Limb darkening measurements from TESS and Kepler light curves of transiting exoplanets

Abstract

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 $h_1^{\prime }=I_{\lambda }(\frac{2}{3})$ and $h_2^{\prime }=h_1^{\prime }-I_{\lambda }(\frac{1}{3})$, where $I_{\lambda }(\mu )$ is the specific intensity emitted in the direction $\mu$, the cosine of the angle between the line of sight and the surface normal vector. These parameters are straightforward to interpret and insensitive to the details of how they are computed. I find that most (but not all) tabulations of limb-darkening data agree well with the observed values of $h_1^{\prime }$ and $h_2^{\prime }$. There is a small but significant offset $\Delta h_1^{\prime }\approx 0.006$ compared to the observed values that can be ascribed to the effect of a mean vertical magnetic field strength $\approx 100$\,G that is expected in the photospheres of these inactive solar-type stars but that is not accounted for by typical stellar model atmospheres. The implications of these results for the precision of planetary radii measured by the PLATO mission are discussed briefly.

arXiv comment12 pages, 11 figures. Accepted for publication in MNRAS

References in corpus (40)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• emcee: The MCMC Hammer
• The chemical composition of the Sun
• The Transiting Exoplanet Survey Satellite
• A new extensive library of PHOENIX stellar atmospheres and synthetic spectra
• batman: BAsic Transit Model cAlculatioN in Python
• Efficient, uninformative sampling of limb darkening coefficients for two-parameter laws
• Homogeneous studies of transiting extrasolar planets. IV. Thirty systems with space-based light curves
• Limb and gravity-darkening coefficients for the TESS satellite at several metallicities, surface gravities, and microturbulent velocities
• Stellar Limb-Darkening Coefficients for CoRot and Kepler
• Using Stellar Limb-Darkening to Refine the Properties of HD 209458b
• Starspots, spin-orbit misalignment, and active latitudes in the HAT-P-11 exoplanetary system
• HST/STIS Optical Transit Transmission Spectra of the hot-Jupiter HD209458b
• ELLC - a fast, flexible light curve model for detached eclipsing binary stars and transiting exoplanets
• The Stagger-grid: A grid of 3D stellar atmosphere models - IV. Limb darkening coefficients
• The effect of stellar limb darkening values on the accuracy of the planet radii derived from photometric transit observations
• A new method to compute limb-darkening coefficients for stellar atmosphere models with spherical symmetry: the space missions TESS, Kepler, Corot, and MOST
• Properties of analytic transit light curve models
• SWEET-Cat 2.0: The Cat just got SWEETer; Higher quality spectra and precise parallaxes from GAIA eDR3
• On stellar limb darkening and exoplanetary transits
• A Transiting Hot Jupiter Orbiting a Metal-Rich Star
• Limb-darkening and exoplanets II: Choosing the Best Law for Optimal Retrieval of Transit Parameters
• Kepler-14b: A massive hot Jupiter transiting an F star in a close visual binary
• Empirical limb-darkening coefficients & transit parameters of known exoplanets from TESS
• An Independent Analysis of Kepler-4b through Kepler-8b
• High-precision stellar limb-darkening in exoplanetary transits
• Comparison of the power-2 limb-darkening law from the Stagger-grid to Kepler light curves of transiting exoplanets
• Transit light curve and inner structure of close-in planets
• Kepler423b: a half-Jupiter mass planet transiting a very old solar-like star
• No X-rays from WASP-18. Implications for its age, activity, and the influence of its massive hot Jupiter
• Spectral variability of photospheric radiation due to faculae I: The Sun and Sun-like stars
• Spherically symmetric model stellar atmospheres and limb darkening II: limb-darkening laws, gravity-darkening coefficients and angular diameter corrections for FGK dwarf stars
• Tidally Distorted Exoplanets: Density Corrections for Short-Period Hot-Jupiters based solely on Observable Parameters
• SAtlas: Spherical Versions of the Atlas Stellar Atmosphere Program
• Suppressed Far-UV Stellar Activity and Low Planetary Mass Loss in the WASP-18 System
• The PLATO Solar-like Light-curve Simulator: A tool to generate realistic stellar light-curves with instrumental effects representative of the PLATO mission
• TOI-150b and TOI-163b: two transiting hot Jupiters, one eccentric and one inflated, revealed by TESS near and at the edge of the JWST CVZ
• Limb Darkening and Planetary Transits: Testing Center-to-limb Intensity Variations and Limb-Darkening Directly from Model Stellar Atmospheres
• Note on the Power-2 Limb Darkening Law
• First release of PLATO consortium stellar limb-darkening coefficients

Cited by in corpus (3)

• Kepler meets Gaia DR3: homogeneous extinction-corrected color-magnitude diagram and binary classification
• The EBLM project -- XIV. TESS light curves for eclipsing binaries with very low mass companions
• KRONOS I: The $1-2.8\mu$m JWST Transmission Spectrum of the 23 Myr V1298 Tau c