Reflected Light Curves, Spherical and Bond Albedos of Jupiter- And Saturn-Like Exoplanets*

Abstract

Reflected light curves observed for exoplanets indicate that a few of them host bright clouds. We estimate how the light curve and total stellar heating of a planet depends 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 broadbands at 0.59-0.72 and 0.39-0.5 μm, and narrowbands at 0.938 (atmospheric window), 0.889 (CH4 absorption band), and 0.24-0.28 μm. 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 and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.

Jupiter’s Phase Variations From Cassini: A Testbed for Future Direct-Imaging Missions

“…At phase angles above 45 degrees, the Cassini data generally have a shallower slope than a Lambertian phase function. In addition at very low phase angles there is an uncharacteristic steep slope to the phase curve, known as the cusp effect, that has been readily apparent since the first ground-based observations were conducted at the turn of the 20th Century (Güssow 1929;Guthnick 1920Guthnick , 1918Muller 1893;Irvine et al 1968) and most recently was discussed in Dyudina et al (2016) as being caused by large cloud particles sharpening the backscattering peak. Dyudina et al (2016) employ models incorporating Henyey-Greenstein functions to study this effect in detail.…”

Dynamic mineral clouds on HD 189733b

“…Cahoy et al 2010;Barstow et al 2014;Garcia Munoz & Isaak 2015;Dyudina et al 2016) and more qualitatively captures the Mie backscattering lobe at optical wavelengths.…”

“…However, a small but not insignificant probability of backscattering is not completely captured by this approximation at optical wavelengths (e.g. Kattawar 1975;Draine 2003;Hood et al 2008;Dyudina et al 2016). To address this, we apply a two-term Henyey-Greenstein (TTHG) function (e.g.…”

“…To address this, we apply a two-term Henyey-Greenstein (TTHG) function (e.g. Pfeiffer & Chapman 2008;Cahoy et al 2010;Dyudina et al 2016) given by…”

Exoplanet Reflected-light Spectroscopy with PICASO

“…However these values are certainly not universal. Jupiter, Saturn, Uranus and Neptune all exhibit slightly different forward/back scattering peaks (Sudarsky et al 2005;Dyudina et al 2016). For observations of exoplanets, these parameters will have to be fit for.…”