2004/02/17 by Piotr M. Kowalski, P. M. Kowalski, D. Saumon · 39 citations
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Astrophysics #Atmosphere (unit) #Atmospheric Ozone and Climate #Calibration and Measurement Techniques #Limb darkening #Optics #Physics #Radiative equilibrium #Radiative transfer #Reflection (computer programming) #Refraction #Refractive index #Stars #Stellar atmosphere #Stellar, planetary, and galactic studies #Thermodynamics #White dwarf #astro-ph
paper · pdf · doi:10.1086/386280
published in The Astrophysical Journal 607(2), 970-981 (IOP Publishing) · 20 pages, 7 figures, accepted for publication in ApJ
arxiv created 2004/02/17 · openalex publication_date 2004/05/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the problem of radiative transfer in stellar atmospheres where the index of refraction departs from unity and is a function of density and temperature. We present modified Feautrier and Λ-iteration methods to solve the equation of radiative transfer with refraction in a plane-parallel atmosphere. These methods are general and can be used in any problem with one-dimensional geometry where the index of refraction is a monotonically varying function of vertical optical depth. We present an application to very cool white dwarf atmospheres in which the index of refraction departs significantly from unity. We investigate how ray curvature and total internal reflection affect the limb darkening and the pressure-temperature structure of the atmosphere. Refraction results in a much weakened limb-darkening effect. We find that through the constraint of radiative equilibrium, total internal reflection warms the white dwarf atmosphere near the surface (τ ≲ 1). This effect may have a significant impact on studies of very cool white dwarf stars.