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

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 $Δu_2 \approx 0.2$ 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 $Δu_1, Δu_2 \approx 0.2$ 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.

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