Empirical limb-darkening coefficients & transit parameters of known exoplanets from TESS

TL;DR

This study empirically derives limb-darkening coefficients and refines transit parameters for 176 known exoplanets observed by TESS, revealing significant discrepancies with theoretical models, especially for cooler stars below 5000 K.

Contribution

It provides the first large-scale empirical limb-darkening coefficients for TESS data and compares them with models, highlighting limitations in current theoretical predictions.

Findings

Significant offsets between empirical and theoretical limb-darkening coefficients.

Discrepancies up to 0.2 in quadratic limb-darkening parameters for cool stars.

Most theoretical models fail to accurately predict limb-darkening for stars cooler than 5000 K.

Abstract

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 allows us to extract empirical limb-darkening coefficients (LDCs) for the widely used quadratic law, but also updated transit parameters (including ephemerides refinements) as a byproduct. Comparing our empirically obtained LDCs with theoretical predictions, we find significant offsets when using tabulated \textit{TESS} LDCs. Specifically, the $u_2$ coefficients obtained using \textsc{phoenix} models show the largest discrepancies depending on the method used to derive them, with offsets that can reach up to $\Delta u_2 \approx 0.2$ on average. Most of those average offsets disappear, however, if one uses the SPAM algorithm introduced by Howarth (2011) to calculate the LDCs instead. Our results suggest, however, that for stars cooler than about 5000 K, no methodology is good enough to explain the limb-darkening effect: we observe a sharp deviation between measured and predicted LDCs on both quadratic LDCs of order $\Delta u_1, \Delta u_2 \approx 0.2$ for those cool stars. We recommend caution when assuming limb-darkening coefficients as perfectly known thus, in particular for these cooler stars when analyzing \textit{TESS} transit lightcurves.