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Simulations of Core Convection and Dynamo Activity in A-type Stars

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?.

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Simulations of Core Convection and Dynamo Activity in A-type Stars

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

  2. Motivating issues for 3-D simulations • What is nature of penetration and overshooting from convective cores? • Does the convection drive differential rotation within the core, and in what manner? • 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?

  3. Computational Approach for 3-D Simulations • Utilize 3-D Anelastic Spherical Harmonic (ASH) code in full spherical geometry • Simulate 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% • Realistic stratification, radiative opacity • Simplified physics: perfect gas, subgrid turbulent transport

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

  5. Evolution of convective patterns Radial velocity in longitude-latitude mapping

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

  7. Penetration into radiative envelope Prolate convective core, spherical overshooting region

  8. Variation of penetration with radiative zone stiffness • Simulations provide upper bound to extent of overshooting • In stiffest, most turbulent case: dov ~ 0.21+/- 0.05 Hp stiffer

  9. Character of differential rotation • Central columns of slow rotation • More turbulent flows yield greater angular velocity contrasts laminar turbulent

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

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

  12. Intricate magnetic field Evolving banded azimuthal field

  13. Radial field in cutaway Complexity in interleaved radial fields

  14. Topology of core magnetism • Field on finer scales than flow (Pm > 1) • Tangled radial field, but B organized into ribbon-like structures Vr Br B

  15. Global views of complex structures Vr Br B

  16. Evolution seen in time-longitude maps Vr Br

  17. Magnetism reduces differential rotation Angular velocity contrasts lessened by magnetic field MHD HYDRO

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

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

  20. Wandering of the poles

  21. Our findings • Global simulations of magnetized core convection reveal dynamo action, differential rotationandprolate penetration • Resulting complex magnetic fields weaken differential rotation • Core magnetic fields likely screened by radiative envelope • Possibly magnetic buoyancy instability could bring fields outward

  22. Angular Momentum Flux 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: Transport of angular momentum by diffusion, advection and meridional circulation

  23. Model’s Parameters for a 2Msol Star Cartoon view Star Properties M=2Msol, Teff=8570 K R=1.9 Rsol, L=19 Lsol W=Wsol or W=2Wsol P=28 days or 14 days Eq of State = Ideal Gas Law Nuclear energy source ~ re0T8 No composition gradient m Innermost Core r~0.02R omitted Numerical methods:anelastic approximation, spectral code (spherical harmonics in (q,j) & Chebyshev polynomials in r),semi-implicit temporal scheme.

  24. Angular Momentum Balance R R total total V MC V MC The transport of angular momentum by theReynolds stressesis directed toward the equator (opposite to meridional circulation) and is at theorigin of the equatorial acceleration

  25. For our stiffest and morecomplex case we find a mean overshooting extent d~0.21+/- 0.05 Hp Mean Overshooting Extent in 2Msol Star Pressure Scale Height Hp~8 109 cm More Complex flows Stiffer Stratification for Radiative Envelope 1D model dS/dr~10-2

  26. Baroclinicity Vj dVj/dz cst*dS/dq difference b-c A variation of few degree K between the equator (cold) and the poles (hot) is established for a contrast of W of 30%. But angular velocity is mostly dynamical in origin.

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