Spherically symmetric model stellar atmospheres and limb darkening II: limb-darkening laws, gravity-darkening coefficients and angular diameter corrections for FGK dwarf stars

Limb darkening is a fundamental ingredient for interpreting observations of planetary transits, eclipsing binaries, optical/infrared interferometry and microlensing events. However, this modeling traditionally represents limb darkening by a simple law having one or two coefficients that have been derived from plane-parallel model stellar atmospheres, which has been done by many researchers. More recently, researchers have gone beyond plane-parallel models and considered other geometries. We previously studied the limb-darkening coefficients from spherically symmetric and plane-parallel model stellar atmospheres for cool giant and supergiant stars, and in this investigation we apply the same techniques to FGK dwarf stars. We present limb-darkening coefficients, gravity-darkening coefficients and interferometric angular diameter corrections from Atlas and SAtlas model stellar atmospheres. We find that sphericity is important even for dwarf model atmospheres, leading to significant differences in the predicted coefficients.Comment: 9 pages, 8 figures. Accepted for publication in A&

Limb Darkening and Planetary Transits II: Intensity profile correction factors for a grid of model stellar atmospheres

The ability to observe extrasolar planets transiting their stars has profoundly changed our understanding of these planetary systems. However, these measurements depend on how well we understand the properties of the host star, such as radius, luminosity and limb darkening. Traditionally, limb darkening is treated as a parameterization in the analysis, but these simple parameterizations are not accurate representations of actual center-to-limb intensity variations (CLIV) to the precision needed for interpreting these transit observations. This effect leads to systematic errors for the measured planetary radii and corresponding measured spectral features. We compute synthetic planetary transits using model stellar atmosphere CLIV and corresponding best-fit limb-darkening laws for a grid spherically symmetric model stellar atmospheres. From these light curves we measure the differences in flux as a function of the star's effective temperature, gravity, mass, and the inclination of the planet's orbit.Comment: 10 pages, 8 figures, submitted to AAS journals. Comments welcom

Indicators of Mass in Spherical Stellar Atmospheres

Mass is the most important stellar parameter, but it is not directly observable for a single star. Spherical model stellar atmospheres are explicitly characterized by their luminosity ($L_\star$), mass ($M_\star$) and radius ($R_\star$), and observations can now determine directly $L_\star$ and $R_\star$. We computed spherical model atmospheres for red giants and for red supergiants holding $L_\star$ and $R_\star$ constant at characteristic values for each type of star but varying $M_\star$, and we searched the predicted flux spectra and surface-brightness distributions for features that changed with mass. For both stellar classes we found similar signatures of the star's mass in both the surface-brightness distribution and the flux spectrum. The spectral features have been use previously to determine $\log_{10} (g)$, and now that the luminosity and radius of a non-binary red giant or red supergiant can be observed, spherical model stellar atmospheres can be used to determine the star's mass from currently achievable spectroscopy. The surface-brightness variations with mass are slightly smaller than can be resolved by current stellar imaging, but they offer the advantage of being less sensitive to the detailed chemical composition of the atmosphere.Comment: 24 pages, 9 figure

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

Wigner crystallization in transition metal dichalcogenides: A new approach to correlation energy

We introduce a new approach for the correlation energy of one- and two-valley two-dimensional electron gas (2DEG) systems. Our approach is based on a random phase approximation at high densities and a classical approach at low densities, with interpolation between the two limits. This approach gives excellent agreement with available Quantum Monte Carlo (QMC) calculations. We employ the two-valley 2DEG model to describe the electron correlations in monolayer transition metal dichalcogenides (TMDs). The zero-temperature transition from a Fermi liquid to a quantum Wigner crystal phase in monolayer TMDs is obtained using density-functional theory within the local-density approximation. Consistent with QMC, we find that electrons crystallize at $r_s=30.5$ in one-valley 2DEG. For two-valleys, we predict Wigner crystallization at $r_s= 29.5$, indicating that valley degeneracy has little effect on the critical $r_s$, in contrast to an earlier claim.Comment: 5 pages, 3 figure

Limb Darkening and Planetary Transits: Testing Center-to-limb Intensity Variations and Limb-Darkening Directly from Model Stellar Atmospheres

The transit method, employed by MOST, \emph{Kepler}, and various ground-based surveys has enabled the characterization of extrasolar planets to unprecedented precision. These results are precise enough to begin to measure planet atmosphere composition, planetary oblateness, star spots, and other phenomena at the level of a few hundred parts-per-million. However, these results depend on our understanding of stellar limb darkening, that is, the intensity distribution across the stellar disk that is sequentially blocked as the planet transits. Typically, stellar limb darkening is assumed to be a simple parameterization with two coefficients that are derived from stellar atmosphere models or fit directly. In this work, we revisit this assumption and compute synthetic planetary transit light curves directly from model stellar atmosphere center-to-limb intensity variations (CLIV) using the plane-parallel \textsc{Atlas} and spherically symmetric \textsc{SAtlas} codes. We compare these light curves to those constructed using best-fit limb-darkening parameterizations. We find that adopting parametric stellar limb-darkening laws lead to systematic differences from the more geometrically realistic model stellar atmosphere CLIV of about 50 -- 100 ppm at the transit center and up to 300 ppm at ingress/egress. While these errors are small they are systematic, and appear to limit the precision necessary to measure secondary effects. Our results may also have a significant impact on transit spectra.Comment: 12 pages, 14 figures, accepted for publication in ApJ after revision

SAtlas: Spherical Versions of the Atlas Stellar Atmosphere Program

Context: The current stellar atmosphere programs still cannot match some fundamental observations of the brightest stars, and with new techniques, such as optical interferometry, providing new data for these stars, additional development of stellar atmosphere codes is required. Aims: To modify the open-source model atmosphere program Atlas to treat spherical geometry, creating a test-bed stellar atmosphere code for stars with extended atmospheres. Methods: The plane-parallel Atlas has been changed by introducing the necessary spherical modifications in the pressure structure, in the radiative transfer and in the temperature correction. Results: Several test models show that the spherical program matches the plane-parallel models in the high surface gravity regime, and matches spherical models computed by Phoenix and by MARCS in the low gravity case.Comment: 10 pages, 10 figures, Accepted for publication in A&