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This paper is part of an effort to correct the transmission spectra of atransiting planet orbiting an active star. In Paper I (Cracchiolo et al. 2020)we have demonstrated a methodology to minimize the potential bias induced byunocculted star spots on the transmission spectrum, assuming a spot modelparameterized by filling factor and temperature. In this work we introduce thelimb darkening effect, therefore the position of the spot in the stellar diskand the impact parameter of the transiting planet now play a key role. Themethod is tested on simulations of planetary transits of three representativekinds of planetary systems, at ARIEL resolution. We find that a realistictreatment of the limb darkening is required to reliably estimate both the spotsparameters and the transmission spectrum of the transiting planet. Furthermore,we show that the influence of the spots onthe retrieval of the planetarytransmission spectrum is significant for spots close to the center of the star,covering a fraction greater than 0.05 and with a temperature contrast greaterthan 500 K, and that for these cases our method can confidently extract thetransmission spectrum and the impact parameter of the transiting planet forboth cases of occulted and not occulted spots, provided that we have anaccurate characterization of the stellar parameters and a reliable simulator ofthe instrument performances.

Correcting the effect of stellar spots on ARIEL transmission spectra II.The limb darkening effect