MDI velocity data from the 1996, 1997, and 1998 Dynamics campaigns. We have tracked sets of regions (each 15 degrees in diameter and spaced 7.5 degrees apart in latitude and longitude), creating a `dense-pack' mosaic of such tiles that oversamples the spatial domain. The tiles cover the solar disc to a distance of up to 52.5 degrees from center. A single dense-pack mosaic is prepared by tracking each of 189 regions for 1664 minutes (27.7 hrs). Such mosaics now cover more than two full Carrington rotations in 1996 and one-third of a rotation each in both 1997 and 1998. This is the best spatial and temporal coverage of any ring-diagram study carried out to date. We are able to compare the mean flows determined over 9-day averages for data from the different SOI-MDI Dynamics campaigns, as well as examine the daily flow maps, allowing us to study possible changes in the convection during the rising magnetic activity of the current solar cycle. We also present movies of the daily variations in the flows within this dense pack for given depths that show the evolution of the complex velocity field. The longitudinally-averaged meridional flow varies with latitude but remains relatively constant with depth below the upper shear layer at 2 Mm down to a depth of about 16 Mm. The averaged zonal flow increases with depth within this same layer and agrees well with the rotation rates found from global modes. However, with the high-degree wave-field data from this analysis we are better able to resolve the shear layer within the upper convection zone. We see bands of faster and slower average zonal flows in both hemispheres; these are present at all depths studied. Title: Helioseismic Studies of Differential Rotation in the Solar Envelope by the Solar Oscillations Investigation Using the Michelson Doppler Imager Authors: Schou, J.; Antia, H. M.; Basu, S.; Bogart, R. S.; Bush, R. I.; Chitre, S. M.; Christensen-Dalsgaard, J.; Di Mauro, M. P.; Dziembowski, W. A.; Eff-Darwich, A.; Gough, D. O.; Haber, D. A.; Hoeksema, J. T.; Howe, R.; Korzennik, S. G.; Kosovichev, A. G.; Larsen, R. M.; Pijpers, F. P.; Scherrer, P. H.; Sekii, T.; Tarbell, T. D.; Title, A. M.; Thompson, M. J.; Toomre, J. Bibcode: 1998ApJ...505..390S Altcode: The splitting of the frequencies of the global resonant acoustic modes of the Sun by large-scale flows and rotation permits study of the variation of angular velocity Ω with both radius and latitude within the turbulent convection zone and the deeper radiative interior. The nearly uninterrupted Doppler imaging observations, provided by the Solar Oscillations Investigation (SOI) using the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft positioned at the L1 Lagrangian point in continuous sunlight, yield oscillation power spectra with very high signal-to-noise ratios that allow frequency splittings to be determined with exceptional accuracy. This paper reports on joint helioseismic analyses of solar rotation in the convection zone and in the outer part of the radiative core. Inversions have been obtained for a medium-l mode set (involving modes of angular degree l extending to about 250) obtained from the first 144 day interval of SOI-MDI observations in 1996. Drawing inferences about the solar internal rotation from the splitting data is a subtle process. By applying more than one inversion technique to the data, we get some indication of what are the more robust and less robust features of our inversion solutions. Here we have used seven different inversion methods. To test the reliability and sensitivity of these methods, we have performed a set of controlled experiments utilizing artificial data. This gives us some confidence in the inferences we can draw from the real solar data. The inversions of SOI-MDI data have confirmed that the decrease of Ω with latitude seen at the surface extends with little radial variation through much of the convection zone, at the base of which is an adjustment layer, called the tachocline, leading to nearly uniform rotation deeper in the radiative interior. A prominent rotational shearing layer in which Ω increases just below the surface is discernible at low to mid latitudes. Using the new data, we have also been able to study the solar rotation closer to the poles than has been achieved in previous investigations. The data have revealed that the angular velocity is distinctly lower at high latitudes than the values previously extrapolated from measurements at lower latitudes based on surface Doppler observations and helioseismology. Furthermore, we have found some evidence near latitudes of 75° of a submerged polar jet which is rotating more rapidly than its immediate surroundings. Superposed on the relatively smooth latitudinal variation in Ω are alternating zonal bands of slightly faster and slower rotation, each extending some 10° to 15° in latitude. These relatively weak banded flows have been followed by inversion to a depth of about 5% of the solar radius and appear to coincide with the evolving pattern of ``torsional oscillations'' reported from earlier surface Doppler studies. Title: Pumping of Magnetic Fields by Turbulent Penetrative Convection Authors: Tobias, Steven M.; Brummell, Nicholas H.; Clune, Thomas L.; Toomre, Juri Bibcode: 1998ApJ...502L.177T Altcode: A plausible scenario for solar dynamo action is that the large-scale organized toroidal magnetic field is generated by the action of strong radial shear at the base of the solar convection zone, whereas the weaker poloidal field is regenerated by cyclonic convection throughout the convection zone. We show, using high-resolution three-dimensional numerical simulations, that the required transport of magnetic field from the convection zone to the overshoot region can be achieved on a convective rather than diffusive timescale by a pumping mechanism in turbulent penetrative compressible convection. A layer of magnetic field initially placed in the convection zone is swept down by strong sinking plumes, locally amplified, and deposited in the stable region at the base of the convection zone, despite the opposing action of magnetic buoyancy. The rate of transport is insensitive to the strength of the initial imposed field. Title: Phase Inversion: Inferring Solar Subphotospheric Flow and Other Asphericity from the Distortion of Acoustic Waves Authors: Gough, Douglas; Merryfield, William J.; Toomre, Juri Bibcode: 1998ApJ...501..882G Altcode: A method is proposed for analyzing an almost monochromatic train of waves propagating in a single direction in an inhomogenous medium that is not otherwise changing in time. An effective phase is defined in terms of the Hilbert transform of the wave function, which is related, via the JWKB approximation, to the spatial variation of the background state against which the wave is propagating. The contaminating effect of interference between the truly monochromatic components of the train is eliminated using its propagation properties. Measurement errors, provided they are uncorrelated, are manifest as rapidly varying noise; although that noise can dominate the raw phase-processed signal, it can largely be removed by low-pass filtering. The intended purpose of the analysis is to determine the distortion of solar oscillations induced by horizontal structural variation and material flow. It should be possible to apply the method directly to sectoral modes. The horizontal phase distortion provides a measure of longitudinally averaged properties of the Sun in the vicinity of the equator, averaged also in radius down to the depth to which the modes penetrate. By combining such averages from different modes, the two-dimensional variation can be inferred by standard inversion techniques. After taking due account of horizontal refraction, it should be possible to apply the technique also to locally sectoral modes that propagate obliquely to the equator and thereby build a network of lateral averages at each radius, from which the full three-dimensional structure of the Sun can, in principle, be determined as an inverse Radon transform. Title: Subphotospheric Convective Flows Determined by Ring-Diagram Analyses of SOI-MDI Observations Authors: Haber, D.; Hindman, B.; Toomre, J.; Bogart, R.; Schou, J.; Hill, F. Bibcode: 1998ESASP.418..791H Altcode: 1998soho....6..791H The variation of large-scale velocity flows with depth and location on the sun places important constraints on theoretical models of the solar convection zone and dynamo. High-degree oscillations can be viewed as nearly plane waves that are advected and distorted by the underlying flows. By conducting observations over limited regions of the solar surface to obtain `ring diagram' power spectra, we can deduce spatially-averaged horizontal flows with depth below that region. Previous analyses of ring diagrams have already suggested the presence of strong shearing flows below the surface. We have now implemented a highly efficient technique for determining these horizontal flows with depth and report here on a systematic analysis of full-disk Doppler velocity data taken continuously with a one-minute cadence during portions of the two-month dynamics observing program with SOI-MDI in 1996. The square regions examined span about 15-circ, and are studied for time intervals each of about 1536 mins (~25 hrs). A lattice of such squares is considered: their centers are spaced 15-circ apart in longitude and there are seven such regions across the solar disk at +20-circ, 0-circ, -20-circ latitude. Another set of regions is placed along the central meridian at 10-circ and 15-circ intervals in latitude. Properties of the underlying large-scale subphotospheric flows and their temporal variations so revealed are presented in detail. Title: Slow Poles and Shearing Flows from Heliospheric Observations with MDI and GONG Spanning a Year Authors: Schou, J.; Christensen-Dalsgaard, J.; Howe, R.; Larsen, R. M.; Thompson, M. J.; Toomre, J. Bibcode: 1998ESASP.418..845S Altcode: 1998soho....6..845S We invert one year of coeval high-resolution rotational splitting data (up to degree l 250) from GONG and SOI-MDI. The first 4 months of MDI data uncovered several new features in the rotation of the solar convective envelope: surface and subsurface zonal bands corresponding to the so-called torsional oscillations, superimposed on the overall smooth latitudinal surface rotation; a drop in the near-polar surface rotation rate below the rate extrapolated from lower latitudes; and an indication of a prograde jet-like feature at high latitudes at a depth of about 5 percent of the solar radius. Using the 1 year of data from the MDI and GONG instruments, we test the robustness and stationarity of these features. As an aid to testing the robustness of our inferences, we use two independent inversion methods (2-D regularized least squares and SOLA) and apply them to the splitting data obtained from both GONG and MDI. Title: Helioseismology: What are We Learning About the Sun? Authors: Toomre, Juri Bibcode: 1998ASPC..154..275T Altcode: 1998csss...10..275T Helioseismology studies the internal structure and dynamics of the Sun, utilizing very precise measurements of the frequencies of sound waves that propagate throughout the solar interior and are observed at the surface. Efforts to accurately and precisely measure the mode frequencies from a single observing site have met with fundamental limitations imposed by the day-night cycle. Such difficulties have recently been overcome as nearly uninterrupted Doppler imaged observations of the full solar disk have become available both from the ground-based six-station Global Oscillation Network Group (GONG) project and from the SOI Michelson Doppler Imager (SOI-MDI) aboard the SOHO spacecraft in continuous sunlight orbiting the Sun-Earth L_1 Lagrangian point. Thus helioseismology has entered a major new phase of intensive scientific study as coordinated scientific teams have started to analyze both the GONG and SOI data. We review some of the basic principles and motivations of helioseismology, and then discuss some of the preliminary scientific results obtained by the teams through inversion of the global-mode frequencies and their splittings, dealing with the structure of the solar interior and the physics of stellar models, and an assessment of the differential rotation profile with depth and latitude. The inversions confirm that the surface latitudinal variation of the rotation rate carries through much of the convection zone. At the base of the convection zone there is a currently unresolved adjustment layer with latitudinally independent rotation at greater depths. A shearing layer just below the surface is discernible at low to mid latitudes. Such global investigations are supplemented by local area analyses via ring diagrams and time-distance methods, which enable one to probe the subsurface variation of large-scale flows and thermal structures with depth beneath selected regions of the Sun. Title: Correlation Tracking of Mesogranules from SOI-MDI Doppler Images to Reveal Supergranular Flow Fields Authors: De Rosa, Marc L.; Toomre, Juri Bibcode: 1998ESASP.418..753D Altcode: 1998soho....6..753D We present evidence that mesogranules on the sun are advected horizontally by the underlying supergranular flow field. Correlation tracking of mesogranules, as observed in full-disk SOI-MDI Doppler images, reveal that the flow field experienced by the mesogranules is composed of several long-lived regions of divergent fluid. These outflow regions correlate well with the locations of supergranules present on related Doppler images. The flow fields also contain regions where the fluid is converging or is moving slowly, both corresponding to areas of the related Doppler images where no organized supergranular outflows exist. Typical velocities are of order 200 m s-1. The data used in this study consist of 30-circ-square patches of the photospheric velocity field extracted from full-disk SOI-MDI Dopplergrams. Time series were created by tracking each patch in a frame corotating with the surface plasma. Images of mesogranulation superimposed on supergranulation were created by removing the velocity signals due to rotation and acoustic oscillations. The supergranular signal is isolated by spatially smoothing each image, while the mesogranular signal is isolated by taking the residual of the smoothed and unsmoothed images. The correlation tracking calculation was performed on the time series of mesogranulation, from which the surface flow-fields analyzed in this study were deduced. Title: Turbulent Solar Convection and its Coupling with Rotation Authors: Elliott, J. R.; Miesch, M. S.; Toomre, J.; Cluney, T. C.; Glatzmaier, G. A. Bibcode: 1998ESASP.418..765E Altcode: 1998soho....6..765E Previous numerical simulations of global-scale solar convection in rotating spherical shells of fluid have been restricted by computational resources to deal with nearly laminar flow regimes. Disparities between the differential rotation profiles that such models predict and those deduced from helioseismology, coupled with recent advances in high performance computing, encouraged us to begin pursuing numerical simulations of global-scale convection in turbulent parameter regimes. We anticipate that rotationally-constrained turbulence can possess inverse cascades that yield large-scale coherent vorticity structures and strong mean flows which coexist with less persistent smaller-scale turbulence, and yield angular velocity profiles that may be quite different than those obtained with laminar convection. We have developed a new code for studying penetrative anelastic convection in rotating spherical shells which is highly optimized for massively parallel supercomputer architechtures, and as a result, is capable of achieving more turbulent flow regimes than previously possible. We present results from such simulations, which are providing new insight into the nature of turbulent solar convection and its coupling to differential rotation. Title: Some Comments on Phase Inversions Authors: Gough, D. O.; Sekii, T.; Toomre, J. Bibcode: 1998ESASP.418..789G Altcode: 1998soho....6..789G The method of phase inversion have been proposed and tested for simple cases by Gough, Merryfield and Toomre(1991,1993,1998) for detection of inhomogeneity in media by observing wave propagation. We discuss some of the difficulties that are encountered with the procedure in practice, and what might be done to overcome them in transferring the technique to the solar case, such as in the study of horizontal inhomogeneity in the solar cavity along the equator using the MDI sectoral-mode data. A complication seems to arise, aside from observational problems, from the fact that the waves are not only scattered by inhomogeneity, but are also excited and damped, as is observed in the broadening of the ridges in the k-ω diagram. Title: Turbulent Compressible Convection with Rotation. II. Mean Flows and Differential Rotation Authors: Brummell, Nicholas H.; Hurlburt, Neal E.; Toomre, Juri Bibcode: 1998ApJ...493..955B Altcode: The effects of rotation on turbulent, compressible convection within stellar envelopes are studied through three-dimensional numerical simulations conducted within a local f-plane model. This work seeks to understand the types of differential rotation that can be established in convective envelopes of stars like the Sun, for which recent helioseismic observations suggest an angular velocity profile with depth and latitude at variance with many theoretical predictions. This paper analyzes the mechanisms that are responsible for the mean (horizontally averaged) zonal and meridional flows that are produced by convection influenced by Coriolis forces. The compressible convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers encompassing both laminar and turbulent flow conditions under weak and strong rotational constraints.

When the nonlinearities are moderate, the effects of rotation on the resulting laminar cellular convection leads to distinctive tilts of the cell boundaries away from the vertical. These yield correlations between vertical and horizontal motions that generate Reynolds stresses that can drive mean flows, interpretable as differential rotation and meridional circulations. Under more vigorous forcing, the resulting turbulent convection involves complicated and contorted fluid particle trajectories, with few clear correlations between vertical and horizontal motions, punctuated by an evolving and intricate downflow network that can extend over much of the depth of the layer. Within such networks are some coherent structures of vortical downflow that tend to align with the rotation axis. These yield a novel turbulent alignment mechanism, distinct from the laminar tilting of cellular boundaries, that can provide the principal correlated motions and thus Reynolds stresses and subsequently mean flows. The emergence of such coherent structures that can persist amidst more random motions is a characteristic of turbulence with symmetries broken by rotation and stratification. Such structure is here found to play a crucial role in defining the mean zonal and meridional flows that coexist with the convection. Though they are subject to strong inertial oscillations, the strength and type of the mean flows are determined by a combination of the laminar tilting and the turbulent alignment mechanisms. Varying the parameters produces a wide range of mean motions. Among these, some turbulent solutions exhibit a mean zonal velocity profile that is nearly constant with depth, much as deduced by helioseismology at midlatitudes within the Sun. The solutions exhibit a definite handedness, with the direction of the persistent mean flows often prescribing a spiral with depth near the boundaries, also in accord with helioseismic deductions. The mean helicity has a profile that is positive in the upper portion of the domain and negative in the lower portion, a property bearing on magnetic dynamo processes that may be realized within such rotating layers of turbulent convection. Title: Differential rotation in turbulent compressible convection Authors: Brummell, N. H.; Toomre, J.; Hurlburt, N. Bibcode: 1997ASSL..225..223B Altcode: 1997scor.proc..223B Numerical simulations of 3D compressible convection in a local rectilinear geometry show that zonal and meridional mean flows, $\overline{u}(z)$ and $\overline{v}(z)$, can be produced when rotation is included. A wide variety of mean profiles can be achieved depending upon the parameters, including behaviour equivalent (within the limitations of the model) to that inferred from helioseismic solar observations. Title: Rotation and Zonal Flows in the Solar Envelope from the SOHO/MDI Observations Authors: Scherrer, P. H.; Schou, J.; Bogart, R. S.; Bush, R. I.; Hoeksema, J. T.; Kosovichev, A. G.; Antia, H. M.; Chitre, S. M.; Christensen-Dalsgaard, J.; Larsen, R. M.; Pijpers, F. P.; Eff-Darwich, A.; Korzennik, S. G.; Gough, D. O.; Sekii, T.; Howe, R.; Tarbell, T.; Title, A. M.; Thompson, M. J.; Toomre, J. Bibcode: 1997AAS...191.7310S Altcode: 1997BAAS...29.1322S We report on the latest inferences concerning solar differential rotation that have been drawn from the helioseismic data that are now available from the Solar Oscillations Investigation (SOI) using the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO). That spacecraft is positioned in a halo orbit near the Sun-Earth Lagrangian point L_1, in order to obtain continuous Doppler-imaged observations of the sun with high spatial fidelity. Doppler velocity, intensity and magnetic field images are recorded, based on modulations of the 676.8 nm Ni I solar absorption line. The high spatial resolution of MDI thereby permits the study of many millions of global resonant modes of solar oscillation. Determination and subsequent inversion of the frequencies of these modes, including the degeneracy-splitting by the rotation of the sun, enables us to infer how the sun's angular velocity varies throughout much of the interior. The current MDI data are providing substantial refinements to the helioseismic deductions that can be made about differential rotation both within the convection zone and in its transition to the radiative interior. The shearing layer evident in the angular velocity Omega just below the solar surface is becoming better defined, as is the adjustment layer or tachocline near the base of the convection zone. The MDI data are also revealing a prominent decrease in Omega at high latitudes from the rotation rate expressed by a simple three-term expansion in latitude that was originally deduced from surface Doppler measurements. Further, there are indications that a submerged polar vortex involving somewhat faster Omega than its surroundings exists at about 75(deg) in latitudes. Title: Global-scale numerical simulation of solar turbulent convection and its coupling to rotation Authors: Elliott, J. R.; Miesch, M.; Toomre, J.; Clune, T. C.; Glatzmaier, G. A. Bibcode: 1997AAS...191.7403E Altcode: 1997BAAS...29.1324E The larger scales of convection in the sun are influenced by rotation, leading to a redistribution of angular momentum which is seen as differential rotation. Previous numerical simulations of such global-scale convection in rotating spherical shells of fluid have been restricted by computational resources to deal with nearly laminar flow regimes for the resolved scales of motion, though provisions were made for diffusive transport by nominally turbulent unresolved scales. The disparities between the differential rotation profiles that those models predict (angular velocity nearly constant on cylinders) and those deduced from the frequency splittings of p modes (nearly constant on radii in the convection zone), coupled with recent advances in high performance computing, encouraged us to begin pursuing numerical simulations of global-scale convection in turbulent parameter regimes. We anticipate that rotationally-constrained turbulence can possess inverse cascades that yield large-scale coherent vorticity structures and strong mean flows which coexist with less persistent smaller-scale turbulence, and yield angular velocity profiles that may be quite different than those obtained with laminar convection. The dominant challenge to all turbulence simulations is to be able to explicitly describe the dynamics over a broad enough range of length scales. To this end, we have developed a new code for studying rotating anelastic convection in spherical shells, employing expansions in spherical harmonics to resolve horizontal structures and in Chebyshev polynomials to resolve radial structures. Appropriate optimization techniques, including expedient use of inter-processor transposes and sophisticated load balancing, enable the code to achieve high performance on massively parallel architectures, and currently to reach a speed of around 100Mflop/s per node on the Cray T3E. The new code is enabling us to perform simulations of convection at spatial resolutions significantly higher than those of earlier studies, and thereby to begin to investigate fully turbulent parameter regimes. We present the results from such a simulation, which includes the important effects of penetration into the stable interior, and discuss the corresponding differential-rotation profile obtained. Title: The Nature of Supergranulation from SOI-MDI Dopplergrams Authors: De Rosa, Marc L.; Toomre, Juri Bibcode: 1997SPD....28.0257D Altcode: 1997BAAS...29..903D We discuss the distribution of supergranule cell areas and evolutionary characteristics as determined from a series of SOI-MDI dopplergrams. Patches of the photospheric velocity field 30(deg) x30(deg) (heliographic) in size were tracked as they rotated across the disk of the sun. Supergranule boundaries were identified on each tracked image by a pattern recognition algorithm, from which supergranule area distributions and evolutionary trends are found. Title: Persistence of Large-Scale Flows Beneath Quiet Sun: Local-Area Analysis Using MDI Doppler Data Authors: Haber, D.; Toomre, J.; Bogart, R.; Schou, J.; Gonzalez, I.; Hill, F. Bibcode: 1997SPD....28.0201H Altcode: 1997BAAS...29..893H Knowing the large-scale flows that occur in the upper convection zone is critical to our understanding of the processes that govern the solar cycle. Here we apply solar oscillation ring-diagram analysis to several small tracked regions on the sun, approximately 15(deg) on a side, as they rotate across the solar disk, in order to determine the persistence and depth variation of the large-scale flows beneath these regions. We use the Doppler velocity images from the Michelson Doppler Imager (MDI) instrument aboard the Solar Heliospheric Observatory (SOHO) satellite using quiet-sun data taken during the MDI Dynamics campaign of 1996. Three regions at different latitudes were extracted from full-disk Doppler images of 1024 x 1024 pixels (pixel size ~ 2'' square) with a one-minute temporal cadence. Eight sequential 1536-minute time intervals were tracked, remapped onto great-circle grids, spatially and temporally filtered, and apodized in space and time. They were then Fourier transformed in two spatial dimensions and time. The resulting power spectra show characteristic rings at each frequency slice. Shifts in the center positions of the rings are caused by underlying flow fields and can be inverted to map these flows with depth. We use several techniques to fit these shifts in order to assess the stability of the results. Title: Structure and Rotation of the Solar Interior: Initial Results from the MDI Medium-L Program Authors: Kosovichev, A. G.; Schou, J.; Scherrer, P. H.; Bogart, R. S.; Bush, R. I.; Hoeksema, J. T.; Aloise, J.; Bacon, L.; Burnette, A.; de Forest, C.; Giles, P. M.; Leibrand, K.; Nigam, R.; Rubin, M.; Scott, K.; Williams, S. D.; Basu, Sarbani; Christensen-Dalsgaard, J.; Dappen, W.; Rhodes, E. J., Jr.; Duvall, T. L., Jr.; Howe, R.; Thompson, M. J.; Gough, D. O.; Sekii, T.; Toomre, J.; Tarbell, T. D.; Title, A. M.; Mathur, D.; Morrison, M.; Saba, J. L. R.; Wolfson, C. J.; Zayer, I.; Milford, P. N. Bibcode: 1997SoPh..170...43K Altcode: The medium-l program of the Michelson Doppler Imager instrument on board SOHO provides continuous observations of oscillation modes of angular degree, l, from 0 to ∽ 300. The data for the program are partly processed on board because only about 3% of MDI observations can be transmitted continuously to the ground. The on-board data processing, the main component of which is Gaussian-weighted binning, has been optimized to reduce the negative influence of spatial aliasing of the high-degree oscillation modes. The data processing is completed in a data analysis pipeline at the SOI Stanford Support Center to determine the mean multiplet frequencies and splitting coefficients. The initial results show that the noise in the medium-l oscillation power spectrum is substantially lower than in ground-based measurements. This enables us to detect lower amplitude modes and, thus, to extend the range of measured mode frequencies. This is important for inferring the Sun's internal structure and rotation. The MDI observations also reveal the asymmetry of oscillation spectral lines. The line asymmetries agree with the theory of mode excitation by acoustic sources localized in the upper convective boundary layer. The sound-speed profile inferred from the mean frequencies gives evidence for a sharp variation at the edge of the energy-generating core. The results also confirm the previous finding by the GONG (Gough et al., 1996) that, in a thin layer just beneath the convection zone, helium appears to be less abundant than predicted by theory. Inverting the multiplet frequency splittings from MDI, we detect significant rotational shear in this thin layer. This layer is likely to be the place where the solar dynamo operates. In order to understand how the Sun works, it is extremely important to observe the evolution of this transition layer throughout the 11-year activity cycle. Title: Plane-wave analysis of 501 data Authors: Bogart, R. S.; Discher de Sá, L. A.; González Hernández, I.; Patrón Recio, J.; Haber, D. A.; Toomre, J.; Hill, F.; Rhodes, E. J., Jr.; Xue, Y.; SOI Ring Diagrams Team Bibcode: 1997IAUS..181..111B Altcode: No abstract at ADS Title: Internal structure and rotation of the Sun: First results from MDI data Authors: Kosovichev, A. G.; Schou, J.; Scherrer, P. H.; Bogart, R. S.; Bush, R. I.; Hoeksema, J. T.; Aloise, J.; Bacon, L.; Burnette, A.; De Forest, C.; Giles, P. M.; Leibrand, K.; Nigam, R.; Rubin, M.; Scott, K.; Williams, S. D.; Basu, Sarbani; Christensen-Dalsgaard, J.; Däppen, W.; Rhodes, E. J., Jr.; Duvall, T. L., Jr.; Howe, R.; Thompson, M. J.; Gough, D. O.; Sekii, T.; Toomre, J.; Tarbell, T. D.; Title, A. M.; Mathur, D.; Morrison, M.; Saba, J. L. R.; Wolfson, C. J.; Zayer, I.; Milford, P. N. Bibcode: 1997IAUS..181..203K Altcode: No abstract at ADS Title: Dynamics of the solar convection zone Authors: Toomre, J. Bibcode: 1997ppvs.conf..343T Altcode: Introduction Multiple discrete scales of convection Probing of structure and flows with helioseismology Multitude of magnetic structures and dynamo action Structures and inverse cascades in turbulence Dynamical range of solar turbulence Local models of rotating compressible convection Formulation of local ƒ-plane models Nature of rotating turbulent convection Driving of mean flows and implications for differential rotation Penetrative convection and intermittency in transport of heat Global models of spherical convection Formulation of anelastic convection in rotating shells Nature of global convection and the mean flows Reflections Title: Internal rotation and dynamics of the Sun from GONG data Authors: Korzennik, S.; Thompson, M. J.; Toomre, J.; GONG Internal Rotation Team Bibcode: 1997IAUS..181..211K Altcode: No abstract at ADS Title: The seismic structure of the Sun from GONG Authors: Anderson, E.; Antia, H. M.; Basu, S.; Chaboyer, B.; Chitre, S. M.; Christensen-Dalsgaard, J.; Eff-Darwich, A.; Elliott, J. R.; Giles, P. M.; Gough, D. O.; Guzik, J. A.; Harvey, J. W.; Hill, F.; Leibacher, J. W.; Kosovichev, A. G.; Monteiro, M. J. P. F. G.; Richard, O.; Sekii, T.; Shibahashi, H.; Takata, M.; Thompson, M. J.; Toomre, J.; Vauclair, S.; Vorontsov, S. V. Bibcode: 1997IAUS..181..151A Altcode: No abstract at ADS Title: Turbulent Compressible Convection with Rotation. I. Flow Structure and Evolution Authors: Brummell, Nicholas H.; Hurlburt, Neal E.; Toomre, Juri Bibcode: 1996ApJ...473..494B Altcode: The effects of Coriolis forces on compressible convection are studied using three-dimensional numerical simulations carried out within a local modified f-plane model. The physics is simplified by considering a perfect gas occupying a rectilinear domain placed tangentially to a rotating sphere at various latitudes, through which a destabilizing heat flux is driven. The resulting convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers, evaluating conditions where the influence of rotation is both weak and strong. Given the computational demands of these high-resolution simulations, the parameter space is explored sparsely to ascertain the differences between laminar and turbulent rotating convection. The first paper in this series examines the effects of rotation on the flow structure within the convection, its evolution, and some consequences for mixing. Subsequent papers consider the large-scale mean shear flows that are generated by the convection, and the effects of rotation on the convective energetics and transport properties.

It is found here that the structure of rotating turbulent convection is similar to earlier nonrotating studies, with a laminar, cellular surface network disguising a fully turbulent interior punctuated by vertically coherent structures. However, the temporal signature of the surface flows is modified by inertial motions to yield new cellular evolution patterns and an overall increase in the mobility of the network. The turbulent convection contains vortex tubes of many scales, including large-scale coherent structures spanning the full vertical extent of the domain involving multiple density scale heights. Remarkably, such structures align with the rotation vector via the influence of Coriolis forces on turbulent motions, in contrast with the zonal tilting of streamlines found in laminar flows. Such novel turbulent mechanisms alter the correlations which drive mean shearing flows and affect the convective transport properties. In contrast to this large-scale anisotropy, small-scale vortex tubes at greater depths are randomly orientated by the rotational mixing of momentum, leading to an increased degree of isotropy on the medium to small scales of motion there. Rotation also influences the thermodynamic mixing properties of the convection. In particular, interaction of the larger coherent vortices causes a loss of correlation between the vertical velocity and the temperature leaving a mean stratification which is not isentropic. Title: Angular Momentum Transport in Turbulent Compressible Convection Authors: Hurlburt, N. E.; Brummell, N. H.; Toomre, J. Bibcode: 1996AAS...188.6907H Altcode: 1996BAAS...28R.936H We consider the dynamics of compressible convection within a curved local segment of a rotating spherical shell, aiming to resolve the disparity between the differential rotation profiles predicted by previous laminar simulations (angular velocity constant on cylinders) and those deduced from helioseismic inversion of the observed frequency splitting of p modes. By limiting the horizontal extent of the domain under study, we can utilize the available spatial degrees of freedom on current supercomputers to attain more turbulent flows than in the full shell. Our previous study of three-dimensional convection within a slab geometry of an f-plane neglected the effects of curvature, and thus did not admit the generation of Rossby waves. These waves propagate in the longitudinal direction and thus produce rather different spectral characteristics and mean flows in the north-south and east-west directions. By considering motions in a curvilinear geometry in which the Coriolis parameter varies with latitude, we admit the possibility of Rossby waves which couple to the turbulent convection. Here we present simulations with Rayleigh numbers in excess of 10(6) , and Prandtl numbers less than 0.1 in such a curved local segment of a spherical shell using a newly developed code based on compact finite differences. This computational domain takes the form of a curved, periodic channel in longitude with stress-free sidewalls in latitude and radius. Despite the differences in geometry and boundary conditions, the flows maintain similarities with those of our previous f-plane simulations. The surface flows form broad, laminar networks which mask the much more turbulent flows of the interior. The dynamics within this turbulent region is controlled by the interactions of a tangled web of strong vortex tubes. These interactions are further complicated by the effects of curvature. The differential rotation generated by the turbulent convection typically increases with depth and attains a maximum at the base of the layer of about 10 % over the imposed rotation rate. Title: Perspectives in Helioseismology Authors: Gough, D. O.; Leibacher, J. W.; Scherrer, P. H.; Toomre, J. Bibcode: 1996Sci...272.1281G Altcode: Helioseismology is probing the interior structure and dynamics of the sun with ever-increasing precision, providing a well-calibrated laboratory in which physical processes can be studied under conditions that are unattainable on Earth. Nearly 10 million resonant modes of oscillation are observable in the solar atmosphere, and their frequencies need to be known with great accuracy in order to gauge the sun's interior. The advent of nearly continuous imaged observations from the complementary ground-based Global Oscillation Network Group (GONG) observatories and the space-based Solar and Heliospheric Observatory instruments augurs a new era of discovery. The flow of early results from GONG resolves some issues and raises a number of theoretical questions whose answers are required for understanding how a seemingly ordinary star actually operates. Title: Preliminary Ring-Diagram Analysis of Doppler Velocity Fields Observed with MDI on SOHO Authors: Haber, D. A.; Bogart, R. S.; Sa, L. A. D.; Hill, F.; Toomre, J.; Duvall, T. L., Jr. Bibcode: 1996AAS...188.3710H Altcode: 1996BAAS...28Q.879H We analyze properties of high-degree acoustic wave fields over small patches of the sun using high-resolution Doppler velocity observations with the Michelson Doppler Imager (MDI) on the Solar Heliospheric Observatory (SOHO). By studying asymmetric frequency shifts in the acoustic waves that propagate in different horizontal directions, we can make inferences about the underlying large-scale flows which contribute to these shifts. We here analyze two different sets of data obtained from early observations with MDI. One is a continuous 80-hour sequence of full-disk Doppler images with a 60 s cadence and 4'' resolution, the other is an 8-hour sequence of high-resolution images that have 1.2'' resolution. Both sets have 1024 x 1024 pixels but the second set only covers about 36deg on the sun and is centered on the central meridian and somewhat above disk center. In both cases we remap a number of smaller areas of the data and compute three-dimensional Fourier transforms (two in space, one in time) over each patch. The resulting power diagrams have cross-sections in frequency that exhibit power distributed along rings. The detailed shapes and displacements of the rings depend upon the averaged velocities and their gradients, which can be estimated by theory. We measure the displacements of the rings using two different analysis techniques, thereby determining the frequency splittings which are then used in inversion procedures to deduce the underlying smoothed flow fields in each region. The results from the various patches provide preliminary estimates of the flow structures present in the upper convection zone. Title: The Seismic Structure of the Sun Authors: Gough, D. O.; Kosovichev, A. G.; Toomre, J.; Anderson, E.; Antia, H. M.; Basu, S.; Chaboyer, B.; Chitre, S. M.; Christensen-Dalsgaard, J.; Dziembowski, W. A.; Eff-Darwich, A.; Elliott, J. R.; Giles, P. M.; Goode, P. R.; Guzik, J. A.; Harvey, J. W.; Hill, F.; Leibacher, J. W.; Monteiro, M. J. P. F. G.; Richard, O.; Sekii, T.; Shibahashi, H.; Takata, M.; Thompson, M. J.; Vauclair, S.; Vorontsov, S. V. Bibcode: 1996Sci...272.1296G Altcode: Global Oscillation Network Group data reveal that the internal structure of the sun can be well represented by a calibrated standard model. However, immediately beneath the convection zone and at the edge of the energy-generating core, the sound-speed variation is somewhat smoother in the sun than it is in the model. This could be a consequence of chemical inhomogeneity that is too severe in the model, perhaps owing to inaccurate modeling of gravitational settling or to neglected macroscopic motion that may be present in the sun. Accurate knowledge of the sun's structure enables inferences to be made about the physics that controls the sun; for example, through the opacity, the equation of state, or wave motion. Those inferences can then be used elsewhere in astrophysics. Title: The Global Oscillation Network Group (GONG) Project Authors: Harvey, J. W.; Hill, F.; Hubbard, R. P.; Kennedy, J. R.; Leibacher, J. W.; Pintar, J. A.; Gilman, P. A.; Noyes, R. W.; Title, A. M.; Toomre, J.; Ulrich, R. K.; Bhatnagar, A.; Kennewell, J. A.; Marquette, W.; Patron, J.; Saa, O.; Yasukawa, E. Bibcode: 1996Sci...272.1284H Altcode: Helioseismology requires nearly continuous observations of the oscillations of the solar surface for long periods of time in order to obtain precise measurements of the sun's normal modes of oscillation. The GONG project acquires velocity images from a network of six identical instruments distributed around the world. The GONG network began full operation in October 1995. It has achieved a duty cycle of 89 percent and reduced the magnitude of spectral artifacts by a factor of 280 in power, compared with single-site observations. The instrumental noise is less than the observed solar background. Title: Differential Rotation and Dynamics of the Solar Interior Authors: Thompson, M. J.; Toomre, J.; Anderson, E. R.; Antia, H. M.; Berthomieu, G.; Burtonclay, D.; Chitre, S. M.; Christensen-Dalsgaard, J.; Corbard, T.; De Rosa, M.; Genovese, C. R.; Gough, D. O.; Haber, D. A.; Harvey, J. W.; Hill, F.; Howe, R.; Korzennik, S. G.; Kosovichev, A. G.; Leibacher, J. W.; Pijpers, F. P.; Provost, J.; Rhodes, E. J., Jr.; Schou, J.; Sekii, T.; Stark, P. B.; Wilson, P. R. Bibcode: 1996Sci...272.1300T Altcode: Splitting of the sun's global oscillation frequencies by large-scale flows can be used to investigate how rotation varies with radius and latitude within the solar interior. The nearly uninterrupted observations by the Global Oscillation Network Group (GONG) yield oscillation power spectra with high duty cycles and high signal-to-noise ratios. Frequency splittings derived from GONG observations confirm that the variation of rotation rate with latitude seen at the surface carries through much of the convection zone, at the base of which is an adjustment layer leading to latitudinally independent rotation at greater depths. A distinctive shear layer just below the surface is discernible at low to mid-latitudes. Title: High Resolution Numerical Simulations of Global Solar Convection Authors: Miesch, M.; Clune, T.; Toomre, J.; Glatzmaier, G. Bibcode: 1996AAS...188.6908M Altcode: 1996BAAS...28..936M We present a new computer code for simulating anelastic stellar convection in a rotating spherical shell which is based on an existing algorithm, but redesigned to take full advantage of the higher resolution possible on currently available parallel super-computing platforms. Similar previous studies have led to important insights into the dynamics of the solar convection zone, but are unable to reproduce several important features, in particular the latitudinal and radial angular velocity profile inferred from helioseismological inversion. The results from helioseismology imply a differential rotation which is constant on radial lines at mid latitudes in the convection zone, while numerical simulations generally exhibit profiles which tend to be constant on cylindrical surfaces aligned with the rotation axis. Spherical shell simulations by Glatzmaier and other results from convection in plane-parallel geometries suggest that the answer may lie in increasing the spatial resolution of the model. The relatively low resolutions of previous simulations only admit predominantly laminar flows, which are known to exhibit significantly different transport properties than turbulent flows, and which are therefore less applicable to the highly turbulent conditions in solar convection zone. To achieve the highest possible resolution, and therefore the most turbulent flows, on current (and near future) computational resources, our new implementation of Glatzmaier's earlier code is specifically suited to the hierarchical memories characteristic of MPPs, with careful consideration given to achieving both good serial performance as well as good scalability on this class of machines. The former is largely achieved through an extremely efficient implementation of the Legendre transform which constitutes the majority of the computational workload, while the latter is achieved primarily by a relatively complex load-balancing scheme. We discuss the implementation as well as the flow characteristics and transport properties of several simulations achieved on our initial target platform, the IBM SP-2 at the Cornell Theory Center, with spatial resolutions of up to 768 x 1536 x 129 (latitude, longitude, radial). Title: First Helioseismic Results from the Global Oscillation Network Group Authors: Toomre, Juri Bibcode: 1996AAS...188.2901T Altcode: 1996BAAS...28..861T Helioseismology studies the internal structure and dynamics of the sun, utilizing very precise measurements of the frequencies of sound waves that propagate throughout the solar interior and are observed at the surface. Efforts to accurately and precisely measure the mode frequencies from a single observing site have met with fundamental limitations imposed by the inevitable interruptions arising from the day-night cycle. To address such problems, the NSF-sponsored Global Oscillation Network Group (GONG) project has developed a network of six identical instruments around the world providing velocity images nearly continuously, a data processing system that can keep up with the massive data flow, and is supported by a vigorous scientific community structured around GONG teams that have shared in all aspects of the development of the project. Though the primary helioseismic data deals with the frequencies and their splittings for the nearly half-million global acoustic modes detectable with the GONG instruments, the data also allows study of how wave fields are locally influenced by flows and magnetic structures below the solar surface, and further provides direct measures of larger-scale flows at the surface. We shall briefly describe the network, instruments, and data analysis, and then review some of the preliminary scientific results obtained by the teams through inversion of the frequency data, dealing with the structure of the solar interior and the physics of stellar models, and an assessment of the differential rotation profile with depth and latitude. Early results will also be presented concerning nearly steady surface flows of the solar surface. Title: Solar Internal Rotation and Dynamics from GONG Frequency Splittings Authors: Thompson, M. J.; Toomre, J.; GONG Dynamics Inversion Team Bibcode: 1996AAS...188.5305T Altcode: 1996BAAS...28..903T The splitting of the Sun's global mode frequencies by large-scale flows can be used to investigate the rotation profile in both radius and latitude within the convection zone and deeper radiative interior. The inversion of GONG data confirms that the surface latitudinal variation of the rotation rate carries through much of the convection zone. At the base of the convection zone there is a currently unresolved adjustment layer with latitudinally independent rotation at greater depths. A shearing layer just below the surface is discernable at low to mid latitudes. Such global investigations are supplemented by local area analyses via ring diagrams, which enable us to probe the subsurface variation of rotation with depth beneath selected regions of the Sun. Title: First Scientific Results from the GONG Helioseismology Network Authors: Toomre, Juri Bibcode: 1995AAS...18711402T Altcode: 1995BAAS...27.1447T The GONG helioseismology project involves a broad international collaboration among experimentalists and theoreticians keenly interested in studying the internal dynamics and structure of our nearest star. Much of the scientific work is being done by teams of GONG members working together to assess the scientific inferences that can be drawn from the nearly continuous Doppler imaging of the sun that is now available from this network of identical instruments. Though the primary helioseismic data deals with the frequencies and their splittings for the nearly half-million global acoustic modes detectable with the GONG instruments, the data also allows study of how wave fields are locally influenced by flows and magnetic structures below the solar surface, and further provides direct measures of larger-scale flows at the surface. We shall review some of the preliminary scientific results obtained by the teams through inversion of the frequency data obtained from the early operation of the full network, dealing with assessment of differential rotation profiles with depth and latitude deduced from inversion of frequency splittings and of the sound speed profiles, and thus mean structure deduced from the basic mode frequencies. Early results will also be presented concerning nearly steady surface flows, and of magnetic effects seen in the wave fields. Title: Turbulent Dynamics in the Solar Convection Zone Authors: Brummell, Nicholas; Cattaneo, Fausto; Toomre, Juri Bibcode: 1995Sci...269.1370B Altcode: Observations of the sun reveal highly complex flows and magnetic structures that must result from turbulent convection in the solar envelope. A remarkable degree of large-scale coherence emerges from the small-scale turbulent dynamics, as seen in the cycles of magnetic activity and in the differential rotation profile of this star. High-performance computing now permits numerical simulations of compressible turbulence and magnetohydrodynamics with sufficient resolution to show that compact structures of vorticity and magnetic fields can coexist with larger scales. Such structured turbulence is yielding transport properties for heat and angular momentum at considerable variance with earlier models. These simulations are elucidating the coupling of turbulent fluid motions with rotation and magnetic fields, which must control the interlinked differential rotation and magnetic dynamo action. Title: Local-Area Simulations of Rotating Compressible Convection and Associated Mean Flows Authors: Hurlburt, N. E.; Brummel, N. H.; Toomre, J. Bibcode: 1995ESASP.376b.245H Altcode: 1995soho....2..245H; 1995help.confP.245H No abstract at ADS Title: The Sensitivity of Various Mode Sets for Probing Differential Rotation Shear Zones Authors: Christensen-Dalsgaard, J.; Schou, J.; Thompson, M. J.; Toomre, J. Bibcode: 1995ESASP.376b..41C Altcode: 1995soho....2...41C; 1995help.confP..41C The potential of forthcoming datasets from GONG and SOI for resolving long-lived azimuthal jets and shearing flows is investigated. The authors construct various artificial datasets, containing noise resembling that for a one-year observing run. These are then inverted, using a 2-D regularized least squares (RLS) inversion. In particular, the authors investigate the ability of the RLS method to form well-localized averages of the rotation rate, as measured by the averaging kernels, using an extensive mode set as well as subsets thereof. The authors show that it is possible to keep the noise in the solution down to a few nanohertz in much of the solar interior, while obtaining very reasonable resolution, for a GONG-like dataset. Title: Analysis of Helioseismic Wave Fields to Examine Horizontal Structures Authors: Julien, K. A.; Gough, D. O.; Toomre, J. Bibcode: 1995ESASP.376b.155J Altcode: 1995help.confP.155J; 1995soho....2..155J Presents and evaluates a preliminary inversion procedure for carrying out a local area analysis on simulated oscillation data to deduce two-dimensional subsurface structures in the horizontal, representative of thermal variations, potentially as function of depth. Title: Non-Local Transport in Turbulent MHD Convection Authors: Miesch, M.; Brandenburg, A.; Zweibel, E.; Toomre, J. Bibcode: 1995ESASP.376b.253M Altcode: 1995help.confP.253M; 1995soho....2..253M No abstract at ADS Title: Plane-Wave Analysis of Solar Acoustic-Gravity Waves: a (slightly) New Approach Authors: Bogart, R. S.; Sá, L. A. D.; Duvall, T. L.; Haber, D. A.; Toomre, J.; Hill, F. Bibcode: 1995ESASP.376b.147B Altcode: 1995soho....2..147B; 1995help.confP.147B Plane-wave decomposition of acoustic-gravity wave effects observed in the photosphere provides a computationally efficient technique for probing the structure of the upper convective zone and boundary, where the flat-Sun approximation is reasonably accurate. The authors describe the technique to be used for systematic plane-wave analysis of MDI data as part of the SOI data analysis pipeline, and the SOI analysis plan. The authors present estimates of sensitivity and discuss the effects of using different planar mappings. The technique is compared with previous approaches to the 3-dimensional plane-wave problem. Title: Local-Area Analysis of High-Degree Solar Oscillations: New Ring-Fitting Procedures Authors: Haber, D. A.; Toomre, J.; Hill, F.; Gough, D. O. Bibcode: 1995ESASP.376b.141H Altcode: 1995help.confP.141H; 1995soho....2..141H Local-area analysis of five-minute solar oscillations using ring diagrams to determine subphotospheric velocity flows is on the brink of becoming an important tool in understanding convective zone dynamics. One of the main problems up to this point has been the large computational burden of fitting the rings. The authors present a faster method for carrying out the ring fits using data obtained with the High-l Helioseismometer at Kitt Peak. The authors first eliminate serious sources of noise, then use a perturbation approach to fit the azimuthally averaged spectrum. The parameters so determined are held constant while fitting the entire ring diagram. Title: Turbulent Rotating Compressible Convection in Spherical Domains Authors: Hurlburt, N. E.; Brummell, N. H.; Toomre, J. Bibcode: 1995SPD....26..406H Altcode: 1995BAAS...27..955H No abstract at ADS Title: Inversion for Background Inhomogeneity from Phase Distortion of Two-Dimensional Wave Fields Authors: Julien, K.; Gough, D.; Toomre, J. Bibcode: 1995ASPC...76..196J Altcode: 1995gong.conf..196J No abstract at ADS Title: Global-Scale Solar Turbulent Convection and its Coupling to Rotation Authors: Glatzmaier, G. A.; Toomre, J. Bibcode: 1995ASPC...76..200G Altcode: 1995gong.conf..200G No abstract at ADS Title: Spherical Core Convection in Rotating A-Type Stars Authors: Dolez, N.; Glatzmaier, G. A.; Toomre, J. Bibcode: 1995ASPC...76..653D Altcode: 1995gong.conf..653D No abstract at ADS Title: Maintenance of Differential Rotation in Turbulent Compressible Convection with Rotation Authors: Brummell, N. H.; Xie, X.; Toomre, J.; Baillie, C. Bibcode: 1995ASPC...76..192B Altcode: 1995gong.conf..192B No abstract at ADS Title: Modelling Astrophysical Turbulent Convection Authors: Brummell, N.; Toomre, J. Bibcode: 1995ASPC...77...15B Altcode: 1995adass...4...15B Numerical simulations of highly turbulent flows in astrophysics benefit greatly from recent advances in high performance computing. Yet such three-dimensional modelling raises major problems in capturing, moving, and analyzing the resulting massive data sets necessary to sample the evolving intricate dynamics. Thus archiving, networking, and visualization are as essential as the actual act of computing when it comes to real scientific progress. Title: Solar Convection Zone Dynamics and Rotation Authors: Toomre, J.; Brummell, N. H. Bibcode: 1995ESASP.376a..47T Altcode: 1995soho....1...47T; 1995heli.conf...47T Reviews a range of approaches to study the basic dynamics of convection, along with its ability to redistribute angular momentum in rotating systems. The authors then describe results of three-dimensional simulations of turbulent compressible convection constrained by effects of rotation, both within spherical shells and within local area f-planes. The turbulence possesses intense vortex tubes with intricate interactions and instabilities, and more persistent and spatially-coherent downflow networks, along with strong mean flows when the rotational constraint is prominent. These theoretical studies reveal that transition to turbulent states have associated with them significant changes in flow asymmetries and transports, and that such turbulent convection can drive substantial mean flows which are distinctly different from those in which the convection is dominantly laminar. Title: Hunting for Azimuthal Jets and Shearing Flows in the Solar Convection Zone Authors: Christensen-Dalsgaard, J.; Schou, J.; Thompson, M. J.; Toomre, J. Bibcode: 1995ASPC...76..212C Altcode: 1995gong.conf..212C No abstract at ADS Title: Solar Oscillation Ring Diagrams: Benefits of Great Circle Remapping Authors: Haber, D.; Toomre, J.; Hill, F.; Gough, D. Bibcode: 1995ASPC...76..272H Altcode: 1995gong.conf..272H No abstract at ADS Title: Astrophysical Convection and Turbulence Authors: Toomre, J. Bibcode: 1994AAS...184.5002T Altcode: 1994BAAS...26..942T The vigorous turbulence that results from convective instability within rotating stars serves to not only transport heat but also redistribute angular momentum and chemical species, and can yield magnetic dynamo action. A hallmark of such turbulence constrained by rotation and stratification is that large-scale coherent structures and strong mean flows can coexist with the intense smaller-scale turbulence. Helioseismology is suggesting that the resulting differential rotation within the convection zone of a star like the sun yields serious puzzles about the interaction of convection and rotation. Understanding such nonlinear dynamics at a fundamental level raises formidable challenges because of the broad range of scales of motion that must be resolved. High-performance computing offers the opportunity to make substantial inroads in studying the properties of such astrophysical turbulence. An interdisciplinary team of researchers at several institutions is working jointly on problems in geophysical and astrophysical fluid dynamics (GAFD) turbulence to utilize massively parallel architectures to increase the spatial resolution in three-dimensional simulations employing variously pseudo-spectral, finite-difference, multi-grid and PPM approaches in studying the intense turbulence encountered in both planetary and stellar settings. The scale of these simulations requires corresponding progress in the computational sciences, both in order to develop and optimize software for massively-parallel computers and to capture and visualize the resulting massive data sets. A selection of highlights from our turbulence research will be presented, turning for instance to local-area models of turbulent compressible convection within stellar envelopes. The turbulence possesses both intense vortex filaments with intricate interactions and instabilities, and more persistent and spatially-coherent downflow networks, along with strong mean flows when the rotational constraint is prominent. We also consider the convective turbulence and mixing achieved within the full nuclear burning cores of rotating A-type stars, finding that such penetrative convection drives substantial differential rotation. Title: Penetration below a Convection Zone Authors: Hurlburt, Neal E.; Toomre, Juri; Massaguer, Josep M.; Zahn, Jean-Paul Bibcode: 1994ApJ...421..245H Altcode: Two-dimensional numerical simulations are used to investigate how fully compressible nonlinear convection penetrates into a stably stratified zone beneath a stellar convection zone. Estimates are obtained of the extent of penetration as the relative stability S of the stable to the unstable zone is varied over a broad range. The model deals with a perfect gas possessing a constant dynamic viscosity. The dynamics is dominated by downward-directed plumes which can extend far into the stable material and which can lead to the excitation of a broad spectrum of internal gravity waves in the lower stable zone. The convection is highly time dependent, with the close coupling between the lateral swaying of the plumes and the internal gravity waves they generate serving to modulate the strength of the convection. The depth of penetration delta, determined by the position where the time-averaged kinetic flux has its first zero in the stable layer, is controlled by a balance between the kinetic energy carried into the stable layer by the plumes and the buoyancy braking they experience there. A passive scalar is introduced into the unstable layer to evaluate the transport of chemical species downward. Such a tracer is effectively mixed within a few convective overturning times down to a depth of delta within the stable layer. Analytical estimates based on simple scaling laws are used to interpret the variation of delta with S, showing that it first involves an interval of adiabatic penetration if the local Peclet number of the convection exceeds unity, followed by a further thermal adjustment layer, the depths of each interval scaling in turn as S-1 and S-1/4. These estimates are in accord with the penetration results from the simulations. Title: Seismology of the Sun Authors: Christensen-Dalsgaard, J.; Gough, D. O.; Toomre, J. Bibcode: 1994snft.book..418C Altcode: No abstract at ADS Title: Compressible Convection with Ionization. II. Thermal Boundary-Layer Instability Authors: Rast, Mark P.; Toomre, Juri Bibcode: 1993ApJ...419..240R Altcode: Rast & Toomre (1993, Paper I) examined the effects of ionization-state changes on the stability, flow asymmetry, and flux transport properties of two-dimensional compressible convection. Here we employ the same single-atomic-level hydrogen model and analyze vigorously time-dependent nonlinear solutions. Ionization- state-dependent variations in thermal diffusivity of the fluid can result in thermal boundary-layer instability and plume formation. The interval between pluming events depends on the growth rate of the instability and both the scale and the velocity of the underlying convective motions. Such instabilities can occur at either boundary, depending on the positioning of the partially ionized region within the domain. Here we concentrate on simulations in which the instability is manifest in the upper thermal boundary layer, and results in cool plume formation. Temperature fluctuations and associated buoyancy forces in the plumes are maintained as long as heat exchange and compressional heating result primarily in ionization of the fluid rather than in temperature equilibration, and this can lead to supersonic vertical flows in an otherwise subsonic flow field. These flows serve to excite acoustic oscillations, the phase of which can be abruptly altered by subsequent plume events. For high rates of plume initiation, the fundamental acoustic period of the domain is greater than the time span between two descents. Such ionization effects are expected to influence the dynamics of granulation and acoustic mode excitation in the Sun and other stars, and likewise the coupling of convection with pulsations that occurs in stars such as white dwarfs and Cepheid variables. Additionally, it is possible that thermal instabilities analogous to those seen in these simulations occur not only in the photosphere but also at the base of stellar convective envelopes owing to temperature-sensitive variations in the radiative conductivity of fluid there. Title: Compressible Convection with Ionization. I. Stability, Flow Asymmetries, and Energy Transport Authors: Rast, Mark P.; Toomre, Juri Bibcode: 1993ApJ...419..224R Altcode: The influence of nonideal effects associated with ionization upon the dynamics and thermodynamics of compressible convection is studied. Linear and finite-amplitude analyses and fully nonlinear two-dimensional simulations of a plane-parallel layer of single-atomic-level hydrogen fluid are undertaken. Ionization significantly influences both the global transport properties and the local dynamics of convective flows by modifying the particle number density, specific heat, and internal energy content of the fluid. Strong temperature fluctuations and corresponding buoyancy forces develop locally in the fluid wherever rapid changes in ionization state occur. These can result in narrow regions of intense vertical flow. The flow asymmetries seen in simulations of compressible ideal-gas convection can either be enhanced or diminished depending on the vertical positioning of the partially ionized region within the domain. Additionally, the enthalpy flux achieved by ionizing convection is dominated in regions of partial ionization by latent-heat transport. The enthalpy carried by downflow plumes can be considerably elevated, and the cancellation between kinetic energy and enthalpy fluxes observed in the downflows in some simulations of ideal gas turbulence may thus be offset by partial ionization of the fluid. Such ionization effects are likely to influence the character of convective motions within stellar envelopes. Convective transport properties may differ substantially between the partially ionized and the deeper fully ionized regions of a star, and since ionization zone placement also varies with respect to both the photosphere and the lower thermal boundary, between stellar types and during the course of stellar evolution. Title: Turbulent Compressible Convection with Rotation Authors: Brummell, N. H.; Toomre, J.; Hurlburt, N. E. Bibcode: 1993BAAS...25.1192B Altcode: No abstract at ADS Title: Ionization Effects in Three-dimensional Solar Granulation Simulations Authors: Rast, Mark P.; Nordlund, Ake; Stein, Robert F.; Toomre, Juri Bibcode: 1993ApJ...408L..53R Altcode: These numerical studies show that ionization influences both the transport and dynamical properties of compressible convection near the surface of the Sun. About two-thirds of the enthalpy transported by convective motions in the region of partial hydrogen ionization is carried as latent heat. The role of fast downflow plumes in total convective transport is substantially elevated by this contribution. Instability of the thermal boundary layer is strongly enhanced by temperature sensitive variations in the radiative properties of the fluid, and this provides a mechanism for plume initiation and cell fragmentation in the surface layers. As the plumes descend, temperature fluctuations and associated buoyancy forces are maintained because of the increased specific heat of the partially ionized material. This can result is supersonic vertical flows. At greater depths, ionization effects diminish, and the plumes are decelerated by significant entrainment of surrounding fluid. Title: Large-Eddy Simulations of Compressible Convection on Massively Parallel Computers Authors: Xie, Xin; Toomre, Juri Bibcode: 1993ApJ...405..747X Altcode: We report preliminary implementation of the large-eddy simulation (LES) technique in 2D simulations of compressible convection carried out on the CM-2 massively parallel computer. The convective flow fields in our simulations possess structures similar to those found in a number of direct simulations, with roll-like flows coherent across the entire depth of the layer that spans several density scale heights. Our detailed assessment of the effects of various subgrid scale (SGS) terms reveals that they may affect the gross character of convection. Yet, somewhat surprisingly, we find that our LES solutions, and another in which the SGS terms are turned off, only show modest differences. The resulting 2D flows realized here are rather laminar in character, and achieving substantial turbulence may require stronger forcing and less dissipation. Title: Interaction of Externally-Driven Acoustic Waves with Compressible Convection Authors: Jones, P.; Merryfield, W.; Toomre, J. Bibcode: 1993ASPC...42...45J Altcode: 1993gong.conf...45J No abstract at ADS Title: Inversion for Background Inhomogeneity from Phase Distortions of One-Dimensional Wave Trains Authors: Gough, D. O.; Merryfield, W. J.; Toomre, J. Bibcode: 1993ASPC...42..257G Altcode: 1993gong.conf..257G No abstract at ADS Title: Acoustic Excitation by Thermal Boundary Layer Instability in a Partially Ionized Convecting Fluid Authors: Rast, M. P.; Toomre, J. Bibcode: 1993ASPC...42...41R Altcode: 1993gong.conf...41R No abstract at ADS Title: Thermal convection and penetration. Authors: Toomre, J. Bibcode: 1993afd..conf..325T Altcode: Contents: 1. Introduction. 2. Boussinesq convection in simple geometries. 3. Anelastic modal convection. 4. Two-dimensional fully compressible convection. 5. Three-dimensional fully compressible convection. 6. Final reflections. Title: Ionization Effects on Solar Granulation Dynamics Authors: Rast, M. P.; Nordlund, A.; Stein, R. F.; Toomre, J. Bibcode: 1993ASPC...42...57R Altcode: 1993gong.conf...57R No abstract at ADS Title: Turbulent Compressible Convection with Rotation Authors: Brummell, N. H.; Hurlburt, N. E.; Toomre, J. Bibcode: 1993ASPC...42...61B Altcode: 1993gong.conf...61B No abstract at ADS Title: Laboratory and theoretical models of planetary-scale instabilities and waves Authors: Hart, John E.; Toomre, Juri Bibcode: 1991gsap.rept...47H Altcode: Meteorologists and planetary astronomers interested in large-scale planetary and solar circulations recognize the importance of rotation and stratification in determining the character of these flows. The two outstanding problems of interest are: (1) the origins and nature of chaos in baroclinically unstable flows; and (2) the physical mechanisms responsible for high speed zonal winds and banding on the giant planets. The methods used to study these problems, and the insights gained, are useful in more general atmospheric and climate dynamic settings. Because the planetary curvature or beta-effect is crucial in the large scale nonlinear dynamics, the motions of rotating convecting liquids in spherical shells were studied using electrohydrodynamic polarization forces to generate radial gravity and centrally directed buoyancy forces in the laboratory. The Geophysical Fluid Flow Cell (GFFC) experiments performed on Spacelab 3 in 1985 were analyzed. The interpretation and extension of these results have led to the construction of efficient numerical models of rotating convection with an aim to understand the possible generation of zonal banding on Jupiter and the fate of banana cells in rapidly rotating convection as the heating is made strongly supercritical. Efforts to pose baroclinic wave experiments for future space missions using a modified version of the 1985 instrument have led us to develop theoretical and numerical models of baroclinic instability. Some surprising properties of both these models were discovered. Title: Simulation of Effects of Atmospheric Seeing on the Observation of High-Degree Solar Oscillations Authors: Hill, Frank; Gough, Douglas; Merryfield, William J.; Toomre, Juri Bibcode: 1991ApJ...369..237H Altcode: Numerical simulations of the effects of atmospheric seeing distortions on observations of solar oscillations of intermediate and high degree are performed. The simulations involve a representation of about 100 p-modes of oscillation, with degrees l = 50-150 (intermediate-degree) and 150-450 (high-degree), formed from the complement of a sexated mode set. These modes are superposed on a steady large-scale convective background, and projected onto the plane of the sky. Image motion is modeled by displacement maps generated from two-dimensional turbulence power spectra; the maps are scaled so that the rms amplitude of the displacements has values of 2-5 arcsec. The distorted velocity field is then Fourier analyzed to produce simulated (l, nu) power diagrams, where nu is the temporal cyclic frequency. The results show that power in the mode ridges is diminished as atmospheric seeing worsens, particularly at high degrees. Redistribution of power produces an apparent decrease in the frequencies of the oscillations as measured by the centroids of the ridges in the power spectra. It is found that time-averaging the observations is quite effective in reducing the noise. Title: Turbulent Compressible Convection Authors: Cattaneo, Fausto; Brummell, Nicholas H.; Toomre, Juri; Malagoli, Andrea; Hurlburt, Neal E. Bibcode: 1991ApJ...370..282C Altcode: Numerical simulations with high spatial resolution (up to 96-cubed gridpoints) are used to study three-dimensional, compressible convection. A sequence of four models with decreasing viscous dissipation is considered in studying the changes in the flow structure and transport properties as the convection becomes turbulent. Title: Nonlinear Behavior of Solar Gravity Modes Driven by 3He in the Core. II. Numerical Simulations Authors: Merryfield, William J.; Toomre, Juri; Gough, Douglas Bibcode: 1991ApJ...367..658M Altcode: The nonlinear behavior of gravity-mode oscillations driven by He-3-destroying reactions in the solar core has been examined by numerically integrating equations describing a very simplified model. The results of a previous bifurcation analysis, which suggest that such oscillations are unlikely to attain amplitudes sufficient to trigger core convection, are verified. These results are extended to models whose nuclear reaction rates and thermal stratification represent the core somewhat more accurately. Nonlinear processes give rise to a preference for the oscillations to develop as standing waves rather than traveling waves, thus breaking the degeneracy between these two types of motion which exists in linearized theory. Study of the large-amplitude behavior of the oscillations is hindered by a tendency for the model to become thermally unstable. Title: On the Analysis of Physical Wave Trains Authors: Gough, D. O.; Merryfield, W. J.; Toomre, J. Bibcode: 1991LNP...388..265G Altcode: 1991ctsm.conf..265G When a wave train whose constituent frequencies and wave numbers are unresolved by observation propagates through an inhomogeneous medium, beating between the components can contaminate deductions one might naively draw about the inhomogeneous background. This is a severe problem to anyone confronted with analysing helioseismic data with a view to determining the structure of giant convective cells. We propose a procedure for analysing wave trains, based on approximating a packet as a single representative pure wave. We present some preliminary results of analysing artificial data. For simplicity, we have deliberately excluded some of the effects of wave interference, which must be faced by any means of analysis. Therefore we do not claim to have found a complete procedure for analysing real data. Title: Challenges to Theories of the Structure of Moderate-Mass Stars Authors: Gough, Douglas; Toomre, Juri Bibcode: 1991LNP...388.....G Altcode: 1991ctsm.conf.....G No abstract at ADS Title: The Organization of Turbulent Convection Authors: Brummell, Nicholas; Cattaneo, Fausto; Malagoli, Andrea; Toomre, Juri; Hurlburt, Neal E. Bibcode: 1991LNP...388..187B Altcode: 1991ctsm.conf..187B Highly resolved numerical simulations are used to study three-dimensional, compressible convection. The viscous dissipation is sufficiently low that the flow divides itself in depth into two distinct regions: (i) an upper thermal boundary layer containing a smooth flow with a granular appearance, and (ii) a turbulent interior pierced by the strongest downflows from the surface layer. Such downflows span the whole depth of the unstable layer, are temporally coherent, and are thermodynamically well correlated. A remarkable property of such convection, once it becomes turbulent, is that the enthalpy and kinetic fluxes carried by the strong downflows nearly cancel, for they are of opposite sense and nearly equal in amplitude. Thus, although the downflows serve to organize the convection and are the striking feature that emerges from effects of compressibility, it is the small-scale, disorganized turbulent motions (between the coherent downflow structures that serve as the principal carriers of net convected flux. Title: The role of f modes in the inversion of high-ℓ rotational splittings Authors: Haber, Deborah A.; Hill, Frank; Toomre, Juri Bibcode: 1991LNP...388...87H Altcode: 1991ctsm.conf...87H The contribution of the solar f modes of oscillation to the inversion of high-degree rotational splitting data is examined. We find that the f modes play an important role in such inversions as revealed by the magnitude of their weighting coefficients c i . This may be attributed to the single-peaked structure of the f-mode kernels, which is similar to that of the desired averaging kernels and in contrast to the many-peaked shape of the higher-order kernels. The high weight placed on the f modes in the inversions raises issues for observational techniques since the f modes possess modest power levels and their detection is influenced by the choice of spatial filtering. Title: Program at ITP: Helioseismology — Probing the interior of a star Authors: Gough, Douglas; Toomre, Juri Bibcode: 1991LNP...388....1G Altcode: 1991ctsm.conf....1G The research program in helioseismology carried out at the Institute for Theoretical Physics (ITP) at the University of California, Santa Barbara during the six-month interval from January to June 1990 involved 61 scientists of diverse disciplines: theorists, observers and instrumentalists in physics, astrophysics and geophysics. The main topics of research and joint discussion included mode excitation and decay, the internal structure of the sun and its sensitivity to the physics of the equation of state and opacity, seismological inverse procedures, and solar rotation and convection-zone dynamics. Title: Vertically Coherent Compressible Convective Flows in a Layer with a High Density Contrast Authors: Xie, Xin; Toomre, Juri Bibcode: 1991LNP...388..171X Altcode: 1991ctsm.conf..171X Two-dimensional simulations are used to study compressible convection in a plane-parallel layer of ideal gas with a high density contrast across the layer. The convective flows are found to consist of rolls which are coherent throughout the entire vertical domain, similar to the results of a number of earlier investigations. Motions near the upper boundary are supersonic, though the Rayleigh number is moderate. The major effect of a high density stratification is to significantly rarefy the fluid in the upper part of the domain, hence increase its thermal diffusivity. The consequence appears to be twofold: Firstly, enhanced thermal diffusion makes non-adiabatic cooling more efficient, thus helps the flows to become supersonic more easily. Secondly, sufficient diffusion can broaden shocks to such an extent that it actually turns them into smooth transition regions. Title: Effects of spatial filtering on high-ℓ power spectra and rotational splitting inversions Authors: Haber, Deborah A.; Hill, Frank; Toomre, Juri Bibcode: 1991LNP...388..259H Altcode: 1991ctsm.conf..259H The effects of the spatial filtering algorithm on the results of an inversion of high-degree solar oscillation data are examined. In attempting to isolate sectoral modes, the Fourier transforms in longitude are accompanied by three different spatial filterings in the orthogonal direction. The filters are: simple averaging in the plane of the sky, averaging along lines of constant heliographic longitude with uniform weighting, and another with weighting based on appropriate Legendre functions. The choice of spatial filter changes the distribution of power in the two-dimensional spectrum of the oscillations, particularly in the f and p 1 ridges. These variations in the power distribution affect the determination of the rotational splittings, thereby influencing the results of inversions which emphasize information contained in the low-order ridges. Title: Seismic observations of the solar interior. Authors: Gough, Douglas; Toomre, Juri Bibcode: 1991ARA&A..29..627G Altcode: Contents: 1. Introduction. 2. Solar evolution. 3. Properties of modes. 4. Observational principles. 5. Inversion of data. 6. Inference of hydrostatic structure. 7. The neutrino problem. 8. Rotation and other subsurface flows. 9. Mode excitation and decay. 10. Solar cycle variations. 11. Asteroseismology. Title: Interaction of Acoustic Oscillations with Time-Dependent Compressible Convection Authors: Jones, P. W.; Merryfield, W. J.; Toomre, J. Bibcode: 1991LNP...388..213J Altcode: 1991ctsm.conf..213J We present the results of numerical simulations in which acoustic waves are driven into a two-dimensional layer of compressible fluid which is undergoing convection. The energetics of the waves are analyzed by computing the work integrals associated with the modulation of the gas and turbulent pressures. We find that the relative importance of the turbulent pressure component of the work integral increases prominently with increasing wave frequency. Also, the time dependence of the convection leads to temporal irregularity in the component of wave driving and damping associated with the convection-pulsation coupling. We speculate that such irregularity may contribute to the aperiodicity observed in the light curves of Mira variables and other pulsating red giant stars. Title: Large Eddy Simulations of Compressible Convection Authors: Xie, Xin; Toomre, Juri Bibcode: 1991LNP...388..147X Altcode: 1991ctsm.conf..147X Large-eddy simulation (LES) technique has been applied to two-dimensional compressible convection in a plane-parallel layer of ideal gas with intermediate density contrast. The general flow patterns consist of a series of rolls in the horizontal which are coherent throughout the entire vertical domain, much like findings by a number of investigators. The horizontal component of the subgrid-scale (SGS) force appears to enhance fluctuations of pressure and density, which in turn cause the resultant force, say f pg arising from pressure gradient and gravity terms, to increase in magnitude in such a way that f pg, besides balancing the inertial terms, can essentially offset the vertical component of the SGS force. Consequently, compared to a solution obtained omitting the SGS terms, the flow field of the LES solution only shows moderate differences. There is some indication that the overall SGS effect tends to reduce the asymmetry between the vertical flows in the interior of the domain while enhancing it in the base region. Title: Three-dimensional compressible convection at low Prandtl numbers. Authors: Toomre, Juri; Brummell, Nicholas; Cattaneo, Fausto; Hurlburt, Neal E. Bibcode: 1990CoPhC..59..105T Altcode: Numerical simulations are used to study fully compressible thermal convection at large Rayleigh numbers. The authors present results from a sequence of three-dimensional simulations that reveal a transition from gradually-evolving laminar convection to nearly turbulent convection as the Prandtl number is reduced from a value of unity to one-tenth. Title: Nonlinear Behavior of Solar Gravity Modes Driven by 3He in the Core. I. Bifurcation Analysis Authors: Merryfield, William J.; Toomre, Juri; Gough, Douglas Bibcode: 1990ApJ...353..678M Altcode: The nonlinear development of solar gravity modes driven by He-3 burning in the solar core is investigated by means of an idealized dynamical model. Possible outcomes that have been suggested in the literature include the triggering of subcritical direct convection, leading to core mixing, and the saturation of the excitation processes, leading to sustained finite-amplitude oscillations. The present simple model suggests that the latter is the more likely. The limiting amplitude of the oscillations is estimated, ignoring possible resonances with other gravity modes, to be of order 10 km/s at the solar surface. Such oscillations would be easily observable. That large-amplitude gravity modes have not been observed suggests either that these modes are not unstable in the present era or that they are limited to much smaller amplitudes by resonant coupling. Title: Supersonic Convection Authors: Cattaneo, Fausto; Hurlburt, Neal E.; Toomre, Juri Bibcode: 1990ApJ...349L..63C Altcode: Numerical simulations with high spatial resolution are used to study that the combined effects of stratification, pressure gradients, and nonadiabatic processes can lead to the formation of regions of supersonic motions near the upper thermal boundary layer. Within these regions, the dynamics is dominated by nonstationary shock structures. These form near the downflow sites and propagate upstream along the boundary layer to the upflow regions where they weaken and eventually disappear. The shock cycle, consisting of the formation, propagation, and disappearance of shock structures, has a time scale comparable to the sound crossing time over a portion of the convective cell, giving rise to vigorous time dependence in the convection. Title: Laboratory and theoretical models of planetary-scale instabilities and waves Authors: Hart, John E.; Toomre, Juri Bibcode: 1989gsap.rept...59H Altcode: The continuous low-g environment of the orbiting space shuttle provided a setting for conducting geophysical fluid model experiments with a completely consistent representation of sphericity and the resultant radial gravity found on astrogeophysical objects. This is possible because in zero gravity an experiment can be constructed that has its own radial buoyancy forces. The dielectric forces in a liquid, which are linearly dependent on fluid temperature, give rise to an effectively radial buoyancy force when a radial electrostatic field is applied. The Geophysical Fluid Flow Cell (GFFC) experiment is an implementation of this idea in which fluid is contained between two rotating hemispheres that are differentially heated and stressed with a large ac voltage. The GFFC flew on Spacelab 3 in May 1985. Data in the form of global Schlieren images of convective patterns were obtained for a large variety of configurations. These included situations of rapid rotation (large Taylor numbers), low rotation, large and small thermal forcing, and situations with applied meridional temperature gradients. The analysis and interpretation of the GFFC-85 data are being conducted. Improvements were developed to the GFFC instrument that will allow for real-time (TV) display of convection data and for near-real-time interactive experiments. These experiments, on the transition to global turbulence, the breakdown of rapidly rotating convective planforms and other phenomena, are scheduled to be carried out on the International Microgravity Laboratory (IML-1) aboard the shuttle in June 1990. Title: Preflare activity. Authors: Priest, E. R.; Gaizauskas, V.; Hagyard, M. J.; Schmahl, E. J.; Webb, D. F.; Cargill, P.; Forbes, T. G.; Hood, A. W.; Steinolfson, R. S.; Chapman, G. A.; Deloach, A. C.; Gary, G. A.; Jones, H. P.; Karpen, J. T.; Martres, M. -J.; Porter, J. G.; Schmieder, B.; Smith, J. B., Jr.; Toomre, J.; Woodgate, B.; Waggett, P.; Bentley, R.; Hurford, G.; Schadee, A.; Schrijver, J.; Harrison, R.; Martens, P. Bibcode: 1989epos.conf....1P Altcode: Contents: 1. Introduction. 2. Magnetohydrodynamic instability. 3. Preflare magnetic and velocity fields. 4. Coronal manifestations of preflare activity. Title: Two and Three-Dimensional Simulations of Compressible Convection Authors: Cattaneo, F.; Hurlburt, N. E.; Toomre, J. Bibcode: 1989ASIC..263..415C Altcode: 1989ssg..conf..415C No abstract at ADS Title: Nonlinear studies of solar gravity modes driven by nuclear burning of the 3He in the core. Authors: Merryfield, W. J.; Toomre, J.; Gough, Douglas O. Bibcode: 1988ESASP.286...21M Altcode: 1988ssls.rept...21M The finite-amplitude behavior of gravity-mode oscillations driven within the deep interior of the sun has been studied by means of a simple idealized model. Such g modes may be self-excited by their ability to extract energy from the nuclear burning of 3He in the core. Both a nonlinear bifurcation analysis and numerical simulations of the behavior of this instability suggest that the growth of 3He-driven oscillations is likely be limited to an amplitude which is insufficient to induce convective instability in the core, a process which has been proposed as a mechanism for core mixing. The numerical results also indicate that if the oscillations are linarly unstable then the degeneracy in linear theory between standing and travelling g modes is broken by nonlinear effects. The oscillations thus develop into a left- or right-travelling wave rather than a standing wave or other superposition of horizontally propagating waves. Title: Local effects of a major flare on solar five-minute oscillations. Authors: Haber, D. A.; Toomre, J.; Hill, Frank; Gough, Douglas O. Bibcode: 1988ESASP.286..301H Altcode: 1988ssls.rept..301H Doppler velocity images of the full Sun were obtained both during and after a major white-light flare. These velocities were interpolated onto a cylindrical coordinate system centered on the flare and decomposed into radially propagating waves defined by Hankel functions. For a similar analysis of quiet Sun regions the authors find fairly comparable power in incoming and outgoing waves irrespective of the presence of the flare. However, for the flaring region, there is 14% greater power in incoming as opposed to outgoing waves when there is no flare, but 5% greater power in outgoing than in incoming waves during the flare. This result suggests that the flare may have excited outgoing waves which counteracted the more usual absorption of incoming acoustic waves by sunspots. Title: Whirlpool traced by granulation Authors: Toomre, Juri Bibcode: 1988Natur.335..202T Altcode: No abstract at ADS Title: Magnetic Fields Interacting with Nonlinear Compressible Convection Authors: Hurlburt, Neal E.; Toomre, Juri Bibcode: 1988ApJ...327..920H Altcode: Two-dimensional numerical simulations are used to study fully compressible convection in the presence of an imposed magnetic field. Highly nonlinear flows are considered that span multiple density scale heights. The convection tends to sweep the initially uniform vertical magnetic field into concentrated flux sheets with significant magnetic pressures. These flux sheets are partially evacuated, and effects of buoyancy and Lorentz forces there can serve to suppress motions. The flux sheets can be surrounded by a sheath of descending flow. If the imposed magnetic field is sufficiently strong, the convection can become oscillatory. The unstably stratified fluid layer has an initial density ratio (bottom to top of layer) of 11. Surveys of solutions at fixed Rayleigh number sample Chandrasekhar numbers from 1 to 1000 and magnetic Prandtl numbers from 1/16 to 1. These nonlinear simulations utilize a two-dimensional numerical scheme based on a modified two-step Lax-Wendroff method. Title: Simulations of the Interaction of Radial Stellar Pulsations with Compressible Convection Authors: Merryfield, W. J.; Toomre, J. Bibcode: 1988BAAS...20..702M Altcode: No abstract at ADS Title: Topology of Plumes in Nonlinear Compressible Convection Authors: Toomre, J.; Cattaneo, F.; Hurlburt, N. E. Bibcode: 1988BAAS...20..678T Altcode: No abstract at ADS Title: Helioseismology: Theoretical Background and Challenges Authors: Toomre, J. Bibcode: 1988BAAS...20..729T Altcode: No abstract at ADS Title: Solar Equatorial Rotation Rate Inferred from Inversion of Frequency Splitting of High-Degree Modes Authors: Hill, F.; Gough, D. O.; Toomre, J.; Haber, D. A. Bibcode: 1988IAUS..123...45H Altcode: The equatorial rotation rate has been inferred as a function of depth through the outer 16 Mm of the Sun from observations of high-degree five-minute oscillations. The results imply that the solar rotation rate increases with depth by 0.023 μHz reaching a maximum at about 2 Mm below the surface, then decreases by 0.037 μHz down to 16 Mm. Title: Response of the Solar 5-MINUTE Oscillations to a Major Flare Authors: Haber, D. A.; Toomre, J.; Hill, F. Bibcode: 1988IAUS..123...59H Altcode: Solar five-minute oscillations of intermediate-degree l were observed both before and after a very strong white-light flare. The data were projected onto both equatorial and polar sectoral modes and Fourier transformed in time. Comparing the resulting power spectra, the authors find a substantial increase in power in the p5 ridge of the equatorial modes on the day after the flare. When data from all the ridges are considered, there is an average increase in power of only a few percent the day after the flare. Title: Traveling waves and chaos in thermosolutal convection Authors: Deane, A. E.; Knobloch, E.; Toomre, J. Bibcode: 1987PhRvA..36.2862D Altcode: Numerical experiments on two-dimensional thermosolutal convection reveal oscillations in the form of traveling, standing, modulated, and chaotic waves. Transitions between these wave forms and steady convection are investigated and compared with theory. Such rich nonlinear behavior is possible in fluid layers of wide horizontal extent, and provides an explanation for waves observed in recent laboratory experiments with binary fluid mixtures. Title: Solar oscillations and convective flows as probes of structure in the subphotosphere Authors: Toomre, Juri; Gebbie, Katharine B. Bibcode: 1987jila.rept.....T Altcode: Application of inverse theory to the observation of high-degree five-minute solar oscillations has led to the detection of horizontal flows below the solar surface that are a combination of solar rotation and giant convection cells. The distinctive displacements in the centroids of the ridges evident in the power diagrams of the oscillations from one observing day to the next arise from different patterns of giant cells being rotated into view. Such observation of frequency splittings for the high degree oscillation modes, combined with refinements in the inversion of the data using optimal averaging and spectral expansions, has shown that helioseismology should permit detailed mapping of velocity and thermal structures below the solar surface. Extensive theoretical studies of fully compressible magnetoconvection have shown that flows are indeed able to concentrate magnetic fields into concentrated flux sheets that are substantially evacuated of gas. The magnetic buoyancy instabilities have been extensively studied. Title: A laboratory model of planetary and stellar convection Authors: Hart, J. E.; Toomre, J.; Deane, A. E.; Hurlburt, N. E.; Glatzmaier, G. A.; Fichtl, G. H.; Leslie, F.; Fowlis, W. W.; Gilman, P. A. Bibcode: 1987STIN...8722108H Altcode: Experiments on thermal convection in a rotating, differentially-heated spherical shell with a radial buoyancy force were conducted in an orbiting microgravity laboratory. A variety of convective structures, or planforms, were observed depending on the magnitude of the rotation and the nature of the imposed heating distribution. The results are in agreement with numerical simulations that can be conducted at modest parameter values, and suggest possible regimes of motion in rotating planets and stars. Title: Vector array processor computer equipment Authors: Toomre, Juri Bibcode: 1987colo.rept.....T Altcode: To support the on-going research on Solar Oscillations and Convective Flows as Probes of Structure in the Subphotosphere, a vector array processor system was acquired to augment the existing DEC VAX-11/750 computer system. The fifty-fold average increase in computing speed offered by the array processor would make it feasible to invert solar oscillation data on a regular basis, and thereby permit us to use the five-minutes oscillations of the Sun to probe the turbulent convection zone below the surface of this star. The array processor would also permit us to carry out detailed numerical experiments with compressible convection in the presence of magnetic fields, for the speed and memory of the machine makes it a formidable tool for direct numerical simulations of two- and three-dimensional fluid dynamics. Such theoretical simulations are also needed to study the solar dynamo and its ability to build and transform magnetic fields, an issue central to solar-terrestrial variability and predictions of solar activity. Attached as Appendix A is a cover article in Science Magazine that describes the importance of the work on the Seismology of the Sun that is beginning to emerge from the class of array processors. Title: Spacelab experiments on convection in a rotating spherical shell with radial gravity Authors: Toomre, J.; Hart, J. E.; Glatzmaier, G. A. Bibcode: 1987ASSL..137...27T Altcode: 1987isav.symp...27T Experiments on thermal convection in a rotating, differentially-heated hemispherical shell of fluid with a radial gravity field were carried out in the microgravity environment of Spacelab 3 which was flown on the space shuttle Challenger in May 1985. Schlieren visualizations of these laboratory flows are compared briefly to three-dimensional nonlinear simulations that can be conducted at the more modest heating rates. Title: Nonlinear Compressible Convection Penetrating into Stable Layers and Producing Internal Gravity Waves Authors: Hurlburt, Neal E.; Toomre, Juri; Massaguer, Josep M. Bibcode: 1986ApJ...311..563H Altcode: Penetrative convection spanning multiple scale heights is studied within a simple stellar envelope consisting of three layers: a convectively unstable middle layer bounded above and below by stably stratified polytropes. Two-dimensional numerical simulations are used to investigate the fully compressible nonlinear motions that ensue. The cellular flows display prominent downward-directd plumes surrounded by broader regions of upflow. Such asymmetry arises because pressure fluctuations accentuate buoyancy driving in the concentrated plumes and can even lead to weak buoyancy braking in the surrounding ascending flows. As the plumes plunge downward into a region of stable stratification, they serve to excite a broad spectrum of internal gravity waves there. The induced waves are not passive, for they feed back upon the plumes by deflecting them sideways, thereby modulating the amplitude of the convection in time even in the unstable layer. The penetrative motions that billow upward into the upper stable zone are distinctly weaker, and they cascade back downward toward the unstable zone over a broad horizontal scale. The strong excitation of gravity waves by the convection has implications for gradual mixing deep within a star. Title: Space-laboratory and numerical simulations of thermal convection in arotating hemispherical shell with radial gravity. Authors: Hart, John E.; Glatzmaier, Gary A.; Toomre, Juri Bibcode: 1986JFM...173..519H Altcode: The flight of the Spacelab 3 microgravity laboratory onboard the Space Shuttle Challenger in May 1985 enabled electroconvection experiments to be conducted using the goephysical fluid flow cell instrument. Experimental results are presented which illustrate the variety of convection achieved by varying the imposed radial and latitudinal temperature gradients, rotation rates, and the strength of the electrostatic gravity. These results are compared with those obtained from nonlinear three-dimensional simulations and good agreement is found. Title: Laboratory Experiments on Planetary and Stellar Convection Performed on Spacelab 3 Authors: Hart, J. E.; Toomre, J.; Deane, A. E.; Hurlburt, N. E.; Glatzmaier, G. A.; Fichtl, G. H.; Leslie, F.; Fowlis, W. W.; Gilman, P. A. Bibcode: 1986Sci...234...61H Altcode: Experiments on thermal convection in a rotating, differentially heated hemispherical shell with a radial buoyancy force were conducted in an orbiting microgravity laboratory. A variety of convective structures, or planforms, were observed, depending on the magnitude of the rotation and the nature of the imposed heating distribution. The results are compared with numerical simulations that can be conducted at the more modest heating rates, and suggest possible regimes of motion in rotating planets and stars. Title: Local Response of the Five-Minute Oscillations to a Major Solar Flare Authors: Haber, D. A.; Toomre, J.; Hill, F.; Gough, D. O. Bibcode: 1986BAAS...18Q1011H Altcode: No abstract at ADS Title: Preflare activity. Authors: Priest, E. R.; Gaizauskas, V.; Hagyard, M. J.; Schmahl, E. J.; Webb, D. F.; Cargill, P.; Forbes, T. G.; Hood, A. W.; Steinolfson, R. S.; Chapman, G. A.; Deloach, A. C.; Gary, G. A.; Jones, H. P.; Karpen, J. T.; Martres, M. -J.; Porter, J. G.; Schmieder, B.; Smith, J. B., Jr.; Toomre, J.; Woodgate, B.; Waggett, P.; Bentley, R.; Hurford, G.; Schadee, A.; Schrijver, J.; Harrison, R.; Martens, P. Bibcode: 1986NASCP2439....1P Altcode: Contents: 1. Introduction: the preflare state - a review of previous results. 2. Magnetohydrodynamic instability: magnetic reconnection, nonlinear tearing, nonlinear reconnection experiments, emerging flux and moving satellite sunspots, main phase reconnection in two-ribbon flares, magnetic instability responsible for filament eruption in two-ribbon flares. 3. Preflare magnetic and velocity fields: general morphology of the preflare magnetic field, magnetic field shear, electric currents in the preflare active region, characterization of the preflare velocity field, emerging flux. 4. Coronal manifestations of preflare activity: defining the preflare regime, specific illustrative events, comparison of preflare X-rays and ultraviolet, preflare microwave intensity and polarization changes, non-thermal precursors, precursors of coronal mass ejections, short-lived and long-lived HXIS sources as possible precursors. Title: Influence of spatial filtering on possible anisotropies in solar oscillations. Authors: Hill, Frank; Haber, Deborah A.; Toomre, Juri; November, Laurence J. Bibcode: 1986ASIC..169...85H Altcode: 1986ssds.proc...85H The authors have used full disk Doppler observations of solar oscillations to compare the amplitudes of sectoral modes propagating along the equator with those of similar modes propagating along a great circle aligned with the poles. They find that the amplitudes are generally not equal for the two classes of modes, but the results are sensitive to analysis procedures attempting to isolate the different modes of oscillation. Spatial filtering of the data using spherical harmonics suggests that greater amplitudes are associated with "polar" sectoral modes than with "equatorial" sectoral modes. Title: Properties of solar oscillations. Authors: Toomre, Juri Bibcode: 1986ASIC..169....1T Altcode: 1986ssds.proc....1T Many of the oscillations that can be observed in the atmosphere of the Sun are resonant acoustic or gravity modes of the interior. Accurate measurement of the frequencies of these p and g modes permits deductions about the internal structure and dynamics of this star. Some of the methods of interpretation, involving a close interplay between observation and theory, can be carried over to the study of more distant stars. Title: Theoretical and experimental studies in support of the geophysical fluid flow experiment Authors: Hart, J.; Toomre, J. Bibcode: 1985aprr.nasa.....H Altcode: Meteorologists and astrophysicists interested in large scale planetary and solar circulations have come to recognize the importance of rotation and stratification in determining the character of these flows. In particular, the effect of latitude-dependent Coriolis force on nonlinear convection is thought to play a crucial role in such phenomena as differential rotation on the Sun, cloud band orientation on Jupiter, and the generation of magnetic fields in thermally driven dynamos. The continuous low-gravity environment of the orbiting space shuttle offers a unique opportunity to make laboratory studies of such large-scale thermally driven flows under the constraint imposed by rotation and sphericity. This is possible because polarization forces in a dielectric liquid, which are linearly dependent on fluid temperature, give rise to an effectively radial buoyancy force when a radial electrostatic field is imposed. The Geophysical Fluid Flow Cell (GFFC) is an implementation of this ideal in which fluid is contained between two rotating hemispheres that are differentially heated and stressed with a large a-c voltage. The experiment, to be flown on Spacelab III (currently set for launch April 29, 1985), will explore non-linear mode selection and high Rayleigh number turbulence in a rotating convecting spherical shell of liquid. Experiments will be carried out in a low driving parameter range where some limited numerical experimentation is currently feasible, as well as in a parameter range significantly beyond numerical computation for many years. Title: Seismology of the Sun Authors: Christensen-Dalsgaard, J.; Gough, D.; Toomre, J. Bibcode: 1985Sci...229..923C Altcode: Oscillations of the sun make it possible to probe the inside of a star. The frequencies of the oscillations have already provided measures of the sound speed and the rate of rotation throughout much of the solar interior. These quantities are important for understanding the dynamics of the magnetic cycle and have a bearing on testing general relativity by planetary precession. The oscillation frequencies yield a helium abundance that is consistent with cosmology, but they reinforce the severity of the neutrino problem. They should soon provide an important standard by which to calibrate the theory of stellar evolution. Title: Helioseismology Authors: Leibacher, J. W.; Noyes, R. W.; Toomre, J.; Ulrich, R. K. Bibcode: 1985SciAm.253c..48L Altcode: 1985SciAm.253...48L Oscillations of the sun's surface are due to sound waves resonating in the solar interior. In actual observations, such surface displacements are evidenced in the form of Doppler shifts in the wavelengths of light that are absorbed by the moving gases, and as variations in brightness. The spatial pattern and period of surface oscillation allows investigators to deduce the three-dimensional structure of the resonance, and to infer properties of the solar interior. Reflection and refraction below the solar surface confine sound waves within acoustic cavities. Such trapped waves interfere constructively with themselves as they circle the sun, creating the resonances that are detectable as solar surface oscillations. Title: Helioseismology. Authors: Leibacher, J. W.; Noyes, R. W.; Toomre, J.; Ulrich, R. K. Bibcode: 1985SciAm.253c..34L Altcode: 1985SciAm.253...34L Acoustic waves within the sun are visible as oscillations on the solar surface. Their pattern and period hold clues to structure, composition and dynamics in the sun's interior. Title: Frequent Ultraviolet Brightenings in Solar Active Regions Authors: Porter, J. G.; Toomre, J.; Gebbie, K. B. Bibcode: 1985BAAS...17..629P Altcode: No abstract at ADS Title: Changes in Subsurface Horizontal Velocities Inferred from Observations of High Degree 5-Minute Solar Oscillations Authors: Hill, F.; Toomre, J.; Gough, D. O. Bibcode: 1985BAAS...17..643H Altcode: No abstract at ADS Title: Turbulence and wave particle interactions in solar-terrestrial plasmas Authors: Dulk, G. A.; Goldman, M. V.; Toomre, J. Bibcode: 1985colo.reptQ....D Altcode: Activities in the following study areas are reported: (1) particle and wave processes in solar flares; (2) solar convection zone turbulence; and (3) solar radiation emission. To investigate the amplification of cyclotron maser radiation in solar flares, a radio frequency. (RF) heating model was developed for the corona surrounding the energy release site. Then nonlinear simulations of compressible convection display prominent penetration by plumes into regions of stable stratification at the base of the solar convection zone, leading to the excitation of internal gravity waves there. Lastly, linear saturation of electron-beam-driven Langmuir waves by ambient density fluctuations, nonlinear saturation by strong turbulence processes, and radiation emission mechanisms are examined. An additional section discusses solar magnetic fields and hydromagnetic waves in inhomogeneous media, and the effect of magnetic fields on stellar oscillation. Title: Sensitivity of inferred subphotospheric velocity field to mode selection, analysis technique and noise. Authors: Hill, F.; Gough, D.; Toomre, J. Bibcode: 1984sses.nasa...95H Altcode: 1984sss..conf...95H The horizontal velocity immediately below the photosphere can be inferred from observations of high-degree solar oscillations by an optimal-averaging inversion technique. The authors investigate the sensitivity of the results to various details of both the inversion and the determination of the frequencies. The results are shown to be quite stable to the choice of most parameters, suggesting that this procedure produces reliable estimates of the subsurface velocity. Title: Solar Seismology From Space. A conference at Snowmass, Colorado Authors: Ulrich, R. K.; Harvey, J.; Rhodes, E. J., Jr.; Toomre, J. Bibcode: 1984sses.nasa.....U Altcode: 1984sss..conf.....U No abstract at ADS Title: Overview of solar seismology: oscillations as probes of internal structure and dynamics in the Sun. Authors: Toomre, J. Bibcode: 1984sses.nasa....7T Altcode: 1984sss..conf....7T The physical nature of solar oscillations is reviewed. The nomenclature of the subject and the techniques used to interpret the oscillations are discussed. Many of the acoustic and gravity waves that can be observed in the atmosphere of the Sun are actually resonant or standing modes of the interior; precise measurements of the frequencies of such modes allow deductions of the internal structure and dynamics of this star. The scientific objectives of such studies of solar seismic disturbances, or of solar seismology, will be outlined. The reasons for why it would be very beneficial to carry out further observations of solar oscillations both from ground-based networks and from space will be discussed. Title: Penetrative cellular convection in a stratified atmosphere Authors: Massaguer, J. M.; Latour, J.; Toomre, J.; Zahn, J. -P. Bibcode: 1984A&A...140....1M Altcode: In the present investigation of penetrative convection within a simple compressible model, the middle one of the three layers of differing stratification prior to the onset of convection is a convectively unstable polytrope bounded above and below by two stably stratified polytropes. One- and two-mode steady solutions with hexagonal planforms have been studied for Rayleigh numbers up to aobut 1000 times critical, and for a range of Prandtl numbers, horizontal wavenumbers, and stratifications. These indicate that the penetration into the lower stable layer by downward plumes is substantially larger in a stratified medium than in a Boussinesq fluid, and produces an extended region of adiabatic stratification. The strong asymmetry between upward and downward penetration in compressible media has major implications for the mixing of stable regions above and below stellar convection zones. Title: Frequent ultraviolet brightenings observed in a solar active region with solar maximum mission Authors: Porter, J. G.; Toomre, J.; Gebbie, K. B. Bibcode: 1984ApJ...283..879P Altcode: Observations of the temporal behavior of ultraviolet emission from bright points within an active region of the sun are reported. Frequent and rapid brightenings in Si IV and O IV line emission are seen. The observations suggest that intermittent heating events of modest amplitude are occurring at many sites within an active region. By selecting the brightest site at any given time within an active region and then sampling its behavior in detail within a 120 s interval, it is found that about two-thirds of the samples show variations of the Si IV line intensity. The brightenings typically last about 40-60 s; intensity increases of about 20-100 percent are frequently observed. The results suggest that heating due to magnetic field reconnection within an active region is proceeding almost stochastically. Events involving only a modest release of energy occur the most frequently. Title: Two-dimensional compressible convection extending over multiple scale heights Authors: Hurlburt, N. E.; Toomre, J.; Massaguer, J. M. Bibcode: 1984ApJ...282..557H Altcode: The theoretical description of the dynamics of a stellar convection zone is considered, taking into account one of the most basic issues by studying compressible convection extending over multiple scale heights. A revised version of a code reported by Graham (1975) is employed. Two-dimensional simulations show that nonlinear compressible convection possesses cellular structures with strong localized downward-directed plumes and broader upflows. The horizontal flows which close the circulation within the cell satisfy an approximate Bernoulli integral along a considerable portion of the horizontal trajectory. Attention is given to details regarding the numerical methods, the properties of the numerical solutions, the overall effects of compressibility on nonlinear convection, and a comparison with anelastic modal solutions. Title: Attempt to measure the solar subsurface velocity Authors: Hill, F.; Gough, D.; Toomre, J. Bibcode: 1984MmSAI..55..153H Altcode: Five-minute oscillation modes are advected by horizontal velocities below the solar surface, and thus can be used as probes of rotation and large-scale convective flows. Results of inverse theory applied to observations of high-degree modes carried out on six separate days reveal variations in horizontal velocities with depth from day to day that may be the result of giant convection cells, through noise in the data makes this interpretation somewhat tentative. Title: Solar convection Authors: Toomre, J.; Gebbie, K. B. Bibcode: 1984colo.rept.....T Altcode: A thorough study of convective penetration into the solar atmosphere and convective motions in sub-atmospheric layers on the sun was made. Non-linear anelastic and Boussinesq modal equations were developed and solved to describe solar and stellar convection. An explanation was developed for the lack of penetration of large-scale convective motions into the observable solar atmosphere through the discovery of buoyancy braking near the top of a supposedly unstable layer. Observations of motions in the solar atmosphere led to the discovery of a new scale of solar motion, the so-called mesogranulation. A technique was developed to use changes in the solar five-minute oscillations as a probe of internal solar structure. Using this technique, large-scale, subatmospheric convective eddies were discovered. Title: Simulation of Effects of Atmospheric Seeing on Observations of Solar Five-Minute Oscillations Authors: Merryfield, W. J.; Toomre, J.; Hill, F.; Gough, D. O. Bibcode: 1984BAAS...16..532M Altcode: No abstract at ADS Title: Horizontal Velocities in the Solar Convection Zone Inferred from High Degree 5-Minute Oscillations Authors: Hill, F.; Toomre, J.; Gough, D. O. Bibcode: 1984BAAS...16R.451H Altcode: 1984BAAS...16..451H No abstract at ADS Title: Effects of Spherical Harmonic Filtering on Analysis of Five-Minute Solar Oscillations of High-Degree Authors: Haber, D.; Toomre, J.; Hill, F. Bibcode: 1984BAAS...16Q.533H Altcode: No abstract at ADS Title: Strong Downward Plumes Resulting from Compressibility in Nonlinear Convection and Their Coupling to Gravity Waves Authors: Toomre, J.; Hurlburt, N. E.; Massaguer, J. M. Bibcode: 1984ssdp.conf..222T Altcode: Two-dimensional numerical simulations are used to model fully compressible nonlinear convection spanning multiple scale heights within a stellar envelope. Title: Solar seismology from space. A conference at Snowmass, Colorado, August 17 - 19, 1983. Authors: Ulrich, R. K.; Harvey, J.; Rhodes, E. J., Jr.; Toomre, J. Bibcode: 1984ssfs.book.....U Altcode: No abstract at ADS Title: On the Detection of Subphotospheric Convective Velocities and Temperature Fluctuations Authors: Gough, D. O.; Toomre, J. Bibcode: 1983SoPh...82..401G Altcode: 1983IAUCo..66..401G A procedure is outlined for estimating the influence of large-scale convective eddies on the wave patterns of five-minute oscillations of high degree. The method is applied to adiabatic oscillations, with frequency ω and wave number k, of a plane-parallel polytropic layer upon which is imposed a low-amplitude convective flow. The distortion to the k - ω relation has two constituents: one depends on the horizontal component of the convective velocity and has a sign which depends on the sign of ω/k; the other depends on temperature fluctuations and is independent of the sign of ω/k. The magnitude of the distortion is just at the limit of present observational sensitivity. Thus there is reasonable hope that it will be possible to reveal some aspects of the large-scale flow in the solar convection zone. Title: Nonlinear Anelastic Modal Theory for Solar Convection Authors: Latour, J.; Toomre, J.; Zahn, J. -P. Bibcode: 1983SoPh...82..387L Altcode: 1983IAUCo..66..387L Preliminary solar envelope models have been computed using the single-mode anelastic equations as a description of turbulent convection. This approach provides estimates for the variation with depth of the largest convective cellular flows, akin to giant cells, with horizontal sizes comparable to the total depth of the convection zone. These modal nonlinear treatments are capable of describing compressible motions occurring over many density scale heights. Single-mode anelastic solutions have been constructed for a solar envelope whose mean stratification is nearly adiabatic over most of its vertical extent because of the enthalpy (or convective) flux explicitly carried by the big cell; a sub-grid scale representation of turbulent heat transport is incorporated into the treatment near the surface. The single-mode equations admit two solutions for the same horizontal wavelength, and these are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. It is striking that the upward directed flows experience large pressure effects when they penetrate into regions where the vertical scale height has become small compared to their horizontal scale. The fluctuating pressure can modify the density fluctuations so that the sense of the buoyancy force is changed, with buoyancy braking actually achieved near the top of the convection zone. The pressure and buoyancy work in the shallow but unstable H+ and He+ ionization regions can serve to decelerate the vertical motions and deflect them laterally, leading to strong horizontal shearing motions. It appears that such dynamical processes may explain why the amplitudes of flows related to the largest scales of convection are so feeble in the solar atmosphere. Title: Variability in the power spectrum of solar five-minute oscillations Authors: Hill, F.; Toomre, J.; November, L. J. Bibcode: 1983SoPh...82..411H Altcode: 1983IAUCo..66..411H Two-dimensional power spectra of solar five-minute oscillations display prominent ridge structures in (k, ω) space, where k is the horizontal wavenumber and ω is the temporal frequency. The positions of these ridges in k and ω can be used to probe temperature and velocity structures in the subphotosphere. We have been carrying out a continuing program of observations of five-minute oscillations with the diode array instrument on the vacuum tower telescope at Sacramento Peak Observatory (SPO). We have sought to establish whether power spectra taken on separate days show shifts in ridge locations; these may arise from different velocity and temperature patterns having been brought into our sampling region by solar rotation. Power spectra have been obtained for six days of observations of Doppler velocities using the MgIλ5173 and FeIλ5434 spectral lines. Each data set covers 8 to 11 hr in time and samples a region 256″ × 1024″ in spatial extent, with a spatial resolution of 2″ and temporal sampling of 65 s. We have detected shifts in ridge locations between certain data sets which are statistically significant. The character of these displacements when analyzed in terms of eastward and westward propagating waves implies that changes have occurred in both temperature and horizontal velocity fields underlying our observing window. We estimate the magnitude of the velocity changes to be on the order of 100 m s-1; we may be detecting the effects of large-scale convection akin to giant cells. Title: Search for Solar Giant Cells Using Five-Minute Oscillations as Probes of Velocity Structures Authors: Toomre, J. Bibcode: 1983EOSTr..64..303T Altcode: No abstract at ADS Title: Time-dependent solutions of multimode convection equations Authors: Toomre, J.; Gough, D. O.; Spiegel, E. A. Bibcode: 1982JFM...125...99T Altcode: Truncated modal equations are used to study the time evolution of thermal convection. In the Boussinesq approximation these nonlinear equations are obtained by expanding the fluctuating velocity and temperature fields in a finite set of planforms of the horizontal coordinates. Numerical studies dealing with two or three modes with triad interactions are discussed. Rich time dependence was found in these cases: periodic and aperiodic solutions can be obtained, along with various steady solutions. Three-mode solutions reproduce the qualitative appearance of spoke-pattern convection as observed in experiments at high Prandtl numbers. Though the values of the periods of the time-dependent solutions do not agree with those of the experiments, their variation with Rayleigh number compares favorably. Except at the highest Rayleigh number considered (10,000,000), the theoretical Nusselt numbers agree well with experiment. Title: Internal gravity waves in the solar atmosphere. II - Effects of radiative damping Authors: Mihalas, B. W.; Toomre, J. Bibcode: 1982ApJ...263..386M Altcode: In the solar photosphere, temperature fluctuations associated with acoustic-gravity waves may be rapidly smoothed by the transfer mechanism of radiation between hotter and cooler regions. The present investigation of the radiative effects on internal gravity waves takes into account the parameterization of the radiative energy, employing the Newtonian cooling approximation. A linear analysis of the propagation of internal gravity waves is carried out in a model of the solar atmosphere which is taken to be homogeneous in the horizontal coordinates. Linear wave properties both with and without radiative cooling are summarized, and the variation with height of energy fluxes and of nonlinearities in the waves is discussed. Attention is given to the significance of the obtained results in terms of energy balance in the chromosphere and in relation to spectral line observations. Title: Single-mode theory of diffusive layers in thermohaline convection Authors: Gough, D. O.; Toomre, J. Bibcode: 1982JFM...125...75G Altcode: A two-layer configuration of thermohaline convection is studied, with the principal aim of explaining the observed independence of the buoyancy-flux ratio on the stability parameter when the latter is large. Temperature is destabilizing and salinity is stabilizing, so diffusive interfaces separate the convecting layers. The convection is treated in the single-mode approximation, with a prescribed horizontal planform and wavenumber. Surveys of numerical solutions are presented for a selection of Rayleigh numbers R, stability parameters lambda and horizontal wavenumbers. The solutions yield a buoyancy flux ratio chi that is insensitive to lambda, in accord with laboratory experiments. However chi increases with increasing R, in contradiction to laboratory observations. Title: Nonlinear modal analysis of penetrative convection Authors: Zahn, J. -P.; Toomre, J.; Latour, J. Bibcode: 1982GApFD..22..159Z Altcode: It is pointed out that thermal convection in many astrophysical and geophysical settings occurs in an unstable layer bounded above and below by regions which are stably stratified. The convective motions may extend a substantial distance into the adjacent stable zones. If the motions have little direct effect upon the mean stratification of the stable zone, then they are usually referred to as convective overshooting. The primary objective of the present investigation is to study the dynamics of overshooting at very large Rayleigh numbers, mainly with stellar applications in mind. Numerically this is only feasible if severe simplifications are made in the description of what are likely to be turbulent motions. The approach employed in the investigation utilizes nonlinear modal equations in which the vertical and temporal structure of the convection is described accurately at the expense of the horizontal structure. A summary of the salient properties of penetrative convection is provided on the basis of the results of the conducted studies. Title: Relation of Ephemeral Magnetic Regions to the Low Amplitude Branch of Persistent Vertical Velocities Authors: Gebbie, K. B.; Toomre, J.; Haber, D. A.; Hill, F.; Simon, G. W.; November, L. J.; Gurman, J. B.; Shine, R. A. Bibcode: 1982BAAS...14R.939G Altcode: 1982BAAS...14..939G No abstract at ADS Title: The Lateral Deflection of Large-Scale Convective Flows by Scale Height Effects below the Solar Surface Authors: Hurlburt, N.; Toomre, J. Bibcode: 1982BAAS...14..938H Altcode: No abstract at ADS Title: Solar Five-Minute Oscillations, Subsurface Velocities and Inverse Theory Authors: Gough, D. O.; Hill, F.; Toomre, J. Bibcode: 1982BAAS...14..938G Altcode: No abstract at ADS Title: Vertical flows of supergranular and mesogranular scale observed on the sun with OSO 8 Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W. Bibcode: 1982ApJ...258..846N Altcode: A program of observations was carried out in order to study the penetration of supergranular flows over a broad range of heights in the solar atmosphere. Steady Doppler velocities are determined from observations of a Si II spectral line using the Ultraviolet Spectrometer on the Orbiting Solar Observatory 8 (OSO 8) satellite and Fe I and Mg I lines with the diode-array instrument on the vacuum telescope at Sacramento Peak Observatory (SPO). The heights of formation of these spectral lines span about 1400 km or nearly 11 density scale heights from the photosphere to the middle chromosphere. Steady vertical flows on spatial scales typical of supergranulation and mesogranulation have been detected in the middle chromosphere with OSO 8. The patterns of intensity and steady velocity of granular scale are reproducible in successive data sets. The patterns appear to evolve slowly over the 9 hr period spanned by six orbits. Title: University of Colorado, Boulder, Colorado 80309. Report. Authors: Dulk, G. A.; Shull, J. M.; Toomre, J. Bibcode: 1982BAAS...14..122D Altcode: No abstract at ADS Title: Solar 5-MINUTE Oscillations as Probes of Structure in the Subphotosphere Authors: Hill, F.; Toomre, J.; November, L. J. Bibcode: 1982pccv.conf..139H Altcode: No abstract at ADS Title: Review of Time-Dependent Convection and Attempts to Couple it to Pulsation in Stars Authors: Toomre, J. Bibcode: 1982pccv.conf..170T Altcode: No abstract at ADS Title: Steady flows in the solar transition region observed with SMM Authors: Gebbie, K. B.; Hill, F.; November, L. J.; Gurman, J. B.; Shine, R. A.; Woodgate, B. E.; Athay, R. G.; Tandberg-Hanssen, E. A.; Toomre, J.; Simon, G. W. Bibcode: 1981ApJ...251L.115G Altcode: Steady flows in the quiet solar transition region have been observed with the Ultraviolet Spectrometer and Polarimeter experiment on the Solar Maximum Mission (SMM) satellite. The persistent vertical motions seen at disk center have spatial rms amplitudes of 1.4 km/s in the C II line, 3.9 km/s in Si IV, and 4.2 km/s in C IV. The amplitudes of the more horizontal flows seen toward the limb tend to be somewhat higher. Plots of steady vertical velocity versus intensity seen at disk center in Si IV and C IV show two distinct branches. Title: Internal gravity waves in the solar atmosphere. I - Adiabatic waves in the chromosphere Authors: Mihalas, B. W.; Toomre, J. Bibcode: 1981ApJ...249..349M Altcode: The properties of adiabatic and linear internal gravity waves propagating in a solar wind model are discussed, using nonlinearity criteria unique to gravity waves to estimate wave-breaking heights. The results are used to deduce information on the possible role of gravity waves in the chromospheric energy balance. Maximum vertical velocity amplitudes for gravity waves are estimated to be on the order of 2 km/sec or less, and maximum horizontal velocity amplitudes are less than 6 km/sec, with temperature perturbations as large as 1000-2000 K. It is also estimated that gravity waves with an incident energy flux of one million ergs/sq cm-sec can propagate upward to a maximum height of 900-1000 km above the visible surface before nonlinearities lead to wave breaking, while those with an energy flux of 100,000 ergs/sq cm-sec can reach maximum heights of 1400-1600 km. Title: Stellar convection theory. III - Dynamical coupling of the two convection zones in A-type stars by penetrative motions Authors: Latour, J.; Toomre, J.; Zahn, J. -P. Bibcode: 1981ApJ...248.1081L Altcode: The thermal convection occurring over many density scale heights in an A-type star outer envelope, encompassing both the hydrogen and helium convectively unstable zones, is examined by means of anelastic modal equations. The single-mode anelastic equations for such compressible convection display strong overshooting of the motions into adjacent radiative zones, which would preclude diffusive separation of elements in the supposedly quiescent region between the two unstable zones. In addition, the anelastic solutions reveal that the two zones of convective instability are dynamically coupled by the overshooting motions. The two solutions that the nonlinear single-mode equations admit for the same horizontal wavelength are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. It is suggested that strong horizontal shear flows should be present just below the surface of the star, and that the large-scale motions extending into the stable atmosphere would appear mainly as horizontal flows. Title: The detection of mesogranulation on the sun. Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W. Bibcode: 1981ApJ...245L.123N Altcode: Time averages of velocity measurements at disk center on the quiet sun reveal the presence of a fairly stationary pattern of cellular flow with a spatial scale of 5-10 Mm. Such mesogranulation has a spatial rms vertical velocity amplitude of about 60 m/s superposed on the larger scale supergranular flows. The lifetimes of mesogranules appear to be at least 2 hr. Title: Nonlinear Penetrative Convection in a Compressible Medium Authors: Hurlburt, N.; Toomre, J.; Massaguer, J. M. Bibcode: 1981BAAS...13..912H Altcode: No abstract at ADS Title: Solar Five-Minute Oscillations as Probes of Velocity and Temperature Fields Authors: Hill, F.; Toomre, J.; November, L. J. Bibcode: 1981BAAS...13Q.860H Altcode: 1981BAAS...13..860H No abstract at ADS Title: Nonlinear Anelastic Models of Solar Convection Authors: Toomre, J.; Latour, J.; Zahn, J. -P. Bibcode: 1981BAAS...13Q.907T Altcode: No abstract at ADS Title: Height Dependence of Steady Flows Determined from Coordinated SMM and SPO Observations Authors: Gebbie, K. B.; Hill, F.; Toomre, J.; November, L. J.; Simon, G. W.; Gurman, J. B.; Shine, R. A.; Woodgate, B. E. Bibcode: 1981BAAS...13..914G Altcode: No abstract at ADS Title: OSO 8 Observations of Coherent Chromospheric Oscillations Authors: Hill, F.; Toomre, J.; November, L. J. Bibcode: 1980BAAS...12R.894H Altcode: No abstract at ADS Title: Nonlinear Simulations of Rotational Effects in Supergranules Authors: Hathaway, D. H.; Toomre, J. Bibcode: 1980BAAS...12Q.894H Altcode: No abstract at ADS Title: Steady Flows in the Solar Transition Region Observed with the UVSP Experiment on SMM Authors: Gebbie, K. B.; Hill, F.; Toomre, J.; November, L. J.; Simon, G. W.; Athay, R. G.; Bruner, E. C.; Rehse, R.; Gurman, J. B.; Shine, R. A.; Woodgate, B. E.; Tandberg-Hanssen, E. A. Bibcode: 1980BAAS...12..907G Altcode: No abstract at ADS Title: Two Dimensional Compressible Convection Extending Over Multiple Scale Heights Authors: Hurlburt, N. E.; Toomre, J.; Massaguer, J. M.; Graham, E. Bibcode: 1980BAAS...12S.894H Altcode: No abstract at ADS Title: Anelastic Modal Theory Applied to the Solar Convection Zone Authors: Toomre, J.; Latour, J.; Zahn, J. P. Bibcode: 1980BAAS...12..895T Altcode: No abstract at ADS Title: The Lifetime of Solar Mesogranulation Authors: November, L. J.; Gebbie, K. B.; Hill, F.; Toomre, J.; Simon, G. W. Bibcode: 1980BAAS...12..895N Altcode: No abstract at ADS Title: Axisymmetric Convection Driven by Latitudinal Temperature Gradients in Rotating Spherical Shells. Authors: Hathaway, D. H.; Gilman, P. A.; Miller, J.; Toomre, J. Bibcode: 1980BAAS...12..686H Altcode: No abstract at ADS Title: Overshooting Motions from the Convection Zone and Their Role in Atmospheric Heating Authors: Toomre, J. Bibcode: 1980HiA.....5..571T Altcode: No abstract at ADS Title: Convective instability when the temperature gradient and rotation vector are oblique to gravity. II. Real fluids with effects of diffusion Authors: Hathaway, D. H.; Toomre, J.; Gilman, P. A. Bibcode: 1980GApFD..15....7H Altcode: The linear stability analysis of Hathaway, Gilman and Toomre (1979) (hereafter referred to as Paper I) is repeated for Boussinesq fluids with viscous and thermal diffusion. As in Paper I the fluid is confined between plane parallel boundaries and the rotation vector is oblique to gravity. This tilted rotation vector introduces a preference for roll-like disturbances whose axes are oriented north-south; the preference is particularly strong in the equatorial region. The presence of a latitudinal temperature gradient produces a thermal wind shear which favors axisymmetric convective rolls if the gradient exceeds some critical value. For vanishingly small diffusivities the value of this transition temperature gradient approaches the inviscid value found in Paper I. For larger diffusivities larger gradients are required particularly in the high latitudes. These results are largely independent of the Prandtl number. Diffusion tends to stabilize the large wavenumber rolls with the result that a unique wavenumber can be found at which the growth rate is maximized. These preferred rolls have widths comparable to the depth of the layer and tend to be broader near the equator. The axisymmetric rolls are similar in many respects to the cloud bands on Jupiter provided they extend to a depth of about 15,000 km. Title: Mesogranulation -- An Intermediate Scale of Motion on the Sun Authors: Toomre, J.; November, L. J.; Gebbie, K. B.; Simon, G. W. Bibcode: 1979BAAS...11..641T Altcode: No abstract at ADS Title: Convective Instability in Rotating Layers with Thermal Winds and Application to Jupiter Authors: Hathaway, D. H.; Gilman, P. A.; Toomre, J. Bibcode: 1979BAAS...11Q.618H Altcode: No abstract at ADS Title: The height variation of supergranular velocity fields determined from simultaneous OSO 8 satellite and ground-based observations. Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W. Bibcode: 1979ApJ...227..600N Altcode: Results are reported for simultaneous satellite and ground-based observations of supergranular velocities in the sun, which were made using a UV spectrometer aboard OSO 8 and a diode-array instrument operating at the exit slit of an echelle spectrograph attached to a vacuum tower telescope. Observations of the steady Doppler velocities seen toward the limb in the middle chromosphere and the photosphere are compared; the observed spectral lines of Si II at 1817 A and Fe I at 5576 A are found to differ in height of formation by about 1400 km. The results show that supergranular motions are able to penetrate at least 11 density scale heights into the middle chromosphere, that the patterns of motion correlate well with the cellular structure seen in the photosphere, and that the motion increases from about 800 m/s in the photosphere to at least 3000 m/s in the middle chromosphere. These observations imply that supergranular velocities should be evident in the transition region and that strong horizontal shear layers in supergranulation should produce turbulence and internal gravity waves. Title: Convective Instability when the Temperature Gradient and Rotation Vector are Oblique to Gravity. I. Fluids without Diffusion Authors: Hathaway, D. H.; Toomre, J.; Gilman, P. A. Bibcode: 1979GApFD..13..289H Altcode: No abstract at ADS Title: Compressible Convection in the Outer Envelope of A-type Stars Authors: Toomre, J.; Latour, J.; Zahn, J. -P. Bibcode: 1978BAAS...10..677T Altcode: No abstract at ADS Title: The Variation with Height of Supergranular Velocity Fields Authors: Gebbie, K. B.; November, L. J.; Toomre, J.; Simon, G. W. Bibcode: 1978BAAS...10Q.672G Altcode: No abstract at ADS Title: Vertical and Horizontal Components of Supergranulation Velocity Fields Observed with OSO-8 Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W. Bibcode: 1977BAAS....9..337N Altcode: No abstract at ADS Title: Anelastic Stellar Convection Theory Applied to A-type Stars. Authors: Toomre, J.; Latour, J.; Zahn, J. -P. Bibcode: 1977BAAS....9..337T Altcode: No abstract at ADS Title: Violent Tides Between Galaxies Authors: Toomre, Alar; Toomre, Juri Bibcode: 1977nass.book..271T Altcode: No abstract at ADS Title: Numerical solutions of single-mode convection equations Authors: Toomre, J.; Gough, D. O.; Spiegel, E. A. Bibcode: 1977JFM....79....1T Altcode: In the Boussinesq approximation, single-mode equations describing thermal convection are constructed by expanding the fluctuating velocity and temperature fields in a complete set of functions (or planforms) of the horizontal coordinates and retaining just one term. Numerical solutions of the single-mode equations are investigated, chief consideration being given to hexagonal planforms. Extensive surveys of steady solutions are presented for various Rayleigh numbers, Prandtl numbers, and horizontal wavenumbers. The dependences on Rayleigh number and Prandtl number at very large Rayleigh number are in satisfactory agreement with the results of asymptotic expansions. Title: Stellar convection theory. II. Single-mode study of the second convection zone in an A-type star. Authors: Toomre, J.; Zahn, J. -P.; Latour, J.; Spiegel, E. A. Bibcode: 1976ApJ...207..545T Altcode: The anelastic modal equations presented in Paper I are considered in their simplest version: only one mode is retained in the representation of the fluctuating dynamic and thermodynamic variables of convection theory. These single-mode equations are used to examine the structure of the second convection zone of an A-type star. Two- and three-dimensional numerical solutions are obtained for a range of parameters in the theory, and a simple analysis is provided for their interpretation. The principal results are for three-dimensional motions, since these are most likely to be relevant to stellar convection. Such motions produce a convective heat flux several orders of magnitude greater than predicted by standard mixing-length theory for the same situation; we find that convection carries up to 6 percent of the total flux. The most significant astrophysical implication of our results is that they suggest strong overshooting into the adjacent radiative zones. We anticipate that mixing will extend to the overlying hydrogen convection zone. This would rule out some interpretations of metallic-line stars which invoke diffusive element separation between the two convection zones. Subject headings: convection - stars: interiors - stars: metallic-line Title: Stellar convection theory. I. The anelastic modal equations. Authors: Latour, J.; Spiegel, E. A.; Toomre, J.; Zahn, J. -P. Bibcode: 1976ApJ...207..233L Altcode: Methods are developed for dealing with the various dynamical problems that arise because of convective zones in stars. A system of equations for stellar convection is derived from the full equations of compressible fluid dynamics with the aid of two major approximations. The first of these is the anelastic approximation, which involves both the filtering out of acoustic waves and a suitable linearization of the fluctuating thermodynamic variables. The second one approximates the horizontal structure of convection by expanding the motion in a set of horizontal cellular platforms and severely truncating the expansion. The resulting system of partial differential equations, referred to as the anelastic modal equations, is outlined along with suggested boundary conditions and techniques for solving the equations. Ways of assessing the overall validity of the present treatment are discussed. Title: Supergranulation Velocity Fields Observed in the Solar Transition Region with OSO-8 Authors: November, L. J.; Toomre, J.; Gebbie, K. B.; Simon, G. W.; Bruner, E. C., Jr.; Chipman, E. G.; Lites, B. W.; Shine, R. A.; Orrall, F. Q.; Athay, R. G.; White, O. R. Bibcode: 1976BAAS....8..311N Altcode: No abstract at ADS Title: The Second Convection Zone in an A-type Star Authors: Latour, J.; Spiegel, E. A.; Toomre, J.; Zahn, J. P. Bibcode: 1975BAAS....7..526L Altcode: No abstract at ADS Title: Modal equations for cellular convection Authors: Gough, D. O.; Spiegel, E. A.; Toomre, J. Bibcode: 1975JFM....68..695G Altcode: We expand the fluctuating flow variables of Boussinesq convection in the planform functions of linear theory. Our proposal is to consider a drastic truncation of this expansion as a possible useful approximation scheme for studying cellular convection. With just one term included, we obtain a fairly simple set of equations which reproduces some of the qualitative properties of cellular convection and whose steady-state form has already been derived by Roberts (1966). This set of 'modal equations' is analyzed at slightly supercritical and at very high Rayleigh numbers. In the latter regime the Nusselt number varies with Rayleigh number just as in the mean-field approximation with one horizontal scale when the boundaries are rigid. However, the Nusselt number now depends also on the Prandtl number in a way that seems compatible with experiment. The chief difficulty with the approach is the absence of a deductive scheme for deciding which planforms should be retained in the truncated expansion. Title: What Velocities are Consistent with the Interpretation of Supergranulation as Penetrative Convection? Authors: Gebbie, K. B.; Toomre, J. Bibcode: 1975BAAS....7Q.363G Altcode: No abstract at ADS Title: Highly stretched meshes as functionals of solutions Authors: Gough, D. O.; Spiegel, E. A.; Toomre, J. Bibcode: 1975LNP....35..191G Altcode: No abstract at ADS Title: Violent tides between galaxies. Authors: Toomre, A.; Toomre, J. Bibcode: 1973SciAm.229f..38T Altcode: 1973SciAm.229...38T No abstract at ADS Title: Violent Tides between Galaxies Authors: Alar; Toomre, Juri Bibcode: 1973SciAm.229f..38A Altcode: No abstract at ADS Title: Radial Velocities in the Tail of NGC 4676A Authors: Theys, J. C.; Spiegel, E. A.; Toomre, Juri Bibcode: 1972PASP...84..851T Altcode: A spectrum of ffie long tail of NGC 4676A shows [011] x3727 in emission. The radial velocity measured from one plate varies by about 400 km sec-1 along the length of the tail. Key words: peculiar galaxy - radial velocities Title: Galactic Bridges and Tails Authors: Toomre, Alar; Toomre, Juri Bibcode: 1972ApJ...178..623T Altcode: This paper argues that the bridges and tails seen in some multiple galaxies are just tidal relics of close encounters. These consequences of the brief but violent tidal forces are here studied in a deliberately simple-minded fashion: Each encounter is considered to involve only two galaxies and to be roughly parabolic; each galaxy is idealized as just a disk of noninteracting test particles which initially orbit a central mass point. As shown here, the two-sided distortions provoked by gravity alone in such circumstances can indeed evolve kinematically into some remarkably narrow and elongated features: (i) After a relatively direct passage of a small companion, the outer portions of the primary disk often deform both into a near-side spiral arm or "bridge" extending toward this satellite, and into a far-side "counterarm." (ii) A similar encounter with an equal or more massive partner results typically in a long and curving "tail" of escaping debris from the far side of the victim disk, and in an avalanche of near-side particles, most of which are captured by the satellite. Besides extensive pictorial surveys of such tidal damage, this paper offers reconstructions of the orbits and outer shapes of four specific interacting pairs: Arp 295, M51 + NOC 5195, NGC 4676, and NOC 4038/9. Those models can be found in the fairly self-explanatory figures 19, 21, 22, and 23. Also discussed are some closely related issues of eccentric bound orbits, orbital decay, accretion, and forced spiral waves. Title: Spectra of Extragalactic Rings. Authors: Theys, J. C.; Spiegel, E. A.; Toomre, J. Bibcode: 1972BAAS....4..213T Altcode: No abstract at ADS Title: Model of the Encounter Between NGC 5194 and 5195. Authors: Toomre, A.; Toomre, J. Bibcode: 1972BAAS....4..214T Altcode: No abstract at ADS Title: Theorectical Model of NGC 4038/39. Authors: Toomre, Alar; Toomre, Juri Bibcode: 1971BAAS....3..390T Altcode: No abstract at ADS Title: On Intergalactic Bridges. Authors: Toomre, Alar; Toomre, Juri Bibcode: 1970BAAS....2R.350T Altcode: No abstract at ADS