An approach for calculating exo-Earth yield of a 6 m IR/O/UV telescope for various broad bandwidth metrics

The Astro2020 Decadal Survey recommended a "future large IR/O/UV telescope optimized for observing habitable exoplanets and general astrophysics" to be ready by end of the decade and that mission "to search for biosignatures from a robust number of about ~25 habitable zone [exo]planets." The search for multiple biosignatures requires high quality spectra of broad bandwidth and sufficient signal-to-noise. The combination of spectral resolution, bandwidth, and signal-to-noise-ratio impacts the number of exo-Earths that can be spectrally characterized. Broader bandwidths and higher signal-to-noise lead to increased integration time and is likely to reduce the number of targets around which an Earth-size, habitable zone exoplanet could be sufficiently characterized. An increased integration will also consume a larger share of mission time dedicated to exoplanet direct imaging, possibly resulting in fewer exoplanets with higher quality spectra. Previous work (Morgan et al. 2022), evaluated the number of Earth-size, habitable zone exoplanets that could be spectrally characterized for a range of spectral resolutions, signal-to-noise ratios, and bandwidths for a 6-m diameter exoplanet direct imaging mission for coronagraph-only, starshade-only, and hybrid coronagraph-starshade architectures for three cases: the nominal case of a blind-search survey, the bounding case of perfect-prior knowledge which is useful to determine if target depletion occurs, and the partial-prior knowledge case of a hypothetical extreme precision radial velocity survey. In this paper, we expand the broadband spectra metric from 400 - 1000 nm to include UV (at a low spectral resolution) and the near infrared up to 2 microns. We introduce an approach for expressing the yield for each coronagraph sub-band that contains both the lower bound of the blind search base and the upper bound of the perfect prior case (a depth-of-search indicator), and includes the cumulative exposure time required to reach target depletion for each sub-band.