Power-2 limb-darkening coefficients for the uvby, UBVRIJHK, SDSS ugriz, Gaia, Kepler, TESS, and CHEOPS photometric systems II. PHOENIX spherically symmetric stellar atmosphere models

The Spanish MEC (AYA2015-71718-R, ESP2017-87676-C5-2-R, PID2019-107061GB-C64, and PID2019-109522GB-C52) is gratefully acknowledged for its support during the development of this work. A.C. acknowledges financial support from the grant CEX2021-001131-S funded by MCIN/AEI/ 10.13039/501100011033. This research has made use of the SIMBAD database, operated at the CDS, Strasbourg, France, of NASA’s Astrophysics Data System Abstract Service and of SVO Filter Profile supported from the Spanish MINECO through grant AYA2017-84089.Context. The phenomenon of limb-darkening is relevant to many topics in astrophysics, including the analysis of light curves of eclipsing binaries, optical interferometry, measurement of stellar diameters, line profiles of rotating stars, gravitational microlensing, and transits of extrasolar planets Aims. Multiple parametric limb-darkening laws have been presented, and there are many available sources of theoretical limb-darkening coefficients (LDCs) calculated using stellar model atmospheres. The power-2 limb-darkening law allows a very good representation of theoretically predicted intensity profiles, but few LDCs are available for this law from spherically symmetric model atmospheres. We therefore present such coefficients in this work. Methods. We computed LDCs for the space missions Gαiα, Kepler, TESS, and CHEOPS and for the passbands uνby, UBVRIJHK, and SDSS ugriz, using the PHOENIX-COND spherical models. We adopted two methods to characterise the truncation point, which sets the limb of the star: the first (M1) uses the point where the derivative dI(r)/dr is at its maximum - where I(r) is the specific intensity as a function of the normalised radius r - corresponding to μcri, and the second (M2) uses the midpoint between the point μcri and the point located at μcn-1. The LDCs were computed adopting the Levenberg-Marquardt least-squares minimisation method, with a resolution of 900 equally spaced μ points, and covering 823 model atmospheres for a solar metallicity, effective temperatures of 2300-12000 K, log g values from 0.0 to 6.0, and microturbulent velocities of 2 km s-1. As our previous calculations of LDCs using spherical models included only 100 μ points, we also updated the calculations for the four-parameter law for the passbands listed above, and compared them with those from the power-2 law. Results. Comparisons between the quality of the fits provided by the power-2 and four-parameter laws show that the latter presents a lower merit function, X2, than the former for both cases (M1 and M2). This is important when choosing the best approach for a particular science goal.The Spanish MEC (AYA2015-71718-R, ESP2017-87676-C5-2-R, PID2019-107061GB-C64, PID2019-109522GB-C52)MCIN/AEI/ 10.13039/501100011033 CEX2021-001131-SCDSNASA’s Astrophysics Data System Abstract ServiceThe Spanish MINECO AYA2017-8408

Probing the Stellar Surface of HD 209458 from Multicolor Transit Observations

Multicolor photometric observations of a planetary transit in the system HD 209458 are analyzed. The observations, made in the Stromgren photometric system, allowed a recalculation of the basic physical properties of the star-planet system. This includes derivation of linear limb-darkening values of HD 209458, which is the first time that a limb-darkening sequence has observationally been determined for a star other than the Sun. As the derived physical properties depend on assumptions that are currently known with limited precision only, scaling relations between derived parameters and assumptions are given. The observed limb-darkening is in good agreement with theoretical predictions from evolutionary stellar models combined with ATLAS model atmospheres, verifying these models for the temperature (Teff ~ 6000K), surface gravity (log g ~ 4.3) and mass (~ 1.2 Msol) of HD 209458.Comment: 16 pages, 8 figures, uses elsart.cls, accepted for New Astronom

MECI: A Method for Eclipsing Component Identification

We describe an automated method for assigning the most probable physical parameters to the components of an eclipsing binary, using only its photometric light curve and combined colors. With traditional methods, one attempts to optimize a multi-parameter model over many iterations, so as to minimize the chi-squared value. We suggest an alternative method, where one selects pairs of coeval stars from a set of theoretical stellar models, and compares their simulated light curves and combined colors with the observations. This approach greatly reduces the parameter space over which one needs to search, and allows one to estimate the components' masses, radii and absolute magnitudes, without spectroscopic data. We have implemented this method in an automated program using published theoretical isochrones and limb-darkening coefficients. Since it is easy to automate, this method lends itself to systematic analyses of datasets consisting of photometric time series of large numbers of stars, such as those produced by OGLE, MACHO, TrES, HAT, and many others surveys.Comment: 25 pages, 7 figures, accepted for publication in Ap

Absolute dimensions of eclipsing binaries. XVII. A metal-weak F-type system, perhaps with preference for Y = 0.23-0.24

V1130 Tau is a bright (m_V = 6.56), nearby (71 +/- 2 pc) detached system with a circular orbit (P = 0.80d). The components are deformed with filling factors above 0.9. Their masses and radii have been established to 0.6-0.7%. We derive a [Fe/H] abundance of -0.25 +/- 0.10. The measured rotational velocities, 92.4 +/- 1.1 (primary) and 104.7 +/- 2.7 (secondary) km/s, are in fair agreement with synchronization. The larger 1.39 Msun secondary component has evolved to the middle of the main-sequence band and is slightly cooler than the 1.31 Msun primary. Yonsai-Yale, BaSTI, and Granada evolutionary models for the observed metal abundance and a 'normal' He content of Y = 0.25-0.26, marginally reproduce the components at ages between 1.8 and 2.1 Gyr. All such models are, however, systematically about 200 K hotter than observed and predict ages for the more massive component, which are systematically higher than for the less massive component. These trends can not be removed by adjusting the amount of core overshoot or envelope convection level, or by including rotation in the model calculations. They may be due to proximity effects in V1130 Tau, but on the other hand, we find excellent agreement for 2.5-2.8 Gyr Granada models with a slightly lower Y of 0.23-0.24. V1130 Tau is a valuable addition to the very few well-studied 1-2 Msun binaries with component(s) in the upper half of the main-sequence band, or beyond. The stars are not evolved enough to provide new information on the dependence of core overshoot on mass (and abundance), but might - together with a larger sample of well-detached systems - be useful for further tuning of the helium enrichment law.Comment: Accepted for publication in Astronomy & Astrophysic

Limb darkening in spherical stellar atmospheres

(Abridged) Context. Stellar limb darkening, I({\mu} = cos{\theta}), is an important constraint for microlensing, eclipsing binary, planetary transit, and interferometric observations, but is generally treated as a parameterized curve, such as a linear-plus-square-root law. Many analyses assume limb-darkening coefficients computed from model stellar atmospheres. However, previous studies, using I({\mu}) from plane- parallel models, have found that fits to the flux-normalized curves pass through a fixed point, a common {\mu} location on the stellar disk, for all values of T eff, log g and wavelength. Aims. We study this fixed {\mu}-point to determine if it is a property of the model stellar atmospheres or a property of the limb-darkening laws. Furthermore, we use this limb-darkening law as a tool to probe properties of stellar atmospheres for comparison to limb- darkening observations. Methods. Intensities computed with plane-parallel and spherically-symmetric Atlas models (characterized by the three fundamental parameters L\star, M\star and R\star) are used to reexamine the existence of the fixed {\mu}-point for the parametrized curves. Results. We find that the intensities from our spherical models do not have a fixed point, although the curves do have a minimum spread at a {\mu}-value similar to the parametrized curves. We also find that the parametrized curves have two fixed points, {\mu}1 and {\mu}2, although {\mu}2 is so close to the edge of the disk that it is missed using plane-parallel atmospheres. We also find that the spherically- symmetric models appear to agree better with published microlensing observations relative to plane-parallel models.Comment: 8 pages, 8 figures, figures 4 and 6 have lower resolution. A&A in pres

On the Selection of Photometric Planetary Transits

We present a new method for differentiating between planetary transits and eclipsing binaries based on the presence of the ellipsoidal light variations. These variations can be used to detect stellar secondaries with masses ~0.2 M_sun orbiting sun-like stars at a photometric accuracy level which has already been achieved in transit surveys. By removing candidates exhibiting this effect it is possible to greatly reduce the number of objects requiring spectroscopic follow up with large telescopes. Unlike the usual candidate selection method, which are primarily based on the estimated radius of the orbiting object, this technique is not biased against bona-fide planets and brown dwarfs with large radii, because the amplitude of the effect depends on the transiting object's mass and orbital distance. In many binary systems, where a candidate planetary transit is actually due to the partial eclipse of two normal stars, the presence of flux variations due to the gravity darkening effect will show the true nature of these systems. We show that many of the recent OGLE-III photometric transit candidates exhibit the presence of significant variations in their light curves and are likely to be due to stellar secondaries. We find that the light curves of white dwarf transits will generally not mimic those of small planets because of significant gravitationally induced flux variations. We discuss the relative merits of methods used to detect transit candidates which are due to stellar blends rather than planets. We outline how photometric observations taken in two bands can be used to detect the presence of stellar blends.Comment: ApJ, 11 pages, 2 figures, 1 table, replaced with accepted versio

Spurious Eccentricities of Distorted Binary Components

I discuss the effect of physical distortion on the velocities of close binary components and how we may use the resulting distortion of velocity curves to constrain some properties of binary systems, such as inclination and mass ratio. Precise new velocities for 5 Cet convincingly detect these distortions with their theoretically predicted phase dependence. We can even use such distortions of velocity curves to test Lucy's theory of convective gravity darkening. The observed distortions for TT Hya and 5 Cet require the contact components of those systems to be gravity darkened, probably somewhat more than predicted by Lucy's theory but clearly not as much as expected for a radiative star. These results imply there is no credible evidence for eccentric orbits in binaries with contact components. I also present some speculative analyses of the observed properties of a binary encased in a non-rotating common envelope, if such an object could actually exist, and discuss how the limb darkening of some recently calculated model atmospheres for giant stars may bias my resuts for velocity-curve distortions, as well as other results from a wide range of analyses of binary stars.Comment: 14 pp, 2 tables, 12 fig; under review by Ap

Using limb darkening to measure fundamental parameters of stars

Context. Limb darkening is an important tool for understanding stellar atmospheres, but most observations measuring limb darkening assume various parameterizations that yield no significant information about the structure of stellar atmospheres. Aims. We use a specific limb-darkening relation to study how the best-fit coefficients relate to fundamental stellar parameters from spherically symmetric model stellar atmospheres. Methods. Using a grid of spherically symmetric Atlas model atmospheres, we compute limb-darkening coefficients, and develop a novel method to predict fundamental stellar parameters. Results. We find our proposed method predicts the mass of stellar atmosphere models given only the radius and limb-darkening coefficients, suggesting that microlensing, interferometric, transit and eclipse observations can constrain stellar masses. Conclusions. This novel method demonstrates that limb-darkening parameterizations contain important information about the structure of stellar atmospheres, with the potential to be a valuable tool for measuring stellar masses.Comment: 8 pages, 6 figures, 2 tables, A&A accepte

Observational Tests and Predictive Stellar Evolution

We compare eighteen binary systems with precisely determined radii and masses from 23 to 1.1 M_sol, and stellar evolution models produced with our newly revised code TYCHO. ``Overshooting'' and rotational mixing were suppressed in order to establish a baseline for isolating these and other hydrodynamic effects. Acceptable coeval fits are found for sixteen pairs without optimizing for heavy element or helium abundance. The precision of these tests is limited by the accuracies of the observed effective temperatures. High dispersion spectra and detailed atmospheric modeling should give more accurate effective temperatures and heavy element abundances. PV Cas, a peculiar early A system, EK Cep B, a known post-T Tauri star, and RS Cha, a member of a young OB association, are matched by pre-main sequence models. Predicted mass loss agrees with upper limits from IUE for CW Cep A and B. Relatively poor fits are obtained for binaries having at least one component in the mass range 1.7 < M/M_sol <2.6, whose evolution is sensitive to mixing. These discrepancies are robust and consistent with additional mixing in real stars. The predicted apsidal motion implies that massive star models are systematically less centrally condensed than the real stars. If these effects are due to overshooting, then the overshooting parameter alpha_OV increases with stellar mass. The apsidal motion constants are controlled by radiative opacity under conditions close to those directly measured in laser experiments, making this test more stringent than possible before.Comment: 38 pages, 9 figures (color versions of figures 1,2,3,4, and 9 are available separately). Accepted for publication in the Astrophysical Journa