Solar Surface Dynamics convection & waves Bob Stein - MSU Dali Georgobiani - MSU Dave Bercik - MSU Regner Trampedach - MSU Aake Nordlund - Copenhagen Mats.

Solar Surface Dynamicsconvection & waves

Bob Stein - MSU

Dali Georgobiani - MSU

Dave Bercik - MSU

Regner Trampedach - MSU

Aake Nordlund - Copenhagen

Mats Carlsson - Oslo

Viggo Hansteen - Oslo

Andrew McMurry - Oslo

Tom Bogdan - HAOO

Simulations

Computation

• Solve– Conservation equations

• mass, momentum & internal energy

– Induction equation– Radiative transfer equation

• 3D, Compressible

• EOS includes ionization

• Open boundaries– Fix entropy of inflowing plasma at bottom

Equations

Method

• Spatial derivatives - Finite difference– 6th order compact or 3rd order spline

• Time advance - Explicit– 3rd order predictor-corrector or Runge-Kutta

• Diffusion∂f∂t

⎛

⎝ ⎜

⎞

⎠ ⎟ diffusive

=∇ •αν∇f

α =max|Δ3 f |−1,0,1( )

max|Δf |−1,0,1( )

Boundary Conditions

• Periodic horizontally• Top boundary: Transmitting

– Large zone, adjust < mass flux, ∂u/∂z=0, energy ≈ constant, drifts slowly with mean state

• Bottom boundary: Open, but No net mass flux– (Node for radial modes so no boundary work)– Specify entropy of incoming fluid at bottom – (fixes energy flux)

• Top boundary: B potential field• Bottom boundary: inflows advect 1G or 30G

horizontal field, or B vertical

Wave Reflection

Acoustic Wave Gravity wave

Radiation Transfer

• LTE

• Non-gray - multigroup

• Formal Solution Calculate J - B by integrating Feautrier equations along one vertical and 4 slanted rays through each grid point on the surface.

Simplifications

• Only 5 rays

• 4 Multi-group opacity bins

• Assume L C

Opacity is binned, according to its magnitude, into 4 bins.

• Wavelengths with same (z) are grouped together, so

• integral over and sum over commute

Advantage

integral over and sum over commute

Solar Magneto-Convection

Energy Fluxes

ionization energy 3X larger energy than thermal

Fluid Parcels

reaching the

surface Radiate away their

Energy and

Entropy

Z

SE

Q

Entropy

Green & blue are low entropy downflows, red is high entropy upflowsLow entropy plasma rains down from the surface

A Granule is a fountainvelocity arrows, temperature color

Stratified convective flow:diverging upflows, turbulent downflows

Velocity arrows, temperature fluctuation image (red hot, blue cool)

Vorticity

Downflows are turbulent, upflows are more laminar.

Velocity at Surface and Depth

Horizontal scale of upflows increases with depth.

Vorticitysurface and

depth.

Turbulent downdrafts

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Velocity Distribution

Up Down

Entropy Distribution

Vorticity Distribution

Down

Up

Magnetic Field Reorganization

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Simulation Results: B Field lines

Field Distribution

simulation observed

Both simulated and observed distributions are stretched exponentials.

Flux Emergence & Disappearance

Emerging Magnetic Flux Tube

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Magnetic Field Lines, t=0.5 min

Magnetic Field Lines, t=3.5 min

Magnetic Field Lines: t=6 min

Micropores

David Bercik - Thesis

Strong Field Simulation

• Initial Conditions– Snapshot of granular convection (6x6x3 Mm)– Impose 400G uniform vertical field

• Boundary Conditions– Top boundary: B -> potential field– Bottom boundary: B -> vertical

• Results– Micropores

Micropore

Intensity image + B contours @ 0.5 kG intervals (black) + Vz=0 contours (red).

“Flux Tube” Evacuationfield + temperature contours

“Flux Tube” Evacuationfield + density contours

Observables

)(kPk

Solar velocity spectrum

MDI doppler (Hathaway) TRACE correlation

tracking (Shine)

MDI correlation tracking (Shine)

3-D simulations (Stein & Nordlund)

v ~ k

v ~ k-1/3

!constant v ≈l

Line Profiles

Line profile without velocities. Line profile with velocities.

simulation

observed

Convection produces line shifts, changes in line widths. No microturbulence, macroturbulence.

Average profile is combination of lines of different shifts & widths.

average profile

Stokes Profiles of Flux Tubenew SVST, perfect seeing

Gra

nula

tion

Spectrum of granulation

Simulated intensity spectrum and distribution agree with observationsafter smoothing with telescope+seeing point spread function.

Granule Statistics

Emergent Intensity, mu=0.5

Magnetic Field Strength

Stokes Image - Quiet SunSynthetic Observation - La Palma Telescope MTF +

Moderate Seeing

Surface IntensityStokes V

6 Mm

6 MmQuickTime™ and a

decompressorare needed to see this picture.

Stokes Image - Quiet Sun Synthetic Observation - La Palma Telescope MTF +

Excellent Seeing


6 Mm



Stokes Image - Quiet Sun Synthetic Observation - Perfect Telescope & Seeing


6 Mm



Atmospheric DynamicsAtmospheric Dynamics

Dynamic Effects• Non-linear effects

– The mean of a dynamic atmosphere is not equal to a static atmosphere

– e.g. Planck function is a non-linear function of temperature, (except in the infrared)

– Trad > Tgas

• Slow rates– Not enough time to reach equilibrium– e.g. Ionization and recombination slow

compared to dynamic times in chromosphere electron density > than LTE

3D EffectsInhomogeneous T (see only cool gas), Pturb

Raises atmosphere 1 scale height

p-mode frequencies1D Standard model 3D Convection model

P-Mode Excitation

Modes are excited by PdV work of turbulent and non-adiabatic gas pressure fluctuations.

Pressure fluctuation Mode compression

Mode mass

P-Mode Excitation

Triangles = simulation, Squares = observations (l=0-3)Excitation decreases both at low and high frequencies

Excitation: Turbulence vs. Entropy

Excitation: Up vs. Down Flows

P-Mode Excitation

P-Mode excitation• Decreases at low frequencies because of

mode properties:– mode mass increases toward low frequencies– mode compression decreases toward low

frequencies

• Decreases at high frequencies because of convection properties:– Turbulent and non-adiabatic gas pressure

fluctuations produced by convection and convective motions are low frequency.

Fast & Slow MHD Waves, t=27.5

Fast magnetic wave Slow acoustic wave

Waves generated by piston in low beta strong magnetic field.

Velocity || B, t=58.5black lines=B, white lines = beta

Velocity B, t=58.5 sfast waves are refracting sideways & down

⊥

Fast & Slow MHD Waves - 2

Fast magnetic wave has passed through top of computational domain.

It is being refracted to the side and back down.

Slow acoustic wave propagates along B

Downward propagating fast waves couple to transmitted fast and slow waves at = 1 surfaceβ

Fast & Slow MHD Waves - 3

Slow acoustic wave shocks.

Downward propagating fast magnetic wave couples to fast acoustic and slow magnetic waves at the beta=1 surface.

The Future

• Supergranulation scale magneto-convection– What are supergranules? – Emergence of magnetic flux– Disappearance of magnetic flux– Maintenance of the magnetic network– Pores and sunspots

The End

Solar Surface Dynamics convection & waves Bob Stein - MSU Dali Georgobiani - MSU Dave Bercik - MSU Regner Trampedach - MSU Aake Nordlund - Copenhagen Mats.

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