Exo-Earth/Super-Earth Yield of JWST plus a Starshade External Occulter

We examine the scientific viability of an imaging mission to find exo-Earths combining the James Webb Space Telescope (JWST) with a starshade external occulter under a realistic set of astrophysical assumptions. We define an exo-Earth as a planet of 1 to 10 Earth masses orbiting in the habitable zone (HZ) of a solar-type star. We show that for a survey strategy that relies on a single image to detect an exo-Earth, roughly half of all exo-Earth detections will be false alarms. Here, a false alarm is a mistaken identification of a planet as an exo-Earth. We consider two survey strategies designed to mitigate the false alarm problem. The first is to require that for each potential exo-Earth, a sufficient number of detections are made to measure the orbit. When the orbit is known we can determine if the planet is in the habitable zone. With this strategy, we find that the number of exo-Earths found is on average 0.9, 1.9 and 2.7 for {\eta}_Earth = 0.1, 0.2 and 0.3. Here, {\eta}_Earth is the frequency of exo-Earths orbiting solar-type stars. There is a ~40% probability of finding zero exo-Earths for {\eta}_Earth = 0.1. A second strategy can be employed if a space astrometry mission has identified and measured the orbits and masses of the planets orbiting nearby stars. We find that with prior space-based astrometry from a survey of 60 nearby stars, JWST plus an external occulter can obtain orbital solutions for the majority (70% to 80%) of the exo-Earths orbiting these 60 stars. The exo-Earth yield is approximately five times higher than the yield for the JWST plus occulter mission without prior astrometry. With prior astrometry, the probability that an imaging mission will find zero exo-Earths is reduced to below 1% for the case of {\eta}_Earth = 0.1.