2015ApJ...799...87B

We use N_t, the number of exoplanets observed in time t, as a science metric to study direct-search missions like Terrestrial Planet Finder. In our model, N has 27 parameters, divided into three categories: 2 astronomical, 7 instrumental, and 18 science-operational. For various "27-vectors" of those parameters chosen to explore parameter space, we compute design reference missions to estimate N_t. Our treatment includes the recovery of completeness c after a search observation, for revisits, solar and antisolar avoidance, observational overhead, and follow-on spectroscopy. Our baseline 27-vector has aperture D = 16 m, inner working angle IWA = 0.039'', mission time t = 0-5 yr, occurrence probability for Earth-like exoplanets η = 0.2, and typical values for the remaining 23 parameters. For the baseline case, a typical five-year design reference mission has an input catalog of ∼4700 stars with nonzero completeness, ∼1300 unique stars observed in ∼2600 observations, of which ∼1300 are revisits, and it produces N₁∼ 50 exoplanets after one year and N₅∼ 130 after five years. We explore offsets from the baseline for 10 parameters. We find that N depends strongly on IWA and only weakly on D. It also depends only weakly on zodiacal light for Z < 50 zodis, end-to-end efficiency for h > 0.2, and scattered starlight for ζ < 10^–10. We find that observational overheads, completeness recovery and revisits, solar and antisolar avoidance, and follow-on spectroscopy are all important factors in estimating N.