# Reflected spectroscopy of small exoplanets III: probing the UV band to
measure biosignature gasses

Mario Damiano Jet Propulsion Laboratory, California Institute of Technology,
Pasadena, CA 91109, USA  Renyu Hu Jet Propulsion Laboratory, California
Institute of Technology, Pasadena, CA 91109, USA  Division of Geological and
Planetary Sciences, California Institute of Technology, Pasadena, CA 91125,
USA  Bertrand Mennesson Jet Propulsion Laboratory, California Institute of
Technology, Pasadena, CA 91109, USA

(Received May 12th, 2023; Accepted August 7th, 2023)

###### Abstract

Direct-imaging observations of terrestrial exoplanets will enable their
atmospheric characterization and habitability assessment. Considering the
Earth, the key atmospheric signatures for the biosphere is O2 and the
photochemical product O3. However, this O2-O3 biosignature is not detectable
in the visible wavelengths for most of the time after the emergence of
oxygenic photosynthesis life (i.e., the Proterozoic Earth). Here we
demonstrate spectroscopic observations in the ultraviolet wavelengths for
detecting and characterizing O2 and O3 in Proterozoic Earth-like planets,
using ExoReLℜ. For an O2 mixing ratio 2 to 3 orders of magnitude less than the
present-day Earth, and an O3 mixing ratio of $10^{-7}-10^{-6}$, we find that
O3 can be detected and its mixing ratio can be measured precisely (within
$~{}1$ order of magnitude) in the ultraviolet ($0.25-0.4\ \mu$m) in addition
to visible-wavelength spectroscopy. With modest spectral resolution ($R=7$)
and S/N ($\sim 10$) in the ultraviolet, the O3 detection is robust against
other potential gases absorbing in the ultraviolet (e.g., H2S and SO2), as
well as the short-wavelength cutoff between 0.2 and 0.25 $\mu$m. While the O3
detection does not rely on the near-infrared spectra, extending the wavelength
coverage to the near-infrared ($1-1.8\ \mu$m) would provide essential
information to interpret the O3 biosignature, including the mixing ratio of
H2O, the cloud pressure, as well as the determination of the dominant gas of
the atmosphere. The ultraviolet and near-infrared capabilities should thus be
evaluated as critical components for future missions aiming at imaging and
characterizing terrestrial exoplanets, such as the Habitable Worlds
Observatory.

methods: statistical – planets and satellites: rocky exoplanets – atmospheres
– technique: spectroscopic – radiative transfer

††journal: AJ

##  1 Introduction

High-contrast imaging of exoplanets promises to enable the spectroscopic
characterization of temperate and rocky exoplanets in our interstellar
neighborhood. Laboratory studies have successfully achieved the necessary
level of starlight suppression required for imaging an earth-like planet
orbiting a Sun-like star using starshade technology (e.g., Harness et al.
(2021)) and significant progress has been made toward high contrast imaging
using coronagraphy (e.g., Trauger & Traub (2007); Seo et al. (2019)). The
Nancy Grace Roman Space Telescope (Roman; Spergel et al. (2015); Akeson et al.
(2019)) is set to demonstrate high-precision/performance coronagraph
technology in space (Mennesson et al., 2022). Future large astrophysics
missions combined with starlight suppression technologies could potentially
discover small exoplanets in habitable zones around nearby stars and examine
their atmospheres across ultraviolet (UV), visible (VIS), and near-infrared
(NIR) wavelengths (Roberge & Moustakas (2018); Seager et al. (2019); Gaudi et
al. (2020); HabEx Final Report111https://www.jpl.nasa.gov/habex/documents/;
LUVOIR Final Report222https://asd.gsfc.nasa.gov/luvoir/reports/). In light of
these progresses, the Astro2020 decadal survey recommended the development of
a flagship mission to discover Earth-like habitable exoplanets via direct
imaging (National Academies of Sciences et al. (2021)), which is now referred
to as the Habitable Worlds Observatory (HWO).

As such, the characterization of exoplanetary atmospheres through spectroscopy
has become a key frontier in the search for potentially habitable worlds.
While existing (e.g., JWST) and upcoming telescopes (e.g., Nancy Grace Roman
Space Telescope, Roman) have predominantly focused on observations in the
visible and near-infrared (NIR) wavelength ranges (JWST Transiting Exoplanet
Community Early Release Science Team et al., 2023; Feinstein et al., 2023;
Rustamkulov et al., 2023; Alderson et al., 2023; Ahrer et al., 2023), the
ultraviolet (UV) band offers unique opportunities to probe the presence of
crucial atmospheric species, such as O2 and O3, that may serve as potential
biosignatures.

In previous works, the use of reflected light spectroscopy to characterize gas
giants, sub-Neptunes, and terrestrial exoplanets has been investigated (Lupu
et al., 2016; Feng et al., 2018; Batalha et al., 2019; Damiano & Hu, 2020;
Damiano et al., 2020; Carrión-González et al., 2020; Damiano & Hu, 2021, 2022;
Robinson & Salvador, 2023). These studies demonstrated the effectiveness of
using reflected light spectroscopy for the atmospheric characterization of
small planets, particularly for characterizing the atmospheres of terrestrial
exoplanets beyond modern Earth analogs. Collectively, it has been shown that
(1) an optimal definition of Bayesian prior functions leads to a better
interpretation of the reflected spectrum by reducing the possibility of
degeneracies, (2) The VIS band alone, ranging from approximately 0.4 to 1
$\mu$m, has limitations in fully characterizing terrestrial planets, as it is
unable to extract information on CO2 levels, cloud formations, and surface
details, (3) the NIR wavelength band ($\sim 1-1.8\ \mu$m) is necessary for
reliably characterizing terrestrial exoplanet atmospheres from modern Earth-
like to Archean Earth-like and CO2-dominated.

The detection of O2 and O3 in exoplanetary atmospheres is of paramount
importance, as their presence can be indicative of biological processes
occurring on a planet (Meadows et al., 2018). The UV band ($\sim 0.2-0.4\
\mu$m) provides a promising mean of detecting these species due to their
strong absorption in this wavelength range. In the Solar System, the Earth’s
atmosphere exhibits strong O2 and O3 absorption bands in the UV region (e.g.,
Turnbull et al., 2006; Kaltenegger et al., 2007), which have played a
significant role in shaping the planet’s ability of a life-bearing world.

The Earth’s atmosphere has experienced several evolutionary phases before
reaching its current state. The Archean and Proterozoic eons are two
significant periods preceding the present. The Archean Eon, which occurred
from around 4 billion to 2.5 billion years ago, is of great importance due to
the critical developments in the Earth’s crust and the evolution of life
during this time. This period saw the creation of the Earth’s first stable
continental crusts, which contributed to shaping the planet’s geological
features and set the stage for the development of continents and ocean basins.
The atmosphere during this time was characterized by a significant presence of
CH4 and CO2 in an N2-dominated scenario (e.g., Catling & Zahnle (2020)).

The Proterozoic Eon, spanning from approximately 2.5 billion to 500 million
years ago, is also a crucial period in Earth’s history. Its significance lies
primarily in the critical developments in life’s evolution on our planet
during this time. These advancements established the groundwork for the
emergence of more diverse and complex life forms in subsequent eons.
Additionally, the Proterozoic Eon witnessed the Great Oxygenation Event (GOE),
which led to a dramatic increase in oxygen levels in the atmosphere. This
event had a profound impact on the planet’s climate, geology, and habitability
for future life forms (Young, 2009; Planavsky et al., 2014). Nonetheless, the
concentrations of O2 and O3 during this period would not have been adequate to
display notable absorption signatures in the visible wavelength band, but they
would have been sufficient to profoundly affect the UV waveband. Consequently,
this scenario is the focus of this study.

We employ our state-of-the-art Bayesian retrieval method, ExoReLℜ(Damiano &
Hu, 2020, 2021, 2022), to explore the constraints on O2 and O3 in the
atmospheres of terrestrial exoplanets akin to Proterozoic Earth through
reflected spectroscopy across UV, VIS, and NIR wavelength bands. Our retrieval
framework, which builds upon the methodology presented in the previous works
on reflected spectroscopy of small exoplanets (Damiano & Hu, 2021, 2022),
allows us to identify and characterize the dominant atmospheric species
without relying on prior assumptions about the background atmosphere. This
capability is crucial for accurately assessing the potential habitability of
exoplanets with diverse atmospheric compositions.

To assess the detectability of O2 and O3 in the UV band, we simulate two
Proterozoic Earth’s analog planetary atmospheric scenarios, which encompass
0.1% and 1% of O2 of modern Earth’s mixing ratio and the corresponding level
of O3 predicted by photochemical models (Reinhard et al., 2017). We explore
the sensitivity of our retrieval method to variations in observational
parameters such as the wavelength coverage (e.g., the implications of the UV
coverage starting at either 0.20 or 0.25 $\mu$m). Additionally, we compare the
constraints obtained from observations that include UV with those derived from
only visible and NIR bands, to evaluate the added value of including the UV
wavelengths in the characterization of exoplanetary atmospheres.

The paper is organized as follows: Sec. 2 describes the retrieval algorithm,
atmospheric scenarios, and the simulation of reflected light spectra. Sec. 3
presents the results of our retrievals and the constraints on O2 and O3. In
Sec. 4, we discuss the implications of our findings for the detection of
potential biosignatures in exoplanetary atmospheres, as well as the design of
future missions aimed at characterizing habitable worlds. Sec. 5 then
summarizes the key conclusions of this study.

##  2 Methods

###  2.1 Retrieval Setup

We used ExoReLℜ to carry out atmospheric retrievals on synthesized spectra.
The details of the algorithm are described in our previous two papers about
the atmospheric characterization of small exoplanets, i.e. Damiano & Hu (2021,
2022). The key features of the algorithm are summarized here:

  * •

Implemented centered log-ratio (CLR) of mixing ratios for atmospheric chemical
compounds as free parameters;

  * •

Developed new set of prior functions (detailed in Damiano & Hu, 2021) to
ensure no gas is preferred as the dominant gas a priori;

  * •

Included water clouds as type of condensates in the atmosphere;

  * •

Used optical properties from Palmer & Williams (1974) for cross sections and
single-scattering albedo of water droplets;

  * •

The volume mixing ratio of water and the cloud density are correlated to
ensure physical consistency between water in the gas form and condensation
into water clouds;

  * •

Cloud parameterization includes cloud top pressure (Ptop), cloud depth (Dcld),
and condensation ratio (CR);

  * •

Introduced surface pressure and surface albedo as fixed or free parameters in
the model.

The full list of free parameters used here is reported in Tab. 1, along with
the ranges and the type of priors for the free parameters.

Parameter | Symbol | Range | Prior type
---|---|---|---
Surface pressure [Pa] | P0 | 3.0 - 11.0 | log-uniform
Cloud top [Pa] | P${}_{top,H_{2}O}$ | 0.0 - 8.0 | log-uniform
Cloud depth [Pa] | D${}_{H_{2}O}$ | 0.0 - 8.5 | log-uniform
Condensation ratio | CR${}_{H_{2}O}$ | -12.0 - 0.0 | log-uniform
VMR H2O | H2O | -25.0 - 25.0 | CLR1
VMR CH4 | CH4 | -25.0 - 25.0 | CLR1
VMR SO2 | SO2 | -25.0 - 25.0 | CLR1
VMR CO2 | CO2 | -25.0 - 25.0 | CLR1
VMR O2 | O2 | -25.0 - 25.0 | CLR1
VMR O3 | O3 | -25.0 - 25.0 | CLR1
Surface albedo | Ag | 0.0 - 1.0 | linear-uniform
Surface gravity [cgs] | g | 1.0 - 5.0 | log-uniform
Table 1: Priors for the free parameters used in the retrievals presented in
this work. NOTE - 1 Damiano & Hu (2021)

Finally, we used MultiNest (Feroz et al., 2009; Buchner et al., 2014) as
Bayesian algorithm to explore the multi-dimensional free parameter space. We
used 1000 live points and a Bayesian tolerance of 0.5 to be able to capture
any possible degeneracies.

###  2.2 Simulated Atmospheric Scenarios

In our previous work (Damiano & Hu, 2022), we presented four different case
studies to asses the impact on retrieved parameters by the probed wavelength
range for terrestrial exoplanets. Among the four scenarios, we included an
Archean Earth-like and a Modern Earth-like atmosphere. To characterize these
two scenarios, the use of the UV wavelength band was not required as the
Modern Earth shows strong absorption features of both O2 and O3 in the VIS
wavelength band, while the Archean Earth does not contain enough O2 and O3 to
show significant absorption in either visible or UV wavelengths. In the
history of the Earth evolution, the passage from the Archean to Modern
environment is characterized by the Proterozoic Eon, when the atmospheric O2
was substantial but lower than the modern Earth’s mixing ratio by at least two
orders of magnitude (Planavsky et al., 2014). In the Proterozoic Earth-like
scenario, while the presence of O2 and O3 is not negligible and a product of
the biosphere, they do not have enough atmospheric abundance to produce
detectable absorption features in the VIS wavelength band. In this case the UV
band can be useful, where small amount of O2 and O3 produce strong signatures
(Reinhard et al., 2017).

Here we simulate a 1M⊕, 1R⊕ planet at 1AU from a Sun-like star. We surround
the planet with two different atmospheric Proterozoic-like scenarios to
explore the capability of reflected light spectroscopy in different wavelength
bands. The first scenario is a Proterozoic Earth-like planet containing 1% of
the O2 concentration of the Modern Earth value, while in the second scenario
we dropped the O2 concentration to 0.1% of Modern Earth concentration value.
We modeled the concentration of O2 and O3 to be consistent with each other by
considering the results presented in (Reinhard et al., 2017). The true value
used to simulate the spectra are reported in Tabs. 2 and 3, while the
generated spectra are shown in Fig. 1.

Figure 1: Simulated spectra of the two Proterozoic Earth-like scenario
considered in this study.

Finally, in the final reports for HabEx and LUVOIR, concerns have been raised
about the potential for degenerate solutions between O3 and other chemical
compounds within the UV wavelength range. In particular, SO2 and H2S show
strong absorption features close to that of the ozone (Fig. 2). A closer look
reveals that the features do not overlap with each other, signaling that
degeneracy on the detection of O3 is possible but not likely. To test this
assumption, we included SO2 as free parameter of the retrieval to see if we
would detect it at a modest spectral resolution ($R=7$) in any of the studied
cases.

Figure 2: Absorption features of different gases in the UV wavelength band. In
particular, O3, SO2, and H2S absorption features are compared.

In all scenarios, we study the impact of including and excluding the UV and
the NIR portion of the reflected light spectra in the retrieval. In this work,
we set the “UV” wavelengths to $0.2/0.25-0.4\ \mu$m, the “VIS” wavelengths to
$0.4-1.0\ \mu$m and the “NIR” wavelengths to $1.0-1.8\ \mu$m, and adopt a
baseline spectral resolution of R$=$7, R$=$140, and R$=$40 for the UV, VIS,
and NIR bands, respectively. These assumptions are approximately consistent
with the large mission studies (Roberge & Moustakas, 2018; Gaudi et al.,
2020).

Figure 3: Simulated data and best fit retrievals for the Proterozoic Earth-
like scenario with 1% of Modern Earth O2. VIS/UV/NIR spectrum predicted when
fitting: VIS data only (blue curve), UV+ VIS data only (orange curve, same as
blue curve, except in the UV), VIS + NIR data only (green curve), UV + VIS +
NIR data only (red curve, same as green curve, except in the UV).

Lastly, to simulate the error associated to each of the data points, we
considered the maximum value of the spectrum and we divided it by the desired
S/N, 20 in this study. This effectively assumes that the noise is dominated by
the background and not the planet, likely valid for spectroscopy of
terrestrial planets (e.g., Hu et al., 2021). In the UV band, this corresponds
to an average S/N=9 for the 1% O2 scenario and S/N=12 for the 0.1% O2
scenario. We then added a Gaussian deviation to the data to simulate the
random realization of the observation.

##  3 Results

In this section, we present the results of the retrieval process applied to
the two scenarios presented in Sec. 2.2.

###  3.1 1% of Modern Earth’s O2

The retrieval results are reported in Tab. 2, and the posterior distributions
are shown in Appendix A. The simulated data and the best-fit spectra are shown
in Figure 3.

Table 2: Atmospheric parameters used to simulate the Proterozoic Earth-like scenario (1% of Modern Earth O2) and the retrieval results. The error bars of the retrieval median results correspond to the 95% confidence interval (i.e., 2$\sigma$). NOTE - parameters highlighted with the asterisk are derived from the other free parameters. Color code: green strongly constrained within 3$\sigma$, orange weakly constrained within 3$\sigma$, and red not constrained or outside 3$\sigma$.  Parameter | Input | VIS | UV$+$VIS | VIS$+$NIR | UV$+$VIS$+$NIR
---|---|---|---|---|---
$Log(P_{0})$ [Pa] | $5.00$ | $9.76^{+1.15}_{-1.18}$ | $9.78^{+1.15}_{-1.25}$ | $5.45^{+0.67}_{-0.52}$ | $5.32^{+0.64}_{-0.41}$
$Log(P_{top,H_{2}O})$ [Pa] | $4.85$ | $3.47^{+3.65}_{-3.19}$ | $3.48^{+3.74}_{-3.30}$ | $5.09^{+0.65}_{-0.52}$ | $4.96^{+0.55}_{-0.36}$
$Log(D_{cld,H_{2}O})$ [Pa] | $4.30$ | $3.61^{+3.88}_{-3.34}$ | $3.79^{+3.93}_{-3.57}$ | $4.65^{+0.69}_{-0.58}$ | $4.52^{+0.56}_{-0.43}$
$Log(CR_{H_{2}O})$ | $-3.00$ | $-5.67^{+5.20}_{-5.83}$ | $-5.74^{+5.45}_{-5.93}$ | $-5.06^{+2.19}_{-4.40}$ | $-4.79^{+1.92}_{-4.02}$
$Log(VMR_{H_{2}O})$ | $-2.01$ | $-7.37^{+0.26}_{-0.28}$ | $-7.35^{+0.26}_{-0.28}$ | $-2,28^{+0.55}_{-0.56}$ | $-2.12^{+0.42}_{-0.44}$
$Log(VMR_{CH_{4}})$ | $-4.30$ | $-7.74^{+0.57}_{-5.77}$ | $-7.64^{+0.54}_{-5.79}$ | $-4.53^{+0.54}_{-0.73}$ | $-4.37^{+0.39}_{-0.62}$
$Log(VMR_{SO_{2}})$ | $-$ | $-$ | $-11.02^{+2.19}_{-2.80}$ | $-$ | $-8.71^{+0.83}_{-1.42}$
$Log(VMR_{CO_{2}})$ | $-3.40$ | $-$ | $-$ | $-5.94^{+2.92}_{-3.88}$ | $-5.75^{+2.79}_{-3.84}$
$Log(VMR_{O_{2}})$ | $-2.71$ | $-8.54^{+2.73}_{-5.13}$ | $-8.44^{+2.73}_{-5.10}$ | $-3.84^{+1.77}_{-5.94}$ | $-2.61^{+0.65}_{-6.14}$
$Log(VMR_{O_{3}})$ | $-6.30$ | $-9.61^{+3.48}_{-4.19}$ | $-6.11^{+0.16}_{-0.19}$ | $-7.73^{+1.75}_{-2.36}$ | $-6.32^{+0.24}_{-0.26}$
$Log(VMR_{N_{2}})^{*}$ | $-0.005$ | $-0.01^{+0.01}_{-0.01}$ | $-0.01^{+0.01}_{-0.01}$ | $-0.01^{+0.01}_{-0.01}$ | $-0.01^{+0.01}_{-0.01}$
$A_{g}$ | $0.2$ | $0.54^{+0.43}_{-0.50}$ | $0.51^{+0.47}_{-0.48}$ | $0.25^{+0.38}_{-0.24}$ | $0.22^{+0.39}_{-0.21}$
$Log(g\ [cgs])$ | $2.99$ | $3.05^{+0.01}_{-0.01}$ | $3.05^{+0.01}_{-0.01}$ | $2.99^{+0.02}_{-0.02}$ | $3.00^{+0.02}_{-0.02}$
$\mu^{*}$ | $27.93$ | $28.01^{+0.01}_{-0.01}$ | $28.01^{+0.01}_{-0.01}$ | $27.97^{+0.03}_{-0.13}$ | $27.95^{+0.04}_{-0.12}$

We run ExoReLℜ on the simulated data while considering different combination
of the wavelength band probed. Starting with the VIS band only, we decided not
to fit for SO2 and CO2 as the spectral features of these gasses are present in
UV and NIR. By inspecting the posterior distribution functions (PDFs) (blue
model of Fig. 7), the solution on which the retrieval process converged is not
compatible with the true values used to synthesize the data in the first
place. Even though the code has been able to identify the background gas, i.e.
N${}_{2}-$dominated atmosphere, it is not able to constrain the rest of the
atmospheric components. The clouds parameters are not constrained at all,
showing a flat posterior. This is not surprising as we exposed the weaknesses
of considering the VIS band alone in the context of the characterization of
the reflected light for small rocky planets in our previous work (Damiano &
Hu, 2022).

Adding the UV band to the VIS gives information on the O2 and O3 absorption.
Looking at the PDFs (orange model of Fig. 7), it is possible to see that
surface and clouds parameters are still not correctly constrained. However, by
inspecting the PDFs of oxygen and ozone, we find that the UV indeed provides
the constraint of these two gases, and their PDFs do not show a broad
posterior distribution anymore. Finally, we note that fitting SO2, in this
case, does not impact whatsoever the constraint on the O2 and O3 as the
converged VMR value for SO2 is equal to $-11.02^{+2.19}_{-2.80}$, practically
absent.

Moving on to the VIS plus NIR case (green model of Fig. 7), the general nature
of the planet is correctly identified: the background gas is correctly found,
and the majority of the other gases are constrained except for CO2 and O3 as
the VMR of CO2 is too low to show substantial features, and because O3 does
not contain absorption bands in the VIS or NIR. Interestingly, O2 is weakly
constrained even though its VMR is quite low. This is because O2 shows
multiple but small absorption bands in the VIS and NIR wavelength range (see
Fig. 1). The surface pressure of the planet has been correctly identified as
well ass the surface albedo. The cloud parameters are also correctly
constrained.

Finally, adding UV to VIS and NIR observations again measures the mixing ratio
of O3. By inspecting the PDFs (red model of Fig. 7), we can confirm that the
nature of the planet has been correctly retrieved as the totality of the
parameters converged to the true values. Also in this case, SO2 does not
impact the convergence of the detection of O3.

We have also performed a test to reveal effect on the retrieval when
considering a different lower limit of the UV band. As it may be difficult to
reach 0.2 $\mu$m, we tested the case in which the UV is defined starting from
0.25 $\mu$m. Fig. 4 shows the effect on the retrieval results of O2 and O3. We
find that a UV wavelength range of $0.25-0.4\ \mu$m would also allow
measurments of O3, as well as O2 when the NIR coverage is also available. The
retrieved PDFs for both gases are broader compared to the UV wavelength range
of $0.2-0.4\ \mu$m, and the impact is more evident for O2 as there is a strong
absorption feature of O2 between 0.2 and 0.25 $\mu$m (Fig. 2).

Finally, we noticed a minor and secondary improvement in the posterior
distribution when UV is considered in addition to VIS and NIR bands. In Fig.
7, for example, the top pressure of the clouds is better constrained than the
VIS+NIR case. However, when UV is considered along with VIS only (VIS vs.
UV+VIS), we do not see any improvement. Moreover, we underline that the
difference is only noticeable for the 1% O2 level suggesting a correlation
with the detection of O2 in the UV and NIR bands. The improvement vanishes
once the UV is cut to 250 nm or for the 0.1% O2 level.

Figure 4: Effect of the lower wavelength cutoff of the UV band on the PDFs of
O2 and O3 for the Proterozoic Earth-like with 1% of Modern Earth’s O2. The
results of the retrieval does not change appreciably. The constraints are
moderately affected as the distributions are broadened. Blue curves correspond
to the results shown in Tale 2, with the default 0.2 um UV lower bound.

###  3.2 0.1% of Modern Earth’s O2

The Proterozoic Earth-like scenario with 0.1% of Modern Earth’s O2 is
identical to the 1% case except for the input VMR of O2 and O3. The retrieval
results are reported in Tab. 3, and the posterior distributions are shown in
Appendix B. The simulated data and the best-fit spectra are shown in Figure 5.

Figure 5: Simulated data and best fit retrievals for the Proterozoic Earth-like scenario with 0.1% of Modern Earth O2. VIS/UV/NIR spectrum predicted when fitting: VIS data only (blue curve), UV+ VIS data only (orange curve, same as blue curve, except in the UV), VIS + NIR data only (green curve), UV + VIS + NIR data only (red curve, same as green curve, except in the UV). Table 3: Atmospheric parameters used to simulate the Proterozoic Earth-like scenario (0.1% of Modern Earth O2) and the retrieval results. The error bars of the retrieval median results correspond to the 95% confidence interval (i.e., 2$\sigma$). NOTE - parameters highlighted with the asterisk are derived from the other free parameters. Color code: green strongly constrained within 3$\sigma$, orange weakly constrained within 3$\sigma$, and red not constrained or outside 3$\sigma$.  Parameter | Input | VIS | UV$+$VIS | VIS$+$NIR | UV$+$VIS$+$NIR
---|---|---|---|---|---
$Log(P_{0})$ [Pa] | $5.00$ | $9.67^{+1.25}_{-1.28}$ | $9.62^{+1.28}_{-1.23}$ | $5.32^{+1.07}_{-0.87}$ | $5.26^{+0.78}_{-0.81}$
$Log(P_{top,H_{2}O})$ [Pa] | $4.85$ | $3.18^{+3.59}_{-2.97}$ | $3.60^{+3.35}_{-3.39}$ | $3.88^{+1.05}_{-2.06}$ | $3.84^{+0.84}_{-1.44}$
$Log(D_{cld,H_{2}O})$ [Pa] | $4.30$ | $3.93^{+3.58}_{-3.61}$ | $3.73^{+3.73}_{-3.51}$ | $4.37^{+0.45}_{-0.61}$ | $4.52^{+0.42}_{-0.40}$
$Log(CR_{H_{2}O})$ | $-3.00$ | $-5.98^{+5.60}_{-5.59}$ | $-5.65^{+5.33}_{-5.86}$ | $-8.40^{+6.29}_{-3.24}$ | $-8.64^{+4.93}_{-3.08}$
$Log(VMR_{H_{2}O})$ | $-2.01$ | $-7.00^{+0.23}_{-0.19}$ | $-6.99^{+0.21}_{-0.18}$ | $-1.51^{+0.98}_{-0.59}$ | $-1.54^{+0.51}_{-0.58}$
$Log(VMR_{CH_{4}})$ | $-4.30$ | $-10.80^{+3.05}_{-4.36}$ | $-10.84^{+3.07}_{-3.55}$ | $-3.98^{+1.00}_{-0.60}$ | $-4.00^{+0.58}_{-0.54}$
$Log(VMR_{SO_{2}})$ | $-$ | $-$ | $-11.31^{+1.91}_{-3.27}$ | $-$ | $-8.96^{+0.81}_{-1.91}$
$Log(VMR_{CO_{2}})$ | $-3.40$ | $-$ | $-$ | $-5.50^{+5.13}_{-3.64}$ | $-6.96^{+4.94}_{-3.48}$
$Log(VMR_{O_{2}})$ | $-3.71$ | $-10.24^{+3.86}_{-4.35}$ | $-10.35^{+4.11}_{-4.02}$ | $-5.63^{+3.20}_{-3.26}$ | $-7.48^{+3.78}_{-3.08}$
$Log(VMR_{O_{3}})$ | $-6.70$ | $-10.22^{+4.34}_{-4.72}$ | $-6.64^{+0.13}_{-0.14}$ | $-7.12^{+1.52}_{-2.70}$ | $-6.68^{+0.13}_{-0.12}$
$Log(VMR_{N_{2}})^{*}$ | $-0.005$ | $-0.01^{+0.01}_{-0.01}$ | $-0.01^{+0.01}_{-0.01}$ | $-0.01^{+0.01}_{-2.61}$ | $-0.01^{+0.01}_{-0.03}$
$A_{g}$ | $0.2$ | $0.49^{+0.42}_{-0.47}$ | $0.52^{+0.45}_{-0.48}$ | $0.44^{+0.31}_{-0.37}$ | $0.28^{+0.38}_{-0.25}$
$Log(g\ [cgs])$ | $2.99$ | $3.04^{+0.01}_{-0.01}$ | $3.04^{+0.01}_{-0.01}$ | $3.00^{+0.01}_{-0.01}$ | $2.99^{+0.1}_{-0.02}$
$\mu^{*}$ | $27.92$ | $28.01^{+0.01}_{-0.01}$ | $28.01^{+0.01}_{-0.01}$ | $27.73^{+2.76}_{-0.87}$ | $27.74^{+0.21}_{-0.61}$

Also in this case, the VIS alone (blue model of Fig. 8) will not yield any
significant constraints. The cloud and surface parameters are either flat or
very broad. The background gas has been identified, but the chemical
composition of the amotsphere shows significant biases with respect to the
truth.

Adding UV data points to the visible observations results in the detection and
constraints of O3 (orange model of Fig. 8), while O2 remains undetected by
showing no constraints and a broad distribution that encompass almost the
entire range probed.

Fitting the NIR band in addiction to the VIS provides constraints on the
surface and cloud parameters (green model of Fig. 8). The general nature of
the planet is identified with constraints on the background gas, i.e. N2, and
other minor gases like H2O and CH4. Like the previous scenario (1% O2), O2 and
O3 are not constrained.

Including the UV band in addition to VIS and NIR allows for the clear
constrain of O3 (red model of Fig. 8). All the other parameters except for CO2
and O2 are constrained. In this scenario, fitting for the presence of SO2 does
not impact the PDFs, highlighting once again that SO2 and O3 are well distinct
in the UV band.

Figure 6: Similar to Fig. 4 but for the scenario with 0.1% modern Earth O2.

Finally, repeating the retrieval process for a truncated UV band, i.e.
starting from 0.25 $\mu$m rather than 0.2 $\mu$m, results in a broadening of
the posterior distribution of O3, while O2 remains undetected (see Fig. 6).

##  4 Discussion

The Proterozoic period is placed in between the Archean and the Modern Earth
in terms of Earth’s atmospheric evolution, and it lasted for $\sim 2$ billion
years, or $\sim 40\%$ of Earth’s history. During this period, the biosphere
has already been outputting O2 from photosynthesis, but geochemical evidence
indicates that atmospheric O2 mixing ratio remained low (Planavsky et al.,
2014), preventing remote-sensing detection in the visible wavelengths in
similar way to modern-Earth-like planets (e.g., Feng et al., 2018; Damiano &
Hu, 2022). However, due to nonlinear dependency of the photochemical O3 mixing
ratio on O2, as well as the strong absorption of O3, spectroscopy in the UV
band may detect the O2-O3 biosignature via O3 on a Proterozoic-Earth-like
planet (Reinhard et al., 2017). Here we demonstrated, using rigorous spectral
retrievals, that the detection of O3 is indeed feasible, and only requires a
modest spectral resolution of $R=7$ in a wavelength range of $0.25-0.4\ \mu$m.

This thus gives us a compelling science case for spectroscopic observations in
the UV ($0.25-0.4\ \mu$m) for the Habitable World Observatory. Since the
atmospheric concentration of O2 and O3 was not sufficient to show significant
absorption features in the VIS or NIR wavelength bands for a good part of
Earth history, not having the capabilities of starlight suppression and
spectroscopy in the UV could mean missing half of Earth-like planets with an
oxygenic biosphere. As O2 and O3 remain the leading biosignature gases for
terrestrial exoplanets of FGK stars (Meadows et al., 2018), it is vital to
provide sensitivity to O3 at low mixing ratios ($10^{-7}-10^{-6}$,
corresponding to the estimated Proterozoic level), which is feasible in the
UV.

We also reaffirm the importance of probing the NIR band to successfully
constrain the nature of the planet. The addition of the spectra in $1-1.8\
\mu$m result in the constraints of the surface/cloud properties and,
importantly, the mixing ratio of H2O. These pieces of information are
essential to establish the hydrological cycle and surface habitability of an
exoplanet, upon which the biosignature interpretation would be built. We have
retrieved an N2-dominated atmosphere for all scenarios considered in this
paper, but for a planet with higher CO2 mixing ratios (e.g., the Archean Earth
case in Damiano & Hu, 2022), adding the NIR band is critical for determining
the planet has an N2\- rather than CO2-dominated atmosphere. The constraints
on H2O and CO2, which are available when the NIR spectroscopy is obtained,
also help delineate any geochemical/photochemical false positive scenarios for
the O2-O3 biosignature (see a review in Meadows et al., 2018). In the case of
the 1% O2 levels, decent (but not good, i.e., broad posterior distribution,
-10.0 $\lesssim$ Log(O2) $\lesssim$ -2.0, Fig. 7) constraints on the O2 levels
can be made with the NIR part of the spectrum along with the VIS part,
lessening the need for the UV spectrum.

While not studied here, the UV part of the spectrum can be useful for studying
photochemical hazes in planetary atmospheres. Observations in the UV would
provide additional information on haze-rich planets such as Archean Earth
(Arney et al., 2016), Titan (Trainer et al., 2006), Venus (Titov et al.,
2018), and Jupiter (Anguiano-Arteaga et al., 2022)). The detectability of O3
would not be impacted by the presence of hazes as the O3 absorption shows as a
sharp edge in the UV while the haze absorption typically creates a slope in
the continuum starting from $\sim 0.5\ \mu$m. Future studies could assess the
information on photochemical hazes (e.g., particle size, absorption
coefficient) that could be extracted from the UV and VIS spectra.

Taking into account the results of this work and the previous ones (Feng et
al., 2018; Damiano & Hu, 2022), it is clear that probing the VIS wavelength
band alone is not sufficient for the characterization of terrestrial
exoplanets as many key gases, e.g., CO2, CH4, and O3 present their main
absorption features in the NIR or UV part of the electromagnetic spectrum. The
capabilities in the UV and NIR wavelengths should thus be evaluated as a
critical component for the future missions aiming at imaging and
characterizing terrestrial exoplanets, such as the Habitable World
Observatory.

##  5 Conclusions

In this study, we have investigated the potential of ultraviolet (UV), visible
(VIS), and near-infrared (NIR) observations to characterize terrestrial
exoplanets like the Proterozoic Earth in the context of the direct-imaging
spectroscopy in the reflected starlight. This 2-billion-year period of Earth’s
history is of particular interest, as it represents an intermediate stage
between the Archean and Modern Earth, when oxygenic photosynthesis had
commenced but the O2 level in the atmosphere remained lower than the modern
day.

Our analysis demonstrates the benefits of UV spectroscopy for detecting and
measuring the atmospheric mixing ratios of O3, as well as improving the
measurements of O2. Even with a modest spectral resolution of $R=7$ and an
average S/N of $\sim 10$ for the UV band, the spectra can precisely measure
the mixing ratio of O3 to $\sim 10^{-7}$, without interference of other UV
absorbing gases like SO2. This makes the UV band a crucial wavelength window
for the search for O2-O3 biosignatures on terrestrial exoplanets. Furthermore,
while the O3 detection does not rely on the NIR spectral coverage, the NIR
band would provide essential habitability indicators and contextual
information, including the cloud/surface pressure, atmospheric H2O abundances,
and dominant atmospheric gases (N2 versus CO2). Overall, it becomes clear that
relying solely on the visible (VIS) wavelength band for characterizing small
temperate planets can be limiting. This is because many crucial gases, such as
O3, CO2, and CH4, display their primary absorption characteristics in the UV
(0.25 to 0.4 $\mu$m) or NIR (1.0 to 1.8 $\mu$m) regions of the electromagnetic
spectrum.

Based on our findings, future direct-imaging missions aiming at finding and
characterizing small rocky exoplanets (e.g., the Habitable World Observatory)
should have the capability to probe both the UV and NIR bands, whenever this
is feasible from the perspective of the inner working angle. This will
significantly enhance our ability to detect and characterize biosignatures,
thereby improving our understanding of planetary atmospheres and enhancing our
search of life beyond the Solar System.

## Acknowledgments

We thank Charles Lawrence, Keith Warfield, Rhonda Morgan, and Shawn Domagal-
Goldman for helpful discussion. This work was supported in part by a JPL
strategic initiative for developing tools for scientific optimization of
missions. This research was carried out at the Jet Propulsion Laboratory,
California Institute of Technology, under a contract with the National
Aeronautics and Space Administration.

## Software

ExoReLℜ(Damiano & Hu, 2020, 2021, 2022), Numpy (Oliphant, 2015), Scipy
(Virtanen et al., 2020), Astropy (Price-Whelan et al., 2018), scikit-bio
(scikit-bio development team, 2020), Matplotlib (Hunter, 2007), MultiNest
(Feroz et al., 2009; Buchner et al., 2014), mpi4py (Dalcin & Fang, 2021), and
corner (Foreman-Mackey, 2016).

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##  Appendix A Scenario 1: Proterozoic Earth-like with 1% of Modern Earth’s O2

Earth’s atmosphere has experienced multiple evolutionary stages before
reaching the current state. Between the Archean and Modern epochs, another
important eon in the Earth’s history is called Proterozoic. For this scenario,
we simulate the reflected spectrum of an N2-dominated atmosphere (Figs. 1 and
3). We also include H2O, CH4, CO2, O2, and O3 as minor absorbing gases. We
include a water cloud layer and a surface with albedo of 0.2. We use the
synthesized data as input for ExoReLℜ, and Fig. 7 comprises the resulted
posterior distributions of all the wavelength band combinations discussed in
Sec. 2.2.

Figure 7: The full posterior distributions (corner plots) of the Proterozoic
Earth-like scenario with 1% of Modern Earth’s O2. The different cases explore
a combination of different wavelength bands used for the retrieval process.
The black lines in the corner plots refer to the true value used to simulate
the data.

##  Appendix B Scenario 2: Proterozoic Earth-like with 0.1% of Modern Earth’s
O2

This scenario is similar to the previous one except for the concentration of
O2 and O3. Therefore, we simulate, again, the reflected spectrum of a an
N2-dominated atmosphere with H2O, CH4, CO2, O2, and O3 as minor absorbing
gases (Fig. 1 and 5). We still include a water cloud layer and a surface with
albedo of 0.2. The synthesized data are used as input for ExoReLℜ. We perform
the retrieval with and without the UV and NIR part of the spectrum to explore
the benefit of having a larger wavelength band in addition to the optical. The
result is shown in Fig. 8.

Figure 8: The full posterior distributions (corner plots) of the Proterozoic
Earth-like scenario with 0.1% of Modern Earth’s O2. The different cases
explore a combination of different wavelength bands used for the retrieval
process. The black lines in the corner plots refer to the true value used to
simulate the data.