Revealing peculiar exoplanetary shadows from transit light curves

Context. Until now the search of peculiar exoplanetary shadows, particularly those caused by exorings, was focused on the detection of a second-order photometric difference between the ringed and ringless (circular) transiting shadows. Both scenarios involved the parameter fitting to approximate the corresponding transit light curves (TLCs). As a result, the searched difference was extremely difficult to detect in the noise of the real transit photometry signals. Aims. In this work, we look for photometric manifestations of a non-spherical obscuring matter (e.g., exorings) around different exoplanets, mainly hot Jupiters, using a principally new approach. Methods. We used the transit parameters provided in Kepler database from the NASA Exoplanet Archive, where the fitting of the TLCs gives consistent sets of parameters for the transiting objects, assuming their spherical shape. At the same time, the semimajor axes, expressed in units of the stellar radii (initially, also a subject of the fitting), finally appear to be replaced by the calculated values according the Kepler’s third law and known stellar radii and surface gravity that have been determined through other methods. In the most typical case of a spherical transiting planet, such a replacement does not break the consistency of the whole parameter set. However, in the case of a non-spherical transiter and its non-circular shadow, the real (i.e., calculated according physics) value of the orbital semimajor axis could become inconsistent with the rest of the transit parameter set defined with the standard fitting procedure. The search for such inconsistencies, manifested as the difference between the simulated and observed transit duration, constitutes one of the main goals of this work. Moreover, we elaborate on a particular technique to gain information about the shape of planetary shadow, using the derivatives of the TLC during the ingress and egress phases. Results. We checked the TLCs of 21 hot Jupiters and 2 hot Neptunes. The consistent transit parameters and quasi-circular shadows were found for 11 objects. The analysis of the TLCs of five of the objects is complicated due to the noise problems, leading to the instability of solutions and deformation of shadows due to the low resolution of the derivatives. The remaining seven objects were formally qualified as peculiar outliers and among them, the planets Kepler-45b and Kepler-840b appear to be the most intriguing targets, with the most signifi