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

Matthew BrowningMatthew Browning

Sacha BrunSacha Brun

Juri ToomreJuri Toomre

JILA, Univ Colorado, and JILA, Univ Colorado, and CEA-SaclayCEA-Saclay

Motivating issues Motivating issues for 3-D simulationsfor 3-D simulations

• What is nature of penetration and What is nature of penetration and overshooting from convective overshooting from convective cores?cores?

• Does the convection drive Does the convection drive differential rotationdifferential rotation within the core, and in what manner?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 If so, what are the properties of the

magnetism, and in what way does it feed magnetism, and in what way does it feed back upon the flows?back upon the flows?

Computational Computational Approach for 3-D Approach for 3-D

Simulations Simulations

• Utilize 3-D Utilize 3-D Anelastic Spherical HarmonicAnelastic Spherical Harmonic (ASH) code in full spherical geometry(ASH) code in full spherical geometry

• Simulate 2 solar mass stars, at 1 to 4 times Simulate 2 solar mass stars, at 1 to 4 times solar rotation ratesolar rotation rate

• Model dynamics of inner 30% of star (CZ + Model dynamics of inner 30% of star (CZ + portion of RZ), excluding innermost 3%portion of RZ), excluding innermost 3%

• Realistic stratification, radiative opacityRealistic stratification, radiative opacity• Simplified physics: perfect gas, subgrid Simplified physics: perfect gas, subgrid

turbulent transportturbulent transport

Vigorous convection in the coreVigorous convection in the core

Radial velocity Radial velocity VVrr

at mid-core in at mid-core in hydro simulationshydro simulations

Broad, sweeping Broad, sweeping flows that evolveflows that evolve

Browning, Brun & Browning, Brun & Toomre (2004), Toomre (2004), ApJ v. 601, 512ApJ v. 601, 512

Evolution of convective patternsEvolution of convective patterns

Radial velocity in longitude-latitude mappingRadial velocity in longitude-latitude mapping

Propagation and shearing of patternsPropagation and shearing of patterns

Prograde propagation at Prograde propagation at equator, retrograde at polesequator, retrograde at poles

Global viewsGlobal views Time-longitude mapsTime-longitude maps

VVrr

Penetration into radiative envelopePenetration into radiative envelope

Prolate convective core, spherical overshooting regionProlate convective core, spherical overshooting region

Variation of penetration with Variation of penetration with radiative zone stiffnessradiative zone stiffness

• Simulations Simulations provide provide upper upper boundbound to extent of to extent of overshootingovershooting

• In stiffest, most In stiffest, most turbulent case:turbulent case:

ddovov ~ 0.21 ~ 0.21+/- 0.05+/- 0.05 H Hpp

stifferstiffer

Character of Character of differential rotationdifferential rotation

• Central columns of Central columns of slow rotation slow rotation

• More turbulent flows More turbulent flows yield greater angular yield greater angular velocity contrastsvelocity contrasts

laminarlaminar

turbulentturbulent

Angular momentum transportAngular momentum transport

Analysis of fluxes reveals crucial role of nonlinear Reynolds Analysis of fluxes reveals crucial role of nonlinear Reynolds stresses to establish differential rotationstresses to establish differential rotation

RR

VVMM

MM

VV

RR

radiusradius latitudelatitude

Dynamo activity in new MHD modelsDynamo activity in new MHD models

Convective motions amplify a tiny seed field by many Convective motions amplify a tiny seed field by many orders of magnitudeorders of magnitude

With increasingWith increasingME, drop in KEME, drop in KE

Final ME Final ME ~ 90% KE~ 90% KE

MEME

KEKE

timetime

Intricate Intricate magnetic magnetic

fieldfield

Evolving Evolving banded banded azimuthal fieldazimuthal field

Radial Radial field in field in

cutawaycutaway

Complexity in Complexity in interleaved interleaved radial fieldsradial fields

Topology of core magnetismTopology of core magnetism

• Field on finer scales than flow (Field on finer scales than flow (PPmm > 1) > 1)

• Tangled radial field, but Tangled radial field, but BB organized into ribbon-like structures organized into ribbon-like structures

VVrr BBBBrr

Global views of complex structuresGlobal views of complex structures

VVrr

BB

BBrr

Evolution seen in time-longitude mapsEvolution seen in time-longitude maps

VVrr

BBrr

Magnetism reduces differential rotationMagnetism reduces differential rotation

Angular velocity contrasts lessened by magnetic field Angular velocity contrasts lessened by magnetic field

MHDMHD HYDROHYDRO

Interplay of rotation and magnetismInterplay of rotation and magnetism

MEME

DRKE minimaDRKE minima

Differential rotation quenched when ME > ~ 40% KEDifferential rotation quenched when ME > ~ 40% KE

Fluctuating and mean magnetic fieldsFluctuating and mean magnetic fields

Fluctuating fields much stronger than mean fieldsFluctuating fields much stronger than mean fields

total MEtotal ME

TMETME

PMEPME

FMEFME

radiusradius

Wandering of the polesWandering of the poles

Our findingsOur findings• Global simulations of magnetized Global simulations of magnetized

core convection reveal core convection reveal dynamo dynamo actionaction, , differential rotationdifferential rotation andand prolate penetrationprolate penetration

• Resulting complex magnetic fields weaken Resulting complex magnetic fields weaken differential rotationdifferential rotation

• Core magnetic fields likely screened by Core magnetic fields likely screened by radiative enveloperadiative envelope

• Possibly magnetic buoyancy instability could Possibly magnetic buoyancy instability could bring fields outwardbring 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 totalangular 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 2Msol Star

Star Properties

M=2Msol, Teff=8570 KR=1.9 Rsol, L=19 Lsol

=sol or =2sol

P=28 days or 14 days

Eq of State = Ideal Gas LawNuclear energy source ~ 0T8

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

RR

V

VMC

MC

totaltotal

Mean Overshooting Extent in 2Msol Star

1D modeldS/dr~10-2

MoreComplex

flows

Pressure Scale HeightHp~8 109 cm

Stiffer Stratification for Radiative Envelope

For our stiffest and morecomplex case we find a

mean overshooting extent d~0.21+/- 0.05 Hp

Baroclinicity

A variation of few degree K between the equator (cold) and the poles (hot) is established for a contrast of ofBut angular velocity is mostly dynamicalin origin.

difference b-cV dV/dz cst*dS/d