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Radiative Transfer in 3D Numerical Simulations Robert Stein Department of Physics and Astronomy Michigan State University Åke Nordlund Niels Bohr Institute for Astronomy, Physics, and Geophysics University of Copenhagen
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Radiative Transfer Produces low entropy plasma whose buoyancy work drives convection Determines (with convection and waves) mean atmospheric structure Provides diagnostics of velocity, temperature and magnetic field Reverses p-mode intensity vs. velocity asymmetry
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Energy Conservation Radiative Heating/Cooling
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Radiation Transfer LTE Non-gray Formal Solution Calculate J - B by integrating Feautrier equations along one vertical and 4 slanted rays through each grid point on the surface.
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Solve Feautrier equations along rays through each grid point at the surface
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5 Rays Through Each Surface Grid Point Interpolate source function to rays at each height
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Actually solve for q = P - B
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Finite Difference Equation Problem: at small optical depth the 1 is lost re 1/ 2 in B Solution: store the value - 1, (the sum of the elements in a row) and calculate B = - (1+A+B)
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Interpolate q=P-B from slanted grid back to Cartesian grid
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Simplifications Only 5 rays 4 Multi-group opacity bins Assume L C
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Opacity is binned, according to its magnitude, into 4 bins.
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Line opacities are assumed proportional to the continuum opacity Weight = number of wavelengths in bin
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Advantage Wavelengths with same (z) are grouped together, so integral over and sum over commute
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Radiative Heating/Cooling
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Fluid Parcels that reach the surface Radiate away their Energy and Entropy Z S E Q
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Granulation
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Spectrum of granulation agrees with observations
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Line Profiles
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Convection produces line shifts, changes in line widths. No microturbulence, damping.
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Never See Hot Gas
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3D atmosphere is hotter than 1D atmosphere emitting the same flux, 3D atmosphere is more extended
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Extended atmosphere gives better agreement with p-mode frequencies
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Stokes Profiles - Micropore Synthetic Observation - Perfect Telescope & Seeing
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Stokes Image - Quiet Sun Synthetic Observation - La Palma Telescope MTF + Moderate Seeing Surface IntensityStokes V 6 Mm
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Stokes Image - Quiet Sun Synthetic Observation - La Palma Telescope MTF + Excellent Seeing Surface IntensityStokes V 6 Mm
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Stokes Image - Quiet Sun Synthetic Observation - Perfect Telescope & Seeing Surface IntensityStokes V 6 Mm
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P-Mode Intensity - Velocity Phase
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At fixed height V & T have same profile. Radiation reduces T - more at low
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Height of = 1 varies more at low frequencies where T larger - Reduces T more
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P-Mode Excitation
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The End
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