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Radiative Transfer for Simulations of Stellar Envelope Convection

Radiative Transfer for Simulations of Stellar Envelope Convection. By Regner Trampedach 8/19/04. Hydro-dynamics. Solve Euler equations Conservation of: Mass: d ρ / d t = - u ∙ ∇ ρ - ρ ∇ ∙ u Momentum: ρ d u / d t = - ρ u ∙ ∇ u + ∇ ( T - P gas ) + ρ g

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Radiative Transfer for Simulations of Stellar Envelope Convection

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  1. Radiative Transfer for Simulations of StellarEnvelope Convection By Regner Trampedach 8/19/04

  2. Hydro-dynamics • Solve Euler equations • Conservation of: • Mass: dρ /dt= -u∙∇ρ-ρ∇∙u • Momentum: ρdu/dt= -ρu∙∇u+∇(T-Pgas)+ρ g • Energy: dE/dt = -∇∙uE +(T-Pgas)∇∙u+ρ qrad • Regular horizontal and optimized vertical grid

  3. Vertical Temperature-cut of η -Boo

  4. Applications of the Simulations • Improving stellar structure models • T-τ-relations – atmospheric boundary cond. • Calibration of the mixing-length parameter, α • 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.

  5. Input Physics • Equation of State (EOS) • Pressure for hydro-static support • Response to temperature-/density-changes • Opacity: ff + bf + bb • radiative transfer => • radiative heating: qrad,λ = 4πκ λ(Jλ-Sλ )

  6. FeI Opacity According to LAOL • Hübner et. Al (1977) • Semi-hydrogenic wave-functions • Hundreds of lines...

  7. FeI Opacity According to OP • Seaton et. Al (1994) • Intermediate S-L coupling • Hundreds of millions of lines!

  8. bf-Opacity Before OP/OPAL From Peach (1962)

  9. Confronting Experiment From Nahar, S.N., 2003, Phys. Rev. A (submitted)

  10. Yet... Radiative Transfer • Determines heating/cooling => structure • Determines emergent flux/intensity => link to observations • Transfer Eq. dIλ /dτ λ = (Iλ– Sλ ) solved for more than 105 wavelengths • Not possible in convection simulations

  11. 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 Nbin→ ∞

  12. Selective/Sparse Opacity Sampling

  13. SOS • 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 thoseλ • Paves the way for including velocity-effects • Spans the convective fluctuations better than the opacity binning method • Converges for NSOS→ ∞

  14. Multi-group vs. SOS • SOS, Nλ =50 • Monochrome, ODF, Nλ =2750 • Multi-group, Nbin=4

  15. 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

  16. - and their differences • ___ straight average • - - - RMS average • Systematic diffs for multi-group • >4 times larger RMS differences

  17. 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 forNSOS→ ∞

  18. 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

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