  A critical question in astrobiology is whether exoEarth 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, fE,
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 (15m), LUVOIR-B (8m), HabEx with a starshade (4m,
"HabEx/SS"), HabEx without a starshade (4m, "HabEx/no-SS"); as well as three
estimates of the occurrence rate of EECs (eta_earth): 24%, 5%, and 0.5%. In the
case of a null-detection, we find that for eta_earth = 24%, LUVOIR-A, LUVOIR-B,
and HabEx/SS would constrain fE to <= 0.094, <= 0.18, and <= 0.56,
respectively. This also indicates that if fE is greater than these upper
limits, we are likely to detect O3 on at least 1 EEC. Conversely, we find that
HabEx/no-SS cannot constrain fE, due to the lack of an coronagraph ultraviolet
channel. For eta_earth = 5%, only LUVOIR-A and LUVOIR-B would be able to
constrain fE, to <= 0.45 and <= 0.85, respectively. For eta_earth = 0.5%, none
of the missions would allow us to constrain fE, due to the low number of
detectable EECs. We conclude that the ability to constrain fE is more robust to
uncertainties in eta_earth for missions with larger aperture mirrors. However
all missions are susceptible to an inconclusive null detection if eta_earth is
sufficiently low.
