# Investigating the [C II]-to-H I conversion factor and the H I gas budget of
galaxies at $z\approx 6$ with hydrodynamical simulations

David Vizgan The Cosmic Dawn Center  National Space Institute, DTU Space,
Technical University of Denmark, 2800 Kgs. Lyngby, Denmark  Department of
Astronomy, University of Illinois at Urbana-Champaign, 1002 West Green St.,
Urbana, IL 61801, USA  Kasper E. Heintz  The Cosmic Dawn Center  Niels Bohr
Institute, University of Copenhagen, Lyngbyvej 2, DK-2100 Copenhagen, Denmark
Thomas R. Greve  The Cosmic Dawn Center  National Space Institute, DTU Space,
Technical University of Denmark, 2800 Kgs. Lyngby, Denmark  Department of
Physics and Astronomy, University College London, Gower Place, WC1E 6BT
London, UK  Desika Narayanan  The Cosmic Dawn Center  Department of Astronomy,
University of Florida, Gainesville, Florida 32611  Romeel Davé  Institute for
Astronomy, University of Edinburgh, Edinburgh EH9 3HJ, U.K.  University of the
Western Cape, Bellville, Cape Town 7535, South Africa  Karen P. Olsen
Department of Astronomy and Steward Observatory, University of Arizona,
Tucson, AZ 85721, USA  Gergö Popping  European Southern Observatory, 85478
Garching bei München, Germany  Darach Watson  The Cosmic Dawn Center  Niels
Bohr Institute, University of Copenhagen, Lyngbyvej 2, DK-2100 Copenhagen,
Denmark

###### Abstract

One of the most fundamental, baryonic matter components of galaxies is the
neutral atomic hydrogen (H I). At low redshifts, this component can be traced
directly through the 21-cm transition, but to infer H I gas content of the
most distant galaxies, a viable tracer is needed. We here investigate the
fidelity of the fine structure transition of the (${}^{2}P_{3/2}-^{2}P_{1/3}$)
transition of singly-ionized carbon [C II] at $158\,\mu$m as a proxy for H I
in a set simulated galaxies at $z\approx 6$, following the work by Heintz et
al. (2021). We select 11,125 star-forming galaxies from the simba simulations,
with far-infrared line emissions post-processed and modeled within the Sígame
framework. We find a strong connection between [C II] and H I, with the
relation between this [C II]-to-H I relation ($\beta_{\rm[CII]}$) being anti-
correlated with the gas-phase metallicity of the simulated galaxies. We
further use these simulations to make predictions for the total baryonic
matter content of galaxies at $z\approx 6$, and specifically the H I gas mass
fraction. We find mean values of $M_{\rm HI}/M_{\star}=1.4$, and $M_{\rm
HI}/M_{\rm bar,tot}=0.45$. These results provide strong evidence for H I being
the dominant baryonic matter component by mass in galaxies at $z\approx 6$.

High-redshift galaxies (734); Astronomical simulations (1857); Interstellar
medium (847); Atomic gas (833)

##  1 Introduction

In the process of galaxy formation, the infall of neutral atomic hydrogen (H
I) is a necessary, fundamental ingredient in the formation of stars.
Reservoirs of H I gas condense into molecular hydrogen (H2), which serves as
fuel for star formation. As such, H I is a crucial component for the assembly
of galaxies, and thus governs the first epoch of galaxy formation. At higher
redshifts (z $>$ 3) H I can also reveal large-scale structure of the universe
by tracing the precursors to superclusters of galaxies (e.g. Scott & Rees,
1990).

The main tracer of H I is the $\lambda=$ 21 cm line, which arises from
transitions between the hyperfine structure levels in the ground state of the
hydrogen atom. There are many benefits, in theory, of utilizing the 21 cm line
– for instance, it does not suffer from dust extinction and attenuation like
other lines, and kinematic information about the emitting gas can be derived
from its Doppler shift (Walter et al., 2008). Even though H I has been
observed within our own galaxy (e.g. Kalberla et al., 2005) and for many
galaxies locally (e.g. Thuan & Martin, 1981; Swaters et al., 2002; Walter et
al., 2008), few detections of the 21-cm line emission have been made beyond
$z\approx 0.3$ (Bera et al., 2019), mainly due to the weakness of the
transition and the limited sensitivity (Carilli & Walter, 2013). The current
most distant estimate for a single galaxy has reached $z=0.376$ (Fernández et
al., 2016), with other recent works examining the average 21-cm signal from a
stack of a few thousand galaxies out to $z\approx 1$ (Chowdhury et al., 2020,
2021). Although the evolution of the H I budget across redshift has been
modeled via theoretical predictions (Madau & Dickinson, 2014), our
understanding of the fueling of star formation rate across cosmic time is
incomplete without an understanding of how the contribution of H I to the
total composition of galaxies evolves with redshift, from the epoch of
reionization until today.

To infer the H I gas content of even more distant galaxies, it is clear that a
suitable tracer has to be identified as a proxy. This is similar to how
observations of in particular CO and [C I] has been used as tracers of the
molecular gas content of galaxies through most of cosmic time (e.g.
Papadopoulos & Greve, 2004; Bolatto et al., 2013). We here investigate the
$158\,{\rm\mu m}$ ($1900.5\,{\rm GHz}$) fine-structure transition of singly-
ionized carbon ([Cii]) as a potential tracer of H I. This particular
transition was suggested by Morton & Hu (1975) early on to be a strong cooling
line within H I regions. Further work by Tielens & Hollenbach (1985); Wolfire
et al. (1995); Hollenbach & Tielens (1999); Wolfire et al. (2003) chemically
examined the role of [C II] in the cooling of photodissociation regions (PDRs)
and the cold and warm neutral medium (CNM and WNM, respectively).
Observationally, Madden et al. (1993) found that extended [C II] emission in
NGC 6946 likely emerged from cold, atomic hydrogen clouds. Madden et al.
(1997) investigated a correlation between [C II] luminosity and the H I gas
mass ($M_{\rm H\,{\scriptsize I}}$) in the local irregular galaxy IC 10,
finding that while most [C II] emission arose from dense photodissociation
regions (PDRs), $\sim 20\%$ of the emission could arise from atomic hydrogen
regions in the interstellar medium (ISM) of the galaxy. More recent work
relying on hydrodynamical simulations of galaxies (e.g., Vallini et al., 2015;
Lupi & Bovino, 2020; Ramos Padilla et al., 2021, 2022) have constrained the
fraction of [C II] originating from different ISM phases, showing that it is
more predominantly produced in neutral H I regions at higher redshifts. As [C
II] is one of the strongest cooling lines in the ISM, it is one of the
brightest far-infrared lines and thus easily observable at high redshifts
(Stacey et al., 2010). This makes it a natural candidate as a potential proxy
for H I at $z\approx 6$. With the further evidence to support it as a tracer
of H I in the local universe, and the strong connection found in high-redshift
gamma-ray burst (GRB) sightlines (Heintz et al., 2021), we here wish to
further explore the feasibility of [C II] as a tracer of H I based on
simulations to a) clarify and further investigate the viability of [C II] as a
proxy for H I, b) make predictions for the H I gas mass fraction in galaxies
at $z\approx 6$, c) examine the underlying physics which drive this
correlation.

The paper is structured as follows: In Section 2 we describe the observational
and hydrodynamical simulation samples utilized for the purposes of this work.
In Section 3 we describe the [C II]-HI relation both in equation form and in
terms of a single conversion factor, $\beta_{\rm[C\,{\scriptsize II}]}$, and
analyze the effect of metallicity on $\beta_{\rm[C\,{\scriptsize II}]}$. In
Section 4 we investigate the H I gas budget at z $\approx$ 6\. We conclude
this work in Section 5.

##  2 Simulations & Observational Samples

This work uses a set of simba (Davé et al., 2019) galaxy simulations at
$z=5.93$, with line emission simulated and post-processed using v2 of Sígame
(Olsen et al., 2017). The simba simulation set consists of three cubical
volumes of 25, 50 and $100\,{\rm cMpc}\,h^{-1}$ on a side, all of which are
used in this work to search for galaxies at $z\sim 6$. For each volume, a
total of 10243 gas elements and 10243 dark matter particles are evolved from
$z=249$. Within these three volumes, a total of 11,137 galaxies were selected
via the yt (Turk et al., 2011)-based package caesar; yt is a Python package
used to visualize & analyze volumetric data, and caesar is a six-dimensional
friends-of-friends algorithm which is applied to the simulated gas and stellar
particles to identify and select simba galaxies. The galaxy properties derived
with caesar include star formation rate (SFR), computed by dividing the
stellar mass formed over a 100 Myr timescale (Leung et al., 2020), SFR surface
density, stellar mass ($M_{\rm\star}$), and a SFR-weighted gas-phase
metallicity ($Z$). The ionized, molecular, and atomic gas masses are
calculated via caesar to be equal to the total mass of all gas particles
associated with each respective phase (we refer to Olsen et al., 2017; Vizgan
et al., 2022, for further description of how these gas “particles” are defined
and constructed).

Our final sample consists of 11,125 galaxies, with [C II] luminosities in the
range $L_{\rm[CII]}=10^{3.82}-10^{8.91}$ L⊙ and a molecular gas masses $M_{\rm
mol}=10^{6.25}-10^{10.33}$ M⊙, with a mean $M_{\rm\star}$ of 108.07 M⊙, mean
SFR of 1.9 M${}_{\rm\odot}/$yr, and mean metallicity of 0.18 Z⊙. We refer to
Leung et al. (2020) and Vizgan et al. (2022) for further description and
detailing of simba, Sígame, caesar, and the simulation sample.

In this work, we define the total H I gas mass in each galaxy to be equal to
the sum of its ionized and atomic hydrogen gas mass, independent of galactic
region or radius. Molecular clouds have been shown observationally to also
consist of a substantial fraction of H I and will thereby also contribute to
the total H I gas mass. The fraction of H I in molecular clouds has been
measured to vary between 20 to 80% in our Galaxy (Burgh et al., 2010), so here
we assume that $\sim$50% of the total molecular gas in our simulations is H I.
Similarly, a significant H I volume filling fraction of $\approx 50\%$ has
been derived for interstellar H I within the warm neutral medium in the solar
neighborhood (Heiles & Troland, 2003). The way that Sígame classifies gas
particles as “ionized” in this gas-phase is by requiring that its electron-to-
hydrogen fraction is $x_{e^{-}}>0.5$; consequently, a gas particle in Sígame
will be considered completely ionized beyond $x_{e^{-}}>0.5$, and otherwise
neutral. This is not realistic when considering a real galaxy and we thus
assume $\sim$50% of the ionized gas will contribute to the atomic gas mass
because of this classification. Because of this assumption, the gas masses
derived from simulations should technically be treated as upper limits on the
neutral gas budget.

We supplement our simulation sets with some observational samples of [C II]
observations from the literature. We use H I gas masses (Cormier et al., 2015)
of main-sequence dwarf galaxies with [C II] observations in the local Herschel
Dwarf Galaxy Survey (Madden et al., 2013), which serve as high-redshift
analogs. In addition, we use the X-shooter GRB afterglow legacy sample (XS-
GRB; Selsing et al., 2019), which cover a redshift range between 0.059 and
7.84 and which were detected with the Swift satellite. Metallicities and H I
column densities of these GRBs are taken from Bolmer et al. (2019), and the [C
II] column densities are taken from Heintz et al. (2021).

##  3 The [C II]-to-H I relation

###  3.1 Connecting $L_{\rm[C\,{\scriptsize II}]}$ and $M_{\rm HI}$

Figure 1: Top panel: Histograms of scatter around the best-fit models for the
[C II]-to-H I relation (this work, crimson) and for the [C II]-H2 relation
(Vizgan et al., 2022, violet); the scatter around the former relation is
tighter (0.39 dex) than for the [C II]-H2 relation (0.45 dex). Bottom figure:
The [C II] luminosity vs. H I gas mass relation for our $z\simeq 6$
simulations. We find a very strong linear correlation between these two
quantities, yielding a best-fit of $\log L_{\rm{[C\,{\scriptsize
II}]}}=1.02\log M_{\rm{H\,{\scriptsize I}}}-1.95$. The simulations are color-
coded by the star formation rate, further demonstrating a correlation between
SFR and the log-linear [C II]-H I relation. When accounting only for the
diffuse H I mass derived from Cloudy, the relation changes to $\log
L_{\rm{[C\,{\scriptsize II}]}}=0.84\log M_{\rm{H\,{\scriptsize I}}}+0.55$ with
a scatter of 0.22 dex.

We examine the total [C II] luminosity of the $z\simeq 6$ simulated galaxies
and its connection to the total diffuse H I gas mass in Fig. 1, color-coded as
a function of SFR. In previous work, Vizgan et al. (2022) attempted to test
and verify the use of [C II] as a tracer of the molecular gas based on the
same set of simulated galaxies at $z\approx 6$. They found a sub-linear
relation between $M_{\rm mol}$ and $L_{\rm[C\,{\scriptsize II}]}$, in contrast
with the linear relation described by Zanella et al. (2018), which arose as a
consequence of the Kennicutt-Schmidt Law. By performing a log-linear fit to
the data, we find a strong correlation between the [C II] and H I, yielding a
best-fit relation of

$\log L_{\rm[C\,{\scriptsize II}]}=1.02\log M_{\rm H\,{\scriptsize I}}-1.95.$
(1)

with a root-mean-square (rms) scatter of 0.39 dex. For comparison, we examine
the relation between $L_{\rm[CII]}$ and $M_{\rm mol}$ and SFR within these
simulations. We find that scatter is notably tighter than $L_{\rm[CII]}$ vs.
$M_{\rm mol}$ (0.45 dex) and than $L_{\rm[CII]}$ vs. SFR (0.50 dex) for our
simulations (Vizgan et al., 2022). This is further support of [C II] being
most tightly connected to H I, and thus a more reliable tracer of this gas-
phase. Figure 2 of Vizgan et al. (2022) demonstrated that [C II] emission was
most negligible from H I regions in these simulations; we highlight, though,
that we want to calibrate the inferred HI mass with the total [CII] emission –
irrespective of origin –as this is what we ultimately observe from the high-z
galaxies.

###  3.2 The metallicity dependence of the [C II]-to-H I conversion factor

Figure 2: The [CII]-to-HI conversion factor $\beta_{[\rm CII]}$ vs. SFR-
weighted metallicity. The blue dot is $\beta_{[\rm CII]}=30^{+10}_{-7}\
\mbox{\rm{M}${}_{\odot}$}/\mbox{\rm{L}${}_{\odot}$}$, the conversion factor at
solar metallicities (Heintz et al., 2021). GRBs are taken from Selsing et al.
(2019) (see also Heintz et al., 2021), while the orange points are the
galaxies from Cormier et al. (2015).

Defining the [C II]-to-H I conversion factor as $\beta_{\rm[C\,{\scriptsize
II}]}=M_{\rm H\,{\scriptsize I}}/L_{\rm[C\,{\scriptsize II}]}$ (Heintz et al.,
2021), we derive a median $\log\beta_{\rm[C\,{\scriptsize
II}]}=1.7^{+0.4}_{-0.3}$ M⊙/ L⊙ for our set of simulated galaxies at $z\approx
6$. Heintz et al. (2021) determined that $\beta_{\rm[C\,{\scriptsize
II}]}=M_{\rm HI}/L_{\rm[C\,{\scriptsize II}]}$ evolves with metallicity,
following

$\log M_{\rm H\,{\scriptsize I}}/L_{\rm[C\,{\scriptsize II}]}=(-0.87\pm
0.09)\times\log\left(Z/Z_{\rm\odot}\right)\\\ +(1.48\pm 0.12)$ (2)

This [C II]-to-H I relation is derived from a combination of high-$z$ GRB
afterglows, assuming that their pencil-beam sightlines probe representative
regions of the star-forming ISM, and was found to show remarkable consistency
with direct observations of local galaxies (Heintz et al., 2021).

In Fig. 2 we examine the evolution of $\beta_{\rm[C\,{\scriptsize II}]}$ with
metallicity within our simulations. For comparison, we overplot the
measurements at $z=1.7-6.3$ from the GRB sightlines (Heintz et al., 2021) and
the local set of observations (Cormier et al., 2015). We find an anti-
correlation between $\beta_{\rm[C\,{\scriptsize II}]}$ and $Z$ with our
simulations (with r/pearson coefficient = $-$0.20), in strong agreement with
Heintz et al. (2021) and the local galaxy sample. Additionally, there appears
to be a slight correlation between $\beta_{\rm[C\,{\scriptsize II}]}$ and star
formation rate. The anticorrelation of $\beta_{\rm[C\,{\scriptsize II}]}$ is
mostly a result of the definition; i.e. [C II]/H I is a proxy to
carbon/hydrogen, hence the galaxies which are more-metal rich will have more
carbon available, both in the neutral and ionized states.

##  4 The H I gas mass budget of galaxies at $z\approx 6$

With this set of simulations, we further make predictions of the H I gas mass
fraction of galaxies at $z\approx 6$. Defining the H I gas mass excess as
$M_{\rm H\,{\scriptsize I}}/M_{\rm\star}$, we find a mean and median $M_{\rm
H\,{\scriptsize I}}/M_{\rm\star}=1.4$ and 1.2${}^{+0.9}_{-0.6}$, respectively.
We also predict the fraction of H I by mass to the total baryonic matter
content $M_{\rm bar,tot}=M_{\rm H\,{\scriptsize I}}+M_{\rm
H_{2}}+M_{\rm\star}$. We find a mean and median fraction of $M_{\rm
H\,{\scriptsize I}}/M_{\rm bar,tot}=$ 0.45 and 0.46${}^{+0.12}_{-0.13}$,
respectively. By comparison, the mean $M_{\rm H_{2}}$/$M_{\rm bar,tot}$ is
0.17 and median 0.15${}^{+0.10}_{-0.06}$; the mean $M_{\rm\star}$/$M_{\rm
bar,tot}$ is 0.38, and the median is 0.37${}^{+0.14}_{-0.11}$. We thus predict
that H I is the dominant, baryonic matter component in galaxies at $z\approx
6$.

Several observational works (e.g. Zanella et al., 2018; Dessauges-Zavadsky et
al., 2020) have investigated the use of [C II] as a molecular gas mass tracer.
Vizgan et al. (2022) showed that the $\alpha_{\rm[C\,{\scriptsize II}]}$
derived by Zanella et al. (2018) (Z18) required further calibration, as the
slope of the log-linear[C II]-$M_{\rm mol}$ relation was not near unity.
Dessauges-Zavadsky et al. (2020) used the Z18 $\alpha_{\rm[C\,{\scriptsize
II}]}$ relation to derive the molecular gas budgets of their observations
across redshift.

In Figure 3 we investigate the evolution of the H I gas mass budget, comparing
the data from the ALPINE [C II] survey (e.g. Dessauges-Zavadsky et al., 2020)
with our simulations. The H I gas masses in the ALPINE data are derived first
by deriving metallicities from their SFRs and stellar masses via the high-
redshift mass-metallicity relation in Curti et al. (2020), and then by using
Equation 2 in this work (also see Heintz et al., 2021). We find that the
ALPINE data are in reasonable agreement with the simulations; direct
metallicity measurements from the ALMA sources, which were not available in
the data, would allow for better constraints on the H I gas mass. Nonetheless,
the ALPINE data are consistent with the prediction from simulations that the H
I gas mass content should dominate the ISM at high-redshift. As the ALPINE
team used the work from Zanella et al. (2018) to derive molecular gas masses
for their sources, further work at high-redshift should further examine the
degree to which [C II] luminosity traces the H I, H2, or both gas masses, as
it appears to be a good tracer of both the neutral and molecular gas
reservoirs which occupy the ISMs of high-redshift galaxies.

Figure 3: The evolution of the H I gas mass excess with stellar mass. Our
simulations are color-coded by star formation rate, and the y-axis is scaled
logarithmically. The green stars represent galaxies from the ALPINE survey
Dessauges-Zavadsky et al. (2020) For the ALPINE data, we derive gas-phase
metallicities from their $M_{\rm\star}$ and SFRs using the mass-metallicity
relation in Curti et al. (2020). From there, we use Equation 2 to derive
estimates of their H I gas mass content.

##  5 Conclusions

Previously, [C II] has been used as a tracer of SFR in galaxies (e.g. De Looze
et al., 2014), and more recently as a tracer of H2 gas mass (e.g. Zanella et
al., 2018; Madden et al., 2020; Dessauges-Zavadsky et al., 2020; Vizgan et
al., 2022). In this work, we use a set of simulated galaxies at $z\simeq 6$
(Vizgan et al., 2022) to investigate the utility of [C II] luminosity as a
tracer of atomic (i.e. diffuse) hydrogen gas mass, following the work of
Heintz et al. (2021). We present our main findings below:

  1. 1.

For our simba simulations at $z=6$, we are able to find a strong relationship
between [C II] luminosity and H I gas mass: $\log L_{\rm[C\,{\scriptsize
II}]}=1.02\log M_{\rm H\,{\scriptsize I}}-1.95$. Significantly, the relation
is more tightly correlated (0.39 dex) than the [C II]-to-$\rm{H_{2}}$ (0.45
dex) and [C II]-to-SFR (0.50 dex) correlations described in Vizgan et al.
(2022). Furthermore, we find an anti-correlation of of
$\beta_{\rm[C\,{\scriptsize II}]}$ with metallicity.

  2. 2.

We find that the H I gas mass is a critical baryonic matter component, with
mean $M_{\rm H\,{\scriptsize I}}/M_{\rm\star}=1.4$, and $M_{\rm
H\,{\scriptsize I}}/M_{\rm bar,tot}=0.45$. We conclude that in the high-
redshift universe, galaxies’ ISMs (excluding dust) are dominated by H I
baryonic matter content.

  3. 3.

We compare our work with archival [C II] observational data, finding that
extrapolating H I gas masses from high-redshift [C II] sources in the ALPINE
[C II] survey yields an evolution of the H I gas mass budget over stellar mass
which agrees with predictions from simulations.

We ultimately conclude that [C II] is a viable proxy to infer amount of H I in
galaxies at $z\approx 6$. [C II] is readily available in the high-redshift
universe for large surveys (e.g. the Large ALMA-ALPINE survey at $z\sim 4-6$
(Dessauges-Zavadsky et al., 2020; Le Fèvre et al., 2020; Béthermin et al.,
2020; Faisst et al., 2020, etc.); and REBELS at $z\sim 6-8$ (e.g.; Bouwens et
al., 2021; Heintz et al., 2022). Establishing a proxy for H I is particularly
important as even the next-generation radio facilities such as the SKA will
only be able to detect and measure H I out to z $\approx 2$, and will not be
able to probe the evolution of H I in the universe beyond cosmic noon.

##  6 Acknowledgements

We are grateful the anonymous referee for insights and feedback which
strengthened this work. We thank Robert Thompson for developing caesar, and
the yt team for development and support of yt. This research made use of the
the TOPCAT data analysis software (Taylor, 2005). This research was made
possible by the National Science Foundation (NSF)-funded DAWN-IRES program and
would not be possible without support from the Cosmic Dawn Center (DAWN) in
Copenhagen, Denmark. The Cosmic Dawn Center (DAWN) is funded by the Danish
National Research Foundation under grant No. 140. DV was funded by an Open
Study/Research Award from the Fulbright U.S. Student Program in Denmark. KEH
acknowledges support from the Carlsberg Foundation Reintegration Fellowship
Grant CF21-0103. KPO is funded by NASA under award No 80NSSC19K1651. DN
acknowledges support from the NSF via grant AST 1909153. TRG acknowledges
support from the Carlsberg Foundation (grant no CF20-0534) RD acknowledges
support from the Wolfson Research Merit Award program of the U.K. Royal
Society. simba was run on the DiRAC@Durham facility managed by the Institute
for Computational Cosmology on behalf of the STFC DiRAC HPC Facility. The
equipment was funded by BEIS capital funding via STFC capital grants
ST/P002293/1, ST/R002371/1 and ST/S002502/1, Durham University and STFC
operations grant ST/R000832/1. DiRAC is part of the National e-Infrastructure.

## References

  * Bera et al. (2019) Bera, A., Kanekar, N., Chengalur, J. N., & Bagla, J. S. 2019, ApJ, 882, L7, doi: 10.3847/2041-8213/ab3656
  * Béthermin et al. (2020) Béthermin, M., Fudamoto, Y., Ginolfi, M., et al. 2020, A&A, 643, A2, doi: 10.1051/0004-6361/202037649
  * Bolatto et al. (2013) Bolatto, A. D., Wolfire, M., & Leroy, A. K. 2013, ARA&A, 51, 207, doi: 10.1146/annurev-astro-082812-140944
  * Bolmer et al. (2019) Bolmer, J., Ledoux, C., Wiseman, P., et al. 2019, A&A, 623, A43, doi: 10.1051/0004-6361/201834422
  * Bouwens et al. (2021) Bouwens, R. J., Smit, R., Schouws, S., et al. 2021, arXiv e-prints, arXiv:2106.13719.  https://arxiv.org/abs/2106.13719
  * Burgh et al. (2010) Burgh, E. B., France, K., & Jenkins, E. B. 2010, ApJ, 708, 334, doi: 10.1088/0004-637X/708/1/334
  * Carilli & Walter (2013) Carilli, C. L., & Walter, F. 2013, ARA&A, 51, 105, doi: 10.1146/annurev-astro-082812-140953
  * Chowdhury et al. (2020) Chowdhury, A., Kanekar, N., Chengalur, J. N., Sethi, S., & Dwarakanath, K. S. 2020, Nature, 586, 369, doi: 10.1038/s41586-020-2794-7
  * Chowdhury et al. (2021) Chowdhury, A., Kanekar, N., Das, B., Dwarakanath, K. S., & Sethi, S. 2021, ApJ, 913, L24, doi: 10.3847/2041-8213/abfcc7
  * Cormier et al. (2015) Cormier, D., Madden, S. C., Lebouteiller, V., et al. 2015, A&A, 578, A53, doi: 10.1051/0004-6361/201425207
  * Curti et al. (2020) Curti, M., Mannucci, F., Cresci, G., & Maiolino, R. 2020, MNRAS, 491, 944, doi: 10.1093/mnras/stz2910
  * Davé et al. (2019) Davé, R., Anglés-Alcázar, D., Narayanan, D., et al. 2019, MNRAS, 486, 2827, doi: 10.1093/mnras/stz937
  * De Looze et al. (2014) De Looze, I., Cormier, D., Lebouteiller, V., et al. 2014, A&A, 568, A62
  * Dessauges-Zavadsky et al. (2020) Dessauges-Zavadsky, M., Ginolfi, M., Pozzi, F., et al. 2020, A&A, 643, A5
  * Faisst et al. (2020) Faisst, A. L., Schaerer, D., Lemaux, B. C., et al. 2020, ApJS, 247, 61, doi: 10.3847/1538-4365/ab7ccd
  * Fernández et al. (2016) Fernández, X., Gim, H. B., van Gorkom, J. H., et al. 2016, ApJ, 824, L1, doi: 10.3847/2041-8205/824/1/L1
  * Heiles & Troland (2003) Heiles, C., & Troland, T. H. 2003, ApJ, 586, 1067, doi: 10.1086/367828
  * Heintz et al. (2021) Heintz, K. E., Watson, D., Oesch, P., Narayanan, D., & Madden, S. C. 2021, arXiv e-prints, arXiv:2108.13442.  https://arxiv.org/abs/2108.13442
  * Heintz et al. (2022) Heintz, K. E., Oesch, P. A., Aravena, M., et al. 2022, arXiv e-prints, arXiv:2206.07763.  https://arxiv.org/abs/2206.07763
  * Hollenbach & Tielens (1999) Hollenbach, D. J., & Tielens, A. G. G. M. 1999, Reviews of Modern Physics, 71, 173, doi: 10.1103/RevModPhys.71.173
  * Kalberla et al. (2005) Kalberla, P. M. W., Burton, W. B., Hartmann, D., et al. 2005, A&A, 440, 775, doi: 10.1051/0004-6361:20041864
  * Le Fèvre et al. (2020) Le Fèvre, O., Béthermin, M., Faisst, A., et al. 2020, A&A, 643, A1
  * Leung et al. (2020) Leung, T. K. D., Olsen, K. P., Somerville, R. S., et al. 2020, ApJ, 905, 102
  * Lupi & Bovino (2020) Lupi, A., & Bovino, S. 2020, MNRAS, 492, 2818, doi: 10.1093/mnras/staa048
  * Madau & Dickinson (2014) Madau, P., & Dickinson, M. 2014, ARA&A, 52, 415, doi: 10.1146/annurev-astro-081811-125615
  * Madden et al. (1993) Madden, S. C., Geis, N., Genzel, R., et al. 1993, ApJ, 407, 579, doi: 10.1086/172539
  * Madden et al. (1997) Madden, S. C., Poglitsch, A., Geis, N., Stacey, G. J., & Townes, C. H. 1997, ApJ, 483, 200, doi: 10.1086/304247
  * Madden et al. (2013) Madden, S. C., Rémy-Ruyer, A., Galametz, M., et al. 2013, PASP, 125, 600, doi: 10.1086/671138
  * Madden et al. (2020) Madden, S. C., Cormier, D., Hony, S., et al. 2020, A&A, 643, A141, doi: 10.1051/0004-6361/202038860
  * Morton & Hu (1975) Morton, D. C., & Hu, E. M. 1975, ApJ, 202, 638, doi: 10.1086/154019
  * Olsen et al. (2017) Olsen, K., Greve, T. R., Narayanan, D., et al. 2017, ApJ, 846, 105
  * Papadopoulos & Greve (2004) Papadopoulos, P. P., & Greve, T. R. 2004, ApJ, 615, L29, doi: 10.1086/426059
  * Ramos Padilla et al. (2021) Ramos Padilla, A. F., Wang, L., Ploeckinger, S., van der Tak, F. F. S., & Trager, S. C. 2021, A&A, 645, A133, doi: 10.1051/0004-6361/202038207
  * Ramos Padilla et al. (2022) Ramos Padilla, A. F., Wang, L., van der Tak, F. F. S., & Trager, S. 2022, arXiv e-prints, arXiv:2205.11955.  https://arxiv.org/abs/2205.11955
  * Scott & Rees (1990) Scott, D., & Rees, M. J. 1990, MNRAS, 247, 510
  * Selsing et al. (2019) Selsing, J., Malesani, D., Goldoni, P., et al. 2019, A&A, 623, A92, doi: 10.1051/0004-6361/201832835
  * Stacey et al. (2010) Stacey, G. J., Hailey-Dunsheath, S., Ferkinhoff, C., et al. 2010, ApJ, 724, 957, doi: 10.1088/0004-637X/724/2/957
  * Swaters et al. (2002) Swaters, R. A., van Albada, T. S., van der Hulst, J. M., & Sancisi, R. 2002, A&A, 390, 829, doi: 10.1051/0004-6361:20011755
  * Taylor (2005) Taylor, M. B. 2005, in Astronomical Society of the Pacific Conference Series, Vol. 347, Astronomical Data Analysis Software and Systems XIV, ed. P. Shopbell, M. Britton, & R. Ebert, 29
  * Thuan & Martin (1981) Thuan, T. X., & Martin, G. E. 1981, ApJ, 247, 823, doi: 10.1086/159094
  * Tielens & Hollenbach (1985) Tielens, A. G. G. M., & Hollenbach, D. 1985, ApJ, 291, 722, doi: 10.1086/163111
  * Turk et al. (2011) Turk, M. J., Smith, B. D., Oishi, J. S., et al. 2011, ApJS, 192, 9
  * Vallini et al. (2015) Vallini, L., Gallerani, S., Ferrara, A., Pallottini, A., & Yue, B. 2015, ApJ, 813, 36, doi: 10.1088/0004-637X/813/1/36
  * Vizgan et al. (2022) Vizgan, D., Greve, T. R., Olsen, K. P., et al. 2022, ApJ, 929, 92, doi: 10.3847/1538-4357/ac5cba
  * Walter et al. (2008) Walter, F., Brinks, E., de Blok, W. J. G., et al. 2008, AJ, 136, 2563, doi: 10.1088/0004-6256/136/6/2563
  * Wolfire et al. (1995) Wolfire, M. G., Hollenbach, D., McKee, C. F., Tielens, A. G. G. M., & Bakes, E. L. O. 1995, ApJ, 443, 152, doi: 10.1086/175510
  * Wolfire et al. (2003) Wolfire, M. G., McKee, C. F., Hollenbach, D., & Tielens, A. G. G. M. 2003, ApJ, 587, 278, doi: 10.1086/368016
  * Zanella et al. (2018) Zanella, A., Daddi, E., Magdis, G., et al. 2018, MNRAS, 481, 1976