Extended Data Fig. 5: Empirically derived stellar limb darkening coefficients fit with a quadratic law.

a, the fit u₊ coefficients (black) along with the theoretically predicted values derived from a 3D stellar model (red). The theoretical u₊ values with a constant offset of −0.065 ± 0.022 (purple) is also shown. The theoretical models predict the wavelength-to-wavelength shape of u₊ well. As u₊ is directly related to the intensity of the star at the stellar limb ref. ⁸⁴, these findings suggest WASP-39A is 6% brighter at the limb than models predict. b, similar as a, but for the u₋ coefficient. As the shape of the derived coefficients differs from the model prediction, u₋ was left free to vary in the transmission spectral fits. The error bars are 1-σ standard deviations.