Analytic Models for Albedos, Phase Curves, and Polarization of Reflected Light from Exoplanets

Abstract

New observational facilities are becoming increasingly capable of observing reflected light from transiting and directly imaged extrasolar planets. In this study, we provide an analytic framework to interpret observed phase curves, geometric albedos, and polarization of giant planet atmospheres. We compute the observables for non-conservative Rayleigh scattering in homogeneous semi-infinite atmospheres using both scalar and vector formalisms. In addition, we compute phase curves and albedos for Lambertian, isotropic, and anisotropic scattering phase functions. We provide analytic expressions for geometric albedos and spherical albedos as a function of the scattering albedo for Rayleigh scattering in semi-infinite atmospheres. Given an observed geometric albedo our prescriptions can be used to estimate the underlying scattering albedo of the atmosphere, which in turn is indicative of the scattering and absorptive properties of the atmosphere. We also study the dependence of polarization in Rayleigh scattering atmospheres on the orbital parameters of the planet–star system, particularly on the orbital inclination. We show how the orbital inclination of non-transiting exoplanets can be constrained from their observed polarization parameters. We consolidate the formalism, solution techniques, and results from analytic models available in the literature, often scattered in various sources, and present a systematic procedure to compute albedos, phase curves, and polarization of reflected light.