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

TL;DR

This study compares observed limb-darkening profiles from Kepler and TESS light curves of 43 stars with stellar atmosphere models, revealing good agreement but a small offset likely due to magnetic fields, impacting exoplanet radius measurements.

Contribution

It provides an empirical validation of limb-darkening models using high-quality light curves and identifies a small offset attributable to magnetic effects.

Findings

Most limb-darkening data agree with observations

Detected a small offset possibly caused by magnetic fields

Implications for exoplanet radius precision are discussed

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 $h^{\prime}_1 = I_{\lambda}(\frac{2}{3})$ and $h^{\prime}_2 = h^{\prime}_1 - I_{\lambda}(\frac{1}{3})$, 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 $h^{\prime}_1$ and $h^{\prime}_2$. There is a small but significant offset $\Delta h^{\prime}_1 \approx 0.006$ 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.