Radiative%20Transfer%20for%20Simulations%20of%20Stellar%20Envelope%20Convection

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Radiative Transfer for Simulations of
StellarEnvelope Convection

• By
• Regner Trampedach
• 8/19/04

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Hydro-dynamics

• Solve Euler equations
• Conservation of
• Mass d? /dt -u ? ? -? ? u
• Momentum ? du /dt -? u ? u ? (T - Pgas) ?
  g
• Energy dE /dt -? uE (T - Pgas)?
  u ? qrad
• Regular horizontal and optimized vertical grid

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(No Transcript)
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Vertical Temperature-cut of ? -Boo
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Applications of the Simulations

• Improving stellar structure models
• T-t -relations atmospheric boundary cond.
• Calibration of the mixing-length parameter, a
• Abundance analysis
• Agreement between FeI, FeII and meteoritic
• Lower C, N and O abundances at odds with
  helioseismology
• Synthetic spectra/line-profiles
• No free parameters, e.g., micro-/macro-turb.

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Input Physics

• Equation of State (EOS)
• Pressure for hydro-static support
• Response to temperature-/density-changes
• Opacity ff bf bb
• radiative transfer gt
• radiative heating qrad,? 4p ? ? (J?-S? )

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FeI Opacity According to LAOL

• Hübner et. Al (1977)
• Semi-hydrogenic wave-functions
• Hundreds of lines...

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FeI Opacity According to OP

• Seaton et. Al (1994)
• Intermediate S-L coupling
• Hundreds of millions of lines!

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bf-Opacity Before OP/OPAL

• From Peach (1962)

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Confronting Experiment

• From Nahar, S. N., 2003, Phys. Rev. A (submitted)

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Radiative Transfer

• Determines heating/cooling gt structure
• Determines emergent flux/intensity gt link to
  observations
• Transfer Eq. d I? /dt ? (I? S? ) solved
  for more than 105 wavelengths
• Not possible in convection simulations

• Yet...

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Statistical Methods

• Have used opacity binning (Nordlund 1982) a.k.a.
  the multi-group method
• Works well, and has correct asymptotic behaviour
  in optical thick/thin cases
• Employs a number of somewhat arbitrary bridging
  functions and extrapolations
• Does not converge for N bin? 8

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Selective/Sparse Opacity Sampling
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S O S

• Carefully select NSOS wavelengths
• covering the whole energy spectrum
• that reproduce the full solution, e.g., heating
  qrad, flux Frad, and J and K.
• Perform radiative transfer on those ?
• Paves the way for including velocity-effects
• Spans the convective fluctuations better than the
  opacity binning method
• Converges for NSOS? 8

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Multi-group vs. SOS

• SOS, N? 50
• Monochrome, ODF, N? 2750
• Multi-group, Nbin4

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Horizontal and temporal averages

• 50 bins same as 4 bins!
• Too little cooling in conv/rad trans.
• Too little heating in lower photosph.
• No action at or above T-min

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- and their differences

• ___ straight average
• - - - RMS average
• Systematic diffs for multi-group
• gt4 times larger RMS differences

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Summary

• Developed new radiative transfer scheme
• Performs better than multi-group method
• Much closer to monochromatic solution
• More stable against convective fluctuations
• Reproduce first three moments of I(µ )
• Convergent for NSOS? 8

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Prospects for the Future

• Calculate new and improved EOS-tables
• Use it as basis for new opacity calculation using
  the newest cross-section data
• Implement the SOS radiative transfer scheme in
  the convection simulations
• Build a grid of convection models, using the new
  EOS, opacities and SOS scheme