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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 QuickTime™ and a YUV420 codec decompressor are needed to see this picture. Velocity Distribution Up Down Entropy Distribution Vorticity Distribution Down Up Magnetic Field Reorganization QuickTime™ and a decompressor are needed to see this picture. Simulation Results: B Field lines Field Distribution observed simulation Both simulated and observed distributions are stretched exponentials. Flux Emergence & Disappearance Emerging Magnetic Flux Tube QuickTime™ and a YUV420 codec decompressor are needed to see this picture. 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 QuickTime™ and a decompressor are needed to see this picture. 6 Mm 6 Mm Stokes Image - Quiet Sun Synthetic Observation - La Palma Telescope MTF + Excellent Seeing Stokes V Surface Intensity QuickTime™ and a decompressor are needed to see this picture. 6 Mm 6 Mm Stokes Image - Quiet Sun Synthetic Observation - Perfect Telescope & Seeing Stokes V Surface Intensity QuickTime™ and a decompressor are needed to see this picture. 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