2020MNRAS.499.1627S

The distribution of instellation at the top of a planet's atmosphere or surface is usually calculated using the inverse-square law of radiation. This is based on the assumption that the host star is far enough to be considered a point-sized Lambertian source. This assumption, which works well for the Solar system planets and most exoplanets, must be revised for close-in exoplanets. The objective of this work is to derive accurate instellation patterns for close-in exoplanets, for which the effects of the spherical shape of the star must be taken into account. First, an analytical formula of the insolation as a function of latitude was derived, taking the star and the planet as 3D bodies, and incorporating the limb-darkening effects of the star. Then numerical techniques were used to compute the distribution of the insolation on close-in planets as a function of latitude for a wide range of stellar and planetary properties. There are significant deviations in instellation values and their distribution on close-in exoplanets, due in similar proportions to the physical size of the star and stellar limb-darkening effects. The insolation at the substellar point is always higher - by as much as 21 per cent for known exoplanets - than the standard calculation. The substellar longitude of the terminator can significantly extend on the night-side, from 90° up to 110° for known exoplanets.