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Register a new userLimb and gravity-darkening coefficients for the TESS satellite at several metallicities, surface gravities, and microturbulent velocities
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Antonio Claret
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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.
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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.
We provide here tables of stellar limb-darkening coefficients (LDCs) for the Ariel ESA M4 space mission. These tables include LDCs corresponding to different wavelength bins and white bands for the NIRSpec, AIRS-Ch0 and AIRS-Ch1 spectrographs, and those corresponding to the VISPhot, FGS1 and FGS2 photometers. The LDCs are calculated with the open-source software ExoTETHyS for three complete grids of stellar atmosphere models obtained with the ATLAS9 and PHOENIX codes. The three model grids are complementary, as the PHOENIX code adopts more modern input physics and spherical geometry, while the models calculated with ATLAS9 cover wider ranges of stellar parameters. The LDCs obtained from corresponding models in the ATLAS9 and PHOENIX grids are compared in the main text. All together the models cover the following ranges in effective temperature ($1,500 , K le T_{mbox{eff}} le 50,000 , K$), surface gravity (0.0 dex $le log{g} le 6.0$ dex), and metallicity ($-5.0 le [M/H] le 1.0$).
We present grids of limb-darkening coefficients computed from non-LTE, line-blanketed TLUSTY model atmospheres, covering effective-temperature and surface-gravity ranges of 15--55kK and 4.75 dex (cgs) down to the effective Eddington limit, at 1x, 1x, 0.5x (LMC), 0.2x (SMC), and 0.1x solar. Results are given for the Bessell UBVRIJKHL, Sloan ugriz, Stromgren ubvy, WFCAM ZYJHK, Hipparcos, Kepler, and Tycho passbands, in each case characterized by several different limb-darkening `laws. We examine the sensitivity of limb darkening to temperature, gravity, metallicity, microturbulent velocity, and wavelength, and make a comparison with LTE models. The dependence on metallicity is very weak, but limb darkening is a moderately strong function of log(g) in this temperature regime.
We describe our procedure to determine effective temperatures, rotational velocities, microturbulent velocities, and chemical abundances in the atmospheres of Sun-like stars. We use independent determinations of iron abundances using the fits to the observed Fe I and Fe II atomic absorption lines. We choose the best solution from the fits to these spectral features for the model atmosphere that provides the best confidence in the determined log N(Fe), Vt, and vsini. First, we compute the abundance of iron for a set of adopted microturbulent velocities. To determine the most self-consistent effective temperature and microturbulent velocity in any stars atmosphere, we used an additional constraint where we minimise the dependence of the derived abundances of Fe I and Fe II on the excitation potential of the corresponding lines. We analyse the spectra of the Sun and two well known solar type stars, HD1835 and HD10700 to determine their abundances, microturbulent velocity and rotational velocity. For the Sun abundances of elements obtained from the fits of their absorption features agree well enough (+/- 0.1 dex) with the known values for the Sun. We determined a rotational velocity of vsini = 1.6 +/- 0.3 km/s for the spectrum of the Sun as a star. For HD1835 the self-consistent solution for Fe I and Fe II lines log N(Fe)=+0.2 was obtained with a model atmosphere of 5807/4.47/+0.2 andmicroturbulent velocity Vt = 0.75 km/s, and leads to vsini = 7.2 $pm$ 0.5 km/s. For HD10700 the self-consistent solution log N(Fe) = -4.93 was obtained using a model atmosphere of 5383/4.59/-0.6and microturbulent velocity Vt = 0.5 km/s. The Fe I and Fe II lines give rise to a vsini = 2.4 +/- 0.4 km/s. Using the Teff found from the ionisation equilibrium parameters for all three stars, we found abundances of a number of other elements: Ti, Ni, Ca, Si, Cr. ... Abriged.
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).
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