Probing the capability of future direct imaging missions to spectrally constrain the frequency of Earth-like planets

A critical question in the search for extraterrestrial life is whether exoEarth candidates (EECs) are Earth-like, in that they host life that progressively oxygenates their atmospheres. We propose answering this question statistically by searching for O₂ and O₃ on EECs detected by future direct imaging missions such as HabEx or LUVOIR. In this paper we explore the ability of these missions to constrain the fraction, fE, of EECs that are Earth-like for different estimates of the occurrence rate of EECs (η_earth). A positive detection of O₂ and O₃ on at least 1 EEC would allow us to significantly constrain f_E. However, an important consideration is whether these missions could still allow us to constrain f_E in the event of a null detection, where we do not detect O₂ or O₃ on any observed EEC. To determine this, our approach is to use the Planetary Spectrum Generator to simulate observations of EECs with O₂ and O₃ levels based on Earth’s history. We consider four instrument designs: LUVOIR-A (15 m), LUVOIR-B (8 m), HabEx with a starshade (4 m, “HabEx/SS”), HabEx without a starshade (4 m, “HabEx/no-SS”). We also consider three estimates of η_earth: 24%, 5%, and 0.5%. In the case of a null-detection where we do not detect O₂ and O3 on any EECs we find that for η_earth = 24%, LUVOIR-A, LUVOIR-B, and HabEx/SS would constrain the fraction, f_E , of EECs that are Earth-like, to ≤ 0.094, ≤ 0.18, and ≤ 0.56, respectively, for the most likely range of estimates of Proterozoic O₂. This also indicates that for f_E greater than these upper limits, we are likely to detect O₃ on at least 1 EEC. In contrast, we find that HabEx/no-SS cannot constrain f_E, due in large part to the lack of an ultraviolet channel on the coronagraph. For η_earth = 5%, only LUVOIR-A and LUVOIR-B would be able to constrain fE in the case of a null detection, to ≤ 0.45 and ≤ 0.85, respectively. Finally, for η_earth = 0.5%, none of the missions would allow us to constrain fE in the case of a null detection, as it will likely be difficult to detect EECs in that scenario. We conclude that the value of η_earth has a strong effect on our ability to constrain f_E in the event of a null detection, and although missions with larger aperture mirrors are more robust to uncertainties in η_earth, all are susceptible to an inconclusive null detection if η_earth is sufficiently low.