Rotationally and tidally distorted compact stars A theoretical approach to the gravity-darkening exponents for white dwarfs

Abstract

To the best of our knowledge, there are no specific calculations of gravity-darkening exponents for white dwarfs in the literature. On the other hand, the number of known eclipsing binaries whose components are tidally and/or rotationally distorted white dwarfs is increasing year on year. Our main objective is to present the first theoretical approaches to the problem of the distribution of temperatures on the surfaces of compact stars distorted by rotation and/or tides in order to compare with relevant observational data. We find discrepancies between the gravity-darkening exponents calculated with our methods and the predictions of the von Zeipel theorem, particularly in the cases of cold white dwarfs; although the discrepancy also applies to higher effective temperatures under determined physical conditions. We find physical connections between the gravity-darkening exponents calculated using our modified method of triangles strategy with the convective efficiency (defined here as the ratio of the convective to the total flux). A connection between the entropy and the gravity-darkening coefficients is also found: variations of the former cause changes in the way the temperature is distributed on distorted stellar surfaces. On the other hand, we have generalised the von Zeipel theorem for the case of hot white dwarfs. Such a generalisation allows us to predict that, under certain circumstances, the value of the gravity-darkening exponent may be smaller than 1.0, even in the case of high effective temperatures.

Accepted publication Astronomy&Astrophysics

References in corpus (6)

• Modules for Experiments in Stellar Astrophysics (MESA)
• Convective Overshoot and Macroscopic Diffusion in Pure-Hydrogen Atmosphere White Dwarfs
• Orbital Decay in a 20 Minute Orbital Period Detached Binary with a Hydrogen Poor Low Mass White Dwarf
• Gravity and limb-darkening coefficients for compact stars: DA, DB, and DBA eclipsing white dwarfs
• A new class of Roche lobe-filling hot subdwarf binaries
• Calibration of the mixing length theory for structures of helium-dominated atmosphere white dwarfs

Cited by in corpus (3)

• Theoretical tidal evolution constants for stellar models from the pre-main sequence to the white dwarf stage Apsidal motion constants, moment of inertia, and gravitational potential energy
• Influence of the gravitational darkening effect on the spectrum of a hot, rapidly rotating neutron star
• Influence of the gravitational darkening effect on the spectrum of a hot, rapidly rotating neutron star. II. Iron lines