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Description
Systematic theoretical calculations of Doppler beaming factors are very scarce in the literature, mainly in the case of white dwarfs. Additionally, there are no specific calculations for the limb-darkening coefficients of 3D white dwarf models. The objective of this research is to provide the astronomical community with Doppler beaming calculations for a wide range of effective temperatures, local gravities and hydrogen/metal content for white dwarfs as well as stars on both the main sequence and the giant branch. In addition, for the first time we also present the theoretical calculations of the limb-darkening coefficients for 3D white dwarfs models. We computed Doppler beaming factors for DA, DB and DBA white dwarf models, as well as for main sequence and giant stars covering the transmission curves of the Sloan, UBVRI, HiPERCAM, Kepler, TESS, and Gaia photometric systems. The calculations of the limb-darkening coefficients for 3D models were carried out using the least-squares method for the same mentioned photometric systems. The input physics of the white dwarf models for which we have computed the Doppler beaming factors are: chemical compositions log[H/He]=-10.0 (DB), -2.0 (DBA) and He/H=0 (DA), with logg varying between 5.0 and 9.5 and effective temperatures in the range 3750-100000K. The beaming factors were also calculated assuming non-local thermodynamic equilibrium (NLTE) for the case of DA white dwarfs with T_eff_>40000K. For the mixing-length parameters we adopted ML2/{alpha}=0.8 (DA case) and 1.25 (DB and DBA). The Doppler beaming factors for main sequence and giant stars were computed using the ATLAS9 version, characterized by metallicities ranging from [-2.5, 0.2] solar abundances, with logg varying between 0 and 5.0 and effective temperatures between 3500-50000K. The adopted microturbulent velocity for these models was 2.0km/s. The limb-darkening coefficients were computed for 3D DA and DB white dwarf models calculated with the CO^5^BOLD radiation-hydrodynamics code. The parameter range covered by 3D DA models spans logg values between 7.0 and 9.0, Teff between 6000 and 15000K and He/H=0. The 3D DB models cover a similar parameter range of logg between 7.5 and 9.0, Teff between 12000 and 34000K and logH/He=-10.0. We adopted six laws for the computation of the limb-darkening coefficients: linear, quadratic, square root, logarithmic, power-2, and a general one with four coefficients. The beaming factor calculations which use realistic models of stellar atmospheres show that the black body approximation is not accurate, mainly for the filters u, u', U, g, g' and B. The black body approach is only valid for high effective temperatures and/or long effective wavelengths. Therefore, for more accurate analyses of light curves, we recommend the use of the beaming factors presented in this paper. Concerning limb-darkening, the distribution of specific intensities for 3D models indicates that in general these models are less bright towards the limb than their 1D counterparts, which implies steeper profiles. To describe these intensities better, we recommend the use of the four-terms law (also for 1D models) given the level of precision that is being achieved with Earth-based instruments, as well as space missions such as Kepler, TESS or PLATO in the future.
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