Maximized ExoEarth Candidate Yields for Starshades

The design and scale of a future mission to directly image and characterize potentially Earth-like planets will be impacted, to some degree, by the expected yield of such planets. Recent efforts to increase the estimated yields, by creating observation plans optimized for the detection and characterization of Earth-twins, have focused solely on coronagraphic instruments; starshade-based missions could benefit from a similar analysis. Here we explore how to prioritize observations for a starshade given the limiting resources of both fuel and time, present analytic expressions to estimate fuel use, and provide efficient numerical techniques for maximizing the yield of starshades. We implemented these techniques to create an approximate design reference mission code for starshades and used this code to investigate how exoEarth candidate yield responds to changes in mission, instrument, and astrophysical parameters for missions with a single starshade. We find that a starshade mission operates most efficiently somewhere between the fuel- and exposure-time limited regimes, and as a result, is less sensitive to photometric noise sources as well as parameters controlling the photon collection rate in comparison to a coronagraph. We produced optimistic yield curves for starshades, assuming our optimized observation plans are schedulable and future starshades are not thrust-limited. Given these yield curves, detecting and characterizing several dozen exoEarth candidates requires either multiple starshades or an eta_Earth > ~0.3.