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 $y(λ)$ 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 $\left(\partial{\ln I_o(λ)}/{\partial{\ln g}}\right)_{T_{\rm eff}}$.
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), $-$2.0 (DBA) and He/H = 0 (DA), with log g varying between 5.0 and 9.5 and effective temperatures between 3750 K-100\,000 K. For effective temperatures higher than 40\,000 K, the models were also computed adopting nonlocal thermal equilibirum (DA). The adopted mixing-length parameters are ML2/$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 T$_{\rm eff}$ can be performed upon request.
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 s…
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 ea…
Limb-darkening is a fundamental constraint for modeling eclipsing binary and planetary transit light curves. As observations, for example from Kepler, CoRot, and Most, become more precise then a greater understanding of limb-darkening is necessary. However, limb-darkening is typically modeled as simple parameterizations fit to plane-parallel model stellar atmospheres that ignores stellar atmospheric extension. In this work, I compute linear, quadratic and four-parameter limb-darkening laws from grids of plane-parallel and spherically-symmetric model stellar atmospheres in a temperature and gra…
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 pa…
This paper examines how to compare stellar limb-darkening coefficients evaluated from model atmospheres with those derived from photometry. Different characterizations of a given model atmosphere can give quite different numerical results (even for a given limb-darkening `law'), while light-curve analyses yield limb-darkening coefficients that are dependent on system geometry, and that are not directly comparable to any model-atmosphere representation. These issues are examined in the context of exoplanetary transits, which offer significant advantages over traditional binary-star eclipsing sy…
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…
We present a novel method for measuring the masses of evolved stars from their limb-darkening observations parameterized as a linear-plus-square-root function with two coefficients. The coefficients of the law are related to integrated moments of the intensity and carry information about the extension of the stellar atmosphere, which is correlated to the ratio of the stellar radius to mass, R/M. Here, we show why the limb-darkening law is related to the R/M, and apply this result to limb-darkening observations of the microlensing event EROS-BLG-2000-5.
Stellar limb-darkening is an important tool for constraining the properties of a stellar atmosphere. We present a novel method for relating the fundamental stellar parameters mass and radius to limb-darkening laws using grids of spherical model stellar atmospheres. This method is applied to interferometric observations of the red supergiant Betelgeuse, where an unique measure of the stellar mass is determined.
We present extensive calculations of linear and non-linear limb-darkening coefficients as well as complete intensity profiles appropriate for modeling the light-curves of eclipsing white dwarfs. We compute limb-darkening coefficients in the Johnson-Kron-Cousins UBVRI photometric system as well as the Large Synoptic Survey Telescope (LSST) ugrizy system using the most up-to-date model atmospheres available. In all, we provide the coefficients for seven different limb-darkening laws. We describe the variations of these coefficients as a function of the atmospheric parameters, including the effec…
The variation in area of quiet magnetic network measured over the sunspot cycle should modulate the spatially averaged photospheric temperature gradient, since temperature declines with optical depth more gradually in magnetic flux tube atmospheres. Yet, limb darkening measurements show no dependence upon activity level, even at an rms precision of 0.04%. We study the sensitivity of limb darkening to changes in area filling factor using a 3D MHD model of the magnetized photosphere. The limb darkening change expected from the measured 11 yr area variation lies below the level of measured limb d…
New grids of Atlas9 models have been calculated using revised convection parameters and updated opacity-distribution functions, for chemical compositions intended to be representative of solar, [M/H] = +0.3, +0.5, Large Magellanic Cloud (LMC), and Small Magellanic Cloud (SMC) abundances. The grids cover T(eff) = 3.5-50kK, from log(g) = 5.0 to the effective Eddington limit. Limb-darkening coefficients and synthetic photometry are presented in the UBVRIJHKLM, uvby, ugriz, WFCAM, Hipparcos/Tycho, and Kepler passbands for these models, and for Castelli's comparable `new-ODF' grids. Flux distributi…
Recently there has been a renewed interest in the power-2 limb darkening law for modeling exoplanet transits. This law provides a better match to the intensities generated by spherical stellar atmosphere models than other 2-parameter laws. To help facilitate a wider use of the power-2 law we correct a minor error and, expanding on previous work, suggest a parametrization that can improve the sampling required by some numerical methods such as MCMC.
We introduce a method to measure with high resolution the solar diameter from the ground, through the eclipse observations by reconsidering the definition of the solar edge. The outer part of the Limb Darkening Function (LDF) is recovered using the luminosity evolution of a Baily's Bead and the profile of the lunar limb available from the Kaguya satellite. The method proposed is applied for the videos of the eclipse in January, 15, 2010 recorded by Richard Nugent in Uganda and Andreas Tegtmeier in India. The result shows light from solar limb detected at least 0.65 arcsec beyond the LDF inflec…
A discussion of the solar diameter and its variations must be linked to the limb darkening function (LDF). We introduce a new method to perform high resolution astrometry of the solar diameter from the ground, through the observations of eclipses, using the luminosity evolution of Baily's Bead and the profile of the lunar edge available from satellite data. The method proposed is applied for the videos of the eclipse on 15 January 2010 recorded in Uganda and in India. We obtained a detailed profile constraining the inflection point position. The result suggests reconsidering the evaluations of…
(Abridged) Context. Stellar limb darkening, I(μ = cosθ), 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(μ) from plane- parallel models, have found that fits to the flux-normalized curves pass through a fixed point, a common μ location on the stellar disk, for all values of T eff, log g and wavelength. Aims. We stud…
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 adopti…
The photospheric radius is one of the fundamental parameters governing the radiative equilibrium of a star. We report new observations of the nearest solar-type stars Alpha Centauri A (G2V) and B (K1V) with the VLTI/PIONIER optical interferometer. The combination of four configurations of the VLTI enable us to measure simultaneously the limb darkened angular diameter thetaLD and the limb darkening parameters of the two solar-type stars in the near-infrared H band (lambda = 1.65 microns). We obtain photospheric angular diameters of thetaLD(A) = 8.502 +/- 0.038 mas (0.43%) and thetaLD(B) = 5.999…
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 …
Empirical H- and K-band Limb Darkening for 31 CHARA Stars: A Near-Infrared Benchmark for Stellar-Atmosphere Models
The CHARA Array of Georgia State University（佐治亚州立大学CHARA阵列）；University of Michigan（密歇根大学）；European Southern Observatory（欧洲南方天文台）；Instituto de Alta Investigación, Universidad de Tarapacá（塔拉帕卡大学高等研究院）；European Organisation for Astronomical Research in the Southern Hemisphere (ESO)（欧洲南方天文学研究组织（ESO））；Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS（蔚蓝海岸大学、蔚蓝海岸天文台、法国国家科学研究中心）
We study how the precision of the exoplanet radius determination is affected by our present knowledge of limb darkening in two cases: when we fix the limb darkening coefficients and when we adjust them. We also investigate the effects of spots in one-colour photometry. We study the effect of limb darkening on the planetary radius determination both via analytical expressions and by numerical experiments. We also compare some of the existing limb darkening tables. When stellar spots affect the fit, we replace the limb darkening coefficients, calculated for the unspotted cases, with effective li…
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 approa…
The detection of the first exoplanet paved the way into the era of transit photometry space missions with a revolutionary photometric precision that aim at discovering new exoplanetary systems around different types of stars. With this high precision, it is possible to derive very accurately the radii of exoplanets which is crucial for constraining their type and composition. However, it requires an accurate description of host stars, especially their center-to-limb variation of intensities (so called limb darkening) as it affects the planet-to-star radius ratio determination. We aim at improv…
Transiting exoplanets provide unparalleled access to the fundamental parameters of both extrasolar planets and their host stars. We present limb-darkening coefficients (LDCs) for the exoplanet hunting CoRot and Kepler missions. The LDCs are calculated with ATLAS stellar atmospheric model grids and span a wide range of Teff, log g, and metallically [M/H]. Both CoRot and Kepler contain wide, nonstandard response functions, and are producing a large inventory of high-quality transiting lightcurves, sensitive to stellar limb darkening. Comparing the stellar model limb darkening to results from the…
We compute the emergent stellar spectra from the UV to far infrared for different viewing angles using realistic 3D model atmospheres for a large range in stellar parameters to predict the stellar limb darkening. We have computed full 3D LTE synthetic spectra based on 3D radiative hydrodynamic atmosphere models from the Stagger-grid. From the resulting intensities at different wavelength, we derived coefficients for the standard limb darkening laws considering a number of often-used photometric filters. Furthermore, we calculated theoretical transit light curves, in order to quantify the diffe…
We present a Python package LDTk that automates the calculation of custom stellar limb darkening (LD) profiles and model-specific limb darkening coefficients (LDC) using the library of PHOENIX-generated specific intensity spectra by Husser et al. (2013). The aim of the package is to facilitate analyses requiring custom generated limb darkening profiles, such as the studies of exoplanet transits--especially transmission spectroscopy, where the transit modelling is carried out for custom narrow passbands--eclipsing binaries (EBs), interferometry, and microlensing events. First, LDTk can be used …
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…
The finite-size effect in gravitational microlensing provides a possibility to measure the limb darkening of distant stars. We use the Finite Element Method (FEM) as an inversion tool for discretization and inversion of the magnification-limb darkening integral equation. This method makes no explicit assumption about the shape of the brightness profile more than the flatness of the profile near the center of the stellar disk. From the simulation, we investigate the accuracy and stability of this method and we use regularization techniques to stabilize it. Finally, we apply this method to the s…
Inaccurate limb-darkening models can be a significant source of error in the analysis of the light curves for transiting exoplanet and eclipsing binary star systems. To test the accuracy of published limb-darkening models, I have compared limb-darkening profiles predicted by stellar atmosphere models to the limb-darkening profiles measured from high-quality light curves of 43 FGK-type stars in transiting exoplanet systems observed by the Kepler and TESS missions. The comparison is done using the parameters $h^{\prime}_1 = I_λ(\frac{2}{3})$ and $h^{\prime}_2 = h^{\prime}_1 - I_λ(\frac{1}{3})$, …
Aims: We present a detailed analysis of OGLE 2004-BLG-482, a relatively high-magnification single-lens microlensing event which exhibits clear extended-source effects. These events are relatively rare, but they potentially contain unique information on the stellar atmosphere properties of their source star, as shown in this study. Methods: Our dense photometric coverage of the overall light curve and a proper microlensing modelling allow us to derive measurements of the OGLE 2004-BLG-482 source star's linear limb-darkening coefficients in three bands, including standard Johnson-Cousins I and R…
One of the biggest problems we can encounter while dealing with the limb-darkening coefficients for stellar atmospheric models with spherical symmetry is the difficulty of adjusting both the limb and the central parts simultaneously. In particular, the regions near the drop-offs are not well reproduced for most models, depending on Teff, log g, or wavelength. Even if the law with four terms is used, these disagreements still persist. Here we introduce a new method that considerably improves the description of both the limb and the central parts and that will allow users to test models of stell…
We introduce a new method to perform high resolution astrometry of the solar diameter from the ground, through the observations of eclipses. A discussion of the solar diameter and its variations is linked to the Limb Darkening Function (LDF) using the luminosity evolution of a Baily's Bead and the profile of the lunar limb available from satellite data. The inflexion point of the LDF is defined as the solar limb. The method proposed is applied for the videos of the eclipse in January, 15, 2010 recorded by Richard Nugent in Uganda and Andreas Tegtmeier in India. An upper limit for the inflexion…
In order to perform high resolution astrometry of the solar diameter from the ground, through the observations of eclipses, the study of the limb darkening profile is described. Knowing the profile of the solar limb is useful both to monitor the solar radius over time, and to define the oblateness, which is interesting for the classical tests of general relativity. The Limb Darkening Function (LDF) is studied in order to find the inflexion point, to which the measurements of the solar diameter are referred. The proposed method is applied to the videos of the annular eclipse in January, 15, 201…
Limb darkening is an important stellar phenomenon and must be accounted for in the study of stellar spectra, eclipsing binaries, transiting planetary systems, and microlensing events. The power-2 limb-darkening law provides a good match to the specific intensities predicted by stellar atmosphere models: it is better than other two-parameter laws and is only surpassed by the four-parameter law. Predictions of the limb-darkening coefficients for the power-2 law are not widely available. We therefore compute them, using stellar atmosphere models generated by the ATLAS (plane-parallel) code. Limb-…
Although the main goal of the Transiting Exoplanet Survey Satellite (\textit{TESS}) is to search for new transiting exoplanets, its data can also be used to study in further detail already known systems. The \textit{TESS} bandpass is particularly interesting to study the limb-darkening effect of the stellar host which is imprinted in transit lightcurves, as the widely used \textsc{phoenix} and \textsc{atlas} stellar models predict different limb-darkening profiles. Here we study this effect by fitting the transit lightcurves of 176 known exoplanetary systems observed by \textit{TESS}, which al…
The depth of an exoplanetary transit in the light curve of a distant star is commonly approximated as the squared planet-to-star radius ratio, (R_p/R_s)^2. Stellar limb darkening, however, results in significantly deeper transits. Here we derive analytical solutions to the overshoot of the mid-transit depth caused by stellar limb darkening compared to the (R_p/R_s)^2 estimate for arbitrary transit impact parameters. In turn, this allows us to compute the true planet-to-star radius ratio from the transit depth for a given parameterization of a limb darkening law and for a known transit impact p…
Stellar limb darkening affects a wide range of astronomical measurements and is frequently modelled with a parametric model using polynomials in the cosine of the angle between the line of sight and the emergent intensity. Two-parameter laws are particularly popular for cases where one wishes to fit freely for the limb darkening coefficients (i.e. an uninformative prior) due to the compact prior volume and the fact that more complex models rarely obtain unique solutions with present data. In such cases, we show that the two limb darkening coefficients are constrained by three physical boundary…
Context. One challenge for measuring the Hubble constant using Classical Cepheids is the calibration of the Leavitt Law or period-luminosity relationship. The Baade-Wesselink method for distance determination to Cepheids relies on the ratio of the measured radial velocity and pulsation velocity, the so-called projection factor and the ability to measure the stellar angular diameters. Aims. We use spherically-symmetric model stellar atmospheres to explore the dependence of the p-factor and angular diameter corrections as a function of pulsation period. Methods. Intensity profiles are computed f…
Multi-chromatic observations of classical Cepheids using the CHARA Array interferometer: Surface brightness-colour relation, projection factor, and limb-darkening
Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange（蔚蓝海岸大学，蔚蓝海岸天文台）；European Southern Observatory（欧洲南方天文台）；LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS（巴黎天文台 LIRA 实验室，巴黎文理研究大学，索邦大学，巴黎西岱大学，CY 塞尔吉巴黎大学）；French-Chilean Laboratory for Astronomy, IRL 3386, CNRS（中智天文学联合实验室）；Instituto de Alta Investigación, Universidad de Tarapacá（塔拉帕卡大学高等研究院）；Astronomy Department, University of Michigan（密歇根大学天文学系）
Gravitational microlensing is not only a successful tool for discovering distant exoplanets, but it also enables characterization of the lens and source stars involved in the lensing event. In high magnification events, the lens caustic may cross over the source disk, which allows a determination of the angular size of the source and additionally a measurement of its limb darkening. When such extended-source effects appear close to maximum magnification, the resulting light curve differs from the characteristic Paczynski point-source curve. The exact shape of the light curve close to the peak …
We compare limb darkening laws derived from 3D hydrodynamical model atmospheres and 1D hydrostatic MARCS models for the host stars of the two transiting exoplanet systems HD 209458 and HD 189733. The surface brightness distribution of the stellar disks is calculated using 3D LTE spectrum formation and opacity sampling. We test our predictions using least-squares fits of model light curves to primary eclipses that were observed with the Hubble Space Telescope (HST). The limb darkening law derived from the 3D model of HD 209458 between 2900 A and 5700 A produces significantly better fits to the …
Inaccurate limb-darkening models can be a significant source of error in the analysis of the light curves for transiting exoplanet and eclipsing binary star systems, particularly for high-precision light curves at optical wavelengths. The power-2 limb-darkening law, $I_λ(μ) = 1 - c\left(1-μ^α\right)$, has recently been proposed as a good compromise between complexity and precision in the treatment of limb-darkening. I have used synthetic spectra based on the 3D stellar atmosphere models from the Stagger-grid to compute the limb-darkening for several passbands (UBVRI, CHEOPS, TESS, Kepler, etc.…
We have developed a universal approach to compute accurately the brightness of eclipsing binary systems during the transit of a planet in front of the stellar disk. This approach is uniform for all values of the system parameters and applicable to most limb-darkening laws used in astrophysics. In the cases of linear and quadratic limb-darkening laws we obtained analytical expressions for the light curve and its derivatives in terms of elementary functions, elliptic integrals and piecewise-defined function of one variable. In the cases of logarithmic and square root laws of limb darkening the f…
We release a new grid of stellar limb-darkening coefficients (LDCs, using the quadratic, power-2 and claret-4 laws) and intensity profiles for the Kepler, U, B, V and R passbands, based on STAGGER model atmospheres. The data can be downloaded from Zenodo (doi:10.5281/zenodo.5593162). We compare the newly-released LDCs, computed by ExoTETHyS, with previously published values, based on the same atmospheric models using a so-called "SPAM" procedure. The SPAM method relies on synthetic light curves in order to compute the LDCs that best represent the photometry of exoplanetary transits. We confirm…
Context. The interpretation of stellar pulsations in terms of internal structure depends on the knowledge of the fundamental stellar parameters. Long-base interferometers permit us to determine very accurate stellar radii, which are independent constraints for stellar models that help us to locate the star in the HR diagram. Aims: Using a direct interferometric determination of the angular diameter and advanced three-dimensional (3D) modeling, we derive the radius of the CoRoT target HD 49933 and reduce the global stellar parameter space compatible with seismic data. Methods: The VEGA/CHARA sp…
Limb-darkening is fundamental in determining transit lightcurve shapes, and is typically modeled by a variety of laws that parametrize the intensity profile of the star that is being transited. Confronted with a transit lightcurve, some authors fix the parameters of these laws, the so-called limb-darkening coefficients (LDCs), while others prefer to let them float in the lightcurve fitting procedure. Which of these is the best strategy, however, is still unclear, as well as how and by how much each of these can bias the retrieved transit parameters. In this work we attempt to clarify those poi…
The Total Solar Irradiance varies over a solar cycle of 11 years and maybe over cycles with longer period. Is the solar diameter variable over time too? We introduce a new method to perform high resolution astrometry of the solar diameter from the ground, through the observations of eclipses by reconsidering the definition of the solar edge. A discussion of the solar diameter and its variations must be linked to the Limb Darkening Function (LDF) using the luminosity evolution of a Baily's Bead and the profile of the lunar limb available from satellite data. This approach unifies the definition…
Stellar limb-darkening impacts a wide range of astronomical measurements. The accuracy to which it is modelled limits the accuracy in any covariant parameters of interest, such as the radius of a transiting planet. With the ever growing availability of precise observations and the importance of robust estimates of astrophysical parameters, an emerging trend has been to freely fit the limb-darkening coefficients (LDCs) describing a limb-darkening law of choice, in order to propagate our ignorance of the true intensity profile. In practice, this approach has been limited to two-parameter limb-da…
Limb darkening (LD) is typically parameterised using a range of functional "laws" in models of the light curves of eclipsing binary and transiting planetary systems. The two-coefficient LD laws all suffer from a strong correlation between their coefficients, preventing a reliable determination of both coefficients from high-quality light curves. We use numerical simulations to propose re-parameterisations of the quadratic, logarithmic, square-root and cubic LD laws that show much weaker correlations, and implement them into the JKTEBOP code. We recommend that these re-parameterisations are use…
GIARPS simultaneous optical and infrared high-spectral-resolution observations of Cepheids I. Limb darkening from cross-correlated radial velocities
Université Côte d’Azur（蔚蓝海岸大学）；Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université（巴黎天文台，巴黎文理研究大学，索邦大学，巴黎西岱大学，塞吉-蓬图瓦兹大学）；French-Chilean Laboratory for Astronomy, IRL 3386, CNRS and U. de Chile（中法天文学联合实验室）；Universidad de Concepción（康塞普西翁大学）；Leibniz Institute for Astrophysics（莱布尼茨天体物理研究所）；Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）；European Southern Observatory（欧洲南方天文台）
We release the first grid of stellar limb-darkening coefficients (LDCs) and intensity profiles (IPs) computed by the consortium of the PLAnetary Transits and Oscillations of stars (PLATO), the next medium-class (M3) mission under development by the European Space Agency (ESA) to be launched in 2026. We have performed spectral synthesis with \texttt{TurboSpectrum} on a grid of \texttt{MARCS} model atmospheres. Finally, we adopted \texttt{ExoTETHyS} to convolve the high-resolution spectra ($R=2\times10^5$) with the state-of-the-art response functions for all the PLATO cameras, and computed the L…
This paper is part of an effort to correct the transmission spectra of a transiting planet orbiting an active star. In Paper I (Cracchiolo et al. 2020) we have demonstrated a methodology to minimize the potential bias induced by unocculted star spots on the transmission spectrum, assuming a spot model parameterized by filling factor and temperature. In this work we introduce the limb darkening effect, therefore the position of the spot in the stellar disk and the impact parameter of the transiting planet now play a key role. The method is tested on simulations of planetary transits of three re…
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…
The power-2 law, $I_λ(μ)=1- c (1 - μ^α)$, accurately represents the limb-darkening profile for cool stars. It has been implemented in a few transit models to-date using numerical integration but there is as-yet no implementation of the power-2 law in analytic form that is generally available. An algorithm to implement the power-2 law is derived using a combination of an approximation to the required integral and a Taylor expansion of the power-2 law. The accuracy of stellar and planetary radii derived by fitting transit light curves with this approximation is tested using light curves computed…
