2015ApJ...808..172G

Motivated by the possibility that a coronagraph will be put on the Wide-field Infrared Survey Telescope (WFIRST)/Astrophysics Focused Telescope Assets (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 (). Using a suite of Monte Carlo experiments, we study the dependence of upon the inner working angle (IWA) and minimum achievable contrast () of the direct-imaging observatory; the planet's phase function, geometric albedo, single-scattering albedo, radius, and distance from Earth; and the semimajor 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 largers with respect to the more realistic Rayleigh phase function. For observations made with WFIRST/AFTA's baseline capabilities (,), Jupiter-like planets orbiting stars within 10, 30, and 50 pc of Earth have volume-averaged observability fractions of ∼12%, 3%, and 0.5%, respectively. At 10 pc, such observations yield for low- to modest-eccentricity planets with semimajor axes in the range ∼2-10 AU. If, this range extends to ∼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.