Reflected Light Curves, Spherical and Bond Albedos of Jupiter- and Saturn-like Exoplanets

Abstract

Reflected light curves observed for exoplanets indicate bright clouds at some of them. We estimate how the light curve and total stellar heating of a planet depend on forward and backward scattering in the clouds based on Pioneer and Cassini spacecraft images of Jupiter and Saturn. We fit analytical functions to the local reflected brightnesses of Jupiter and Saturn depending on the planet's phase. These observations cover broad bands at 0.59-0.72 and 0.39-0.5 {\mu}m, and narrow bands at 0.938 (atmospheric window), 0.889 (CH4 absorption band), and 0.24-0.28 {\mu}m. We simulate the images of the planets with a ray-tracing model, and disk-integrate them to produce the full-orbit light curves. For Jupiter, we also fit the modeled light curves to the observed full-disk brightness. We derive spherical albedos for Jupiter, Saturn, and for planets with Lambertian and Rayleigh-scattering atmospheres. Jupiter-like atmospheres can produce light curves that are a factor of two fainter at half-phase than the Lambertian planet, given the same geometric albedo at transit. The spherical albedo is typically lower than for a Lambertian planet by up to a factor of 1.5. The Lambertian assumption will underestimate the absorption of the stellar light and the equilibrium temperature of the planetary atmosphere. We also compare our light curves with the light curves of solid bodies: the moons Enceladus and Callisto. Their strong backscattering peak within a few degrees of opposition (secondary eclipse) can lead to an even stronger underestimate of the stellar heating.