# Bioverse: GMT and ELT Direct Imaging and High-Resolution Spectroscopy
Assessment – Surveying Exo-Earth O2 and Testing the Habitable Zone Oxygen
Hypothesis

Kevin K. Hardegree-Ullman Steward Observatory, The University of Arizona,
Tucson, AZ 85721, USA<EMAIL_ADDRESS>Dániel Apai Steward Observatory,
The University of Arizona, Tucson, AZ 85721, USA<EMAIL_ADDRESS>Lunar
and Planetary Laboratory, The University of Arizona, Tucson, AZ 85721, USA
Sebastiaan Y. Haffert Steward Observatory, The University of Arizona, Tucson,
AZ 85721, USA<EMAIL_ADDRESS>Martin Schlecker Steward Observatory, The
University of Arizona, Tucson, AZ 85721, USA<EMAIL_ADDRESS>Markus
Kasper European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748
Garching bei München, Germany  Jens Kammerer European Southern Observatory,
Karl-Schwarzschild-Straße 2, 85748 Garching bei München, Germany  Kevin Wagner
Steward Observatory, The University of Arizona, Tucson, AZ 85721, USA;
<EMAIL_ADDRESS>
###### Abstract

Biosignature detection in the atmospheres of Earth-like exoplanets is one of
the most significant and ambitious goals for astronomy, astrobiology, and
humanity. Molecular oxygen is among the strongest indicators of life on Earth,
but it will be extremely difficult to detect via transmission spectroscopy. We
used the Bioverse statistical framework to assess the ability to probe Earth-
like O2 levels on hypothetical nearby habitable zone exoplanets (EECs) using
direct imaging and high-resolution spectroscopy on the Giant Magellan
Telescope (GMT) and the Extremely Large Telescope (ELT). We found that O2
could be probed on up to $\sim$5 and $\sim$15 EECs orbiting bright M dwarfs
within 20 pc in a 10-year survey on the GMT and ELT, respectively. Earth-like
O2 levels could be probed on four known super-Earth candidates, including
Proxima Centauri b, within about one week on the ELT and a few months on the
GMT. We also assessed the ability of the ELT to test the habitable zone oxygen
hypothesis – that habitable zone Earth-sized planets are more likely to have
O2 – within a 10-year survey using Bioverse. Testing this hypothesis requires
either $\sim$1/2 of the EECs to have O2 or $\sim$1/3 if $\eta_{\oplus}$ is
large. A northern hemisphere large-aperture telescope, such as the Thirty
Meter Telescope (TMT), would expand the target star pool by about 25%, reduce
the time to probe biosignatures on individual targets, and provide an
additional independent check on potential biosignature detections.

Exoplanet systems (484) — Exoplanets (498) — Exoplanet Atmospheres (487) —
Biosignatures (2018) — Astrobiology (74) — Habitable Zone (696) — Habitable
Planets (695) — Astronomical Simulations (1857) — Bayesian Statistics (1900) —
Parametric Hypothesis Tests (1904)

††software: astroplan (Morris et al., 2018), astropy (Astropy Collaboration et
al., 2013, 2018, 2022), Bioverse (Bixel & Apai, 2021; Hardegree-Ullman et al.,
2023; Schlecker et al., 2024), dynesty (Speagle, 2020), matplotlib (Hunter,
2007), numpy (Harris et al., 2020), pandas (Wes McKinney, 2010; pandas
Development Team, 2020), PyAstronomy (Czesla et al., 2019)

##  1 Introduction

Methods for probing the atmospheres of exoplanets have matured to the point
that we are within reach of biosignature detection on rocky worlds.
Transmission spectroscopy has become a powerful tool to characterize the
atmospheres of planets from the ground (e.g., Snellen et al., 2008, 2010;
Stevenson et al., 2014), and from space with HST (e.g., Charbonneau et al.,
2002; Sing et al., 2016; Zhang et al., 2018) and now JWST (e.g., JWST
Transiting Exoplanet Community Early Release Science Team et al., 2023; Moran
et al., 2023). In the search for biosignatures via transmission spectroscopy,
JWST might prove fruitful in the detection of species such as CH4, H2O, and
CO2 (e.g., Wunderlich et al., 2019), however, it will not be able to detect O2
(Lustig-Yaeger et al., 2019; Wunderlich et al., 2019; Pidhorodetska et al.,
2020), a major byproduct of the biological process of oxygenic photosynthesis
on Earth. Snellen et al. (2013), Rodler & López-Morales (2014), Serindag &
Snellen (2019), López-Morales et al. (2019), Currie et al. (2023), and
Hardegree-Ullman et al. (2023) studied the prospects of detecting O2 via
transmission spectroscopy using upcoming 25–40-meter class telescopes such as
the Giant Magellan Telescope (GMT, Johns et al., 2012), Thirty Meter Telescope
(TMT, Nelson & Sanders, 2008; Sanders, 2013), and European Southern
Observatory Extremely Large Telescope (ELT, Gilmozzi & Spyromilio, 2007).
Hardegree-Ullman et al. (2023) took into account practical ground-based
observing constraints such as transit observability and relative system
velocities to mitigate telluric blending. They concluded that even in a very
optimistic observing scenario where signals from the GMT, TMT, and ELT and all
observable transits could be combined, it will likely take decades to make an
O2 detection on a single transiting habitable zone Earth-sized exoplanet.

This study explores whether direct imaging is more efficient for O2 surveys.
Previous studies suggest it might be possible to detect biosignatures using
reflected light spectroscopy on directly imaged planets (e.g., Snellen et al.,
2015; Lovis et al., 2017). To date, high contrast imaging has been limited to
young, self-luminous gas giants on wide orbits (e.g., Chauvin et al., 2004;
Marois et al., 2008; Lagrange et al., 2009; Macintosh et al., 2015; Keppler et
al., 2018). This is mainly due to telescope apertures limiting the inner
working angle at which a planet is detectable (often similar to the Rayleigh
criterion $\sim$1.22$\lambda/D$, where $\lambda$ is the observing wavelength
and $D$ is the primary mirror diameter) and due to contrast limitations of
current high-contrast imaging systems.

###  1.1 Previous Direct Imaging Studies

There have been numerous studies investigating the potential for a next-
generation space telescope (e.g., LUVOIR, HabEx, LIFE, The LUVOIR Team, 2019;
Gaudi et al., 2020; Quanz et al., 2022) to probe biosignatures in reflected
light with direct imaging and low-resolution spectroscopy (e.g., Feng et al.,
2018; Bixel & Apai, 2021; Damiano & Hu, 2022; Konrad et al., 2022; Robinson &
Salvador, 2023; Susemiehl et al., 2023). Due to the recommendations brought
forth in the Astro2020 Decadal Survey (NASEM, 2021), the Habitable Worlds
Observatory (HWO) is being developed with the goal to identify and directly
image at least 25 potentially habitable worlds using a telescope about the
same size as JWST and optimistically launching in the 2040s. In the meantime,
the GMT, TMT, and ELT are expected to be operational in the early 2030s. The
significantly larger apertures of these telescopes will be able to probe
smaller inner working angles and study the habitable zones of nearby M dwarfs,
which will be inaccessible to HWO.

Ground-based reflected-light spectroscopy of biosignatures necessitates the
use of high resolution spectrographs to mitigate some of the effects of line
blending with Earth’s atmosphere. Sparks & Ford (2002) proposed combining a
coronographic imager to a high spectral resolution integral-field spectrograph
for detection and characterization of exoplanets. As Snellen et al. (2015)
showed, the achievable contrast of a combined high-contrast imaging and high-
resolution spectrograph system is the product of the individual system
achievable contrasts. For example, if each individual system can reach a
contrast of $\sim$10-5, the combined system could reach contrasts of
$\sim$10-10. Snellen et al. (2015) investigated using an optical high-
resolution spectrograph (R=100,000) in combination with an extreme adaptive
optics (AO) system on the ELT to observe a hypothetical 1.5 $R_{\oplus}$
planet in the habitable zone of Proxima Centauri in reflected light (prior to
the discovery of Proxima Centauri b by Anglada-Escudé et al., 2016). They
concluded that such a planet would be detectable in broadband (0.6–0.9 $\mu$m)
reflected light in 10 hours of integration time at a S/N of $\sim$10 after
cross-correlating the hypothetical observed spectrum with a model template
spectrum, but they did not explore specific biosignature detection.

Since its discovery, most of the focus on high-contrast imaging and high-
resolution reflected-light spectroscopy has been on Proxima Centauri b. This
is likely driven by the planet’s location within the habitable zone, and a
measured minimum mass ($M\sin i$) between $1.0~{}M_{\oplus}$ (Damasso et al.,
2020) and $1.27~{}M_{\oplus}$ (Anglada-Escudé et al., 2016). Bixel & Apai
(2017) placed probabilistic mass and radius constraints on Proxima Centauri b
at $M=1.63^{+1.66}_{-0.72}~{}M_{\oplus}$ and
$R=1.07^{+0.38}_{-0.31}~{}R_{\oplus}$, which is consistent with a rocky
composition, but there is still a $\sim$10% chance the planet has a
significant amount of ice or a volatile envelope. We do not yet have enough
information to truly constrain the nature of Proxima Centauri b, so assuming
it is Earth-like or an Earth-analog is an optimistic assumption.

Lovis et al. (2017) proposed upgrades to SPHERE and ESPRESSO on the VLT in
order to observe Proxima Centauri b. They adopted a 3D Global Climate Model
(GCM) atmosphere of Proxima Centauri b from Turbet et al. (2016), assumed
observations at orbital quadrature, and a spectrograph resolution of 220,000.
They concluded a 3.6$\sigma$ detection of O2 could be made in about 60 nights
of telescope time over the course of three years.

Wang et al. (2017) simulated observations of Proxima Centauri b (assuming it
is an Earth-like planet) and a hypothetical Earth-like habitable zone planet
orbiting an M dwarf at 5 pc using a 30-meter class telescope at near-infrared
bands. They used near-infrared (1–2.5 $\mu$m) R=1,000–100,000 Earth-like
exoplanet spectra, considering atmospheric chemistry and using a radiative
transfer model from Hu et al. (2012a, b, 2013); Hu & Seager (2014). For a
100-hour integration time, their simulations yielded S/N$>$10 for H2O, O2,
CO2, and CH4, typically when R$>$10,000 and star-light suppression was
$>10^{-7}$. These simulations simplistically addressed line blending, assuming
the radial velocity of the exoplanet shifts its atmospheric signature by tens
of km s-1. An updated version of this analysis was provided by Zhang et al.
(2024), where they simulated direct imaging of 10 nearby rocky planets at
R=1000 with HARMONI and METIS on the ELT in search of biosignatures. They
indicated that CO2, CH4, and H2O should be detectable on GJ 887 b and Proxima
Centauri b at a S/N$>$5 with integration times on the order of $<$100 hours.

Hawker & Parry (2019) focused on the detectability of Earth-like levels of O2
on Proxima Centauri b with high-resolution spectroscopy and high contrast
imaging on the ELT using HIRES and HARMONI. They concluded a 3–5$\sigma$
detection could be obtained in 30–70 hours of integration time. More recently,
Vaughan et al. (2024) simulated observations of Proxima Centauri b using
HARMONI on the ELT at its highest resolving power of R=17,385. Their
simulations indicated an atmosphere on Proxima Centauri b (assuming it is
Earth-like) could be characterized at 5$\sigma$ in 20–30 hours of integration
time. These observations would be particularly sensitive to CH4, but CO2 would
be harder to detect.

While these previous studies have made significant contributions to assessing
direct imaging capabilities for individual cases, they were intrinsically
constrained in their scope for broader hypothesis testing. Our study seeks to
build upon the above foundational efforts by employing the Bioverse framework,
which allows us to go beyond previous studies by leveraging exoplanet
demographics information, and performing realistic survey simulations and
hypothesis testing.

###  1.2 Bioverse

Bioverse was developed by Bixel & Apai (2021) as a modular framework to
generate and classify exoplanets based on exoplanet demographics, simulate
exoplanet surveys for upcoming telescopes and missions, and compute the
diagnostic power of future surveys in testing population-level hypotheses.
Bioverse folds in state-of-the-art exoplanet occurrence rate calculations,
incorporates a complete nearby star catalog out to $\sim$100 pc, and accounts
for realistic ground-based observing constraints, allowing exploration of the
full potential of a broad statistical survey of nearby exoplanets.

The general workflow of Bioverse starts with generating synthetic populations
of stars with planetary systems and to injecting a statistical trend into that
population. Then, a simulated survey “observes” a sample of the synthetic
planets and collects measurement data according to projected uncertainties and
survey strategies. Next, the hypothesis testing module allows quantification
of how well the injected trend is recovered, and how strongly parameters of
the model shaping the trend can be constrained. This procedure is typically
repeated in a Monte Carlo fashion, varying astrophysical unknowns or features
of the survey, which allows for trade studies on different survey designs.

After introducing the framework in Bixel & Apai (2021), Hardegree-Ullman et
al. (2023) added a stellar catalog based on Gaia Data Release 3, the
capability to determine transit observability for ground-based large-aperture
telescopes, and simulations for oxygen detection via transmission
spectroscopy. Schlecker et al. (2024) introduced selectable mass-radius
relations, a mission simulator for ESA’s PLATO mission (Rauer et al., 2016),
and a runaway greenhouse climate model. Here, we built upon these previous
studies to assess the direct imaging and high resolution spectroscopy
potential for reflected light studies with the GMT and ELT.

In Section 2 we outline the direct imaging observing considerations and
instrument models. We simulate a 10-year survey with the GMT and ELT to probe
Earth-like levels of O2 on habitable zone Earths and super-Earths in Section
3, and follow with testing the habitable zone oxygen hypothesis in Section 4.
In Section 5 we discuss the implications of our simulations, and we summarize
and conclude our results in Section 6.

##  2 Observing Considerations

Earth has evolved from a methane and carbon dioxide-rich atmosphere over 2.4
Gyr ago to its present-day oxygen-rich state due to oxygenic photosynthesis
(e.g., Lyons et al., 2021). While it is likely that habitable zone Earth-sized
exoplanets have atmospheres with diverse compositions and in different states
of evolution, we adopt present-day Earth as a starting point to simplify
simulations. The following simulations are focused on probing present-day
Earth-like atmospheric conditions on rocky, habitable-zone exoplanets.

###  2.1 Planet Generation and Observational Constraints

In order to provide a realistic survey simulation, we used Bioverse to
generate a set of exoplanets orbiting bright stars (Gaia red-band $G_{RP}\leq
10$) out to 20 pc from the Sun based on planet occurrence rates from Bergsten
et al. (2022), which was first introduced to Bioverse in Schlecker et al.
(2024). The underlying parametric model in Bergsten et al. (2022) is derived
from planet radius, orbital period, and stellar host mass distributions in
Kepler’s FGK and early M stars sample, considering planets with radii up to
$3.5~{}R_{\oplus}$ and orbiting out to 100 days. The original SAG 13-based
(Kopparapu et al., 2018) planet occurrence rate module introduced by Bixel &
Apai (2021) was derived from a compilation of Kepler planet occurrence rates
prior to 2017, and did not include a stellar mass dependence. Both of the
planet occurrence rate modules are model-dependent for planets orbiting beyond
100 days.

From the set of generated exoplanets, we only considered planets that meet the
criteria of an exo-Earth candidate (EEC): the planet is within the
conservative habitable zone boundaries between runaway and maximum greenhouse
as defined by Kopparapu et al. (2014), and the planet radius falls between the
range $0.8S^{0.25}<R_{p}<1.4~{}R_{\oplus}$, where $S$ is stellar incident flux
in units of present-day Earth insolation flux. The lower limit is the
theoretical minimum planet size needed to retain an atmosphere (Zahnle &
Catling, 2017), and was previously adopted for use in Bioverse by Bixel & Apai
(2021) and Hardegree-Ullman et al. (2023).

In order to generate realistic surveys, for each EEC we simulated one Earth
year of observations at one hour intervals and computed practical observing
constraints based on the locations of the GMT and ELT. Simple constraints such
as target observability at night and airmass between $z=1.0$ and 2.0 were
modeled using astroplan (Morris et al., 2018). When a planet was observable,
we computed relative radial velocities and planet-to-star contrast ratios.

Since we have to observe O2 on exoplanets through the O2-rich atmosphere of
Earth, we must account for relative radial velocities ($\Delta$RV) in order to
mitigate line blending effects. Relative radial velocities are given by:

$\Delta\mathrm{RV}=\mathrm{RV}_{\star}+\mathrm{RV}_{\mathrm{orb}}-\mathrm{RV}_{\mathrm{bary}},$
(1)

where $\mathrm{RV}_{\star}$ is the radial velocity of the host star,
$\mathrm{RV}_{\mathrm{orb}}$ is the orbital velocity of the exoplanet with
respect to its host star, and $\mathrm{RV}_{\mathrm{bary}}$ is the velocity of
the observer on Earth with respect to the solar system barycenter. The host
star radial velocity comes from the Bioverse stellar catalog (Hardegree-Ullman
et al., 2023), which is based on Gaia Data Release 3. The uncertainties of
these radial velocities are on the order of a few km s-1 (Gaia Collaboration
et al., 2021).

Orbital velocity was computed from:

$\mathrm{RV}_{\mathrm{orb}}=\sqrt{GM_{\star}\left(\frac{2}{r}-\frac{1}{a}\right)}$
(2)

where $G$ is the gravitational constant, $M_{\star}$ is the mass of the host
star, $r$ is the distance of the exoplanet to the host star at the time of
observation, and $a$ is the semi-major axis of the exoplanet. Observer
barycentric velocity at the time of observation was computed using the
baryCorr function from the PyAstronomy package (Czesla et al., 2019). For an
$R=100,000$ spectrograph observing the O2 A-band, severe line blending occurs
when $|\Delta\mathrm{RV}|<13$ km s-1 and $30\ \mathrm{km\
s}^{-1}<|\Delta\mathrm{RV}|<55\ \mathrm{km\ s}^{-1}$ (López-Morales et al.,
2019; Hardegree-Ullman et al., 2023).

For direct imaging observations, the projected distance of the exoplanet from
its host star ($\theta$ [arcsec] = $r$ [au]/$d$ [pc], where $d$ is the
distance to the system) must be larger than the inner working angle of the
observing instrument. The diffraction limit of a telescope is $1.22\lambda/D$.
In practice, we set the observable inner working angle to be greater than
$2\lambda/D$ (e.g., Lovis et al., 2017; Walter et al., 2020). At the
wavelength of the O2 A-band (760 nm), $2\lambda/D$ is 13 mas, 11 mas, and 9
mas for the GMT, TMT, and ELT, respectively.

In order to observe the exoplanet, the contrast ratio between the planet and
the star must be above the detection limit of the instrument. This contrast
ratio is given by:

$\frac{F_{p}(\lambda,\alpha)}{F_{\star}(\lambda)}=A_{g}(\lambda)g(\alpha)\left(\frac{R_{p}}{a}\right)^{2},$
(3)

where $F_{p}(\lambda,\alpha)$ is the exoplanet flux at wavelength $\lambda$
and phase angle $\alpha$, $F_{\star}(\lambda)$ is the host star flux, $A_{g}$
is the geometric albedo, $g(\alpha)$ is the scattering phase function, $R_{p}$
is the exoplanet radius, and $a$ is the exoplanet semi-major axis. Our models
assume a Lambertian phase function:

$g(\alpha)=\frac{\sin\alpha+(\pi-\alpha)\cos\alpha}{\pi},$ (4)

where the illumination phase angle $\alpha=\cos^{-1}(-\sin i\cos\phi)$, $i$ is
the exoplanet inclination angle, and $\phi$ is the orbital phase. Geometric
albedo, inclination angle, and orbital phase were randomly generated from
uniform distributions for each simulated planet within Bioverse.

###  2.2 Instrument Models

In order to provide a realistic simulation of extreme-AO performance, we need
models for planned instruments, which currently include GMagAO-X (Males et
al., 2022) for the GMT and the Planetary Camera and Spectrograph (PCS, Kasper
et al., 2021) for the ELT. However, full end-to-end simulations of these high-
order AO systems are very expensive in terms of computational time and
complexity. Therefore, we used a semi-analytical approach to the performance
simulation (Jolissaint, 2010). The semi-analytical approach assumes that all
temporal evolution of the turbulence is driven by Taylor’s frozen flow. The
frozen flow approximates the short time evolution by shifting the spatial
structure of the turbulence with single wind velocity. The time evolution of
any parameter can then be replaced by a shifted version,
$\varphi(\vec{r},t)=\varphi(\vec{r}-\vec{v}t)$. This time evolution underpins
the semi-analytical model and allows us to express an adaptive optics system
as a series of spatial filters that act on the turbulence Power Spectral
Density (PSD). The AO system is controlled using integral control,
$\mathrm{DM}_{i+1}=\mathrm{DM}_{i}-g\varepsilon_{i}$. Here, $\varepsilon_{i}$
is the wavefront error at time step $i$ and $\mathrm{DM}_{i}$ is the DM shape
at time step $i$. The feedback gain $g$ is a function of spatial frequency and
was optimized following Gendron & Léna (1994); Jolissaint (2010).

We simulated two different representative AO system optimizations. In the
first, the AO system was allowed to run as fast as possible, which is 3 kHz
for both GMagAO-X and PCS. The gain for each spatial frequency was optimized
at this AO loop speed. In the second approach, we optimized the Strehl by
changing both the AO loop speed and modal gains. These two approaches were
used because optimizing for just Strehl does not necessarily lead to the best
contrast. The contrast at small angular separations is driven by the servo lag
error. This error term is a larger contributor on GMT/ELT-sized instruments
than on current instruments (Males & Guyon, 2018). Therefore, it is possible
to increase the contrast at smaller angular separations by running the AO
system faster at the cost of lower Strehl. This leads to a better final
signal-to-noise. The two different approaches are called ‘Max Speed’ and
‘Strehl Optimization’ in this work. A more thorough assessment of which
instrument and observing modes were selected for scientific analysis in
Section 3 is given in Appendix A.

The AO performance depends strongly on the assumed atmospheric conditions. For
our simulations, we followed Prieto et al. (2010) and Thomas-Osip et al.
(2010) for the GMT. The first quartile conditions are $r_{0}=0.22$ m and a
$C_{n}^{2}$ integrated wind velocity of 9.4 m s-1. The second quartile
conditions are $r_{0}=0.17$ m and a mean wind speed of 18.4 m s-1. For the
ELT, we followed Sarazin et al. (2013): the first and second quartile
conditions are $r_{0}=0.24$ m with a velocity of $10$ m s-1 and $r_{0}=0.15$ m
with a velocity of 11 m s-1, respectively.

The design of GMagAO-X is currently further along than that of the other
extreme-AO systems (Males et al., 2022; Haffert et al., 2022). Therefore, we
used the current design parameters for GMagAO-X as reference. Specifically, we
assumed 182 actuators across the pupil and a pyramid wavefront sensor. The
design of PCS is currently still in its conceptual phase and no hard decisions
have been made (Kasper et al., 2021). Therefore, we considered two different
DM sizes for PCS: 200 actuators across the pupil based on the proposed density
for EPICS (Kasper et al., 2010), and 128 actuators across the pupil based on a
more recent ELT extreme-AO design (Madec et al., 2022).

The output of the semi-analytical model is a post-AO PSD. The PSD still has to
be propagated through an actual coronagraphic system to measure the amount of
residual scattered star light. The expected exposure times of our simulations
are on the order of hours. This is much longer than the typical speckle
lifetime of 1 to 10 ms (Males et al., 2021). We can treat the different
spatial frequencies as incoherent because of the many orders of magnitude
differences in characteristic timescales. With that in mind, the propagation
through a coronagraph can be viewed as an incoherent sum of plane waves
(Sauvage et al., 2010; Herscovici-Schiller et al., 2017). Finally, the effects
of quasi-static speckles are ignored in the simulations for two reasons.
First, for high-resolution spectroscopy the speckle lifetime does not matter,
only the amount of residual starlight matters. This is not true for other
post-processing techniques such as Angular Differential Imaging, which is
extremely sensitive to the speckle lifetime. Second, controlling and removing
quasi-static speckles below the residual atmospheric speckles is now possible
(Potier et al., 2022; Haffert et al., 2023; Galicher et al., 2024). Therefore,
no quasi-static speckles were added to our simulations, under the assumption
that the efficiency of quasi-static speckle removal process will continue to
improve over the next few years.

###  2.3 Time Needed to Probe O2

With our new instrument model, we now have to determine how long it will take
to probe O2. For each simulated exoplanet, we first computed the total number
of hours the planet would be observable from the GMT and ELT locations for one
year of observations ($N_{\text{hr-obs}}$) accounting for the aforementioned
ground-based observing limitations and exoplanet orbital properties. Since the
modeled planets change illumination and scattering phase throughout their
orbits, we computed the contrast ratio from Equation 3 at each observable hour
and used the resulting median contrast ratio ($\widetilde{F_{p}/F_{\star}}$)
for our calculations. Tables 1 and 2 show the expected achievable post-
processing contrasts from the instrument models in Section 2.2 for the GMT and
ELT, respectively, at S/N = 5 for a one hour integration of the O2 A-band at
$R=100,000$ for different host magnitudes and angular separations.

It would be ideal to optimize observations based on maximizing Equation 3.
However, this depends on several factors, including well constrained exoplanet
orbits and phases and appropriate relative system velocities coinciding with
Q1 or Q2 observing windows. It is impractical to assume observations will only
happen when all these factors are most optimal, so we opted for a more
conservative median observing situation. For each simulated exoplanet, we
interpolated the host star $G_{RP}$ magnitude and median angular separation
($\tilde{\theta}$) to these tables to yield a 1-hour contrast
($C_{1\text{hr}}$). Total integration time to achieve a S/N = 5 detection of
Earth-like levels of O2 on the simulated planet ($t_{\text{hr-}5\sigma}$) is
given by:

$t_{\text{hr-}5\sigma}=\left(\frac{C_{1\text{hr}}}{\widetilde{F_{p}/F_{\star}}}\right)^{2}.$
(5)

To translate integration time to years of observations:

$t_{\text{yr-}5\sigma}=Q\frac{t_{\text{hr-}5\sigma}}{N_{\text{hr-obs}}},$ (6)

where $Q=2$ for second quartile and $Q=4$ for first quartile observing
conditions.

| GMT, Max Speed, Q1
---|---
Mag|$\theta$ | 15 mas | 30 mas | 50 mas | 100 mas | 120 mas
1 | 5.85E-09 | 4.53E-09 | 3.51E-09 | 2.55E-09 | 2.36E-09
3 | 1.93E-08 | 1.61E-08 | 1.32E-08 | 1.02E-08 | 9.53E-09
5 | 8.01E-08 | 6.89E-08 | 5.85E-08 | 4.68E-08 | 4.41E-08
7 | 4.55E-07 | 4.02E-07 | 3.49E-07 | 2.88E-07 | 2.73E-07
9 | 4.31E-06 | 3.89E-06 | 3.45E-06 | 2.89E-06 | 2.73E-06
10 | 1.82E-05 | 1.66E-05 | 1.50E-05 | 1.26E-05 | 1.16E-05
Table 1: GMT achievable $F_{p}/F_{\star}$ contrast at S/N=5 for 1 hour integration times using high contrast imaging with high-resolution spectroscopy for different host star magnitudes and planet-star angular separations ($\theta$). This table is for a Max Speed AO control system and Q1 observing conditions. For different AO control systems and observing conditions see Table 3 in Appendix A. | ELT, Max Speed, 128 actuators, Q2
---|---
Mag|$\theta$ | 5 mas | 10 mas | 15 mas | 30 mas | 50 mas | 120 mas
1 | 5.00E-09 | 4.07E-09 | 3.89E-09 | 3.11E-09 | 2.58E-09 | 1.97E-09
3 | 1.30E-08 | 1.06E-08 | 1.02E-08 | 8.33E-09 | 7.06E-09 | 5.50E-09
5 | 3.91E-08 | 3.21E-08 | 3.12E-08 | 2.64E-08 | 2.26E-08 | 1.75E-08
7 | 1.49E-07 | 1.22E-07 | 1.19E-07 | 1.02E-07 | 8.82E-08 | 6.85E-08
9 | 7.95E-07 | 6.54E-07 | 6.41E-07 | 5.60E-07 | 4.91E-07 | 3.90E-07
10 | 2.34E-06 | 1.93E-06 | 1.89E-06 | 1.67E-06 | 1.49E-06 | 1.20E-06
Table 2: ELT achievable $F_{p}/F_{\star}$ contrast at S/N=5 for 1 hour
integration times using high contrast imaging with high-resolution
spectroscopy for different host star magnitudes and planet-star angular
separations ($\theta$). This table is for a Max Speed AO control system, 128
deformable mirror actuators, and Q2 observing conditions. For different AO
control systems, actuators, and observing conditions see Table 4 in Appendix
A.

##  3 Survey Simulation

In order to realistically simulate the execution of an observing survey of
nearby EECs, we followed the survey simulation methodology of Hardegree-Ullman
et al. (2023). First, we generated 1000 simulated local neighborhood ($d<20$
pc) exoplanet populations in Bioverse based on exoplanet demographics of
Bergsten et al. (2022) and computed the time it will take to probe Earth-like
O2 levels for each simulated EEC. We then sorted each population of simulated
exoplanets by the number of years it would take to probe O2 and calculated the
median value of the first through nth planets. The results are shown in Figure
1 for optimized instrument and observing modes, which are Max Speed, Q1 for
the GMT, and Max Speed, Q2, 128 actuators for the ELT. An assessment of
different instrument and observing modes is given in Appendix A.

Figure 1 shows that the ELT would be able to survey $\sim$3$\times$ more
planets than the GMT for a survey of similar length, approximately
commensurate with the $\sim$3$\times$ more collecting area. In a 10-year
survey, if all EECs have Earth-like levels of O2, the GMT could probe up to
$\sim$5 planets, and the ELT could probe up to $\sim$15\. Note, that this
simulation did not consider that these planets would likely have overlapping
observing windows, so the number of planets surveyed for O2 is an upper limit.
It is also important to highlight that over 85% of the simulated planets which
could be probed within a 10-year survey across all survey simulations orbit M
dwarfs, and about 75% of these simulated planets are within 13 pc of the Sun
(Figure 2).

Figure 1: Simulation results for a survey of Earth-like concentrations of O2
at 5$\sigma$ on exo-Earth candidates within 20 pc with the ELT (blue dots) and
the GMT (orange stars). A survey of the same duration on both telescopes would
allow the ELT to probe about three times more planets for O2 than the GMT. The
large error bars are driven by the wide range of possible orbital parameters
for our simulated exoplanets.

Figure 2: Distributions of host star $T_{\mathrm{eff}}$ (top) and distance
(bottom) across all EEC survey simulations for EECs that could be probed for
Earth levels of O2 within a 10-year survey. 85% of the detectable simulated
planets orbit M dwarfs, with a peak near spectral type M3. About 3/4 of the
detectable simulated planets are within 13 pc of the Sun. The dashed-dotted
blue lines show the distribution of all bright ($G_{RP}<10$) stars within 20
pc, which highlights that the GMT and ELT will be insensitive to O2 in the
atmospheres of EECs orbiting stars above $\sim$5000 K, and is most sensitive
to stars within about 13 pc.

###  3.1 Super-Earths

Next, we carried out a simulation to explore the observability of O2 in all
super-Earth exoplanets. The previous survey simulation focused on planets
nearly the same size as Earth ($0.8S^{0.25}<R_{p}<1.4~{}R_{\oplus}$). While
not all exoplanets smaller than $1.4~{}R_{\oplus}$ will necessarily be Earth-
like, a larger population including all super-Earth exoplanets would allow us
to observationally constrain the limits of Earth-like planet atmospheres. In
the following simulation, we assessed the ability to probe Earth-like O2
levels on Earth to super-Earth sized planets
($0.8S^{0.25}<R_{p}<1.8~{}R_{\oplus}$), where the upper limit is guided by the
exoplanet radius valley, Fulton et al., 2017; Hardegree-Ullman et al., 2020).
Results from the super-Earth survey simulation are given in Figure 3. We found
that about 1.5$\times$ more planets could be surveyed if the survey is
broadened from Earth-sized to all Earth and super-Earth-sized planets.

Figure 3: Simulation results for a survey of Earth-like concentrations of O2
at 5$\sigma$ on habitable zone Earth and super-Earth-sized candidates
($0.8S^{0.25}<R_{p}<1.8~{}R_{\oplus}$) within 20 pc with the ELT (blue dots)
and the GMT (orange stars). Similar to the exo-Earth simulation in Figure 1,
the ELT could probe about three times more planets than the GMT. Overall, a
super-Earth survey could probe about 1.5 times more planets than a survey of
planets up to 1.4 $R_{\oplus}$.

###  3.2 Known Habitable Zone Exoplanets

Within 20 pc there are five confirmed habitable zone exoplanets which would be
observable from either the GMT or ELT. These exoplanets orbit stars brighter
than ${G_{RP}}=10$ and have minimum masses ($M\sin i$) that make them super-
Earth candidates. These are Proxima Centauri b (Anglada-Escudé et al., 2016),
Ross 128 b (Bonfils et al., 2018), GJ 273 b (Astudillo-Defru et al., 2017),
Wolf 1061 c (Wright et al., 2016), and GJ 667 C c (Anglada-Escudé et al.,
2012). LTT 1445 A d is another nearby candidate super-Earth habitable zone
exoplanet with a relatively bright host star (Lavie et al., 2023). It is worth
noting that all these planets were discovered orbiting M dwarfs using the
radial velocity technique, and it is possible that their mass is significantly
higher than the minimum mass provided by the RV method (see e.g., Bixel &
Apai, 2017). We ran a survey simulation on these planets, assuming uniform
priors on all unknown or loosely constrained parameters such as albedo,
inclination angle, argument of periastron, and longitude of the ascending
node. Results from this simulation are shown in Figure 4. If Earth-like levels
of O2 exist on these planets, it could be probed within days to a few weeks
with the ELT, and within a couple of months with the GMT. For LTT 1445 A d, it
will take several months, and can only be completed on the ELT within a 10
year survey. Given the fact that the existence of these planets is already
established, they will likely be high-priority targets for initial exoplanet
surveys with the GMT and ELT.

Figure 4: Simulation results for a survey of Earth-like concentrations of O2
at 5$\sigma$ for five known, and one candidate (LTT 1445 A d) habitable zone
exoplanets within 20 pc with the ELT (blue) and the GMT (orange). The ELT and
GMT should both be able to probe for O2 on Proxima Centauri b in less than a
month. LTT 1445 A d is the only planet in the simulation for which Earth-like
levels of O2 could not be probed with the GMT, but it could be probed with the
ELT. More precise planet and orbital parameters would minimize the
uncertainties on these observing simulations. The minimum mass
($M_{\oplus}\sin i$) of each planet is given above each relatively-sized point
(Faria et al., 2022; Bonfils et al., 2018; Astudillo-Defru et al., 2017; Lavie
et al., 2023; Anglada-Escudé et al., 2013).

##  4 Hypothesis Testing

Since our survey simulations revealed the possibility of detecting O2 on
several exoplanets in a 10-year survey, particularly with the ELT, in order to
assess the scientific value of such surveys, we now turn to testing related
population-level hypotheses. We refer the reader to Section 5 of Bixel & Apai
(2021) for a full description of Bayesian hypothesis testing with Bioverse. In
general, we want to assess the statistical power of a survey to test a
hypothesis by running survey simulations several times in a Monte Carlo
fashion under the same assumptions (but with randomly drawn parameters) and
determine the fraction of simulations that validate or reject the hypothesis.
Here, we propose and aim to test the “habitable zone oxygen hypothesis”: We
hypothesize that habitable zone Earth-sized exoplanets will be more likely to
have Earth-like levels of O2 than planets outside the habitable zone.

We must first define the statistical effect to inject into our synthetic
planet population. In our model, a planet can have or not have Earth-like
levels of O2. It can further be an EEC if its orbit fulfills
$a_{\mathrm{inner}}<a<a_{\mathrm{outer}}$ and its radius fulfills
$0.8S^{0.25}<R_{p}<1.4~{}R_{\oplus}$. The planet is considered a non-EEC
otherwise, but its atmosphere may still contain Earth-like levels of oxygen.
This population of oxygen-bearing non-EECs can be considered false positives,
and they present a source of noise in the hypothesis testing.

We can now describe the likelihood of a planet having O2 by

$f^{\mathrm{O}_{\mathrm{2}}}=\begin{cases}f^{\mathrm{O}_{\mathrm{2}}}_{\mathrm{EEC}}&\mathrm{if\
}a_{\mathrm{inner}}<a<a_{\mathrm{outer}}\\\ &\mathrm{and\
}0.8S^{0.25}<R_{p}<1.4~{}R_{\oplus}\\\ f^{\mathrm{O}_{\mathrm{2}}}_{\text{non-
EEC}}&\mathrm{if\ }a<a_{\mathrm{inner}}\mathrm{\ or\ }a>a_{\mathrm{outer}}\\\
&\mathrm{and\ }R_{p}>0.8S^{0.25}\\\ 0&\mathrm{if\
}R_{p}<0.8S^{0.25},\end{cases}$ (7)

where $f^{\mathrm{O}_{\mathrm{2}}}_{\mathrm{EEC}}$ is the fraction of EECs
with Earth-like O2 levels, and $f^{\mathrm{O}_{\mathrm{2}}}_{\text{non-EEC}}$
is the fraction of non-habitable zone exoplanets with O2.

Next, we adopt the functional form of the habitable zone oxygen hypothesis,
$H_{\mathrm{HZ}}^{\mathrm{O}_{\mathrm{2}}}$, as

$H_{\mathrm{HZ}}^{\mathrm{O}_{\mathrm{2}}}(a_{\mathrm{eff}})=\begin{cases}f_{\mathrm{HZ}}^{\mathrm{O}_{\mathrm{2}}}\
\ \ \mathrm{if\ }a_{\mathrm{inner}}<a_{\mathrm{eff}}<a_{\mathrm{inner}}+\Delta
a\\\ f_{\mathrm{HZ}}^{\mathrm{O}_{\mathrm{2}}}(f_{\text{non-
HZ}}^{\mathrm{O}_{\mathrm{2}}}/f_{\mathrm{HZ}}^{\mathrm{O}_{\mathrm{2}}})\ \
\mathrm{otherwise.}\end{cases}$ (8)

The model parameter vector $\theta$ consists of the position of the inner edge
of the habitable zone $a_{\mathrm{inner}}$, the width of the habitable zone
$\Delta a$, the fraction of habitable zone planets with O2
$f_{\mathrm{HZ}}^{\mathrm{O}_{\mathrm{2}}}$, and the ratio of non-habitable
zone planets with O2 to habitable zone planets with O2 $f_{\text{non-
HZ}}^{\mathrm{O}_{\mathrm{2}}}/f_{\mathrm{HZ}}^{\mathrm{O}_{\mathrm{2}}}$.

Figure 5: Statistical power of the habitable zone oxygen hypothesis test on
the ELT for different values of $\eta_{\oplus}$ and different fractions of
exo-Earth candidates (EECs, left) and fractions of exo-super Earth candidates
(ESECs, right) with Earth-like levels of O2. Statistical power contours for
50% and 95% are shown in black. More planets with oxygen and/or higher values
for $\eta_{\oplus}$ result in a greater ability to test this hypothesis,
however, the inclusion of all super-Earths does not necessarily improve this
ability. We note that these figures are super-sampled to highlight
differences.

In our test case, we aim to assess the statistical power to test the above
hypothesis in a 10-year survey with the ELT considering different values of
$f^{\mathrm{O}_{\mathrm{2}}}_{\mathrm{EEC}}$ (ten levels between 0.1 and 1)
and $\eta_{\oplus}$ (five levels between 0.075 and 0.3). For simplicity, we
set $f^{\mathrm{O}_{\mathrm{2}}}_{\text{non-EEC}}=1\%$. We imposed log-uniform
priors $a_{\mathrm{inner}}=[0.1,2]$, $\Delta a=[0.01,3]$,
$f_{\mathrm{HZ}}=[0.01,1]$, $f_{\text{non-HZ}}/f_{\mathrm{HZ}}=[0.01,1.0]$.

For each of these realizations, our planetary populations are still subject to
intrinsic stochasticity that may impact the measured diagnostic power of the
survey: planetary orbits and bulk properties are randomly drawn from
distributions informed by exoplanet demographics, leading to random variations
of the sample. To account for this while keeping computational costs
reasonable, we ran ten randomized simulations per grid cell.

Figure 5 shows the statistical power that can be achieved for different
fractions of EECs with Earth-like levels of O2 and $\eta_{\oplus}$. Our
ability to test the habitable zone oxygen hypothesis is contingent on more
than $\sim$1/3 of EECs having Earth-like levels of O2 if EECs are relatively
common, and above $\sim$1/2 for low values of $\eta_{\oplus}$. Figure 3
suggests that a 10-year survey of exo-super Earth candidates (ESECs) could
probe about 1.5$\times$ more planets for Earth-like levels of O2 than a survey
of only Earth-sized planets. As such, we ran the above test with the same
parameters except considering ESECs rather than EECs. Figure 5 shows that
considering ESECs would not necessarily improve the ability to test the
habitable zone oxygen hypothesis. One potential reason for this is that in a
time-limited ground-based survey, a larger target sample would take longer to
survey a significant fraction and test the hypothesis. A higher-resolution
hypothesis grid with more samples per cell could test this more conclusively,
but that is significantly more computationally expensive.

In the previous two hypothesis tests, we considered
$f^{\mathrm{O_{2}}}_{\mathrm{EEC}}$ or $f^{\mathrm{O_{2}}}_{\mathrm{ESEC}}$
for planets up to $1.4~{}R_{\oplus}$ (EEC) and $1.8~{}R_{\oplus}$ (ESEC) for
different values of $\eta_{\oplus}$. Next, instead of varying $\eta_{\oplus}$,
we set $\eta_{\oplus}$ = 8.5% (consistent with the most recent estimates of
$\eta_{\oplus}$ for conservative habitable zone M dwarfs from Bergsten et al.,
2023) and tested the effect of maximum sampled planet size on our ability to
test the habitable zone oxygen hypothesis. Figure 6 shows the results of this
test, indicating the maximum sampled planet size has only a small effect on
the ability to test the habitable zone oxygen hypothesis between $\sim$1.2
$R_{\oplus}$ and 1.8 $R_{\oplus}$.

Figure 6: Statistical power of the habitable zone oxygen hypothesis test on
the ELT for different values of maximum sampled planet size and different
fractions of planet candidates with Earth-like levels of O2. Statistical power
contours for 50% and 95% are shown in black. The maximum sampled planet size
has minor effect on the statistical power between $\sim$1.2 $R_{\oplus}$ and
$\sim$1.8 $R_{\oplus}$. We note that this figure is super-sampled.

##  5 Discussion

The detection of O2 in the atmospheres of Earth-analogs, if found, will no
doubt have profound impacts on astronomy and astrobiology. Our simulations
show that Earth-like O2 levels could be probed on EECs with the GMT and ELT
with planned instrumentation. There are already a half-dozen known probable
super-Earths which may be ideal candidates to start searching for oxygen
(Section 3.2), and planets like Proxima Centauri b could be high-priority
science targets for the GMT and ELT.

It is important to note that the GMT and ELT will be mostly sensitive to
exoplanets orbiting M dwarf stars (Figure 2), and particularly those in the
habitable zone. These exoplanets will not be accessible to the Habitable
Worlds Observatory, which is expected to primarily focus on Sun-like FGK stars
(Mamajek & Stapelfeldt, 2024). The nature of the habitability of M dwarf
exoplanets is extensively studied in the literature (e.g., Shields et al.,
2013, 2016; Meadows et al., 2018a; Airapetian et al., 2020; Lobo et al., 2023)
and is beyond the scope of this paper.

###  5.1 O2 as an Atmospheric Biosignature

Life on Earth has a complex evolutionary history with O2. About 2.4 billion
years ago, cyanobacteria took in solar energy and produced O2 as a waste
product of oxygenic photosynthesis. Eventually, enough oxygen had accumulated
in the ocean to begin escaping into the atmosphere during the “Great Oxidation
Event,” ushering in the Proterozoic eon and the evolution of complex life. A
second great atmospheric accumulation of oxygen occurred between about 800 and
600 million years ago, leading to present-day levels of oxygen and animal life
(Canfield, 2005; Kump, 2008; Sessions et al., 2009; Lyons et al., 2014, 2021).
In this study, we focused on the ability to probe present-day Earth-like
levels of O2 on rocky exoplanets. From 600 Mya to present day, Earth oxygen
levels fluctuated between $\sim$10 and 30%, settling at $\sim$21% today (Costa
et al., 2014). Chaloner (1989) suggest that O2 concentrations of $\sim$35% are
the upper limit to sustain terrestrial vegetation due to the increased
potential for combustibility. We leave the exploration of the limits of O2
detectability to future studies.

###  5.2 Other Atmospheric Biosignatures

O2 on Earth is almost exclusively produced by oxygenic photosynthesis (Segura
et al., 2005), and its present-day abundance, which is difficult to replicate
by individual abiotic mechanisms (Meadows, 2017), makes it a favorable
biosignature to search for in the atmospheres of exoplanets. However, there
are still mechanisms that could produce an oxygen-rich atmosphere, such as
water photolysis on a pure H2O world (Wordsworth & Pierrehumbert, 2014). This
necessitates robust elimination of false-positive abiotic O2 production
scenarios. One way to do this is by observing multiple biosignatures (Meadows
et al., 2018b).

CH4 is another exoplanet biosignature candidate, as its primary production
mechanism on Earth is from methanogenic bacteria in anaeorbic environments
(Segura et al., 2005; Thauer & Shima, 2008). Abiotic CH4 can be produced by
volcanic and geothermal processes, or by gas-water-rock reactions (Etiope &
Sherwood Lollar, 2013; Guzmán-Marmolejo et al., 2013), but on Earth,
biological production of CH4 outweighs abiotic production by an order of
magnitude (Kelley et al., 2005; Segura et al., 2005). The thermodynamic
disequilibrium of CH4 and O2 on Earth (Hitchcock & Lovelock, 1967; Sagan et
al., 1993), makes the disequilibrium pair a particularly enticing
biosignature. Additionally, for M dwarf planets, which will be the primary
targets for biosignature searches via direct imaging with the GMT and ELT, the
photochemical lifetime of CH4 is $\sim$200 years, compared to $\sim$10 years
on Earth (Segura et al., 2005; Arney, 2019), which might make it easier to
detect on such planets.

CO2 and CH4 are another disequilibrium pair that may indicate life. This pair
is particularly important for exoplanets with an Archean-like atmospheric
composition when those two species dominated in the O2 deficient environment
(Haqq-Misra et al., 2008). CH4 could be produced abiotically via mantle
outgassing, but this would also produce abundant CO (Krissansen-Totton et al.,
2018). A biologically active planet would likely have depleted CO levels
because this would be the preferred energy source for methanogens over CO2,
making the absence of CO a biological check on the CO2–CH4 pair (Zahnle et
al., 2011; Krissansen-Totton et al., 2018).

Figure 7 shows the habitable zone accessibility of the biosignatures O2, CH4,
CO2, and CO at red-optical and near-infrared wavelengths for an inner-working
angle of $2\lambda/D$ for the GMT, TMT, ELT, and JWST/HWO at distances of 5
and 10 pc. We have also included H2O, which is the basis of our definition of
a habitable zone planet (Kopparapu et al., 2014). Our study focused on the O2
A-band at 0.76 $\mu$m, which could be probed in the atmospheres of most inner
habitable zone planets orbiting stars up to M4 V by the GMT, TMT, and ELT out
to $\sim$10 pc. Toward near-infrared wavelengths, the inner working angle
decreases, diminishing the ability to probe some bands of biosignatures such
as CO and CO2 in the atmospheres of exoplanets orbiting later-type and more
distant stars. We leave the exploration of the ability to probe other
biosignatures with the GMT, TMT, and ELT to future studies.

Figure 7: The ability to probe H2O (blue dashed), O2 (green dashed dotted),
CH4 (orange dotted), CO2 (pink dashed), and CO (black dotted) in the
atmospheres of exoplanets in the habitable zones of G2 V through M8 V stars at
$2\lambda/D$ for distances of 5 pc (left) and 10 pc (right). Lines are shown
for a $\sim$6-meter JWST or anticipated HWO diameter aperture (orange solid),
the GMT (blue solid), the TMT (green solid), and ELT (yellow solid). If a
habitable zone region falls above the line for a telescope, the biosignature
could be accessible to that facility at an inner working angle of
$2\lambda/D$.

###  5.3 A Statistical Interpretation of Biosignatures

Even if it is possible to probe multiple biosignatures on an exoplanet,
interpretation of detections/non-detections on a single planet will vary (see
e.g., Madhusudhan et al., 2023; Wogan et al., 2024; Tsai et al., 2024).
Therefore, it is crucial to survey a large number of planets to study biotic
and abiotic processes and interpret biosignatures statistically (Apai et al.,
2019). Here, we focused on the potential to probe Earth-like levels of O2 on a
statistical level on hypothetical nearby exoplanets using direct imaging and
high-resolution spectroscopy. Studying exoplanets on a population level with
large-aperture ground-based telescopes will allow testing of the habitable
zone oxygen hypothesis and other statistical trends connected to small-planet
atmosphere diversity and planet formation processes.

###  5.4 Thirty Meter Telescope

The TMT is the only 25–40-meter class telescope planned for the northern
hemisphere. It should be noted that there are about 9,700 stars within 20 pc
of the Sun brighter than 10th magnitude above a declination of 30∘. This is
about 25% of bright, nearby stars which are inaccessible to the GMT and ELT. A
northern hemisphere large-aperture telescope is critical to maximize the
search for biosignatures. Additionally, about 2/3 of the targets observable
from a large-aperture telescope at 20∘ or 30∘ latitude overlap with the
targets observable from the GMT and ELT in the southern hemisphere.

Having multiple facilities capable of searching for biosignatures is
advantageous. When we are looking for $\sim$5$\sigma$ biosignature detections
over years of observations and hundreds of datasets, it will be important to
have independent verification from, e.g., different telescopes and processing
techniques to minimize false-positive scenarios. Multiple facilities can both
expedite data collection on individual targets and potentially expand the
target pool amenable to biosignature surveys if data from different
instruments can be combined, and since weather conditions at one facility
become less of an observing bottleneck. Hoeijmakers et al. (2018) successfully
demonstrated combining more than 2,000 high-resolution reflected light spectra
from different 2–8-meter class telescopes to measure the albedo of the hot
Jupiter $\tau$ Boötis b and achieved a planet-to-star contrast of $\sim$10-5.
The GMT, TMT, and ELT will be able to build upon these methods to reach
smaller planets and potentially detect biosignatures.

The Planetary Systems Imager (PSI) is a planned second-generation instrument
for the TMT which will have extreme-AO and high resolution spectroscopic
capabilities (Jensen-Clem et al., 2021, 2022). We did not model the potential
of TMT+PSI in this paper because a detailed instrument model is not yet
available. However, assuming similar performance to the ELT and GMT systems,
the TMT could probe a $\sim$50% larger sample than the GMT and – equivalently
– probe a sample $\sim$66% the size of the ELT sample in a 10 year survey,
commensurate with the difference in telescope collecting area.

##  6 Summary and Conclusions

The Bioverse survey simulation and hypothesis testing framework enables
comprehensive and quantitative assessments of the capabilities of upcoming
ground-based telescopes and space missions to study exoplanets. We expanded
the Bioverse framework to assess the ability of the ELT and the GMT to probe
Earth-like levels of O2 on nearby ($<$20 pc) habitable zone Earth-sized
exoplanets via extreme adaptive optics direct imaging and high resolution
spectroscopy. The following list summarizes the main conclusions of this work:

  * •

Accounting for recent planet occurrence rate calculations, relative system
velocities, and realistic target observability, we conducted a survey
simulation to determine how many exo-Earths
($0.8S^{0.25}<R_{p}<1.4~{}R_{\oplus}$) and super-Earths
($0.8S^{0.25}<R_{p}<1.8~{}R_{\oplus}$) could be probed for Earth-like levels
of O2 at 5$\sigma$ with the GMT and ELT. In 10 years, the GMT could survey up
to $\sim$5 and $\sim$7 Earths and super-Earths, respectively, while the ELT
could survey up to $\sim$14 and $\sim$23 (Figures 1 and 3).

  * •

Six known, habitable zone super-Earth candidates (Proxima Centauri b, Ross 128
b, GJ 273 b, Wolf 1061 c, LTT 1445 A d, and GJ 667 C c) are ideal targets to
search for O2. Given favorable orbital and exoplanet atmosphere parameters,
Earth-like levels of O2 could be probed in a matter of about one week to a few
weeks of observing for four of these planets with the ELT, and about a month
with the GMT (Figure 4).

  * •

A 10-year survey with the ELT could determine if habitable zone exo-Earths are
more likely to have O2. The diagnostic power of the survey to test this
habitable zone oxygen hypothesis is sensitive to the fraction of EECs with
Earth-like levels of O2 and the value of $\eta_{\oplus}$, but not very
sensitive to maximum planet size (Figures 5 and 6).

  * •

The construction of a northern-hemisphere large-aperture telescope like the
TMT would increase the potential target star sample by 25%. Multiple
facilities can provide independent verification of biosignature detections,
expedite data collection on individual exoplanets, and potentially expand the
exoplanet target sample on which to search for biosignatures.

The upcoming 25–40-meter class telescopes are going to be the first facilities
capable of robustly detecting biosignatures with extreme adaptive optics
direct imaging and high resolution spectroscopy. This method is much more
promising than transmission spectroscopy in the search for O2 (Hardegree-
Ullman et al., 2023), and a handful of high-priority target planets are
already available. The ability to validate biosignature detections and test
the habitable zone oxygen hypothesis and other biosignature hypotheses,
however, depends on probing a larger sample of planets than has been currently
discovered.

##  7 Acknowledgments

We acknowledge the work of Bryan Wang to improve the Bioverse code. KKH-U
acknowledges Megan Weiner Mansfield for general discussions about M dwarf
exoplanet atmospheres and Suri Rukdee for discussions about the LTT 1445 A
system.

This material is based upon work supported by the National Aeronautics and
Space Administration under Agreement No. 80NSSC21K0593 for the program “Alien
Earths.” The results reported herein benefited from collaborations and/or
information exchange within NASA’s Nexus for Exoplanet System Science (NExSS)
research coordination network sponsored by NASA’s Science Mission Directorate.

This material is based upon High Performance Computing (HPC) resources
supported by the University of Arizona TRIF, UITS, and Research, Innovation,
and Impact (RII) and maintained by the UArizona Research Technologies
department.

This research has made use of NASA’s Astrophysics Data System.

Author contributions: KKH-U and DA developed the project and planned its
implementation. DA funded the project through the “Alien Earths” program and
provided regular feedback and guidance as the project progressed. KKH-U
updated the Bioverse code, performed the calculations and analysis, and
drafted the manuscript. SYH created the GMT and ELT instrument models and
computed contrast tables for O2. MS assisted with Bioverse code issues and
hypothesis test implementation. MK provided early models of PCS performance.
MK and JK gave project input regarding the ELT and hypothesis testing. KW
provided guidance on practical direct imaging observations. All authors
contributed suggestions and edits to the manuscript.

##  Appendix A Different Instrument Modes

For both the GMT and ELT, we first assessed different instrument setups and
observing conditions. The GMagAO-X on GMT setup assumes a baseline number of
182 deformable mirror actuators, and we looked at two different AO control
system optimization strategies: Max Speed, and Strehl Optimization. For PCS on
the ELT, additional calculations were made for both a 128 or 200 actuator
setup. Table 3 shows results for the different AO control systems and
observing conditions for the GMT, and Table 4 shows results for different AO
control systems, actuator counts, and observing conditions for the ELT.

Except for survey durations longer than 10 years on the ELT, Max Speed yields
faster O2 detections than Strehl Optimization. There is a trade-off for
observing in different conditions. Observing in Q2 conditions allows more
observing time, but it will take longer to build up signal on a target. From
these simulations, Q1 vs Q2 observing only makes marginal differences
depending on the instrument setup. The large uncertainties (computed as the
16th and 84th percentile of the first through nth planets in the sorted
universes; see Figure 1 for typical uncertainties for all models) effectively
place all instrument setup results within 1$\sigma$. Nonetheless, we selected
the GMT Max Speed Q1 and the ELT Max Speed, 128 actuators, Q2 instrument
setups to perform additional optimistic simulations due to their marginally
better performance than the other instrument setups for surveys with a
duration of up to 10 years (Figure 8).

| Max Speed, Q1 | Max Speed, Q2
---|---|---
Mag|$\theta$ | 15 mas | 30 mas | 50 mas | 100 mas | 120 mas | 15 mas | 30 mas | 50 mas | 100 mas | 120 mas
1 | 5.85E-09 | 4.53E-09 | 3.51E-09 | 2.55E-09 | 2.36E-09 | 1.24E-08 | 9.52E-09 | 6.91E-09 | 4.48E-09 | 4.04E-09
3 | 1.93E-08 | 1.61E-08 | 1.32E-08 | 1.02E-08 | 9.53E-09 | 3.43E-08 | 2.76E-08 | 2.17E-08 | 1.61E-08 | 1.49E-08
5 | 8.01E-08 | 6.89E-08 | 5.85E-08 | 4.68E-08 | 4.41E-08 | 1.24E-07 | 1.07E-07 | 8.91E-08 | 6.98E-08 | 6.55E-08
7 | 4.55E-07 | 4.02E-07 | 3.49E-07 | 2.88E-07 | 2.73E-07 | 6.77E-07 | 6.01E-07 | 5.20E-07 | 4.26E-07 | 4.04E-07
9 | 4.31E-06 | 3.89E-06 | 3.45E-06 | 2.89E-06 | 2.73E-06 | 7.07E-06 | 6.46E-06 | 5.77E-06 | 4.89E-06 | 4.65E-06
10 | 1.82E-05 | 1.66E-05 | 1.50E-05 | 1.26E-05 | 1.16E-05 | 3.58E-05 | 3.34E-05 | 3.04E-05 | 2.58E-05 | 2.42E-05
Mag | Strehl Optimization, Q1 | Strehl Optimization, Q2
1 | 7.33E-09 | 5.43E-09 | 3.92E-09 | 2.55E-09 | 2.32E-09 | 1.24E-08 | 9.52E-09 | 6.91E-09 | 4.48E-09 | 4.04E-09
3 | 2.77E-08 | 2.05E-08 | 1.48E-08 | 9.58E-09 | 8.70E-09 | 4.22E-08 | 3.25E-08 | 2.38E-08 | 1.59E-08 | 1.45E-08
5 | 1.38E-07 | 1.01E-07 | 7.16E-08 | 4.34E-08 | 3.84E-08 | 2.11E-07 | 1.61E-07 | 1.15E-07 | 7.08E-08 | 6.27E-08
7 | 4.78E-07 | 3.53E-07 | 2.54E-07 | 1.64E-07 | 1.49E-07 | 8.31E-07 | 6.34E-07 | 4.56E-07 | 2.88E-07 | 2.58E-07
9 | 2.53E-06 | 1.87E-06 | 1.34E-06 | 8.48E-07 | 7.63E-07 | 3.73E-06 | 2.87E-06 | 2.10E-06 | 1.40E-06 | 1.28E-06
10 | 4.39E-06 | 3.34E-06 | 2.54E-06 | 1.85E-06 | 1.74E-06 | 1.08E-05 | 8.26E-06 | 6.00E-06 | 3.82E-06 | 3.42E-06
Table 3: GMT achievable $F_{p}/F_{\star}$ contrast at S/N=5 for 1 hour integration times using high contrast imaging with high-resolution spectroscopy for different host star magnitudes and planet-star angular separations ($\theta$). Tables are given for different AO control systems (Max Speed and Strehl Optimization) and Q1 and Q2 observing conditions. | Max Speed, 128 actuators, Q1 | Max Speed, 128 actuators, Q2
---|---|---
Mag|$\theta$ | 5 mas | 10 mas | 15 mas | 30 mas | 50 mas | 120 mas | 5 mas | 10 mas | 15 mas | 30 mas | 50 mas | 120 mas
1 | 2.55E-09 | 2.08E-09 | 1.99E-09 | 1.55E-09 | 1.25E-09 | 9.36E-10 | 5.00E-09 | 4.07E-09 | 3.89E-09 | 3.11E-09 | 2.58E-09 | 1.97E-09
3 | 7.12E-09 | 5.84E-09 | 5.64E-09 | 4.64E-09 | 3.90E-09 | 2.95E-09 | 1.30E-08 | 1.06E-08 | 1.02E-08 | 8.33E-09 | 7.06E-09 | 5.50E-09
5 | 2.48E-08 | 2.04E-08 | 1.99E-08 | 1.68E-08 | 1.43E-08 | 1.09E-08 | 3.91E-08 | 3.21E-08 | 3.12E-08 | 2.64E-08 | 2.26E-08 | 1.75E-08
7 | 1.03E-07 | 8.49E-08 | 8.30E-08 | 7.14E-08 | 6.17E-08 | 4.78E-08 | 1.49E-07 | 1.22E-07 | 1.19E-07 | 1.02E-07 | 8.82E-08 | 6.85E-08
9 | 5.72E-07 | 4.72E-07 | 4.64E-07 | 4.06E-07 | 3.57E-07 | 2.82E-07 | 7.95E-07 | 6.54E-07 | 6.41E-07 | 5.60E-07 | 4.91E-07 | 3.90E-07
10 | 1.62E-06 | 1.34E-06 | 1.32E-06 | 1.17E-06 | 1.03E-06 | 8.24E-07 | 2.34E-06 | 1.93E-06 | 1.89E-06 | 1.67E-06 | 1.49E-06 | 1.20E-06
Mag | Max Speed, 200 actuators, Q1 | Max Speed, 200 actuators, Q2
1 | 2.24E-09 | 1.83E-09 | 1.72E-09 | 1.27E-09 | 9.48E-10 | 6.18E-10 | 4.06E-09 | 3.33E-09 | 3.13E-09 | 2.27E-09 | 1.66E-09 | 1.01E-09
3 | 6.39E-09 | 5.24E-09 | 5.03E-09 | 4.02E-09 | 3.27E-09 | 2.31E-09 | 1.07E-08 | 8.77E-09 | 8.32E-09 | 6.31E-09 | 4.92E-09 | 3.39E-09
5 | 2.34E-08 | 1.93E-08 | 1.87E-08 | 1.56E-08 | 1.31E-08 | 9.73E-09 | 3.39E-08 | 2.79E-08 | 2.70E-08 | 2.21E-08 | 1.83E-08 | 1.33E-08
7 | 1.07E-07 | 8.78E-08 | 8.58E-08 | 7.37E-08 | 6.35E-08 | 4.89E-08 | 1.46E-07 | 1.20E-07 | 1.17E-07 | 9.95E-08 | 8.50E-08 | 6.46E-08
9 | 7.13E-07 | 5.88E-07 | 5.77E-07 | 5.07E-07 | 4.46E-07 | 3.52E-07 | 9.95E-07 | 8.22E-07 | 8.07E-07 | 7.07E-07 | 6.21E-07 | 4.93E-07
10 | 2.22E-06 | 1.83E-06 | 1.80E-06 | 1.60E-06 | 1.42E-06 | 1.13E-06 | 3.42E-06 | 2.82E-06 | 2.78E-06 | 2.48E-06 | 2.21E-06 | 1.78E-06
Mag | Strehl Optimization, 128 actuators, Q1 | Strehl Optimization, 128 actuators, Q2
1 | 2.55E-09 | 2.08E-09 | 1.99E-09 | 1.55E-09 | 1.25E-09 | 9.36E-10 | 5.00E-09 | 4.07E-09 | 3.89E-09 | 3.11E-09 | 2.58E-09 | 1.97E-09
3 | 8.29E-09 | 6.78E-09 | 6.44E-09 | 4.94E-09 | 3.91E-09 | 2.86E-09 | 1.57E-08 | 1.28E-08 | 1.21E-08 | 9.37E-09 | 7.48E-09 | 5.46E-09
5 | 3.03E-08 | 2.48E-08 | 2.35E-08 | 1.76E-08 | 1.36E-08 | 9.60E-09 | 5.62E-08 | 4.57E-08 | 4.30E-08 | 3.20E-08 | 2.44E-08 | 1.65E-08
7 | 1.46E-07 | 1.20E-07 | 1.13E-07 | 8.14E-08 | 5.90E-08 | 3.59E-08 | 1.88E-07 | 1.53E-07 | 1.44E-07 | 1.07E-07 | 8.11E-08 | 5.57E-08
9 | 5.94E-07 | 4.85E-07 | 4.57E-07 | 3.30E-07 | 2.40E-07 | 1.49E-07 | 9.28E-07 | 7.53E-07 | 7.06E-07 | 5.08E-07 | 3.68E-07 | 2.24E-07
10 | 1.20E-06 | 9.77E-07 | 9.20E-07 | 6.70E-07 | 4.93E-07 | 3.18E-07 | 1.81E-06 | 1.47E-06 | 1.38E-06 | 9.99E-07 | 7.34E-07 | 4.70E-07
Mag | Strehl Optimization, 200 actuators, Q1 | Strehl Optimization, 200 actuators, Q2
1 | 2.91E-09 | 2.37E-09 | 2.23E-09 | 1.59E-09 | 1.13E-09 | 6.42E-10 | 4.06E-09 | 3.33E-09 | 3.13E-09 | 2.27E-09 | 1.66E-09 | 1.01E-09
3 | 1.09E-08 | 8.92E-09 | 8.37E-09 | 5.96E-09 | 4.21E-09 | 2.33E-09 | 1.36E-08 | 1.11E-08 | 1.05E-08 | 7.58E-09 | 5.50E-09 | 3.35E-09
5 | 3.68E-08 | 3.01E-08 | 2.82E-08 | 2.02E-08 | 1.44E-08 | 8.38E-09 | 5.10E-08 | 4.18E-08 | 3.93E-08 | 2.83E-08 | 2.04E-08 | 1.21E-08
7 | 1.40E-07 | 1.14E-07 | 1.07E-07 | 7.72E-08 | 5.56E-08 | 3.33E-08 | 2.56E-07 | 2.10E-07 | 1.97E-07 | 1.40E-07 | 9.86E-08 | 5.33E-08
9 | 7.10E-07 | 5.79E-07 | 5.44E-07 | 3.88E-07 | 2.76E-07 | 1.56E-07 | 1.06E-06 | 8.70E-07 | 8.18E-07 | 5.84E-07 | 4.13E-07 | 2.29E-07
10 | 1.53E-06 | 1.25E-06 | 1.17E-06 | 8.40E-07 | 5.99E-07 | 3.46E-07 | 2.19E-06 | 1.79E-06 | 1.69E-06 | 1.21E-06 | 8.64E-07 | 4.99E-07
Table 4: ELT achievable $F_{p}/F_{\star}$ contrast at S/N=5 for 1 hour
integration times using high contrast imaging with high-resolution
spectroscopy for different host star magnitudes and planet-star angular
separations ($\theta$). Tables are given for different AO control systems (Max
Speed and Strehl Optimization), 128 and 200 deformable mirror actuators, and
Q1 and Q2 observing conditions.

Figure 8: Simulation results for a survey of Earth-like O2 levels at 5$\sigma$
on exo-Earth candidates within 20 pc with different AO control systems and
observing conditions for the GMT (upper left), additionally accounting for
different deformable mirror actuator counts on the ELT (upper right), and
considering an optimized setup for both the GMT and ELT but assessing the
differences between R=100,000 and R=500,000 (lower panel).

A higher resolution spectrograph produces narrower and deeper absorption and
emission lines. For O2, higher resolution gives access to more relative system
velocity space. We modeled an $R=500,000$ spectrograph coupled to our AO
systems, for which severe line blending in the O2 A-band occurs when
$|\Delta\mathrm{RV}|<10$ km s-1 and $40\ \mathrm{km\
s}^{-1}<|\Delta\mathrm{RV}|<48\ \mathrm{km\ s}^{-1}$ (López-Morales et al.,
2019; Hardegree-Ullman et al., 2023). As noted by Fowler et al. (2023), post-
processing efficiency does not change at $R>100,000$, so we are able to use
Tables 3 and 4 for our $R=500,000$ calculations. The lower panel of Figure 8
shows the results for $R=500,000$ compared to $R=100,000$, with a $\sim$1 or 2
planet increase in planets surveyed for a survey of 10 years, suggesting a
higher resolution spectrograph is not necessarily a good investment for this
science case.

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