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Register a new userGravity and limb-darkening coefficients for compact stars: DA, DB, and DBA eclipsing white dwarfs
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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.
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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 these photometric systems. The beaming factor calculations, which use realistic models of stellar atmospheres, show that the black body approximation is not accurate, particularly 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 toward the limb than their 1D counterparts, which implies steeper profiles. To describe these intensities better, we recommend the use of the four-term law (also for 1D models) given the level of precision that is being achieved with Earth-based instruments and space missions such as Kepler and TESS (and PLATO in the future).
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.
We report on a comparison of spectroscopic analyses for hydrogen (DA) and helium atmosphere (DB) white dwarfs with Gaia Data Release 2 (DR2) parallaxes and photometry. We assume a reddening law and a mass-radius relation to connect the effective temperatures (Teff) and surface gravities (log g) to masses and radii. This allows the comparison of two largely independent sets of fundamental parameters for 7039 DA and 521 DB stars with high-quality observations. This subset of the Gaia white dwarf sample is large enough to detect systematic trends in the derived parameters. We find that spectroscopic and photometric parameters generally agree within uncertainties when the expectation of a single star is verified. Gaia allows the identification of a small systematic offset in the temperature scale between the two techniques, as well as confirming a small residual high-mass bump in the DA mass distribution around 11,000-13,000 K. This assessment of the accuracy of white dwarf fundamental parameters derived from Gaia is a first step in understanding systematic effects in related astrophysical applications such as the derivation of the local stellar formation history, initial-to-final mass relation, and statistics of evolved planetary systems.
We present new gravity and limb-darkening coefficients for a wide range of effective temperatures, gravities, metallicities, and microturbulent velocities. These coefficients can be used in many different fields of stellar physics as synthetic light curves of eclipsing binaries and planetary transits, stellar diameters, line profiles in rotating stars, and others. The limb-darkening coefficients were computed specifically for the photometric system of the space mission TESS and were performed by adopting the least-square method. In addition, the linear and bi-parametric coefficients, by adopting the flux conservation method, are also available. On the other hand, to take into account the effects of tidal and rotational distortions, we computed the passband gravity-darkening coefficients $y(lambda)$ using a general differential equation in which we consider the effects of convection and of the partial derivative $left(partial{ln I(lambda)}/{partial{ln g}}right)_{T_{rm eff}}$. To generate the limb-darkening coefficients we adopt two stellar atmosphere models: ATLAS (plane-parallel) and PHOENIX (spherical, quasi-spherical, and $r$-method). The specific intensity distribution was fitted using five approaches: linear, quadratic, square root, logarithmic, and a more general one with four terms. These grids cover together 19 metallicities ranging from 10$^{-5}$ up to 10$^{+1}$ solar abundances, 0 $leq$ log g $leq$ 6.0 and 1500 K $leq$ T$_{rm eff}$ $leq$ 50000 K. The calculations of the gravity-darkening coefficients were performed for all plane-parallel ATLAS models.
We present a detailed spectroscopic and photometric analysis of DA and DB white dwarfs drawn from the Sloan Digital Sky Survey with trigonometric parallax measurements available from the Gaia mission. The temperature and mass scales obtained from fits to $ugriz$ photometry appear reasonable for both DA and DB stars, with almost identical mean masses of $langle M rangle = 0.617~M_odot$ and $0.620~M_odot$, respectively. The comparison with similar results obtained from spectroscopy reveals several problems with our model spectra for both pure hydrogen and pure helium compositions. In particular, we find that the spectroscopic temperatures of DA stars exceed the photometric values by $sim$10% above $T_{rm eff}sim14,000$~K, while for DB white dwarfs, we observe large differences between photometric and spectroscopic masses below $T_{rm eff}sim16,000$~K. We attribute these discrepancies to the inaccurate treatment of Stark and van der Waals broadening in our model spectra, respectively. Despite these problems, the mean masses derived from spectroscopy --- $langle M rangle = 0.615~M_odot$ and $0.625~M_odot$ for the DA and DB stars, respectively --- agree extremely well with those obtained from photometry. Our analysis also reveals the presence of several unresolved double degenerate binaries, including DA+DA, DB+DB, DA+DB, and even DA+DC systems. We finally take advantage of the Gaia parallaxes to test the theoretical mass-radius relation for white dwarfs. We find that 65% of the white dwarfs are consistent within the 1$sigma$ confidence level with the predictions of the mass-radius relation, thus providing strong support to the theory of stellar degeneracy.
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