Solar Convection Simulations

Bob Stein

David BensonQuickTime™ and aGIF decompressor

are needed to see this picture.

Solar Convection

1. Transports energy (from core nuclear reactions) through outer 1/3 of Sun

2. Drives the dynamics of the solar atmosphere

3. Generates the solar magnetic field

4. Excites the p-mode oscillations

The Simulation Code•Conservative Compressible (M)HD equations• LTE non-gray radiation transfer• Realistic tabular EOS and opacities

No free parameters (except for resolution & diffusion model).

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∂ρ∂t

= −∇ • ρu

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∂ρui∂t

= −∂

∂x jρuiu j + Pδij + ρυ

∂ui∂x j

+∂u j∂x i

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥+ ρgi + J × B( )i

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∂ρe∂t

= −∇ • ρeu− P∇ • u+ ρν∂ui∂x j

+∂u j∂x i

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2

+ηJ 2 +Qrad

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∂B∂t

= −∇ × E, E = −u× B +ηJ, J =∇ × B /μ0

48 Mm

48

Mm

20

Mm

(Developed with Danish collaborator Aake Nordlund)

Numerical Method

• Spatial differencing– 6th-order finite difference – Staggered variables

• Time advancement– 3rd order Runga-Kutta

• Parallelized– OpenMP,

single parallel region– Scales linearly from 64-250

processors as domain size increases

Results are used to:

• Understand spectral line-formation in the atmosphere

• Calculate the solar (and stellar) abundances• Understand the excitation of solar oscillations• Calibrate local helioseismic inversion methods• Study magnetic flux emergence• Calculate the influence of magnetic fields on

observables• Input to chromospheric & coronal modeling

Spectral Line Formation

1D models micro & macro-turbulence due to convective overshoot.

Spatially resolved profiles

New abundance determinations

Inhomogeneous T (see only cool gas), & Pturb

Raises atmosphere One scale height

3D atmosphere not same as 1D atmosphere

(By Martin Asplund and former grad student Regner Trampedach)

Acoustic (p-mode) Oscillations

Observed Simulated

P-Modes Excitedby PdV work

Triangles = simulation, Squares = observations (l=0-3)

Excitation decreases at lowfrequencies because oscillationmode inertia increases andcompressibility (dV) decreases.

Excitation decreases at highfrequencies because convectivepressure fluctuations have longperiods.

(by former grad. studentsDali Georgobiani & Regner Trampedach)

Local Helioseismologyuses wave travel times through the atmosphere

(by former grad. Student Dali Georgobiani)

Magnetic Flux Emergence

Magnetic field lines rise up through theatmosphere and open out to space

QuickTime™ and aGIF decompressor

are needed to see this picture.

G-bandimages from simulation

at disk center & towards limb

(by Norwegian collaboratorMats Carlsson)

Notice:Hilly appearance of granulesBright points, where magnetic field is strongStriated bright walls of granules, when looking through magnetic fieldDark micropore, where especially large magnetic flux