Simulations of Core Convection and Dynamo Activity in A-type Stars Matthew Browning Sacha Brun Juri Toomre JILA, Univ Colorado, and CEA-Saclay

Motivating issues for 3-D simulations What is nature of penetration and overshooting from convective cores?What is nature of penetration and overshooting from convective cores? Does the convection drive differential rotation within the core, and in what manner?Does the convection drive differential rotation within the core, and in what manner? Is magnetic dynamo action realized?Is magnetic dynamo action realized? If so, what are the properties of the magnetism, and in what way does it feed back upon the flows?If so, what are the properties of the magnetism, and in what way does it feed back upon the flows?

Computational Approach for 3-D Simulations Utilize 3-D Anelastic Spherical Harmonic (ASH) code in full spherical geometryUtilize 3-D Anelastic Spherical Harmonic (ASH) code in full spherical geometry Simulate 2 solar mass stars, at 1 to 4 times solar rotation rateSimulate 2 solar mass stars, at 1 to 4 times solar rotation rate Model dynamics of inner 30% of star (CZ + portion of RZ), excluding innermost 3%Model dynamics of inner 30% of star (CZ + portion of RZ), excluding innermost 3% Realistic stratification, radiative opacityRealistic stratification, radiative opacity Simplified physics: perfect gas, subgrid turbulent transportSimplified physics: perfect gas, subgrid turbulent transport

Vigorous convection in the core Radial velocity V r at mid-core in hydro simulations Broad, sweeping flows that evolve Browning, Brun & Toomre (2004), ApJ v. 601, 512

Evolution of convective patterns Radial velocity in longitude-latitude mapping

Propagation and shearing of patterns Prograde propagation at equator, retrograde at poles Prograde propagation at equator, retrograde at poles Global views Time-longitude maps VrVrVrVr

Penetration into radiative envelope Prolate convective core, spherical overshooting region

Variation of penetration with radiative zone stiffness Simulations provide upper bound to extent of overshootingSimulations provide upper bound to extent of overshooting In stiffest, most turbulent case:In stiffest, most turbulent case: d ov ~ / H p stiffer

Character of differential rotation Central columns of slow rotationCentral columns of slow rotation More turbulent flows yield greater angular velocity contrastsMore turbulent flows yield greater angular velocity contrasts laminar turbulent

Angular momentum transport Analysis of fluxes reveals crucial role of nonlinear Reynolds stresses to establish differential rotation Analysis of fluxes reveals crucial role of nonlinear Reynolds stresses to establish differential rotation R V M M V R radius latitude

Dynamo activity in new MHD models Convective motions amplify a tiny seed field by many orders of magnitude With increasing ME, drop in KE Final ME ~ 90% KE ME KE time

Intricate magnetic field Evolving banded azimuthal field

Radial field in cutaway Complexity in interleaved radial fields

Topology of core magnetism Field on finer scales than flow (P m > 1)Field on finer scales than flow (P m > 1) Tangled radial field, but B  organized into ribbon-like structuresTangled radial field, but B  organized into ribbon-like structures VrVrVrVr BBBB BrBrBrBr

Global views of complex structures VrVrVrVr BBBB BrBrBrBr

Evolution seen in time-longitude maps VrVrVrVr BrBrBrBr

Magnetism reduces differential rotation Angular velocity contrasts lessened by magnetic field MHDHYDRO

Interplay of rotation and magnetism ME DRKE minima Differential rotation quenched when ME > ~ 40% KE

Fluctuating and mean magnetic fields Fluctuating fields much stronger than mean fields total ME TME PME FME radius

Wandering of the poles

Our findings Global simulations of magnetized core convection reveal dynamo action, differential rotation and prolate penetrationGlobal simulations of magnetized core convection reveal dynamo action, differential rotation and prolate penetration Resulting complex magnetic fields weaken differential rotationResulting complex magnetic fields weaken differential rotation Core magnetic fields likely screened by radiative envelopeCore magnetic fields likely screened by radiative envelope Possibly magnetic buoyancy instability could bring fields outwardPossibly magnetic buoyancy instability could bring fields outward

Angular Momentum Flux Transport of angular momentum by diffusion, advection and meridional circulation Because of our choice of stress free boundary conditions, the total angular momentum L is conserved. Its transport can be expressed as the sum of 3 fluxes (non magnetic case): F_tot = F_viscous + F_Reynolds + F_meridional_circulation Or in spherical coordinates:

Model’s Parameters for a 2M sol Star Star Properties M=2M sol, T eff =8570 K R=1.9 R sol, L=19 L sol  =  sol or  =2  sol P=28 days or 14 days Eq of State = Ideal Gas Law Nuclear energy source ~  0 T 8 No composition gradient  Innermost Core r~0.02R omitted Numerical methods: anelastic approximation, spectral code (spherical harmonics in (  ) & Chebyshev polynomials in r),semi-implicit temporal scheme. Cartoon view

The transport of angular momentum by the Reynolds stresses is directed toward the equator (opposite to meridional circulation) and is at the origin of the equatorial acceleration Angular Momentum Balance R R V V MC total

Mean Overshooting Extent in 2M sol Star 1D model dS/dr~10 -2 More Complex flows Pressure Scale Height Hp~ cm Stiffer Stratification for Radiative Envelope For our stiffest and more complex case we find a mean overshooting extent d~0.21+/ Hp

Baroclinicity A variation of few degree K between the equator (cold) and the poles (hot) is established for a contrast of  of  But angular velocity is mostly dynamical in origin. difference b-cVV dV  /dz cst*dS/d 