The Direct Detectability of Giant Exoplanets in the Optical

Motivated by the possibility that a coronagraph will be put on WFIRST/AFTA, we explore the direct detectability of extrasolar giant planets (EGPs) in the optical. We quantify a planet's detectability by the fraction of its orbit for which it is in an observable configuration ($f_\mathrm{obs}$). Using a suite of Monte Carlo experiments, we study the dependence of $f_\mathrm{obs}$ upon the inner working angle (IWA) and minimum achievable contrast ($C_\mathrm{min}$) of the direct-imaging observatory; the planet's phase function, geometric albedo, single-scattering albedo, radius, and distance from Earth; and the semi-major axis distribution of EGPs. We calculate phase functions for a given geometric or single-scattering albedo, assuming various scattering mechanisms. We find that the Lambertian phase function can predict significantly larger $f_\mathrm{obs}$'s with respect to the more realistic Rayleigh phase function. For observations made with WFIRST/AFTA's baseline capabilities ($C_\mathrm{min}\sim10^{-9}$, $\mathrm{IWA}\sim0.2''$), Jupiter-like planets orbiting stars within 10, 30, and 50 parsecs of Earth have volume-averaged observability fractions of ${\sim}$12%, 3%, and 0.5%, respectively. At 10 parsecs, such observations yield $f_\mathrm{obs}>1\%$ for low- to modest-eccentricity planets with semi-major axes in the range ${\sim}2 - 10$ AU. If $C_\mathrm{min}=10^{-10}$, this range extends to ${\sim}35$ AU. We find that, in all but the most optimistic configurations, the probability for detection in a blind search is low (${<}\,5\%$). However, with orbital parameter constraints from long-term radial-velocity campaigns and Gaia astrometry, the tools we develop in this work can be used to determine both the most promising systems to target and when to observe them.