Download The Dynamic Sun

Solar Surface Dynamics
convection & 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 
 
    f
t diffusive
max | 3 f | 1,0,1 

max | f |1, 0,1 
Boundary Conditions
• Periodic horizontally
• Top boundary: Transmitting
– Large zone, adjust <r>  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 kL kC
Opacity is binned, according to
its magnitude, into 4 bins.
Advantage
• Wavelengths with same t(z) are grouped
together, so
• integral over
t and sum over l 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
t
r
Q
E
S
Entropy
Green & blue are low entropy downflows, red is high entropy upflows
Low entropy plasma rains down from the surface
A Granule is a fountain
velocity 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.
Vorticity
surface 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
observed
simulation
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” Evacuation
field + temperature contours
“Flux Tube” Evacuation
field + density contours
Observables
Solar velocity spectrum
3-D
k P(k
) simulations
(Stein & Nordlund)
MDI correlation
tracking (Shine)
v  constant !
MDI doppler
(Hathaway)
TRACE correlation
tracking (Shine)
v~k
v ~ k-1/3
Line Profiles
observed
simulation
Line profile without velocities.
Line profile with velocities.
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 Tube
new SVST, perfect seeing
Granulation
Spectrum of granulation
Simulated intensity spectrum and distribution agree with observations
after smoothing with telescope+seeing point spread function.
Granule Statistics
Emergent Intensity, mu=0.5
Magnetic Field Strength
Stokes Image - Quiet Sun
Synthetic Observation - La Palma Telescope MTF +
Moderate Seeing
Stokes V
Surface Intensity
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6 Mm
6 Mm
Stokes Image - Quiet Sun
Synthetic Observation - La Palma Telescope MTF +
Excellent Seeing
Stokes V
Surface Intensity
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6 Mm
6 Mm
Stokes Image - Quiet Sun
Synthetic Observation - Perfect Telescope & Seeing
Stokes V
Surface Intensity
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6 Mm
6 Mm
Atmospheric 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 Effects
Inhomogeneous T (see only cool gas), Pturb
Raises atmosphere 1 scale height
p-mode frequencies
1D 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=58.5
black lines=B, white lines = beta
Velocity  B, t=58.5 s
fast waves are refracting sideways & down
Fast & Slow MHD Waves - 2
Slow acoustic wave propagates along B
Fast magnetic wave has passed through top of computational domain.
It is being refracted to the side and back down.
Downward propagating fast waves couple to
transmitted fast and slow waves at  = 1 surface
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