Gravity and limb-darkening coefficients for compact stars: DA, DB, and DBA eclipsing white dwarfs

Abstract

The main objective of the present work is to extend these investigations by computing the gravity and limb-darkening coefficients for white dwarf atmosphere models with hydrogen, helium, or mixed compositions (types DA, DB, and DBA). We computed gravity and limb-darkening coefficients for DA, DB, and DBA white dwarfs atmosphere models, covering the transmission curves of the Sloan, UBVRI, Kepler, TESS, and Gaia photometric systems. Specific calculations for the HiPERCAM instrument were also carried out. For all calculations of the limb-darkening coefficients we used the least-squares method. Concerning the effects of tidal and rotational distortions, we also computed for the first time the gravity-darkening coefficients $y(\lambda)$ for white dwarfs using the same models of stellar atmospheres as in the case of limb-darkening. A more general differential equation was introduced to derive these quantities, including the partial derivative $\left(\partial{\ln I_o(\lambda)}/{\partial{\ln g}}\right)_{T_{\rm eff}}$. Six laws were adopted to describe the specific intensity distribution: linear, quadratic, square root, logarithmic, power-2, and a more general one with four coefficients. The computations are presented for the chemical compositions log[H/He] = $-$10.0 (DB), $-$2.0 (DBA) and He/H = 0 (DA), with log g varying between 5.0 and 9.5 and effective temperatures between 3750 K-100\,000 K. For effective temperatures higher than 40\,000 K, the models were also computed adopting nonlocal thermal equilibirum (DA). The adopted mixing-length parameters are ML2/$\alpha = 0.8$ (DA case) and 1.25 (DB and DBA). The results are presented in the form of 112 tables. Additional calculations, such as for other photometric systems and/or different values of log[H/He], $\log g,$ and T$_{\rm eff}$ can be performed upon request.