Benjamin P. Brown

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 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.

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 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.

Rapidly Rotating Suns and Active Nests of Convection

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.

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 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.

PROPERTIES OF 42 SOLAR-TYPE KEPLER TARGETS FROM THE ASTEROSEISMIC MODELING PORTAL

Recently the number of main-sequence and subgiant stars exhibiting solar-like oscillations that are resolved into individual mode frequencies has increased dramatically. While only a few such data sets were available for detailed modeling just a decade ago, the Kepler mission has produced suitable observations for hundreds of new targets. This rapid expansion in observational capacity has been accompanied by a shift in analysis and modeling strategies to yield uniform sets of derived stellar properties more quickly and easily. We use previously published asteroseismic and spectroscopic data sets to provide a uniform analysis of 42 solar-type Kepler targets from the Asteroseismic Modeling Portal. We find that fitting the individual frequencies typically doubles the precision of the asteroseismic radius, mass, and age compared to grid-based modeling of the global oscillation properties, and improves the precision of the radius and mass by about a factor of three over empirical scaling relations. We demonstrate the utility of the derived properties with several applications.

BUOYANT MAGNETIC LOOPS IN A GLOBAL DYNAMO SIMULATION OF A YOUNG SUN

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.

Buoyant Magnetic Loops Generated by Global Convective Dynamo Action

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.

ENERGY CONSERVATION AND GRAVITY WAVES IN SOUND-PROOF TREATMENTS OF STELLAR INTERIORS. PART I. ANELASTIC APPROXIMATIONS

Typical flows in stellar interiors are much slower than the speed of sound. To follow the slow evolution of subsonic motions, various sound-proof equations are in wide use, particularly in stellar astrophysical fluid dynamics. These low-Mach number equations include the anelastic equations. Generally, these equations are valid in nearly adiabatically stratified regions like stellar convection zones, but may not be valid in the sub-adiabatic, stably stratified stellar radiative interiors. Understanding the coupling between the convection zone and the radiative interior is a problem of crucial interest and may have strong implications for solar and stellar dynamo theories as the interface between the two, called the tachocline in the Sun, plays a crucial role in many solar dynamo theories. Here, we study the properties of gravity waves in stably stratified atmospheres. In particular, we explore how gravity waves are handled in various sound-proof equations. We find that some anelastic treatments fail to conserve energy in stably stratified atmospheres, instead conserving pseudo-energies that depend on the stratification, and we demonstrate this numerically. One anelastic equation set does conserve energy in all atmospheres and we provide recommendations for converting low-Mach number anelastic codes to this set of equations.

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

The 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)

Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors. II. Lagrangian Constrained Analysis

The speed of sound greatly exceeds typical flow velocities in many stellar and planetary interiors. To follow the slow evolution of subsonic motions, various sound-proof models attempt to remove fast acoustic waves while retaining stratified convection and buoyancy dynamics. In astrophysics, anelastic models typically receive the most attention in the class of sound-filtered stratified models. Generally, anelastic models remain valid in nearly adiabatically stratified regions like stellar convection zones, but may break down in strongly sub-adiabatic, stably stratified layers common in stellar radiative zones. However, studying stellar rotation, circulation, and dynamos requires understanding the complex coupling between convection and radiative zones, and this requires robust equations valid in both regimes. Here we extend the analysis of equation sets begun in Brown et al., which studied anelastic models, to two types of pseudo-incompressible models. This class of models has received attention in atmospheric applications, and more recently in studies of white-dwarf supernova progenitors. We demonstrate that one model conserves energy but the other does not. We use Lagrangian variational methods to extend the energy conserving model to a general equation of state, and dub the resulting equation set the generalized pseudo-incompressible (GPI) model. We show that the GPI equations suitably capture low-frequency phenomena in both convection and radiative zones in stars and other stratified systems, and we provide recommendations for converting low-Mach number codes to this equation set.