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

Context. The distribution of the specific intensity over the stellar disk is an essential tool for modeling the light curves in eclipsing binaries, planetary transits, and stellar diameters through interferometric techniques, line profiles in rotating stars, gravitational microlensing, etc. However, the available theoretical calculations are mostly restricted to stars on the main sequence or the giant branch, and very few calculations are available for compact stars. Aims. 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). Methods. 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(λ) 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 (∂ln Io(λ)/∂ln g)Teff. Results. 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 and 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/α = 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 Teff can be performed upon request

Doppler beaming factors for white dwarfs, main sequence stars, and giant stars. Limb-darkening coefficients for 3D (DA and DB) white dwarf models

Context. Systematic theoretical calculations of Doppler beaming factors are scarce in the literature, particularly in the case of white dwarfs. Additionally, there are no specific calculations for the limb-darkening coefficients of 3D white dwarf models. Aims. 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, we present the theoretical calculations of the limb-darkening coefficients for 3D white dwarf models for the first time. Methods. 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. Results. 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 log g varying between 5.0 and 9.5 and effective temperatures in the range 3750-100 000 K. The beaming factors were also calculated assuming non-local thermodynamic equilibrium (NLTE) for the case of DA white dwarfs with Teff > 40 000 K. For the mixing-length parameters, we adopted ML2/α = 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 log g varying between 0 and 5.0 and effective temperatures between 3500 and 50 000 K. The adopted microturbulent velocity for these models was 2.0 km s−1. The limb-darkening coefficients were computed for three-dimensional DA and DB white dwarf models calculated with the CO5BOLD radiation-hydrodynamics code. The parameter range covered by the three-dimensional DA models spans log g values between 7.0 and 9.0 and Teff between 6000 and 15000 K, while He/H = 0. The three-dimensional DB models cover a similar parameter range of log g between 7.5 and 9.0 and Teff between 12 000 and 34 000 K, while log H/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. Conclusions. 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)

A pulsating white dwarf in an eclipsing binary

White dwarfs are the burnt-out cores of Sun-like stars and are the fate of 97 per cent of the stars in our Galaxy. The internal structure and composition of white dwarfs are hidden by their high gravities, which causes all elements apart from the lightest ones to settle out of their atmospheres. The most direct method of probing the inner structure of stars and white dwarfs in detail is via asteroseismology. Here we present a pulsating white dwarf in an eclipsing binary system, enabling us to place extremely precise constraints on the mass and radius of the white dwarf from the lightcurve, independent of the pulsations. This 0.325-solar-mass white dwarf—one member of the SDSS J115219.99+024814.4 system—will serve as a powerful benchmark with which to constrain empirically the core composition of low-mass stellar remnants and to investigate the effects of close binary evolution on the internal structure of white dwarfs

The direct detection of the irradiated brown dwarf in the white dwarf - brown dwarf binary SDSS J141126.20+200911.1

We have observed the eclipsing, post-common envelope white dwarf–brown dwarf binary, SDSS141126.20+200911.1, in the near-IR with the HAWK-I imager, and present here the first direct detection of the dark side of an irradiated brown dwarf in the H band, and a tentative detection in the Ks band. Our analysis of the light curves indicates that the brown dwarf is likely to have an effective temperature of 1300 K, which is not consistent with the effective temperature of 800 K suggested by its mass and radius. As the brown dwarf is already absorbing almost all the white dwarf emission in the Ks band, we suggest that this inconsistency may be due to the UV-irradiation from the white dwarf inducing an artificial brightening in the Ks band, similar to that seen for the similar system WD0137-349B, suggesting this brightening may be characteristic of these UV-irradiated binaries

Circular polarimetry of suspect wind-accreting magnetic pre-polars

We present results from a circular polarimetric survey of candidate detached magnetic white dwarf – M dwarf binaries obtained using the Nordic Optical Telescope, La Palma. We obtained phase resolved spectropolarimetry and imaging polarimetry of seven systems, five of which show clearly variable circular polarisation. The data indicate that these targets have white dwarfs with magnetic field strengths >80 MG. Our study reveals that cyclotron emission can dominate the optical luminosity at wavelengths corresponding to the cyclotron emission harmonics, even in systems where the white dwarfs are only wind-accreting. This implies that a very significant fraction of the the stellar wind of the companion star is captured by the magnetic white dwarf reducing the magnetic braking in pre-CVs. Furthermore, the polarimetric confirmation of several detached, wind-accreting magnetic systems provides observational constraints on the models of magnetic CV evolution and white dwarf magnetic field generation. We also find that the white dwarf magnetic field configuration in at least two of these systems appears to be very complex

SDSS J105754.25+275947.5: a period-bounce eclipsing cataclysmic variable with the lowest-mass donor yet measured

We present high-speed, multicolour photometry of the faint, eclipsing cataclysmic variable (CV) SDSS J105754.25+275947.5. The light from this system is dominated by the white dwarf. Nonetheless, averaging many eclipses reveals additional features from the eclipse of the bright spot. This enables the fitting of a parameterised eclipse model to these average light curves, allowing the precise measurement of system parameters. We find a mass ratio of q = 0.0546 $\pm$ 0.0020 and inclination i = 85.74 $\pm$ 0.21$^{\circ}$. The white dwarf and donor masses were found to be M$_{\mathrm{w}}$ = 0.800 $\pm$ 0.015 M$_{\odot}$ and M$_{\mathrm{d}}$ = 0.0436 $\pm$ 0.0020 M$_{\odot}$, respectively. A temperature T$_{\mathrm{w}}$ = 13300 $\pm$ 1100 K and distance d = 367 $\pm$ 26 pc of the white dwarf were estimated through fitting model atmosphere predictions to multicolour fluxes. The mass of the white dwarf in SDSS 105754.25+275947.5 is close to the average for CV white dwarfs, while the donor has the lowest mass yet measured in an eclipsing CV. A low-mass donor and an orbital period (90.44 min) significantly longer than the period minimum strongly suggest that this is a bona fide period-bounce system, although formation from a white dwarf/brown dwarf binary cannot be ruled out. Very few period-minimum/period-bounce systems with precise system parameters are currently known, and as a consequence the evolution of CVs in this regime is not yet fully understood

Accurate mass and radius determinations of a cool subdwarf in an eclipsing binary

Cool subdwarfs are metal-poor low-mass stars that formed during the early stages of the evolution of our Galaxy. Because they are relatively rare in the vicinity of the Sun, we know of few cool subdwarfs in the solar neighbourhood, and none for which both the mass and the radius are accurately determined. This hampers our understanding of stars at the low-mass end of the main sequence. Here we report the discovery of SDSSJ235524.29+044855.7 as an eclipsing binary containing a cool subdwarf star, with a white dwarf companion. From the light curve and the radial-velocity curve of the binary we determine the mass and the radius of the cool subdwarf and we derive its effective temperature and luminosity by analysing its spectral energy distribution. Our results validate the theoretical relations between mass, radius, effective temperature and luminosity for low-mass, low-metallicity stars

WD1032+011, an inflated brown dwarf in an old eclipsing binary with a white dwarf

We present the discovery of only the third brown dwarf known to eclipse a non-accreting white dwarf. Gaia parallax information and multicolour photometry confirm that the white dwarf is cool (9950 ± 150 K) and has a low mass (0.45 ± 0.05 M⊙), and spectra and light curves suggest the brown dwarf has a mass of 0.067 ± 0.006 M⊙ (70MJup) and a spectral type of L5 ± 1. The kinematics of the system show that the binary is likely to be a member of the thick disc and therefore at least 5-Gyr old. The high-cadence light curves show that the brown dwarf is inflated, making it the first brown dwarf in an eclipsing white dwarf-brown dwarf binary to be so