Empirical Limb-darkening Coefficients and Transit Parameters of Known Exoplanets from TESS

Although the main goal of the Transiting Exoplanet Survey Satellite (TESS) is to search for new transiting exoplanets, its data can also be used to study already-known systems in further detail. The TESS bandpass is particularly interesting to study the limb-darkening effect of the stellar host that is imprinted in transit light curves, as the widely used PHOENIX and ATLAS stellar models predict different limb-darkening profiles. Here we study this effect by fitting the transit light curves of 176 known exoplanetary systems observed by TESS, which allows us to extract empirical limb-darkening coefficients (LDCs) for the widely used quadratic law but also updated transit parameters (including ephemeride refinements) as a by-product. Comparing our empirically obtained LDCs with theoretical predictions, we find significant offsets when using tabulated TESS LDCs. Specifically, the u ₂ coefficients obtained using PHOENIX models show the largest discrepancies depending on the method used to derive them, with offsets that can reach up to Δu ₂ ≈ 0.2, on average. Most of those average offsets disappear, however, if one uses the SPAM algorithm introduced by Howarth 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 ≈ 0.2 for those cool stars. We recommend caution when assuming LDCs as perfectly known, in particular for these cooler stars when analyzing TESS transit light curves.