Mark S. Miesch

Global-Scale Turbulent Convection and Magnetic Dynamo Action in the Solar Envelope

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.

THREE-DIMENSIONAL SPHERICAL SIMULATIONS OF SOLAR CONVECTION. I. DIFFERENTIAL ROTATION AND PATTERN EVOLUTION ACHIEVED WITH LAMINAR AND TURBULENT STATES

Rotationally constrained convection possesses velocity correlations that transport momentum and drive mean —ows such as diUerential rotation. The nature of this transport can be very complex in turbu- lent —ow regimes, where large-scale, coherent vorticity structures and mean —ows can be established by smaller scale turbulence through inverse cascades. The dynamics of the highly turbulent solar convection zone therefore may be quite diUerent than in early global-scale numerical models, which were limited by computational resources to nearly laminar —ows. Recent progress in high-performance computing tech- nology 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 ii banana cells,ˇˇ but the turbulent case is much more complex, with an intricate, rapidly evolving down- —ow 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 lati- tudes and retrograde at high latitudes relative to the local rotation. The diUerential rotation pro—les show some similarity with helioseismic determinations of the solar rotation but still exhibit signi—cantly more cylindrical alignment. Strong, intermittent, vortical down—ow lanes and plumes play an important dynamical role in turbulent —ow regimes and are responsible for signi—cant diUerences relative to laminar —ows with regard to momentum and energy transport and to the structure of the overshoot region at the base of the convection zone. Subject headings: convectionhydrodynamicsstars: interiorsSun: interiorSun: rotation ¨ turbulence

Solar Differential Rotation Influenced by Latitudinal Entropy Variations in the Tachocline

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 tachoclineinduced entropy variations in maintaining the solar differential rotation is discussed. Subject headingg convection — Sun: interior — Sun: rotation

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.

Structure and Evolution of Giant Cells in Global Models of Solar Convection

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.

DYNAMO ACTION IN THE SOLAR CONVECTION ZONE AND TACHOCLINE: PUMPING AND ORGANIZATION OF TOROIDAL FIELDS

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.

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.

Computational aspects of a code to study rotating turbulent convection in spherical shells

Abstract The coupling of highly turbulent convection with rotation within a full spherical shell geometry, such as in the solar convection zone, can be studied with the new anelastic spherical harmonic (ASH) code developed to exploit massively parallel architectures. Inter-processor transposes are used to ensure data locality in spectral transforms, a sophisticated load balancing algorithm is implemented and the Legendre transforms, which dominate the workload for large problems, are highly optimized by exploiting the features of cache memory and instruction pipelines. As a result, the ASH code achieves around 120 Mflop/s per node on the Cray T3E and scales nearly linearly for adequately large problem sizes.

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.