Post on 21-Dec-2015
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
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
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
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.
• Wavelengths with same (z) are grouped together, so
• integral over and sum over commute
Advantage
integral over and sum over commute
Entropy
Green & blue are low entropy downflows, red is high entropy upflowsLow entropy plasma rains down from the surface
Stratified convective flow:diverging upflows, turbulent downflows
Velocity arrows, temperature fluctuation image (red hot, blue cool)
Field Distribution
simulation observed
Both simulated and observed distributions are stretched exponentials.
Emerging Magnetic Flux Tube
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
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
)(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
Convection produces line shifts, changes in line widths. No microturbulence, macroturbulence.
Average profile is combination of lines of different shifts & widths.
average profile
Spectrum of granulation
Simulated intensity spectrum and distribution agree with observationsafter smoothing with telescope+seeing point spread function.
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
Surface IntensityStokes V
6 Mm
6 MmQuickTime™ and a
decompressorare needed to see this picture.
Stokes Image - Quiet Sun Synthetic Observation - Perfect Telescope & Seeing
Surface IntensityStokes V
6 Mm
6 MmQuickTime™ and a
decompressorare needed to see this picture.
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
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
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.
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
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