# Effects of UV stellar spectral uncertainty on the chemistry of terrestrial
atmospheres

D.J. Teal Department of Astronomy, University of Maryland, College Park, MD
20742, USA  NASA Goddard Space Flight Center  Eliza M.-R. Kempton Department
of Astronomy, University of Maryland, College Park, MD 20742, USA  Sandra
Bastelberger Department of Astronomy, University of Maryland, College Park, MD
20742, USA  NASA Goddard Space Flight Center  Center for Research and
Exploration in Space Science and Technology, NASA/GSFC, Greenbelt, MD 20771
Sellers Exoplanet Environments Collaboration, NASA Goddard Space Flight
Center, Greenbelt, MD 20771, USA  Allison Youngblood NASA Goddard Space Flight
Center  Sellers Exoplanet Environments Collaboration, NASA Goddard Space
Flight Center, Greenbelt, MD 20771, USA  Giada Arney NASA Goddard Space Flight
Center  Sellers Exoplanet Environments Collaboration, NASA Goddard Space
Flight Center, Greenbelt, MD 20771, USA

###### Abstract

The upcoming deployment of JWST will dramatically advance our ability to
characterize exoplanet atmospheres, both in terms of precision and sensitivity
to smaller and cooler planets. Disequilibrium chemical processes dominate
these cooler atmospheres, requiring accurate photochemical modeling of such
environments. The host star’s UV spectrum is a critical input to these models,
but most exoplanet hosts lack UV observations. For cases in which the host UV
spectrum is unavailable, a reconstructed or proxy spectrum will need to be
used in its place. In this study, we use the MUSCLES catalog and UV line
scaling relations to understand how well reconstructed host star spectra
reproduce photochemically modeled atmospheres using real UV observations. We
focus on two cases; a modern Earth-like atmosphere and an Archean Earth-like
atmosphere that forms copious hydrocarbon hazes. We find that modern Earth-
like environments are well-reproduced with UV reconstructions, whereas hazy
(Archean Earth) atmospheres suffer from changes at the observable level.
Specifically, both the stellar UV emission lines and the UV continuum
significantly influence the chemical state and haze production in our modeled
Archean atmospheres, resulting in observable differences in their transmission
spectra. Our modeling results indicate that UV observations of individual
exoplanet host stars are needed to accurately characterize and predict the
transmission spectra of hazy terrestrial atmospheres. In the absence of UV
data, reconstructed spectra that account for both UV emission lines and
continuum are the next best option, albeit at the cost of modeling accuracy.

editorials, notices — miscellaneous — catalogs — surveys

††journal: ApJ††software:  astropy (Astropy Collaboration et al., 2013, 2018),
numpy (Harris et al., 2020), scipy (Virtanen et al., 2020), matplotlib
(Hunter, 2007), spectres (Carnall, 2017)

##  1 Introduction

###  1.1 Photochemical Modeling of Exoplanet Atmospheres

The impending launch of the James Webb Space Telescope (JWST) will usher in an
era of precise characterization of exoplanet atmospheres, including
observations of smaller and cooler planets than ever before, and pushing
ultimately toward the study of habitable worlds. As more advanced
observatories come online, the need for models able to accurately predict
observations becomes increasingly crucial. Disequilibrium chemistry in
particular has become important as modelling efforts strive for accuracy.

Processes that drive an atmosphere away from chemical equilibrium include
photochemistry and atmospheric mixing (both vertical and horizontal). Such
processes should impact planets across a range of parameter space. Less
irradiated planets are vulnerable to disequilibrium chemistry because chemical
reactions that restore an atmosphere to thermochemical equilibrium are
strongly temperature dependent and tend to proceed more slowly at cooler
temperatures. As such, the smaller and cooler exoplanets that will be uniquely
observable with JWST are expected to be significantly impacted by
disequilibrium chemical effects, which therefore must be taken into account
when modeling their atmospheres. Conversely, hotter planets experience higher
UV irradiation, commensurate with their higher instellation, and vertical
mixing can be enhanced at higher temperatures (e.g. Parmentier et al., 2013).
For hot Jupiters, the improved wavelength coverage and precision of JWST
observations will highlight departures from chemical equilibrium that may have
been less apparent with prior data sets.

Chemical kinetics codes have been developed to predict the disequilibrium
chemical composition of exoplanetary atmospheres by simultaneously tracking
hundreds of chemical reaction rates and vertical mixing (e.g. Line et al.,
2010; Moses et al., 2011; Kopparapu et al., 2012; Hu et al., 2012; Miller-
Ricci Kempton et al., 2012; Venot et al., 2012; Rimmer & Helling, 2016; Tsai
et al., 2017; Kawashima & Ikoma, 2018). The aforementioned codes use a
numerical differential equation solver to enforce mass continuity throughout a
one-dimensional (1-D) atmosphere, given production and loss rates within each
vertically stratified layer and flux terms acting at layer boundaries.
Production and loss terms arise via the chemical reactions, and fluxes arise
by processes such as eddy diffusion and molecular diffusion. After setting
physically appropriate boundary conditions at the top and bottom of the
atmosphere, a steady-state solution is found by time stepping the solver
forward until the chemical composition of each atmospheric layer remains
stable at a predetermined threshold.

Such chemical kinetics calculations have been applied to the study of
exoplanet atmospheres to investigate the photochemical effects on atmospheric
composition and aerosol production on a wide variety of exoplanet types,
including hot Jupiters (e.g. Zahnle et al., 2009; Line et al., 2010; Moses et
al., 2011, 2013a; Venot et al., 2012), hydrogen-rich Neptunes and sub-Neptunes
(Line et al., 2011; Miller-Ricci Kempton et al., 2012; Moses et al., 2013b;
Venot et al., 2016), and terrestrial exoplanets orbiting a range of host stars
(e.g. Segura et al., 2010; Rugheimer & Kaltenegger, 2018; Wunderlich et al.,
2019). When taken together, these studies have confirmed the suspicion that
cooler planets should generally be more strongly impacted by disequilibrium
chemistry and that such effects should be more readily observable with JWST-
quality spectra.

An important caveat is that photochemical hazes further complicate modeling
predictions and observables. These optically thick particles, hydrocarbon and
sulfurous hazes, are expected to become abundant below $\sim 850$ K in
planetary atmospheres with conditions conducive to forming haze precursor
molecules (Fortney et al., 2013; Morley et al., 2015; Gao et al., 2020). Such
hazes bring about significant departures from equilibrium chemistry solutions
and are expected to have strong observable signatures (e.g. Morley et al.,
2015; Arney et al., 2017; Kawashima & Ikoma, 2018, 2019).

###  1.2 Considering the Host Star’s UV Spectrum

The UV spectrum of a planet’s host star is a critical input to chemical
kinetics models. It is the UV flux that establishes the rates of photolysis
reactions and thereby governs a primary process that drives the atmosphere out
of equilibrium at its upper boundary. Unfortunately, the UV spectra of many
exoplanet host stars have not been measured, which makes it difficult to
accurately model the photochemistry occurring in their planets’ atmospheres.
Currently, the Hubble Space Telescope (HST) is the only astronomical
observatory capable of obtaining high resolution UV spectra of host stars
between 1,000 and 3,000 Å. With HST nearing the end of its lifetime and no
comparable UV missions on the near-term horizon, there is a pressing need to
identify which UV observations of exoplanet host stars must be obtained now to
ensure future success in modeling and interpreting exoplanet spectra obtained
with upcoming facilities like JWST.

With that in mind, considerable HST observing time in recent years has been
applied to UV monitoring of stars that are of particular interest to exoplanet
studies. Notably, the MUSCLES111https://archive.stsci.edu/prepds/muscles/
Treasury Survey (HST GO 13650, PI K. France) obtained UV observations with HST
of 12 M and K stars known to host exoplanets and used these to create high-
resolution flux-calibrated panchromatic spectra (France et al., 2016;
Youngblood et al., 2016; Loyd et al., 2016). Later-type main sequence
exoplanet hosts were targeted because UV observations of such stars were
generally lacking, despite the fact that M stars offer the most favorable
conditions for transit spectroscopy. Furthermore, the planets orbiting M stars
are expected to be more highly impacted by the UV environment of their hosts
which evolve over the course of a host star’s lifetime (Shkolnik & Barman,
2014; Luger & Barnes, 2015). Since later type stars give off more UV radiation
relative to their bolometric luminosities compared to earlier-type stars, this
effect is particularly relevant to the most favorable targets for
characterization of potentially habitable exoplanets. Following on the MUSCLES
survey, the Mega-MUSCLES survey (HST GO 15071, PI C. Froning; Froning et al.,
2019b) expanded the sample of UV-characterized host stars to additional and
even later-type stars, and various other UV studies of exoplanet hosts and the
M-dwarf population are being pursued as well (e.g. Berta-Thompson et al.,
2015; Berta-Thompson, 2017; Bourrier et al., 2018; Waalkes et al., 2019;
Froning et al., 2019a; France et al., 2020; Diamond-Lowe et al., 2021; Loyd et
al., 2021; Pineda et al., 2021).

In the absence of observed UV data, various scaling relations have been
defined to approximate a host star’s UV spectrum based on optical proxies
related to the Ca II H & K lines. Youngblood et al. (2017) determined a
scaling relation between the equivalent width of the Ca II K line and various
UV emission lines using the UV spectra from the MUSCLES survey. Melbourne et
al. (2020) extended this work to also consider the full set of available HST
UV spectra of M dwarfs (a factor of $\sim 7$ increase in sample size) and
found that the $R^{\prime}_{HK}$ index — the Ca II H & K line core intensity
index defined in Rutten (1984) — was the best predictor of UV emission line
strength of the observable proxies that they considered. The advantage of
using optical proxies is that, in principle, a star’s UV spectrum can be
approximated in the absence of observed UV data using information readily
accessible to ground-based observatories. The Ca II H & K lines, at 3969 Å and
3934 Å, respectively, are historically well-observed, and the
$R^{\prime}_{HK}$ index has been cataloged for many stars or can otherwise be
calculated from existing optical spectra.

For models requiring UV spectra as inputs, such as photochemical models,
determining if these reconstructions are sufficient in the absence of
observations allows informed decision-making when choosing stars to observe
before HST is unavailable. This work aims to close the loop on that question
with respect to photochemical modeling in particular. We do this by directly
comparing the outputs of photochemical models run using observed stellar
spectra vs. those run using the Melbourne et al. (2020) reconstructions of the
same UV spectra. We then examine the degree to which the transmission spectra
of each of the modeled exoplanets are altered by the use of the UV
reconstructions, and we comment on implications for interpreting observations
from JWST. In Section 2, we describe our photochemistry-climate model, the UV
observations that we use as inputs to this model, and how we reconstruct the
UV spectra of our input stars. In Section 3 we describe the results of our
photochemical models, with discussion of their resulting transmission spectra
in Section 4. Section 5 explores the impact of various reconstructions of the
UV continuum (rather than the UV emission lines), focusing on the host star GJ
176. Finally, Section 6 summarizes this work and offers discussion of the
implications of our results, as well as motivation for future study.

##  2 Methods

###  2.1 Photochemistry and climate model

We use the Atmos coupled 1-D photochemistry and climate model to simulate the
physical properties of all atmospheres in our study. This model is well-
established in the literature, having been used to investigate the effects of
stellar activity on Earth-like atmospheres (e.g. Segura et al., 2005, 2010),
hazy terrestrial (“Archean”) atmospheres (e.g. Arney et al., 2016, 2017;
Fauchez et al., 2019), and numerous other studies of Earth-like atmospheres
under various conditions (e.g. Kasting et al., 1979; Kopparapu et al., 2017;
Harman et al., 2018; Meadows et al., 2018; Afrin Badhan et al., 2019).

Atmos includes the option to iterate between a photochemical model and a 1-D
climate (radiative-convective equilibrium) model until reaching a steady-state
solution. Atmos’ photochemical model includes a variety of important physical
processes—such as lightning (Harman et al., 2018), haze formation (Arney et
al., 2016), sedimentation and rainout (Arney et al., 2017)—in addition to
standard gas-phase chemical and photolysis reactions. This extensively
developed and recently updated chemical kinetics model works in conjunction
with the included climate model, which determines the 1-D temperature-pressure
profile in radiative-convective equilibrium, to explicitly model temperature-
sensitive processes such as water saturation and humidity (Kasting & Ackerman,
1986; Mischna et al., 2000; Kopparapu et al., 2013). These coupled models
allow for feedback between radiative-convective equilibrium and chemical
steady-state self-consistently.

Atmos provides two well-tested atmospheric templates that we use in this
study: an oxygen-rich, hazeless222Technically, sulfur aerosols are included in
the modern Earth template, but their abundances are trace, and they do not
significantly alter the atmospheric state. modern Earth-like template and a
hazy Archean Earth template suitable for low oxygen conditions. These serve as
the initial conditions for each of our simulations. Table 1 shows the boundary
conditions for each chemistry model, which include species specific to either
atmospheric state. For our modern Earth and Archean models, we use updated and
extended versions of the reaction networks described in Afrin Badhan et al.
(2019), Lincowski et al. (2018) and Arney et al. (2017), with the most up-to-
date version of these reaction networks appearing in the Atmos GitHub
repository333https://github.com/VirtualPlanetaryLaboratory/atmos.

Species | Type | Value | Species | Type | Value
---|---|---|---|---|---
Both models + |  |  |  Modern Earth + |  |
O + | Deposition velocity + | 1.0 + |  O2 + | Fixed Mixing Ratio + | $2.1\times 10^{-1}$
H + | Deposition velocity + | 1.0 + |  H2 + | Fixed Mixing Ratio + | $5.3\times 10^{-7}$
OH + | Deposition velocity + | 1.0 + |  CO + | Flux + | $3.7\times 10^{11}$
HO2 + | Deposition velocity + | 1.0 + |  CH4 + | Flux + | $1.0\times 10^{11}$
H2O2 + | Deposition velocity + |  $2.0\times 10^{-2}$ + |  N2O + | Flux + | $1.53\times 10^{9}$
HCO + | Deposition velocity + | 1.0 + |  H2S + | Flux + | $1.0\times 10^{8}$
H2CO + | Deposition velocity + |  $2.0\times 10^{-1}$ + |  HO2NO2 + | Deposition Velocity + | $0.2$
NO + | Deposition velocity + |  $3.0\times 10^{-4}$ + |  Archean Earth + |  |
NO2 + | Deposition velocity + |  $3.0\times 10^{-3}$ + |  H2 + | Deposition Velocity + | $2.4\times 10^{-4}$
HNO + | Deposition velocity + | 1.0 + |  | Flux + | $1.0\times 10^{10}$
H2SaaH2S deposition is an additional boundary condition alongside the fluxes and is the same across both model templates. This flux, along with fluxes of SO2 and H2, are distributed within the troposphere and meant to account for volcanic outgassing in both models. + | Deposition velocity + |  $2.0\times 10^{-2}$ + |  O2 + | Deposition Velocity + | $1.0\times 10^{-4}$
SO2 + | Deposition velocity + | 1.0 + |  CO + | Deposition Velocity + | $1.2\times 10^{-4}$
| Flux + |  $1.0\times 10^{9}$ + |  H2S + | Flux + | $3.5\times 10^{8}$
H2SO4 + | Deposition velocity + | 1.0 + |  CH4 + | Fixed Mixing Ratio + | $3.5\times 10^{-3}$
HSO + | Deposition velocity + | 1.0 + |  C4H2 (Aerosol) + | Deposition Velocity + | $1.0\times 10^{-2}$
SO4 (Aerosol) + | Deposition velocity + |  $1.0\times 10^{-2}$ + |  C5H4 (Aerosol) + | Deposition Velocity + | $1.0\times 10^{-2}$
S8 (Aerosol) + | Deposition velocity + |  $1.0\times 10^{-2}$ + |  CO2 + | Fixed Mixing Ratio + | $2.0\times 10^{-2}$
O3 + | Deposition velocity + | $7.0\times 10^{-2}$ |  |  |
CH3 + | Deposition velocity + | 1.0 + |  |  |
HNO3 + | Deposition velocity + | $2.0\times 10^{-1}$ |  |  |
Table 1: Static boundary conditions at the surface of our model. Deposition
velocity has units of cm/s. Flux is a constant surface flux of a species
measured in molecules/cm2/s. We note that this does not include top-of-
atmosphere fluxes, such as downward fluxes of CO and O, which are
parameterized in the model based on abundances at the top of the atmosphere
(Arney et al., 2016; Afrin Badhan et al., 2019). Species highlighted in gray
are those that are included as opacity sources in our Exo-Transmit
calculations (Section 2.3).

The latest public version of the Atmos model includes several significant
updates from previously published versions. The changes relevant to this study
are summarized below:

  * •

For the climate model, the $k$-coefficients for H2O and CO2 were updated using
the HITRAN2016 database (Gordon et al., 2017). For H2O, we assume 25 cm-1 line
cut-offs using Lorentz profiles with the plinth removed. For CO2, we use 500
cm-1 line cut-offs using the Perrin and Hartman sub-Lorentzian line profiles
(Perrin & Hartmann (1989); standard values for coarse spectral resolution).
The coefficients were generated using HELIOS-k (Grimm & Heng, 2015).

  * •

The photochemical model uses a 750 bin wavelength grid — the same one from
Lincowski et al. (2018) spanning $1176.5-10000$ Å with a resolution of 100
cm-1. This grid resolves the UV-wavelength range critical to this study
significantly better than the previous 118-bin grid. In particular, important
UV lines such as Lyman-$\alpha$ are no longer spread over a broad wavelength
range. Instead, these lines are better-resolved, resulting in more accurate
calculations of photolysis rates for all molecules. When spread over a wider
wavelength range as in the previous wavelength grid, molecules that are
otherwise not sensitive to a given strong line will have an overestimated
photolysis rate. Similarly, species very sensitive to these lines will have an
underestimated photolysis rate.

  * •

Comprehensive updates have been made to the photolysis cross sections and
quantum yield data for the photochemical model (e.g. H2O cross sections from
Ranjan et al., 2020). The updated cross section and quantum yield data were
sourced from Hébrard et al. (2006), Lincowski et al. (2018), the JPL
Publication 19-5 recommendations (Burkholder et al., 2019) and the MPI-Mainz
UV/VIS Spectral Atlas (Keller-Rudek et al., 2013); and references therein.

  * •

The treatment of hydrocarbon aerosols has been updated such that different
production channels now all contribute to a single particle population.
Previously, each production pathway formed non-interacting, distinct particle
populations with only one pathway providing opacity in the climate model while
the contribution of other pathways was neglected.

  * •

We include new options for hydrocarbon aerosol optical constants, such as new
UV-visible refractive index data for early Earth aerosols (Gavilan et al.,
2017), which are used for the Archean models in this study, and different
monomer sizes (ranging from 10 to 70 nm) for fractal particles.

In addition to the list above, we have also implemented an updated convergence
scheme for coupled photochemistry-climate models involving significant haze
formation (i.e. our Archean Earth models). In contrast to an integrated model
that solves both photochemistry and radiative transfer simultaneously, Atmos
relies on external coupling of historically separate climate and
photochemistry models — the two models are run sequentially in an iterative
fashion. When the Atmos model is run in this manner, the external coupling
between the two models may impede a self-consistent atmospheric solution in
some cases. Feedbacks between molecular and/or aerosol abundances and the
thermal state of the atmosphere can cause the coupled model to oscillate
between two non self-consistent solutions with drastically different
temperature-pressure and chemical profiles. For example, hazy states can lead
to significant atmospheric heating, which in turn will destroy hazes on a
subsequent model run — thus impeding overall model convergence. To avoid this
problem, we use a “short-stepping” method, in which we do not allow the
climate model to fully adjust the temperature-pressure profile to the
radiative forcing exerted by the spectrally active species, and instead we
interrupt the climate code after a limited number of iterative steps before
re-calculating changes to the chemistry with the photochemistry model. Over
many iterations of the coupled code, this allows for more reliable convergence
to a self-consistent atmospheric steady-state solution in radiative-convective
equilibrium. Only in the final step of a coupled model run, once the thermal
structure and chemical composition of the atmosphere appear to have settled
into a stable state, do we finally allow the climate model to run to a
converged solution.

####  2.1.1 Modelling aerosols

Hydrocarbon aerosol particles are thought to have intermittently existed in
Earth’s atmosphere during the Archean period (e.g., Zerkle et al., 2020). Such
hazes are modeled in our Archean Earth template, replicating a complex mixture
of massive molecules with distinct optical properties compared to gas-phase
molecular species. These particles are thought to exist in a variety of
atmospheric types and planetary conditions (Hörst et al., 2018; Fleury et al.,
2019; Zerkle et al., 2020).

The formation of hydrocarbon haze is initiated by the photolysis of CH4 and
then proceeds via complex and poorly understood chemical polymerization
pathways. As a result, it is not feasible to model the entire chemical
reaction network leading to haze production, and we instead follow a common
modeling practice of converting certain high-order gas-phase hydrocarbon
molecules directly into insoluble haze (Pavlov et al., 2001; Lavvas et al.,
2008; Krasnopolsky, 2009; Morley et al., 2015; Arney et al., 2016). For the
purposes of our model we assume two high-order hydrocarbon species will
ultimately condense into haze particles with a 100% conversion efficiency.
These “haze precursors” are C4H2 and C5H4, formed via the reactions:

$\displaystyle\begin{split}&\ch{C2H+C2H2->C4H2+H}\\\
&\ch{C2H+CH2CCH2->C5H4+H}\end{split}$ (1)

Large particles scatter very efficiently, introducing significant opacity to
an atmosphere, which obscures the spectral features of other molecules and
fundamentally alters the thermal balance throughout an atmosphere (Arney et
al., 2016, 2017, 2018; Lavvas & Arfaux, 2021). The refractive index of
experimentally-produced aerosol condensate is influenced by the chemical
composition of the gas mixture in which it was produced, and may also be
dependent on the energy source used to generate the particles (Hasenkopf et
al., 2010; Mahjoub et al., 2012; Gavilan et al., 2017, 2018; He et al., 2018;
Ugelow et al., 2018). Gavilan et al. (2017) found enhanced UV absorption in
oxidized aerosol material produced in early Earth-like N2/CO2/CH4 mixtures
compared to more reducing mixtures. The real and imaginary part of the
refractive index may exhibit strong wavelength dependence, and data covering
the whole UV/Vis/IR range is rarely available, with few exceptions (Khare et
al., 1984).

To contend with these complications, the optical properties of haze particles
require specific treatments in our modeling in order to adequately capture
scattering, absorption, and emission from particles that consist of
agglomerations of hydrocarbons with non-uniform chemical makeup. Several
approaches have been used in previous work, including enhanced Rayleigh
scattering and Mie scattering approximations. In this work, we follow the
approach laid out in Arney et al. (2016), which is to treat the hazes as
fractal aggregates using the mean-field approximation (Botet et al., 1997;
Rannou et al., 1997). Further, we apply the refractive indices of Gavilan et
al. (2017) for early Earth like atmospheres (N2:CO2:CH4= 90:8:2) in the UV-
visible range over which they were reported, and Khare et al. (1984) for the
IR.

The mean-field approximation considers the effects of non-spherical haze
particles on radiative transfer through the atmosphere. Given refractive
indices for a non-spherical particle as a function of wavelength, we can then
calculate the extinction coefficient $Q_{ext}$, single scattering albedo
$W_{0}$, and asymmetry parameter $G$ (Figure 1). These scattering parameters
are employed in the two-stream radiative transfer calculations in both the
Atmos photochemistry routines (for UV wavelengths) and climate routines (for
visible / IR wavelengths) to account for multiple scattering off of aerosol
particles. These same scattering parameters are also used in our transmission
spectroscopy radiative transfer to calculate an effective extinction cross
section $\sigma_{ext}$, further described in Section 2.3 (see Equation 3).

Figure 1: Optical properties for fractal haze (radius $>$ 50 nm) and spherical
monomer (radius $<$ 50 nm) particles across radii modeled the photochemistry
and climate models. $W_{0}$ is the single scattering albedo, $Q_{ext}$ is the
extinction efficiency, $G$ is the asymmetry parameter, and $\sigma_{ext}$ is
the effective haze extinction cross section for transmission spectroscopy.
These are the same optical properties employed in both the Atmos and Exo-
Transmit models. These optical properties are calculated using the fractal
haze model described in (Rannou et al., 1997) and (Botet et al., 1997), with
haze optical properties from Gavilan et al. (2017) and Khare et al. (1984).

As shown in Figure 1, we use a grid of haze optical properties spanning radii
of 1 nm to 2 $\mu$m over wavelengths between 1216 Å and 9000 Å. In our model,
the haze particle radius is determined based the coagulation time scale and
removal times scales through diffusion and sedimentation at a given pressure
level (Arney et al., 2016). Particles are first treated like spherical Mie
scatters as they grow from nucleation size to a size of 50 nm, after which
they are considered fractal aggregates comprised of spherical monomers. This
threshold is chosen to represent previous work done to understand the haze
properties within the Archean Earth and Titan’s atmosphere, though we also
find that our results are robust to other choices in initial particle sizes
(Tomasko et al., 2008; Larson et al., 2015). As hazes form and interact with
the local radiation field, they can significantly alter the thermal balance of
an atmosphere. Previous studies have shown that increasing haze abundance
significantly warms high altitudes where they form, while simultaneously
cooling the planet’s surface (e.g., Pavlov et al., 2001; Arney et al., 2017;
Lavvas & Arfaux, 2021). Furthermore, haze properties, particularly for larger
particles, are sensitive to small changes in temperature (Hörst et al., 2018),
resulting in haze abundance, particle radii, and formation rates varying non-
linearly over different temperatures and levels of irradiation. The use of the
Atmos coupled climate and chemistry models allows us to model and account for
these sensitive feedbacks between haze properties and the thermal structure of
the atmosphere.

###  2.2 UV input spectra for photochemical modeling

Figure 2: The spectra used in this work. The vertical axis represents the
normalized stellar flux, with an arbitrary offset applied. When running Atmos,
each spectrum is re-scaled such that the total insolation is Earth-like for
the modern-Earth and Archean simulations, with the exception of the solar
Archean model. (Claire et al., 2012)For our Archean models using the solar
spectrum as input, a model following Claire et al. (2012) is used to account
for predicted differences in the solar spectrum 2.7 billion years ago. This
treatment is not applied to our M-dwarf models.. The horizontal axis is
wavelength, with the left panel being the full panchromatic MUSCLES spectrum
(in linear flux units) and the right being a zoom-in on the UV wavelength
range over which we reconstruct the spectrum (in log flux units).

In this study, we focus on the validity and accuracy of reconstructed UV
spectra as input to photochemical models. To that end, we select and
reconstruct stellar UV spectra using the following methodology.

Figure 3: MUSCLES spectra (blue) overplotted with our line reconstructions (orange) using the Melbourne et al. (2020) scaling relations. The reconstructed line profiles are 2-Å top-hat profiles, as described in the text. The reconstructed spectra shown here have our zero-continuum treatment applied. Figure 4: Input GJ 176 UV spectra for several of the tested continuum treatments. All cases plotted, save for the baseline observed MUSCLES spectrum case, have the same set of reconstructed emission lines as described in Section 2.2. We additionally run a final set of two Archean Earth models using the continua of GJ 581 (M2.5) and GJ 436 (M3) in place of GJ 176 (M2.5). Star name | Type | Radius ($R_{\cdot}$) |  $T_{eff}$ (K) | $\log_{10}(R^{\prime}_{HK})$
---|---|---|---|---
SunaaThe solar spectrum is not from the MUSCLES catalog, and instead is the default solar spectrum shipped with the Atmos photochemistry model. The model also scales this spectrum based on the age of the Solar System being used, but we do not scale any other spectra with age. | G2 | 1. | 5800 |
GJ 667c | M1.5 | 0.46 | 3450 | -5.47
GJ 832 | M2 | 0.56 | 3590 | -5.22
GJ 581 | M2.5 | 0.3 | 3500 | -5.75
GJ 176 | M2.5 | 0.45 | 3680 | -4.89
GJ 436 | M3 | 0.45 | 3420 | -5.45
GJ 876 | M4 | 0.38 | 3130 | -5.48
GJ 1214 | M4.5 | 0.21 | 2820 | -5.47
GJ 551 (Proxima Centauri) + | M5.5 | 0.14 | 3100 | -5.23
Table 2: Table of MUSCLES stars used in this work. Each of the
$R^{\prime}_{HK}$ values are taken from Melbourne et al. (2020) and the
citations therein. $T_{eff}$ is the star’s effective temperature, and
$R^{\prime}_{HK}$ is the Ca II H & K line core intensity index.

First, we create a set of baseline photochemical models using panchromatic
spectra from the MUSCLES Treasury Survey (France et al., 2016; Loyd et al.,
2016; Youngblood et al., 2016). We use the adaptive, constant-resolution data
products to avoid overestimation of flux when handling negative flux bins and
re-binning to the Atmos wavelength grid444See the MUSCLES documentation at
https://archive.stsci.edu/prepds/muscles/.. This sample contains 8 M-stars
with spectral types ranging from M1.5 to M5.5. In addition, as our 9th host
star, we run baseline models using the solar spectrum template included in the
Atmos code. Figure 2 depicts the normalized spectra for all of the MUSCLES
M-stars, as well as the Sun. In the following analysis, we treat these spectra
as the “ground truth” for the stellar UV, though we discuss the nuances of
this assumption in Section 5.3. Our baseline model grid is made up of 18
individual Atmos runs: models at both modern Earth and Archean Earth initial
conditions are produced for each of the 9 host stars. Table 2 provides a list
of stars used in this work as well as properties relevant to each star’s UV
spectrum reconstruction and transmission spectrum calculations.

Next, we regenerate each of our photochemical models using reconstructed
MUSCLES UV spectra obtained by applying the UV line scaling relations
described in Melbourne et al. (2020). Specifically, these scaling relations
estimate a given line luminosity using the following equation:

$\log_{10}(L_{UV}/L_{bol})=\alpha\log_{10}(R^{\prime}_{HK})+\beta$ (2)

where $R^{\prime}_{HK}$ is the Ca H & K line core intensity index (Rutten,
1984), $\alpha$ and $\beta$ are fit parameters given in Melbourne et al.
(2020), and $L_{UV}$ and $L_{bol}$ are the UV line luminosity and the star’s
bolometric luminosity, respectively. Using the values for $\alpha$, $\beta$,
and $R^{\prime}_{HK}$ from Melbourne et al. (2020), we reconstruct each of 10
UV emission lines using Equation 2. The reconstructed line profiles are taken
to be top-hat profiles with 2-Å width (filling two adjacent bins in the 1
Å-resolution input spectrum grid), centered on the line core, and with total
wavelength-integrated luminosity equivalent to $L_{UV}$. Because the Melbourne
et al. (2020) scaling relations are only for the strongest UV lines, and
because most of the stellar UV flux emanates from these emission lines, we
initially make the simplifying assumption of zero UV continuum flux outside of
the emission line wavelength ranges. Furthermore, the Melbourne et al. (2020)
relations are a linear regression of over 24 M-dwarf stars. Due to intrinsic
scatter in line intensities across the sample, uncertainties arise in these
relations. In this work, we take the reported scaling relation parameters at
face-value. We have performed limited tests to assure that our results do not
differ significantly when accounting for 1-$\sigma$ scatter in these scaling
parameters.

Figure 3 shows the full set of UV reconstructed spectra overlaid on the
MUSCLES spectra. In total, our full set of UV reconstructed photochemistry
models consists of 16 individual Atmos runs — one for each of the MUSCLES
M-stars at both modern Earth and Archean Earth initial conditions. These UV
reconstructed spectra effectively simulate a situation in which no observed UV
data are available for a given exoplanet host star. This most basic
reconstruction — i.e. completely ignoring any possible continuum flux — only
has appreciable flux at the reconstructed lines. The remaining wavelengths are
set to a constant value of $10^{-50}$ erg/cm2/s/Å, which is vanishingly small
but nonzero to avoid numerical instabilities when running the Atmos code.

Finally, we run a subset of models designed to quantify the impact of the UV
continuum treatment on our results. In these cases we focus on the star GJ 176
(M2.5V), which is a representative early M-dwarf from the MUSCLES sample. In
addition to the zero-continuum reconstructions described above, we examine
three other approaches for reconstructing the UV continuum. In the three cases
described below, and shown in Figure 4, the continuum treatment is applied at
all UV wavelengths (5 - 4000 Å) other than those of the reconstructed UV
emission lines, which are produced using the procedure already described
above.

  1. 1.

Blackbody continuum flux — Because a zero continuum level is certainly an
underestimate of the true UV emission, we employ a first approximation of a
blackbody UV continuum at a temperature of 9000 K. We select this temperature
to compensate for increased UV flux not captured by a blackbody of an M
dwarf’s effective temperature. This approach naïvely assumes the bulk of
continuum flux originates from thermal radiation from plasma in the upper
chromosphere (Ayres, 1979; France et al., 2013; Peacock et al., 2019a). We
normalize our blackbody spectrum such that the total UV flux is equal to the
total UV flux for GJ176 in the same wavelength range, minus flux contributions
from the lines we reconstruct. Chromospheric temperatures can vary by several
thousand degrees (Mauas et al., 1997), which will change the continuum flux
from chromospheric emission appreciably. We choose a 9000 K continuum flux
value to roughly follow the continuum flux exhibited in the MUSCLES data for
GJ 176 as a test case based on observations.

  2. 2.

Observed continuum flux — In this approach, we retain the continuum flux
recorded by the observed MUSCLES spectra and stitch this together with the
reconstructed UV emission lines. The goal here is to quantify how much of the
photochemistry is being caused by the observed UV continuum vs. the strong
(reconstructed) emission lines.

  3. 3.

Synthetic continuum flux — Here we replace the continuum with a model UV
spectrum. Specifically, we use the HAZMAT semi-empirical model spectra for
this set of continuum reconstructions (Peacock et al., 2019b), which provide
panchromatic spectra generated by the PHOENIX stellar atmospheric code and
informed by GALEX and HST observations.

  4. 4.

Adjacent spectral type — With this method, we take the observed continuum flux
from a star of a neighboring stellar type and reconstruct the lines given by
the scaling relations.

Figure 4 shows the reconstructed GJ 176 spectra using the first three
continuum treatments from the list above. These comprise a set of 6 additional
photochemical models — one for each continuum treatment at both modern Earth
and Archean Earth conditions. We additionally apply the final continuum
treatment — employing the continuum of an adjacent spectral type — to the
Archean Earth model only, for two different adjacent host star spectra (GJ 581
and GJ 436).

###  2.3 Exo-Transmit transmission spectra

The Exo-Transmit code (Kempton et al., 2017) is used to generate transmission
spectrum observables for each of our model atmospheres. The version of Exo-
Transmit we use has been modified from the original code to accept the non-
equilibrium, vertically-defined chemical abundance profiles output by Atmos,
rather than the equilibrium chemistry models provided. This modification
consists of a major overhaul to the ordering in which chemistry, opacity, and
optical depth data are read in and calculated within the code but otherwise
leaves the transmission spectrum calculation unchanged.

Mixing ratio profiles for species output by Atmos and shaded gray in Table 1
are read into Exo-Transmit, in addition to C2H2, C2H4, C2H6, OCS, NH3, and
HCN, which have null boundary conditions in our models (and therefore do not
show up in Table 1), but form through reactions. The molecular opacities we
use for all species are those included in the public Exo-Transmit GitHub
repository555https://github.com/elizakempton/exo_transmit and documented in
Kempton et al. (2017). The total opacity for each layer is determined by
geometrically weighting the individual species’ opacities by their respective
mixing ratios in each vertical layer of the atmosphere.

Our hazy (Archean) model runs must also include contributions of hydrocarbon
haze particles to the opacity of the atmosphere. To accomplish this, we
include the hydrocarbon aerosols as an additional extinction species in Exo-
Transmit using the following procedure. We first calculate haze extinction
cross sections $\sigma_{ext}$ as a function of particle radius, $r_{par}$,
according to

$\sigma_{ext}=\pi r_{par}^{2}Q_{ext}(1-G^{2})$ (3)

where $Q_{ext}$ is the extinction efficiency, and $G$ is the asymmetry
parameter. (The final term in this equation is a correction based on the
asymmetry parameter to account for the fraction of incoming starlight that is
forward scattered and therefore remains in the beam.) For each atmospheric
layer, the total haze opacity (in units of m-1) is obtained by selecting
$\sigma_{ext}$ at the nearest neighbor to the mean particle radius in that
layer and then multiplying by the haze number density output by Atmos. We use
the same wavelength-dependent haze optical properties from Atmos (Figure 1)
for self-consistency between our Atmos and Exo-Transmit calculations.

##  3 Photochemical modeling results

Figure 5: Modern Earth model results for our baseline case using the MUSCLES
observations (solid curves), and the same models re-run with the (zero-
continuum) Melbourne et al. (2020) UV spectral reconstructions (dashed lines).
These models are effectively haze-free. Vertical temperature-pressure profiles
are plotted to the left, whereas mixing ratio profiles for various species (as
indicated) are plotted in the right-hand panels. Thermal inversions for the
M-dwarf models at $\sim 10^{-3}$ bar are caused by H2O, unlike Earth’s
inversion caused by O3 in the stratosphere.

In this section, we present the results from our photochemical modeling with
Atmos for the baseline (i.e., observed MUSCLES spectrum) case and zero-
continuum UV reconstructions. In general, we find that replacing the UV input
with a reconstructed spectrum changes the abundances of photochemically active
species. The differences prove significant, especially for our hazy (Archean)
models, which exhibit the greatest deviation from our baseline models.

###  3.1 Modern Earth

We first present our Atmos model outputs for modern Earth conditions for each
of the MUSCLES catalog M-stars (Figure 5). These models serve as our baseline
case against which we will compare all of our UV-reconstructed models, and
they also serve as a benchmark for comparison against similar previous works.
For example, Wunderlich et al. (2019) also modeled Earth-like planets orbiting
the MUSCLES M-dwarf host stars using a similar version of the Atmos
photochemistry-climate code but focusing on detectability of specific
atmospheric spectral features.

Overall, our models are in good agreement with Wunderlich et al. (2019), with
minor discrepancies being attributable to differences in model setup between
our study and theirs. For example, in Wunderlich et al. (2019), to preserve
“Earth-like” conditions, the authors ran their models varying the instellation
such that the planetary surface retained the temperature of modern Earth’s
surface; whereas in our own work we retain Earth-like instellation across all
of our models. This choice leads to surface temperatures that are on average
$\sim 25$ K higher in our models compared to the fixed surface temperatures of
Wunderlich et al. (2019). As a result of the different treatment of
instellation, and also presumably due to other subtle differences in model
implementation (e.g. reaction rates, opacities, etc.), the Wunderlich et al.
(2019) version of Atmos’ climate model produces slightly differing
temperature-pressure profiles compared to ours, including noticeably weaker
(but still apparent) thermal inversions for the later-type M-stars.

These changes to the thermal structure of the atmosphere also result in
notable differences in mixing ratios throughout the atmospheres. H2O, which is
parameterized below the tropopause as described in Manabe & Wetherald (1967),
is directly tied to the thermal structure at these altitudes. Furthermore, the
column depths of photochemical species such as O3 differ from the Wunderlich
et al. (2019) models due to the temperature-sensitivity of their formation
conditions.

Overall though, we achieve good qualitative agreement with trends seen in the
Wunderlich et al. (2019) models as a function of spectral type. Both of our
works find more elevated upper-atmosphere temperatures above the tropopause
with later spectral type and increasingly apparent stratospheric thermal
inversions for later-type host stars. We also both identify general trends of
increasing H2O, CH4, CO, and N2O column depths with later spectral type,
accompanied by decreasing O3.

We find that our Atmos models run with the reconstructed (zero-continuum) UV
spectra compare favorably to our baseline models generated from the observed
MUSCLES spectra (dashed lines vs. solid lines in Figure 5). Some variations,
particularly in species dominated by photochemistry such as O3, have
differences in column depth up to a factor of two to three. Some of the
specific host stars, such as GJ 551 (Proxima Centauri), which have observed
line luminosities that vary significantly from those calculated with the
Melbourne et al. (2020) scaling relations, result in Atmos model outputs that
deviate more severely. We find overall though that reconstructed input UV
spectra capture the bulk characteristics of these modern Earth-like
atmospheres, and they therefore serve as suitable input to photochemical
models in place of observations. For focused studies, variation in trace
species or photochemically-dominated species may be significant enough to
warrant a more careful treatment.

###  3.2 Archean Earth

We similarly model a set of baseline Atmos simulations for hazy, Archean
Earth-like atmospheres (Figure 6). These atmospheres have far more
photochemically active species and the potential for strong radiative feedback
from haze formation (Arney et al., 2016). This results in a greater
sensitivity of the Archean Earth models to the UV input spectrum, compared to
our modern Earth simulations.

Vertical abundance profiles for hydrocarbon hazes are shown in the lower
right-hand panel of Figure 6, and the corresponding particle size
distributions in Figure 7. The disparate optical properties for each Atmos
simulation (i.e., from the differing particle size distributions) couple with
the thermal properties at haze-bearing altitudes to impact the chemical
profiles of other species. These differences are non-linear, with feedback
between the climate and photochemistry models playing significant roles in all
characteristics of these more complex, hazy atmospheres.

Figure 6: Same as Figure 5, but for our Archean Earth models including
hydrocarbon haze. Significant hydrocarbon haze “precursors” are generated in
these models, e.g. C2H6, as seen in the bottom middle mixing ratio panel.
Figure 7: Vertical distribution of haze spherical radius. In general, higher
incident UV fluxes produce haze particles that are able to sediment into
larger radii at all altitudes. This is driven by higher abundances of hazes
and haze precursors, which are able to agglomerate and sediment in the
presence of more available haze particles. GJ 551 shows significantly smaller
haze particle radii due to low abundances of haze precursors to polymerize
into particles.

Compared to the modern Earth models, there are not such clear trends with
stellar spectral type for both thermal structure and abundance profiles. GJ
551 — the latest M-star modeled — does tend to be an end-member, but overall
the lack of clear trends with stellar effective temperature imply that these
hazy models are more sensitive to the activity level and exact details of the
stellar UV spectrum than for the more “well-behaved” modern Earth models. Of
note, this increased sensitivity to the stellar UV is accompanied by increased
challenges with model convergence — it generally takes significantly longer
for the hazy Archean Earth models to fully converge, and we typically must
resort to the model “short-stepping” procedure outlined in Section 2.1.

The baseline models demonstrate the sensitivity of haze formation and feedback
to small changes in the UV irradiation, and this is further shown when we use
our reconstructed UV spectra as inputs. The reconstructed UV spectra often do
not accurately reproduce the abundances of certain major species such as CO,
O2, and C2H6 (shown in Figure 6). As for haze formation, in the majority of
models, the abundances of haze particles are up to several orders of magnitude
lower for our reconstructed spectra, resulting in a significant loss of UV
opacity and changes to the thermal structure of the atmospheres.

An exception to our baseline models producing significantly more haze than the
reconstructed models, GJ 551 produces orders of magnitude less haze using the
MUSCLES spectrum as input compared to the reconstructed UV spectrum. This
arises from the substantially higher line and continuum UV flux exhibited by
GJ 551 compared to the other baseline input spectrum cases. This high
irradiation photolyzes haze precursors that would otherwise polymerize into
haze particles in the model. Coupled with oxidation of haze precursors due to
photolysis of CO2 into oxygen radicals, the haze formation rate in the
baseline GJ 551 model is negligible compared to the reconstruction case.

The degree of disagreement between the baseline and reconstructed models, and
especially the systematic discrepancies in haze formation, leads us to suspect
that other portions of the UV input spectra, beyond just the reconstructed
emission lines, may be playing an important role. We revisit this idea in
depth in Section 5. In the meantime, we conclude that the Melbourne et al.
(2020) UV reconstructions may not adequate for modeling the photochemistry in
hydrocarbon haze-producing atmospheres.

##  4 Transmission spectra results

We next examine how our model-derived temperature and abundance profiles
impact the observable properties of the simulated exoplanets — specifically
their transmission spectra between 0.3 and 30 $\mu$m.

###  4.1 Modern Earth

Figure 8: Model transmission spectra of our Earth-like atmospheres. The black
and blue curves are our baseline models with the raw MUSCLES spectrum and
reconstructed (zero continuum) UV spectrum as inputs, respectively. The
lighter colored lines are the full-resolution transmission spectra output by
Exo-Transmit (at a spectral resolution of $R=1000$), while the dark, thick
lines are smoothed for ease of visualization. Transit depths in both cases are
normalized to the transmission spectrum for the baseline (MUSCLES) model. For
reference, the green bars indicate an amplitude of 5 ppm for each host star,
assuming the transiting exoplanet is Earth-size. For larger and/or hotter
planets, these error bars will shrink proportionately. Spectral features of
key molecules are indicated.

As already shown in Figure 5, the dominant absorbing species in the modern
Earth models do not differ significantly between our reconstructed and
baseline scenarios, especially at the $\sim$mbar pressures probed by
transmission spectroscopy. As a result, our Exo-Transmit transmission spectrum
models (Figure 8), show negligible differences in the wavelength-dependent
absorption produced by any of these model atmospheres, when comparing the
reconstructed to baseline cases.

For this set of modern Earth models, the largest absolute change in transit
depth encountered between baseline and reconstructed models is 5 ppm
(indicated by green bars for each of the spectra in Figure 8), which is below
the anticipated noise floor for observatories like JWST. We note that while
the 5 ppm bars in Figure 8 also make it look as though many of the modeled
atmospheres are well out of reach for atmospheric characterization with JWST
(with an expected noise floor for many instruments at the $\sim$10–20 ppm
level; Matsuo et al., 2019; Schlawin et al., 2020, 2021), these bars will
scale down proportionally to both the planet’s radius and its equilibrium
temperature, indicating that, all else being equal, hotter and larger planets
are easier to characterize (further discussed in Section 4.2). That said,
small, Earth-like planets will be characterizable with JWST with sufficient
integration time, such as those of TRAPPIST-1 and some super-Earth TESS
discoveries within the habitable zone (e.g., Deming et al., 2009; Mollière et
al., 2017; Meadows et al., 2018).

Our main finding here is that prominent broadband absorbers such as H2O, CO2,
CO, and CH4 — and therefore the transmission spectra themselves — are
essentially insensitive to UV spectrum reconstruction for a modern Earth
atmospheric scenario.

###  4.2 Archean Earth

Figure 9: Same as Figure 8 but for the Archean Earth models. ’haze’ indicates
features associated with haze particles. For all stars with the exception of
GJ 551, the model produces significantly less haze using the reconstructed UV
spectra. In the case of GJ 551, our reconstruction actually produces more haze
than in the baseline case (see Section 3.2.)

The Archean models behave more dramatically with respect to UV
reconstructions. Figure 9 demonstrates the significant variations between hazy
models produced in the baseline vs. reconstructed scenarios. The most
significant differences between pairs of transmission spectra comes from the
haze opacity itself, seen as a gentle downward slope, most prominent in the
optical and UV. As discussed in Section 3.2, the reconstructed models
generally produce less haze than our baseline models, resulting in shallower
transit depths and more prominent molecular absorption features at wavelengths
shorter than 3 $\mu$m. Differences in the optical scattering slopes between
spectra are related to the differing particle size and vertical haze
distributions. The magnitude of the differences between baseline and
reconstructed transmission spectra also varies considerably with host star,
but with no clear progression as a function of spectral type, in agreement
with our photochemical modeling results from Section 3.2.

Significant discrepancies of up to 20 ppm also arise between our hazy model
transmission spectra at IR wavelengths of $\sim$6, 7, 12, and 20 $\mu$m, as
seen in Figure 9. Differences at 7 and 12 $\mu$m are attributable to
variations in the amount of C2H6 across atmospheres, which is not as
efficiently photolyzed by the reconstructed UV spectra. Differences at 6 and
20 $\mu$m are a result of differences in haze abundance and optical
properties.

The $\sim$20-ppm differences between our baseline and UV reconstructed models
are expected to be marginally distinguishable by JWST, and therefore using
reconstructed UV spectra will potentially have observable consequences for
these Archean Earth atmospheres. Furthermore, larger and/or hotter planets
will produce even larger transmission spectral features, leading to more
obvious differences between baseline and reconstructed scenarios for hazy
atmospheres. More massive planets are more likely to host hydrogen-dominated
atmospheres, resulting in significantly different chemical networks and haze
formation pathways when compared to terrestrial atmospheres (e.g., He et al.,
2020). As a result, differences in bulk composition may impact the nature of
hazes produced (Moran et al., 2020), as well as their vertical distribution
throughout the atmosphere, when compared directly to the terrestrial models we
use in this study.

##  5 UV Continuum treatment results

###  5.1 Continuum models

Figure 10: Temperature-pressure profiles and abundance profiles for different
UV continuum treatments for our modern Earth-like models, specifically using
the GJ 176 input case. “MUSCLES baseline” is the model using the raw
(observed) MUSCLES UV spectrum. The rest of the models shown use the Melbourne
et al. (2020) scaling relations to reproduce the star’s UV emission lines, and
one of our continuum reconstructions, as indicated. The majority of continuum
treatments reproduce the baseline model, and no observationally significant
differences arise across models (see Figure 13), though photochemically
sensitive species such as O3 and N2O deviate for certain continuum treatments.
Figure 11: Same as Figure 10, but for our hazy Archean Earth-like models.
These haze-forming models are much more sensitive to the properties of the
host star’s UV continuum, particularly for hydrocarbon hazes and their
precursors. These lead to observable differences, shown in Figure 13. Figure
12: Transmission spectra for modern Earth models of GJ 176 using different
prescriptions for reconstructing the host star’s UV continuum, as indicated.
The maximum difference of 2 ppm occurs at 1.5 $\mu$m, a CH4 line, between the
baseline and no-continuum case. Figure 13: Same as Figure 12, using hazy
Archean Earth-like models. A maximum difference between the baseline MUSCLES
spectrum and the continuum treatments of 6 ppm occurs at 1.01$\mu$m for the
zero-continuum case. Figure 14: Vertical distribution of compact sphere
equivalent radius for the various continuum treatments. All reconstructions
produce smaller haze particles compared to our GJ 176 MUSCLES baseline case.
In general, particle size varies with the total integrated continuum flux.
However, when using the MUSCLES continuum flux, very small particles are
created compared to any other reconstruction treatments. This is due to
significantly variable photolysis rates, reported in the relevant
supplementary data for each of our cases .

Figures 10 and 11 show the results of using different UV continuum treatments,
described in Section 2.2, for our modern and Archean Earth-like models of GJ
176, respectively. In the hazeless modern Earth atmospheres, the choice of
continuum treatment has an observationally insignificant impact on the
resulting abundance and temperature profiles. The abundances of the most
prominent photoactive species (e.g. O3, N2O) are found to moderately depend on
the magnitude of the continuum flux. Notably, the O3 abundance profile
deviates significantly for all continuum treatments. These deviations do not
prove observationally significant, as shown in Figure 12.

Our hazy Archean Earth-like models prove more sensitive to choice of UV
continuum. Figure 11 demonstrates the severity of these discrepancies, with
the worst case scenarios producing several orders of magnitude less haze than
models using the baseline MUSCLES UV input spectrum. This translates to
molecular species such as CO, O2, and haze precursors like C2H6 differing
significantly as well.

As a result of the sensitivity to the UV continuum in the Archean models, the
model transmission spectra (Figure 13) also differ substantially. This is
especially true in the visible and near-IR where the haze impacts on the
transmission spectra are most apparent. A comparison between the reconstructed
model with zero continuum vs. the one with the observed MUSCLES continuum
(blue vs. orange line in Figure 13) is especially telling of the role that the
UV continuum plays in shaping the properties of hazy atmospheres. Ignoring the
continuum entirely clearly neglects an important haze formation pathway and
also impacts the transmission spectra via changes to thermal structures and
the abundances of other key absorbers.

The HAZMAT reconstruction best reproduces the transmission spectrum generated
from the MUSCLES observations for GJ 176, although the somewhat higher UV
continuum in this reconstruction (see Figure 4) leads to a modest over-
production of haze (seen as a deeper optical transit depth). Overall, we
conclude that the UV continuum treatment definitely plays a non-negligible
role when modeling hazy atmospheres.

###  5.2 Using a neighboring stellar type

Another way to account for continuum flux is to assume that the continuum of
an observed star similar in stellar type will be sufficient for UV
reconstruction. To that end, we provide a brief assessment of the
applicability of such an approach in our GJ 176 reconstruction case.

Rather than using a _model_ of the UV continuum, employing _observed_ UV data
for an actual star may allow us to account for physical effects not adequately
captured by a model spectrum. Furthermore, one could hypothetically attempt to
match a proxy star’s observed continuum to other physical properties of the
star one is reconstructing. For example, if a star with similar activity has
an observed UV spectrum it may be better than a model or a quiescent spectrum
for a neighboring stellar type.

Figure 15 shows the results of using the GJ 176 line reconstructions, as done
previously (Figures 10 and 11), but using two different MUSCLES stars for the
UV continuum fluxes. In this case, we choose the two stars closest in stellar
type compared to GJ 176 (an M2.5V star): GJ 581 (M2.5V) and GJ 436 (M3V). Here
we only model Archean Earth conditions — as Sections 3.1 and 4.1 have already
shown the relative insensitivity of our hazeless (modern Earth) models to the
UV continuum. We reconstruct GJ 176’s UV spectrum using one of the neighboring
star’s UV continuum to fill between our reconstructed lines using the GJ 551
$R^{\prime}_{HK}$ values. At non-UV wavelengths the MUSCLES GJ 176
panchromatic spectrum is used (relevant only for the climate model). Once the
spectrum reconstruction is complete, the full spectrum is re-normalized to
have a total integrated instellation equivalent to Earth-equivalent flux at
the top of the atmosphere.

We find that the continua of both stars do a reasonable job of replicating the
baseline GJ 176 model, but again noticeable differences do arise. Haze
abundances between the three models differ by up to an order of magnitude, and
abundances of various molecules (e.g. CO, CH4, C2H6, O2) similarly disagree by
factors of a few, as seen in Figure 15.

As for the resulting transmission spectra (Figure 16), significant
discrepancies again arise at optical wavelengths due to differing haze
abundances and particle sizes among the three models, and also at $\sim 12$
$\mu$m from C2H6, C2H4, and C2H2 absorption. Interestingly, the M2.5 star GJ
581 does manage to replicate the baseline GJ 176 model (itself an M2.5 star)
with reasonable accuracy, but only longward of 2 $\mu$m. At shorter
wavelengths the differences in haze properties become apparent. These
differences in simulated transmission spectra for two stars of identical
spectral classification indicate that spectral type is not a unique predictor
of photochemical behavior of an exoplanetary atmosphere, nor of its observable
properties.

Figure 15: Model results using two MUSCLES stars of neighboring spectral types
as proxy continua for a GJ176 reconstructed spectrum. Carbon-bearing species
such as CO, CH4, and C2H6 all have significantly different abundances compared
to the baseline case, with the haze nearly an order of magnitude less abundant
in either case. Figure 16: Transmission spectra resulting from the model
results in Figure 15. The different haze abundances shown there are reflected
in the transmission spectra’s haze absorption at wavelengths shortward of
$\sim 2$ $\mu$m. Furthermore, a feature at 10 $\mu$m is caused by different
C2H6 abundances in the model using the GJ 436 continuum as a proxy. Figure 17:
Vertical distribution of haze spherical radius using continuum from MUSCLES
stars of neighboring stellar types compared to GJ 176 (of type M2.5), as in
Figures 15 and 16.

###  5.3 Which UV continuum treatment is correct?

Based on our results, models with photochemical hazes can vary dramatically,
even at an observable level, as a function of the UV continuum treatment
applied. With this in mind, it is important to establish which UV continuum
treatment is the “best” one to use in the absence of UV observations.

From Figures 13 and 16, we see that the HAZMAT and neighboring host star
continuum treatments do the best job of replicating the behavior of our
baseline Archean Earth model for GJ 176 from an observational perspective. In
practice, semi-empirical spectral models have only been generated so far for a
very limited number of host stars (Fontenla et al., 2016; Peacock et al.,
2019a, b; Tilipman et al., 2021), GJ 176 being one of them, and rely on
observations of the host stars’ UV spectra for their models. As a result, in
many cases it may be impractical to use such a model for replicating the UV
continuum of an arbitrary exoplanet host star. Similarly, using observations
of a neighboring spectral type for UV continuum reconstruction is also
problematic, for reasons discussed in Section 5.2 — mainly that spectral type
is not a unique predictor of UV continuum behavior. This also applies to using
continuum flux from a star of the same stellar type, since factors such as
age, composition, and activity level will all affect the strength of the
continuum for a given host star. However, in many situations this may be the
most practical solution, especially as the library of observed M star UV
spectra continues to grow. It should be noted though that the “neighboring
spectral type” approach is not guaranteed to produce accurate outcomes for
photochemical modeling.

Two further caveats to this finding are as follows. First of all, we have only
done a detailed examination of the UV continuum treatment for a single host
star — GJ 176 — and therefore our results may not be fully generalizable.
Secondly, we have based our modeling approach off of the premise that the
observed MUSCLES spectrum represents the ground truth of the host star’s UV
output. Unfortunately, due to the intrinsic UV-faintness of many M dwarfs, the
MUSCLES-reported continuum fluxes are often representative of the photon-
limited noise floor of of the data, rather than a true detection of the
stellar emission (Loyd et al., 2016). As a result, the MUSCLES UV continuum
fluxes may be overestimates of the true UV emission, especially for fainter
stars and at shorter wavelengths.

##  6 Conclusions

To summarize our study and its findings:

  1. 1.

We have used the MUSCLES Treasury survey M-dwarf spectra (France et al., 2016)
coupled with UV reconstructions from Melbourne et al. (2020) to generate
photochemical and transmission spectrum models of terrestrial atmospheres at
Earth-like instellation, with and without hazes.

  2. 2.

We find these reconstructions to be adequate for photochemical modeling of
hazeless (modern Earth-like) terrestrial atmospheres. Deviations from our
baseline models (i.e., those using the MUSCLES observations) are minimal,
though species formed primarily via photochemistry are slightly
underestimated. Models generated from MUSCLES observations and UV
reconstructions produce nearly identical transmission spectra.

  3. 3.

Photochemical models of hazy (Archean Earth) terrestrial planets are much more
sensitive to the UV input spectrum. Chemical abundances, haze formation rates,
and thermal profiles are all significantly impacted by the use of UV
reconstructions of host star spectra. These changes to the atmospheric
structure and chemistry have observable implications in the transmission
spectra of hazy exoplanets.

  4. 4.

We further find that our hazy atmosphere results are sensitive to the UV
continuum flux, which is not modeled in our nominal UV reconstructions.
Changes in continuum fluxes — tested on our models of the early M-star GJ 176
— are also found to impact thermal structures, as well as haze and molecular
abundances, at an observable level, resulting in transit spectra with
significant differences across a broad range of wavelengths.

Given these results, we find that fully observing a host star’s UV spectrum,
including multiple UV emission lines and the underlying continuum, remains the
gold standard for modeling exoplanet atmospheres. While the Melbourne et al.
(2020) reconstructions are a good proxy for M-dwarf stellar spectra for the
purpose of photochemically modeling non-hazy Earth-like atmospheres, they do
not sufficiently capture a star’s UV spectrum for hazy planet modeling. For
that reason, the observed stellar spectrum is especially necessary for
predicting and interpreting transmission spectra of hazy exoplanets.

For cases in which it is not possible to observe the host star’s UV spectrum,
we recommend the following procedure.

  * •

Reconstruct the strongest UV emission lines using the Melbourne et al. (2020)
scaling relations. This requires knowledge of star’s the $R^{\prime}_{HK}$
index as well as an estimate of its bolometric luminosity — both of which
should be readily obtainable through optical characterization. If certain UV
lines (e.g. Ly $\alpha$) have been observed, but the rest of the UV spectrum
has not, one can use those observed line fluxes in tandem with the Melbourne
et al. (2020) scaling relations to fill in the fluxes of the remaining
emission lines. We reiterate here that Melbourne et al. (2020) find
$R^{\prime}_{HK}$ to be the most robust predictor of UV emission line strength
across the M-dwarf spectral class, and therefore UV emission lines—in the
absence of direct observations—should be generated following the
$R^{\prime}_{HK}$ scaling relations.

  * •

To reconstruct the UV continuum, either choose an observation of a star with a
similar spectral type, as done in Section 5.2, or employ a synthetic model of
the UV continuum, such as those provided by the HAZMAT program (Peacock et
al., 2019b). We have found that these two options produce model results most
consistent with our baseline cases using the MUSCLES observed UV spectra. For
cases in which neither of these two approaches are feasible, a blackbody
continuum can be used, following the example of Ayres (1979).

We note that it remains problematic to make use of observations of the stellar
UV continuum in photochemical modeling because in many cases those
observations simply represent the photon noise level, rather than a true
detection of the stellar emission. We therefore recommend deeper observations
of a benchmark set of exoplanet host stars that fully detect and resolve the
UV continuum emission, accompanied by improved modeling of M-dwarf spectra in
the UV. However, such observations may not be feasible for most exoplanet host
stars without a more sensitive far-UV observatory, such as the 6-m
UV/optical/IR observatory recommended by the Astro2020 Decadal Survey
(National Academies of Science, Engineering, and Medicine, 2021).

In order to generate our photochemical models for well-benchmarked cases, the
planetary scenarios we’ve studied have low effective temperatures and masses
compared to many favorable targets for atmospheric characterization. The
trends and conclusions reached in this study can likely be generalized to
larger, warmer exoplanets, although for such planets disequilibrium processes
are less dominant in establishing atmospheric composition. To more accurately
predict trends in such atmospheres would require an extension of this study
covering a broader parameter space.

Stellar activity changes the time-averaged high-energy irradiation of a
planet’s atmosphere, altering the photochemical equilibrium of a planet’s
atmosphere depending on the rate of flaring (Segura et al., 2010) and the
stellar magnetic activity cycle. Some information about the activity for the
MUSCLES target stars is folded into their observed spectra due to flares
occurring during exposure time (France et al., 2016; Loyd et al., 2018),
though this does not provide sufficient information to draw conclusions in our
work. Since the UV flux during flaring events can increase by several orders
of magnitude, understanding how these events change the time-dependent
evolution of these atmospheres would improve upon the results, particularly in
the case of haze-forming atmospheres.

As the community prepares for future space- and ground-based observatories
capable of unprecedented atmospheric characterization, it is critical to
understand what complementary data sets will be required to contextualize and
interpret these future studies. Here, we have focused on the role that UV
observations play in accurate modeling of disequilibrium chemistry in
exoplanetary atmospheres. Our results have implications for addressing
compelling questions in astrobiology, atmospheric evolution, and aerosol
formation — all of which are fundamentally tied to the photochemistry
occurring in a planet’s atmosphere. Our work motivates the use of the aging
HST facility to perform UV observations of exoplanet host stars at high
precision as a critical input to photochemical models. Following the demise of
HST, future UV missions from the flagship to the SmallSat scale, such as the
6-m UV/optical/IR flagship recommended by the Astro2020 decadal to smaller
observatories in the nearer term on the Explorer and SmallSat scales like CUTE
(Fleming et al., 2018) and SPARCS (Ardila et al., 2018) will have an important
role to play in providing further UV information for exoplanet host stars. In
the absence of UV observations, proxy scaling relations and UV reconstruction
techniques remain the best path forward.

D.J.T. and E.M.-R.K. acknowledge funding from the NSF AAG program (grant
#2009095) and from the Hubble Space Telescope theory program (HST-AR-16135).
We thank E.T. Wolf for generating the H2O and CO2 k-coefficient tables used in
the climate model, as well as Nick Wogan for assistance updating photochemical
cross sections in Atmos. G.A. acknowledges support from the Virtual Planetary
Laboratory, a member of the NASA Nexus for Exoplanet System Science (NExSS)
research coordination network Grant 80NSSC18K0829. S.B. acknowledges support
from NASA under award number 80GSFC21M0002. S.B., A.Y., and G.A. acknowledge
support from the Goddard Space Flight Center Sellers Exoplanet Environments
Collaboration (SEEC) for support, which is funded by the NASA Planetary
Science Division’s Internal Scientist Funding Model (ISFM).

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