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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?. - PowerPoint PPT Presentation
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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