Probing the Capability of Future Direct-imaging Missions to Spectrally Constrain the Frequency of Earth-like Planets

A critical question in astrobiology is whether exo-Earth candidates (EECs) are Earth-like, in that they originate life that progressively oxygenates their atmospheres similarly to Earth. We propose answering this question statistically by searching for O2 and O3 on EECs with missions such as HabEx or LUVOIR. We explore the ability of these missions to constrain the fraction, f E, of EECs that are Earth-like in the event of a null detection of O2 or O3 on all observed EECs. We 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”), and HabEx without a starshade (4 m, “HabEx/no-SS”)—as well as three estimates of the occurrence rate of EECs (η earth): 24%, 5%, and 0.5%. In the case of a null detection, we find that for η earth = 24%, LUVOIR-A, LUVOIR-B, and HabEx/SS would constrain f E to ≤0.094, ≤0.18, and ≤0.56, respectively. This also indicates that if f E is greater than these upper limits, we are likely to detect O3 on at least one EEC. Conversely, we find that HabEx/no-SS cannot constrain f E, due to the lack of a coronagraph ultraviolet channel. For η earth = 5%, only LUVOIR-A and LUVOIR-B would be able to constrain f E, to ≤0.45 and ≤0.85, respectively. For η earth = 0.5%, none of the missions would allow us to constrain f E, due to the low number of detectable EECs. We conclude that the ability to constrain f E is more robust to uncertainties in η earth for missions with larger aperture mirrors. However, all missions are susceptible to an inconclusive null detection if η earth is sufficiently low.