Radiative transfer in the refractive atmospheres of very cool white dwarfs

Abstract

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 Lambda-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 1-D 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 where 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 ($τ\wig< 1$). This effect may have a significant impact on studies of very cool white dwarf stars.

arXiv comment20 pages, 7 figures, accepted for publication in ApJ

Cited by in corpus (22)

• Found: The missing blue opacity in atmosphere models of cool hydrogen white dwarfs
• A large stellar evolution database for population synthesis studies: VI. White dwarf cooling sequences
• Isolated neutron stars: Magnetic fields, distances, and spectra
• The spectrum of the recycled PSR J0437-4715 and its white dwarf companion
• Discovery of New Ultracool White Dwarfs in the Sloan Digital Sky Survey
• Gaia photometry for white dwarfs
• Rotational Doppler beaming in eclipsing binaries
• On the Interpretation of High Velocity White Dwarfs as Members of the Galactic Halo
• The origin of peculiar molecular bands in cool DQ white dwarfs
• Spectral analysis of ultra-cool white dwarfs polluted by planetary debris
• On the Dissociation Equilibrium of H2 in Very Cool, Helium-Rich White Dwarf Atmospheres
• Visitors from the Halo: 11 Gyr old White Dwarfs in the Solar Neighborhood
• Spitzer Observations of the Oldest White Dwarfs in the Solar Neighborhood
• A Nearby Old Halo White Dwarf Candidate from the Sloan Digital Sky Survey
• The Mystery Deepens: Spitzer Observations of Cool White Dwarfs
• 11-12 Gyr old White Dwarfs 30 parsecs Away
• Pressure Distortion of the H${}_2$-He Collision-Induced Absorption at the Photosphere of Cool White Dwarf Stars
• The June 2012 transit of Venus. Framework for interpretation of observations
• Infrared absorption of dense helium and its importance in the atmospheres of cool white dwarfs
• The First Mid-Infrared Spectra of Cool White Dwarfs
• Near-UV absorption in very cool DA white dwarfs
• Complex hydrogen chemical equilibrium and Gaia low mass problem in cool white dwarfs