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Basic LTE Relations (Hubeny & Mihalas 4)

Explore Planck (Black Body) Spectrum deep in the atmosphere with limited leakage and understand Boltzmann Excitation Equation. Discover the Maxwellian Velocity Distribution and Saha Ionization Equation for a detailed analysis.

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Basic LTE Relations (Hubeny & Mihalas 4)

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  1. Basic LTE Relations(Hubeny & Mihalas 4) Planck CurveMaxwellian Velocity DistributionBoltzmann Excitation RelationSaha Ionization Equation

  2. Planck (Black Body) Spectrum • Good description of radiation field deep in the atmosphere where little leakage occurs

  3. Planck (Black Body) Spectrum • Wien’s law: peak of the λcurve in Ångstroms • Stefan-Boltzman law:area under the curve, σ = 5.6705x10-5 erg s-1 cm-2 K-4

  4. Planck curve in IDL • Wave=10.*(findgen(1000)+1.); 10,20,…10000 Ångstroms • Teff=30000. ; Kelvin • B=planck(wave,teff) ; Planck function • Applet at jersey.uoregon.edu/vlab

  5. State of Gas in LTE (T, N) • Maxwellian velocity distribution

  6. Boltzmann Excitation Equation • nijk = number density of atoms of excitation state iionization state jchemical species k • Χijk= excitation energy of state i relative to ground state of atom/ion, Χ0jk • gijk = statistical weight (# degenerate sublevels, 2J+1) Ludwig Boltzmann

  7. Partition Functions • Dependent on T • log U(T) tabulated in Gray, Appendix D.2, as function of

  8. Saha Ionization Equation • ΧI = ionization potentialenergy above ground stateto ionize the atom • Listings in Gray, Appendix D.1 Meghnad Saha

  9. Key Variables: T, ne • Hubeny & Mihalas Chap. 17 give a general iterative method to find ne from T and N, where N=total number of particles • Interesting limiting cases …

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