Anelastic Spherical Harmonic Research Articles

GRAND MINIMA AND EQUATORWARD PROPAGATION IN A CYCLING STELLAR CONVECTIVE DYNAMO

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 $\alpha$-$\Omega$ type. The time scales that appear to be relevant to the magnetic polarity reversal are also identified.

2-D and 3-D models of convective turbulence and oscillations in intermediate-mass main-sequence stars

AbstractWe present multidimensional modeling of convection and oscillations in main-sequence stars somewhat more massive than the Sun, using three separate approaches: 1) Using the 3-D planar StellarBox radiation hydrodynamics code to model the envelope convection zone and part of the radiative zone. Our goals are to examine the interaction of stellar pulsations with turbulent convection in the envelope, excitation of acoustic modes, and the role of convective overshooting; 2) Applying the spherical 3-D MHD ASH (Anelastic Spherical Harmonics) code to simulate the core convection and radiative zone. Our goal is to determine whether core convection can excite low-frequency gravity modes, and thereby explain the presence of low frequencies for some hybrid γ Dor/δ Sct variables for which the envelope convection zone is too shallow for the convective blocking mechanism to drive gravity modes; 3) Applying the ROTORC 2-D stellar evolution and dynamics code to calculate evolution with a variety of initial rotation rates and extents of core convective overshooting. The nonradial adiabatic pulsation frequencies of these nonspherical models are calculated using the 2-D pulsation code NRO. We present new insights into pulsations of 1-2 M⊙ stars gained by multidimensional modeling.

MERIDIONAL CIRCULATION IN SOLAR AND STELLAR CONVECTION ZONES

We present a series of 3-D nonlinear simulations of solar-like convection, carried out using the Anelastic Spherical Harmonic (ASH) code, that are designed to isolate those processes that drive and shape meridional circulations within stellar convection zones. These simulations have been constructed so as to span the transition between solar-like differential rotation (fast equator/slow poles) and ``anti-solar' differential rotation (slow equator/fast poles). Solar-like states of differential rotation, arising when convection is rotationally constrained, are characterized by a very different convective Reynolds stress than anti-solar regimes, wherein convection only weakly senses the Coriolis force. We find that the angular momentum transport by convective Reynolds stress plays a central role in establishing the meridional flow profiles in these simulations. We find that the transition from single-celled to multi-celled meridional circulation profiles in strong and weak regimes of rotational constraint is linked to a change in the convective Reynolds stress, a clear demonstration of gyroscopic pumping. Latitudinal thermal variations differ between these different regimes, with those in the solar-like regime conspiring to suppress a single cell of meridional circulation, whereas the cool poles and warm equator established in the anti-solar states tend to promote single-celled circulations. Though the convective angular momentum transport becomes radially inward at mid-latitudes in anti-solar regimes, it is the meridional circulation that is primarily responsible for establishing a rapidly-rotating pole. We conclude with a discussion of how these results relate to the Sun, and suggest that the Sun may lie near the transition between rapidly-rotating and slowly-rotating regimes.

3D simulations of internal gravity waves in solar-like stars

AbstractWe perform numerical simulations of the whole Sun using the 3D anelastic spherical harmonic (ASH) code. In such models, the radiative and convective zones are non-linearly coupled and in the radiative interior a wave-like pattern is observed. For the first time, we are thus able to model in 3D the excitation and propagation of internal gravity waves (IGWs) in a solar-like star's radiative zone. We compare the properties of our waves to theoretical predictions and results of oscillation calculations. The obtained good agreement allows us to validate the consistency of our approach and to study the characteristics of IGWs. We find that a wave's spectrum is excited up to radial order n=58. This spectrum evolves with depth and time; we show that the lifetime of the highest-frequency modes must be greater than 550 days. We also test the sensitivity of waves to rotation and are able to retrieve the rotation rate to within 5% error by measuring the frequency splitting.

MAGNETIC WREATHS AND CYCLES IN CONVECTIVE DYNAMOS

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 3D magnetohydrodynamic (MHD) simulations with the anelastic spherical harmonic (ASH) 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$\Omega_\odot$), 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.

CONVECTION AND DIFFERENTIAL ROTATION IN F-TYPE STARS

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 $M_\odot$ 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 $\Delta\Omega$ $\alpha$ $M^{3.9}$$\Omega_0^{0.6}$. Accompanying the growing differential rotation is a significant latitudinal temperature contrast, with amplitudes of 1000 K or higher in the most rapidly rotating cases. This contrast in turn scales with mass and rotation rate as $\Delta$$T$ $\alpha$ $M^{6.4}$$\Omega_0^{1.6}$. On the other hand, the meridional circulations become much weaker with more rapid rotation and with higher mass, with their kinetic energy decreasing as KE$_{MC}$ $\alpha$ $M^{-1.2}$$\Omega_0^{-0.8}$. 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.

Convection and differential rotation properties of G and K stars computed with the ASH code

AbstractThe stellar luminosity and depth of the convective envelope vary rapidly with mass for G‐ and K‐type main sequence stars. In order to understand how these properties influence the convective turbulence, differential rotation, and meridional circulation, we have carried out 3D dynamical simulations of the interiors of rotating main sequence stars, using the anelastic spherical harmonic (ASH) code. The stars in our simulations have masses of 0.5, 0.7, 0.9, and 1.1 M⊙, corresponding to spectral types K7 through G0, and rotate at the same angular speed as the Sun. We identify several trends of convection zone properties with stellar mass, exhibited by the simulations. The convective velocities, temperature contrast between up‐ and downflows, and meridional circulation velocities all increase with stellar luminosity. As a consequence of the trend in convective velocity, the Rossby number (at a fixed rotation rate) increases and the convective turnover timescales decrease significantly with increasing stellar mass. The three lowest mass cases exhibit solar‐like differential rotation, in a sense that they show a maximum rotation at the equator and minimum at higher latitudes, but the 1.1 M⊙ case exhibits anti‐solar rotation. At low mass, the meridional circulation is multi‐cellular and aligned with the rotation axis; as the mass increases, the circulation pattern tends toward a unicellular structure covering each hemisphere in the convection zone (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Magnetic confinement of the solar tachocline: II. Coupling to a convection zone

The reason for the observed thinness of the solar tachocline is still not well understood. One of the explanations that have been proposed is that a primordial magnetic field renders the rotation uniform in the radiation zone. We test here the validity of this magnetic scenario through 3D numerical MHD simulations that encompass both the radiation zone and the convection zone. The numerical simulations are performed with the anelastic spherical harmonics (ASH) code. The computational domain extends from $0.07\;R_\odot$ to $0.97\;R_\odot$. In the parameter regime we explored, a dipolar fossil field aligned with the rotation axis can not remain confined in the radiation zone. When the field lines are allowed to interact with turbulent unstationary convective motions at the base of the convection zone, 3D effects prevent the field confinement. In agreement with previous work, we find that a dipolar fossil field, even when it is initially buried deep inside the radiation zone, will spread into the convective zone. According to Ferraro's law of iso-rotation, it then imprints on the radiation zone the latitudinal differential rotation of the convection zone, which is not observed.

MAGNETIC CYCLES IN A CONVECTIVE DYNAMO SIMULATION OF A YOUNG SOLAR-TYPE STAR

Young solar-type stars rotate rapidly and many are magnetically active; some undergo magnetic cycles similar to the 22-year solar activity cycle. We conduct simulations of dynamo action in rapidly rotating suns with the 3D MHD anelastic spherical harmonic (ASH) code to explore dynamo action achieved in the convective envelope of a solar-type star rotating at 5 times the current solar rotation rate. Striking global-scale magnetic wreaths appear in the midst of the turbulent convection zone and show 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 time scale. 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 $\Omega$-effect, while the mean poloidal fields are built by turbulent correlations which are not necessarily well represented by a simple $\alpha$-effect. During a reversal the magnetic wreaths propagate towards the polar regions, and this appears to arise from a poleward propagating dynamo wave. The primary response in the convective flows involves the axisymmetric differential rotation which shows variations associated with the poleward propagating magnetic wreaths. 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. [abridged]

Convection and dynamo action in B stars

AbstractMain-sequence massive stars possess convective cores that likely harbor strong dynamo action. To assess the role of core convection in building magnetic fields within these stars, we employ the 3-D anelastic spherical harmonic (ASH) code to model turbulent dynamics within a 10 M⊙ main-sequence (MS) B-type star rotating at 4 Ω⊙. 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.

Global-scale wreath-building dynamos in stellar convection zones

AbstractWhen 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.

PERSISTENT MAGNETIC WREATHS IN A RAPIDLY ROTATING SUN

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 a system rotating at three 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 $\alpha$-effect explains the regeneration of poloidal field.

Modelling the Sun and Stars in 3-D

Stars can be seen as modern physics laboratory from which fundamental processes as diverse as atomic physics or turbulence can be studied and understood. Being able to model accurately their structure, dynamic and evolution is thus of fundamental importance and is the subject of intense research. In this short review we will present some of the numerical simulations in three dimensions performed in recent years to model such complex and nonlinear objects, focussing mostly our discussion on results obtained with the anelastic spherical harmonic (ASH) code. Using the Sun as a reference star, we wish to gain insight and to constrain magnetohydrodynamical processes (such as Reynolds and Maxwell stresses, meridional circulations, differential rotation (i.e. ω -effect), thermal wind, α -effect) at the origin of the solar small and large scale dynamics and magnetism. We will then extend our study to other stars, such as young Suns, massive stars or evolved RGB stars in order to identify which processes are at the origin of their significantly different dynamics.

NUMERICAL SIMULATIONS OF A ROTATING RED GIANT STAR. I. THREE-DIMENSIONAL MODELS OF TURBULENT CONVECTION AND ASSOCIATED MEAN FLOWS

With the development of one-dimensional stellar evolution codes including rotation and the increasing number of observational data for stars of various evolutionary stages, it becomes more and more possible to follow the evolution of the rotation profile and angular momentum distribution in stars. In this context, understanding the interplay between rotation and convection in the very extended envelopes of giant stars is very important considering that all low- and intermediate-mass stars become red giants after the central hydrogen burning phase. In this paper, we analyze the interplay between rotation and convection in the envelope of red giant stars using three-dimensional numerical experiments. We make use of the Anelastic Spherical Harmonics code to simulate the inner 50% of the envelope of a low-mass star on the red giant branch. We discuss the organization and dynamics of convection, and put a special emphasis on the distribution of angular momentum in such a rotating extended envelope. To do so, we explore two directions of the parameter space, namely, the bulk rotation rate and the Reynolds number with a series of four simulations. We find that turbulent convection in red giant stars is dynamically rich, and that it is particularly sensitive to the rotation rate of the star. Reynolds stresses and meridional circulation establish various differential rotation profiles (either cylindrical or shellular) depending on the convective Rossby number of the simulations, but they all agree that the radial shear is large. Temperature fluctuations are found to be large and in the slowly rotating cases, a dominant ? = 1 temperature dipole influences the convective motions. Both baroclinic effects and turbulent advection are strong in all cases and mostly oppose one another.

Stellar Convection and Magnetism across the H-R diagram: Theory and Models

Stars constitute undoublty one of the elementary blocks of the Universe and play as such a central role in determining for instance its chemical evolution. They can be seen as modern physics laboratory from which fundamental processes as diverse as atomic physics or turbulence can be studied and understood. Being able to model accurately their structure, dynamic and evolution is thus of fundamental importance and is the subject of intense research. In this short lecture we will first discuss the basic equations and processes, such as convection, turbulence, rotation, instabilities and dynamo action that are at the origin of the magnetic field observed in stars. We will then present some of the numerical simulations in three dimensions performed in recent years to model such complex objects and their nonlinear behavior, focussing mainly on results obtained with the anelastic spherical harmonic (ASH) code. Using the Sun as a reference star, we wish to gain insight the various magnetohydrodynamical processes that shape its large scale dynamics and magnetism, such as the Reynolds and Maxwell stresses, and the ω and α-effects. We will then extend our study to other stars, such as young Suns, massive stars or evolved RGB stars in order to identify which processes are at the origin of their significantly different dynamics.

3‐D non‐linear evolution of a magnetic flux tube in a spherical shell: The isentropic case

AbstractWe present recent 3‐D MHD numerical simulations of the non‐linear dynamical evolution of magnetic flux tubes in an adiabatically stratified convection zone in spherical geometry, using the anelastic spherical harmonic (ASH) code.We seek to understand the mechanism of emergence of strong toroidal fields from the base of the solar convection zone to the solar surface as active regions. We confirm the results obtained in cartesian geometry that flux tubes that are not twisted split into two counter vortices before reaching the top of the convection zone. Moreover, we find that twisted tubes undergo the poleward‐slip instability due to an unbalanced magnetic curvature force which gives the tube a poleward motion both in the non‐rotating and in the rotating case. This poleward drift is found to be more pronounced on tubes originally located at high latitudes. Finally, rotation is found to decrease the rise velocity of the flux tubes through the convection zone, especially when the tube is introduced at low latitudes. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Challenges of magnetism in the turbulent Sun

AbstractThree-dimensional global modelling of turbulent convection coupled to rotation and magnetism within the Sun are revealing processes relevant to many stars. We study spherical shells of compressible convection spanning many density scale heights using the MHD version of the anelastic spherical harmonic (ASH) code on massively parallel supercomputers. The simulations reveal that strong magnetic fields can be realized in the bulk of the solar convection zone while still attaining differential rotation profiles that make good contact with helioseismic findings. We find that the Maxwell and Reynolds stresses present in such a turbulent layer play an important role in redistributing angular momentum, with the latter maintaining the differential rotation, aided by baroclinic forcing at the base of the convection zone which is consistent with a tachocline there. The dynamo processes generate strong non-axisymmetric and intermittent fields and weak mean (axisymmetric) fields, but do not possess a regular cyclic magnetism. The explicit inclusion of penetrative convection into the tachocline below is modifying such behavior, serving to build strong toroidal magnetic fields there that may yield more prominent mean fields that have the potential of erupting upward.

Spectral magnetohydrodynamic simulations of the sun and stars

The purpose of this lecture is two fold: first, to describe a powerful numerical technic, namely the spectral method, to solve the compressible (anelastic) magnetohydrodynamic (MHD) equations in spherical geometry and then to discuss some recent numerical applications to study stellar dynamics and magnetism. We thus start by describing the semi-implicit, anelastic spherical harmonic (ASH) code. In this code, the main field variables are projected into spherical harmonics for their horizontal dimensions and into Chebyshev polynomials for their radial direction. We then present, high resolution 3–D MHD simulations of the convective region of A- and G-type stars in spherical shells. We have chosen to model A and G-type stars because they represent good proxies to study and understand stellar dynamics and magnetism given their strikingly different internal “up-side-down” structure and magnetic activity level. In particular, we discuss the nonlinear interactions between turbulent convection, rotation and magnetic fields and the possibility for such flows and fields to lead to dynamo action. We find that both core and envelope turbulent convective zones are efficient at inducing strong mostly non-axisymmetric fields near equipartition but at the expense of damping the differential rotation present in the purely hydrodynamic progenitor solutions.

Simulations of Core Convection in Rotating A‐Type Stars: Magnetic Dynamo Action

Core convection and dynamo activity deep within rotating A-type stars of 2 M☉ 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.

Magnetohydrodynamic 3-D Models of the Solar Convection Zone

We have conducted 3-D simulations of the complex magnetohydrodynamics of the solar convective envelope in spherical shells using our anelastic spherical harmonics (ASH) code (Brun & Toomre 2002). We here briefly discuss the properties of the kinetic and current helicities established in such systems.