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Published byDominick Cummings Modified over 8 years ago
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Simulated Solar Plages Robert Stein, David Benson - Mich. State Univ. USA Mats Carlsson - University of Oslo, NO Bart De Pontieu - Lockheed Martin Solar & Astrophysics Lab., USA Goran Scharmer - Royal Swedish Academy of Sciences, SE Aake Nordlund - Copenhagen University, DK
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Movie by Mats Carlsson
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METHOD Solve conservation equations for: mass, momentum, internal energy & induction equation
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Conservation Equations Mass Momentum Energy Magnetic Flux
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Numerical Method Spatial differencing –6 th -order staggered finite difference, 3 points either side Spatial interpolation –5 th order, staggered Time advancement –3 rd order Runga-Kutta
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Radiation Heating/Cooling LTE Non-gray, 4 bin multi-group Formal Solution Calculate J - B by integrating Feautrier equations along one vertical and 4 slanted rays through each grid point on the surface. Produces low entropy plasma whose buoyancy work drives convection
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5 Rays Through Each Surface Grid Point Interpolate source function to rays at each height
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Opacity is binned, according to its magnitude, into 4 bins.
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Solve Transfer Equation for each bin i
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Equation of State Tabular EOS includes ionization, excitation H, He, H 2, other abundant elements
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Boundary Conditions Ghost zones loaded Density: top hydrostatic, bottom logarithmic Velocity: symmetric (normal derivative =0) Energy (per unit mass): top = slowly evolving average, bottom fixed entropy in inflows Magnetic (Electric field): top -> potential, bottom -> fixed value in inflows, damped in outflows
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Fluid Parcels reaching the surface Radiate away their Energy and Entropy Z S E Q
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Unipolar Field Impose uniform vertical field on snapshot of hydrodynamic convection Boundary Conditions: B -> potential at top, B vertical at bottom B rapidly swept into intergranular lanes
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Magnetic Field Lines - initially vertical
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Magnetic Field & Velocity (@ surface) Up Down
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G-band image & magnetic field contours (-.3,1,2 kG)
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G-band Bright Points = large B, but some large B dark
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G-band & Magnetic Field Contours:.5, 1, 1.5 kG (gray) 20 G (red/green)
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G-band images from simulation at disk center & towards limb (by Mats Carlsson) Notice: Hilly appearance of granules Striated bright walls of granules Micropore at top center Dark bands moving across granules
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Comparison with observations Simulation, mu=0.6 Observation, mu=0.63
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Center to Limb Movie by Mats Carlsson
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G-Band Center to Limb Appearance
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Individual features
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Magnetic field
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Vertical velocity
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Height where tau=1
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Temperature structure
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Magnetic concentrations: cool, low low opacity. Towards limb, radiation emerges from hot granule walls behind. On optical depth scale, magnetic concentrations are hot, contrast increases with opacity
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G-band images from simulation at disk center & towards limb (by Mats Carlsson) Notice: Dark bands moving across granules
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Temperature fluctuations + Velocity
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The End
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