Revised instellation patterns for close-in exoplanets

TL;DR

This paper develops a new analytical and numerical approach to accurately calculate the distribution of stellar radiation on close-in exoplanets, accounting for the star's size and limb darkening, revealing significant deviations from traditional models.

Contribution

It introduces an analytical formula and numerical methods to model insolation patterns on close-in exoplanets considering stellar size and limb darkening effects, improving accuracy over standard point-source assumptions.

Findings

Insolation at the substellar point can be up to 21% higher than standard calculations.

The substellar longitude of the terminator can extend up to 110 degrees on the nightside.

Significant deviations in insolation distribution are due to star size and limb darkening effects.

Abstract

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 3-D 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 susbtellar point is always higher -- by as much as 21% for known exoplanets -- than the standard calculation. The substellar longitude of the terminator can significantly extend on the nightside, from 90 degrees up to 110 degrees for known exoplanets.