We carried out VRI and Gunn z observations of the obscured globular cluster Liller 1. The cluster is so reddened (A_V_=~9.0) that it is at the detection limit in V. The RGB in I vs. (I-z) shows a strong curvature. Recalling that the nearly solar metallicity globular clusters NGC 6553 and NGC 6528 present similar blanketing effects only in the visible bandpasses, we conclude that Liller 1 is considerably more metal-rich than these clusters. The CMD comparison of Liller 1 with the inner bulge field around it (located =~5deg from the nucleus), suggests that the cluster is as metallic as the most metallic fraction of this inner bulge population. Similarly deep I and z observations at =~0.5deg away from Liller 1, at the nominal position of Grindlay 1 do not reveal any cluster.
The degree of complexity of physics due to proximity effects in close binary stars is one of the most important challenges in theoretical stellar physics. The knowledge of how the specific intensity is distributed over the stellar disk is primordial to model the light curves of eclipsing binaries and planetary transits correctly. In order to provide theoretical input for light curve modelling codes, we present new calculations of gravity- and limb darkening coefficients for a wide range of effective temperatures, gravities, metallicities and microturbulent velocities. We have computed limb darkening coefficients for several atmosphere models, covering the transmission curves of the Kepler, CoRoT and Spitzer space missions as well as more widely used passbands (Stroemgren, Johnson-Cousins, Sloan). In addition to these computations, which were computed by adopting the Least-Square Method, we also performed calculations for the bi-parametric approximations by adopting the Flux Conservation Method to provide users with an additional tool to estimate the theoretical error bars. To facilitate the modelling of the effects of tidal and rotational distortions, we computed the GDCs y({lambda}) using the same models of stellar atmospheres as in the case of limb-darkening. Compared to previous work, a more general differential equation was used which now takes into account local gravity variations and the effects of convection. The limb darkening coefficients were computed with a larger numerical resolution (100um points instead of 15 or 17 as is often used in the ATLAS models) and five equations were used to describe the specific intensities (linear, quadratic, root-square, logarithmic and a 4-coefficient law (Equation 5)). Concerning the GDCs, the influence of the local gravity on y({lambda}) is shown as well as the effects of convection, which turn out to be very significant for cool stars. The results are tabulated for log(g)'s ranging from 0.0 to 5.0,-5.0<=log[M/H]<=+1, 2000K<=Teff<=50000K and for 5 values of the microturbulent velocity (0, 2, 4, 6, 8). ATLAS and PHOENIX plane-parallel atmosphere models were used for all the computations.
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. 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 <{\partial}lnI_o_(lambda)/{\partial}lng)_Teff_. 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 logg varying between 5.0 and 9.5 and effective temperatures between 3750K-100000K. For effective temperatures higher than 40000K, the models were also computed adopting nonlocal thermal equilibrium (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], logg, and Teff can be performed upon request.
We present new calculations of limb and gravity-darkening coefficients to be used as input in many fields of stellar physics such as synthetic light curves of double-lined eclipsing binaries and planetary transits, studies of stellar diameters or line profiles in rotating stars. We compute the limb-darkening coefficients specifically for the photometric system of the satellite MOST (Microvariability and Oscillations in STars). All computations were performed by adopting the least-square method, but for completeness we also performed calculations for the linear and bi-parametric approaches by adopting the flux conservation method. The passband gravity-darkening coefficients y({lambda}) were computed by adopting a more general differential equation, which also takes the effects of convection into account. We used two stellar atmosphere models: ATLAS (plane-parallel) and PHOENIX (spherical and quasi-spherical). We adopted six laws to describe the specific intensity distribution: linear, quadratic, square root, logarithmic, exponential, and a more general one with four terms. The covered ranges of T_eff_, log g, metallicities, and microturbulent velocities are [1500-50000K, 0-5.5,-5.0-1.0, 0-8km/s], respectively.
Model stellar atmospheres are fundamental tools for understanding stellar observations from interferometry, microlensing, eclipsing binaries and planetary transits. However, the calculations also include assumptions, such as the geometry of the model. We use intensity profiles computed for both plane-parallel and spherically symmetric model atmospheres to determine fitting coefficients in the BVRIHK, CoRoT and Kepler wavebands for limb darkening using several different fitting laws, for gravity-darkening and for interferometric angular diameter corrections. Comparing predicted variables for each geometry, we find that the spherically symmetric model geometry leads to different predictions for surface gravities logg<3. In particular, the most commonly used limb-darkening laws produce poor fits to the intensity profiles of spherically symmetric model atmospheres, which indicates the need for more sophisticated laws. Angular diameter corrections for spherically symmetric models range from 0.67 to 1, compared to the much smaller range from 0.95 to 1 for plane-parallel models.
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.
Using up-to-date model atmospheres (Heiter et al. 2002A&A...392..619H) with the turbulent convection approach developed by Canuto, Goldman & Mazzitelli (1996ApJ...473..550C, CGM), quadratic, cubic and square root limb darkening coefficients (LDC) are calculated with a least square fit method for the Stroemgren photometric system. This is done for a sample of solar metallicity models with effective temperatures between 6000 and 8500K and with logg between 2.5 and 4.5. A comparison is made between these LDC and the ones computed from model atmospheres using the classical mixing length prescription with a mixing length parameter {alpha}=1.25 and {alpha}=0.5. For CGM model atmospheres, the law which reproduces better the model intensity is found to be the square root one for the u band and the cubic law for the v band. The results are more complex for the b and y bands depending on the temperature and gravity of the model. Similar conclusions are reached for Mixing Length Theory (MLT) {alpha}=0.5 models. As expected much larger differences are found between CGM and MLT with {alpha}=1.25. In a second part, the weighted limb-darkening integrals, b_ell_, and their derivatives with respect to temperature and gravity, are then computed using the best limb-darkening law. These integrals are known to be very important in the context of photometric mode identification of non-radial pulsating stars. The effect of convection treatment on these quantities is discussed and as expected differences in the b_ell_ coefficients and derivatives computed with CGM and MLT {alpha}=0.5 are much smaller than differences obtained between computations with CGM and MLT {alpha}=1.25. The limb darkening coefficients are given here for the u, v, b and y bands and for CGM models, MLT {alpha}=0.5 models and MLT {alpha}=1.25 models.
The knowledge of how the specific intensity is distributed over the stellar disk is crucial for interpreting the light curves of extrasolar transiting planets, double-lined eclipsing binaries, and other astrophysical phenomena. To provide theoretical inputs for light curve modelling codes, we present new calculations of limb-darkening coefficients for the spherically symmetric PHOENIX models. The limb-darkening coefficients were computed by covering the transmission curves of Kepler, CoRoT, and Spitzer space missions, as well as the passbands of the Stromgren, Johnson-Cousins, Sloan, and 2MASS. These computations adopted the least-square method. In addition, we also calculated the linear and bi-parametric approximations by adopting the flux conservation method as an additional tool for estimating the theoretical error bars in the limb-darkening coefficients. Six laws were used to describe the specific intensity distribution: linear, quadratic, square root, logarithmic, exponential, and a more general one with 4 terms. The computations are presented for the solar chemical composition, with logg varying between 2.5 and 5.5 and effective temperatures between 1500K-4800K. The adopted Microturbulent velocity and the mixing-length parameters are 2.0km/s and 2.0, respectively. Model are for solar metallicity.
We present an extension of our investigations on limb-darkening coefficients computed with spherical symmetrical PHOENIX models. The models investigated in this paper cover the range 5000K<=Teff<=10000K and complete our previous studies of low effective temperatures computed with the same code. The limb-darkening coefficients are computed for the transmission curves of the Kepler, CoRoT, and Spitzer space missions and the Stroemgren, Johnson-Cousins, Sloan, and 2MASS passbands. These computations were performed by adopting the least-squares method. We have used six laws to describe the specific intensity distribution: linear, quadratic, square root, logarithmic, exponential, and a general law with four terms. The computations are presented for the solar chemical composition and cover the range 3.0<=logg<=5.5. The adopted microturbulent velocity and the mixing-length parameter are 2.0km/s and 2.0.
We describe the construction of a highly reliable sample of ~7000 optically faint periodic variable stars with light curves obtained by the asteroid survey LINEAR across 10000deg^2^ of the northern sky. The majority of these variables have not been cataloged yet. The sample flux limit is several magnitudes fainter than most other wide-angle surveys; the photometric errors range from ~0.03mag at r=15 to ~0.20mag at r=18. Light curves include on average 250 data points, collected over about a decade. Using Sloan Digital Sky Survey (SDSS) based photometric recalibration of the LINEAR data for about 25 million objects, we selected ~200000 most probable candidate variables with r<17 and visually confirmed and classified ~7000 periodic variables using phased light curves. The reliability and uniformity of visual classification across eight human classifiers was calibrated and tested using a catalog of variable stars from the SDSS Stripe 82 region and verified using an unsupervised machine learning approach. The resulting sample of periodic LINEAR variables is dominated by 3900 RR Lyrae stars and 2700 eclipsing binary stars of all subtypes and includes small fractions of relatively rare populations such as asymptotic giant branch stars and SX Phoenicis stars. We discuss the distribution of these mostly uncataloged variables in various diagrams constructed with optical-to-infrared SDSS, Two Micron All Sky Survey, and Wide-field Infrared Survey Explorer photometry, and with LINEAR light-curve features. We find that the combination of light-curve features and colors enables classification schemes much more powerful than when colors or light curves are each used separately. An interesting side result is a robust and precise quantitative description of a strong correlation between the light-curve period and color/spectral type for close and contact eclipsing binary stars ({beta} Lyrae and W UMa): as the color-based spectral type varies from K4 to F5, the median period increases from 5.9hr to 8.8hr. These large samples of robustly classified variable stars will enable detailed statistical studies of the Galactic structure and physics of binary and other stars and we make these samples publicly available.
