E. da Cunha The dust properties of star-forming galaxies in the first billion
years

17 2022 10.1017/xxxxx 373

Proceedings IAU Symposium

# The dust properties of star-forming galaxies in the first billion years

Elisabete da Cunha  International Centre for Radio Astronomy Research,
University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D)

###### Abstract

The Atacama Large Millimetre/Sub-millimetre Array (ALMA) is obtaining the
deepest observations of early galaxies ever achieved at (sub-)millimetre
wavelengths, and detecting the dust emission of young galaxies in the first
billion years of cosmic history, well in the epoch of reionization. Here I
review some of the latest results from these observations, with special focus
on the REBELS large programme, which targets a sample of 40 star-forming
galaxies at $z\simeq 7$. ALMA detects significant amounts of dust in very
young galaxies, and this dust might have different properties to dust in
lower-redshift galaxies. I describe the evidence for this, and discuss
theoretical/modelling efforts to explain the dust properties of these young
galaxies. Finally, I describe two additional surprising results to come out of
the REBELS survey: (i) a new population of completely dust-obscured galaxies
at $z\simeq 7$, and (ii) the prevalence of spatial offsets between the
ultraviolet and infrared emission of UV-bright, high-redshift star-forming
galaxies.

###### keywords:

galaxies: evolution – galaxies: high-redshift – galaxies: ISM – dust,
extinction

##  1 Introduction

Interstellar dust plays a critical role in galaxy assembly. Dust grains are a
site of efficient molecule formation, specifically H2, the fuel for new star
formation (e.g., Hirashita & Ferrara 2002). Dust grains also affect how we
observe galaxy assembly: the cosmic infrared background is equivalent in power
to the cosmic optical background (e.g., Dole et al. 2006), implying that about
half of all the UV/optical light produced by stars in the Universe is
reprocessed by dust. In fact, we know that dust-obscured star formation
contributes significantly to the total star formation rate (SFR) density of
the Universe (e.g., Madau & Dickinson 2014). Recent studies show that dust-
obscured star formation dominates the cosmic SFR density out to at least
$z\simeq 3$ (e.g., Zavala et al. 2021), and it still provides an important
contribution at higher redshifts, although the exact amount of dust-obscured
star formation at the earliest redshifts ($z\gtrsim 6$, i.e., in the epoch of
reionization, or ‘cosmic dawn’) is still uncertain.

The main limitation in measuring obscured star formation at the highest
redshifts has been the difficulty to detect and measure the dust emission of
individual high-redshift galaxies using far-infrared/sub-millimetre facilities
such as the Herschel Space Observatory and single-dish sub-mm observatories.
Due to their poor resolution and sensitivity (see, e.g., figure 10 of Casey et
al. 2014), observations with these facilities suffer from important confusion
noise, which limited the study of high-redshift sources to only the brightest
objects, such as quasars (e.g., Bertoldi et al. 2003) and sub-millimetre
galaxies (SMGs; e.g., Walter et al. 2012; Riechers et al. 2013).
Alternatively, several studies attempted to overcome the confusion limits and
detect fainter galaxies using stacking (e.g., Schreiber et al. 2015) and de-
blending techniques (e.g., Liu et al. 2018; Jin et al. 2018), but these
approaches have limitations. With its unprecedented sensitivity and spatial
resolution at (sub-)millimetre wavelengths, the Atacama Large Millimetre/Sub-
millimetre Array (ALMA), has revolutionised this field, allowing us to
directly detect, for the first time, the dust (and gas) emission from
individual, normal star-forming galaxies at $z>6$ (see Hodge & da Cunha 2020
for a recent review). In this paper, I briefly review what recent ALMA
observations are revealing about the interstellar dust properties of star-
forming galaxies in the first billion years.

##  2 ALMA observations of Lyman-break galaxies

###  2.1 Different dust properties at high-redshift?

Figure 1: Three model dust emission spectral energy distributions (SEDs) at
$z=6$ normalized at the same ALMA Band 6 (230 GHz) flux of 0.1 mJy. This
illustrates how sources with the same Band 6 flux can have inferred infrared
luminosities, $L_{\mathrm{IR}}$, that vary by almost two orders of magnitude
depending on the adopted dust temperature, $T_{\mathrm{dust}}$. To constrain
the temperatures and luminosities, we need multi-band observations at higher
frequencies (e.g., in the ALMA bands shown in grey) sampling the dust SED
closer to its peak.

Before direct dust detections with ALMA, high-redshift studies routinely
corrected the observed UV emission of distant galaxies for dust attenuation
using the so-called ‘IRX-$\beta$’ relation between the ultraviolet spectral
slope ($\beta$) and the infrared excess (IRX, defined as the ratio of infrared
to ultraviolet luminosity). Local starburst galaxies follow a tight relation
in the IRX vs $\beta$ diagram (Meurer et al., 1999), which can be explained if
stars are behind a screen of dust with properties similar to those of dust in
the Milky Way (Calzetti et al., 1994). Before the advent of ALMA, high-
redshift galaxies were assumed to follow a similar relation. However, early
ALMA follow-up of known Lyman-break galaxies (LBGs) at $z>4$ in Band 6
($\simeq 1$ mm) found infrared luminosities that were lower than those
predicted by the local starburst IRX-$\beta$ relation. This was found in a
variety of targeted observations and stacks of $z>4$ LBGs (e.g., Capak et al.
2015; Bouwens et al. 2016; Fudamoto et al. 2017; Barisic et al. 2017; Bowler
et al. 2018; Schouws et al. 2022): the lower IR excesses were more consistent
with a steeper dust extinction curve similar, to the one observed in the Small
Magellanic Cloud. Taken at face value, this result would imply that
interstellar dust in EoR galaxies has fundamentally different properties than
dust in low-redshift galaxies. This led to speculation that perhaps these
galaxies have different dust properties due to their lower metallicities. This
also implied that dust properties evolve rapidly in the early universe, since
studies at $z<4$ seemed to show properties already consistent to Milky Way
dust (e.g., Fudamoto et al. 2020). However, these results are plagued by the
large uncertainty in measuring the total infrared luminosity of a galaxy from
a single 1-mm ALMA measurement without knowing the dust temperature (see Fig.
1 and discussion in section 3.3 of Hodge & da Cunha 2020).

###  2.2 The need for robust dust temperatures

In all the aforementioned studies, a dust temperature had to be assumed to
extrapolate the single-band ALMA measurement to a total IR luminosity, and
most studies assumed temperatures around 40 K, similar to local and
intermediate-redshift star-forming galaxies. Faisst et al. (2017) argued that
local analogues to high-redshift LBGs have higher dust temperatures
($T_{\mathrm{dust}}\sim 60-90\,\mathrm{K}$), and that adopting such
temperatures would bring the ALMA detections (and upper limits) more in
agreement with Milky-Way dust in the IRX-$\beta$ relation. Theoretical work
also seems to support hotter dust at high redshifts (e.g., Behrens et al.
2018; Narayanan et al. 2018; Ma et al. 2019; Liang et al. 2019; McAlpine et
al. 2019; Sommovigo et al. 2020).

Figure 2: Comparison between dust physical properties derived from fitting the
dust emission with simple isothermal models when using an optically-thin
assumption ($x$-axes) vs a general opacity model ($y$-axes): (a) dust
temperature; (b) dust emissivity index; (c) dust luminosity; (d) dust mass.
The points shown are 27 SMGs with well-sampled dust SEDs studied in da Cunha
et al. (2021). While the dust luminosity and emissivity index are quite robust
to optical depth assumptions, assuming the wrong optical depth can introduce
biases in the derived dust temperatures and dust masses (see more details in
da Cunha et al. 2021). Figure first published in da Cunha et al. (2021).

These higher dust temperatures need to be confirmed through multi-frequency
observations with ALMA, preferably sampling close to the peak of the dust
emission, to measure $T_{\mathrm{dust}}$. For galaxies at $z\gtrsim 6$, such
observations are time consuming even with ALMA, but they have been achieved
for a handful of galaxies so far. Faisst et al. (2020) followed-up four $z\sim
5.5$ galaxies in Band 8 (sampling rest-frame $\sim 100\mu$m, close to the peak
of dust emission), which, combined with existing Bands 6 and 7 observations,
allowed them to measure dust temperatures $T_{\mathrm{dust}}\sim
30-40\,\mathrm{K}$. In another recent study, Bakx et al. (2021) combined Band
9 observations with observations in three other bands (Bands 6, 7, and 8), to
constrain a dust temperature of $T_{\mathrm{dust}}=42\,\mathrm{K}$ for a
galaxy at $z=7.13$.

It is worth noting that having ALMA high-frequency observations that sample
the peak of the dust emission (or even beyond the peak) is critical for robust
constraints on the dust temperature (and hence, luminosity). But even with
multi-band observations, potential degeneracies with the dust emissivity index
and dust opacity assumptions need to be taken into account (e.g., da Cunha et
al. 2021; Jin et al. 2022; Witstok et al. 2022). For example, in a detailed
study of the dust emission of SMGs, da Cunha et al. (2021) show that with only
three ALMA bands sampling the dust emission SED, it is very difficult to
distinguish between optically thin dust emission and dust that it optically
thick at far-infrared wavelengths – but important systematics can be
introduced in the derived dust temperatures and masses (Fig. 2).

###  2.3 Is dust in galaxies really getting hotter with redshift?

As mentioned before, theoretical simulations predict an increase of the dust
temperature with redshift, which is generally explained by several factors
such as stronger radiation fields, lower dust masses, and more compact dust-
emitting regions at high redshifts. Empirically, an increase of dust
temperature with redshift has also been observed, e.g., by Schreiber et al.
(2018), though we note that this is still somewhat controversial as it could
be a result of selection effects: since there is a positive correlation
between dust temperature and dust luminosity, and flux-limited samples
detecting higher luminosity sources at higher redshifts (e.g., Dudzevičiūtė et
al. 2020). In fact, the direct temperature measurements of sources at
$z\gtrsim 6$ with multi-band ALMA observations described above (Faisst et al.,
2020; Bakx et al., 2021) do not follow the extrapolation of the temperature-
redshift relation of Schreiber et al. (2018): their temperatures are about 10
to 20 K lower than predicted by that relation. If these temperatures are
typical for high-redshift galaxies, then the dust temperatures might not be
high enough to reconcile the IR excesses with Milky Way-like dust attenuation
in the IRX-$\beta$ relation, which would indicate that indeed galaxies at the
EoR have different dust properties. However, it is to be expected that there
is a spread in dust temperatures at any given redshift (depending on different
galaxy properties), so larger samples of galaxies t $z\gtrsim 6$ with ALMA
continuum observations are needed. One such samples comes from the REBELS
survey described below.

##  3 Results from the REBELS survey

###  3.1 Continuum detections in REBELS

Figure 3: Empirical relation between the redshift and the dust temperature of
galaxies. The REBELS sources are plotted as colourful stars. The inset shows
that the average dust temperature of REBELS sources fall short of the
extrapolation of the $T_{\mathrm{dust}}$-redshift relation of Schreiber et al.
(2018). Figure first published in Sommovigo et al. (2022).

The Reionization Epoch Bright Emission Line Survey (REBELS) is an ALMA Large
Programme targeting [OIII] and [CII] lines and their underlying dust continuum
(at $\sim 90$ and $160\mu$m) in 40 UV-bright LBGs at $z>6.5$ (Bouwens et al.,
2022). From this sample, 18 sources have been detected in the continuum so far
(Inami et al., 2022), which more than tripled the previous number of dust
continuum detections at $z>6.5$. The inferred infrared luminosities of these
continuum-detected sources imply that about half of their star formation is
dust-obscured. One of the detections, REBELS-25, is noteworthy as it is an
ultra-luminous infrared galaxy (ULIRG, with
$L_{\mathrm{IR}}>10^{12}\,L_{\odot}$) at $z=7.4$ (Hygate et al., submitted).

So far the REBELS sources are only continuum-detected in one ALMA band,
therefore we cannot directly measure the dust temperature from fitting the
dust SEDs. But Sommovigo et al. (2022) estimate the temperatures of REBELS
sources using a novel analytical method that uses only the [CII] line and its
underlying dust continuum (Sommovigo et al., 2021). They find an average
$T_{\mathrm{dust}}\simeq 46\,\mathrm{K}$ for the REBELS sources (Fig. 3) –
broadly consistent with the more direct multi-band measurements of Faisst et
al. (2020); Bakx et al. (2021) for galaxies at similar redshifts.

###  3.2 Dust-obscured star formation and its contribution to the cosmic SFR
density at $z\simeq 7$

Figure 4: Redshift evolution of the cosmic star formation rate density. The
purple and orange filled circles/triangles show the estimated contribution by
the REBELS sources at $z\simeq 7$. Figure first published in Algera et al.
(2022).

The dust temperature estimates of REBELS sources by Sommovigo et al. (2022)
are used to extrapolate from the single continuum measurements to obtain their
total infrared luminosities, and infer their dust-obscured star formation
rates. Algera et al. (2022) find that between 30% and 60% of the star
formation rate in these galaxies is obscured. They find that this fraction
depends on the stellar mass of the sources, similar to what is found at lower
redshifts (Whitaker et al. 2017; the fraction of dust-obscured SFR increases
with stellar mass). They also use these results to quantify the contribution
of dust-obscured star formation to the cosmic star formation rate density at
$z\sim 7$. Since REBELS is not a blind, volume-limited survey, but a targeted
survey, infrared luminosity functions cannot be directly directly derived.
Their method involves first finding a relation between the dust luminosity and
stellar mass, and then integrating across the (known) stellar mass function at
$z=7$ (Algera et al. 2022; see also, Barrufet et al., submitted). Algera et
al. (2022) find that dust-obscured star formation at high redshifts is more
important than previously assumed: it can contribute up to a third of the
total cosmic SFR density at $z\simeq 7$ (Fig. 4). This implies also that the
cosmic SFR density does not decrease as fast as previously predicted at $z>3$.
While there are caveats attached to this result (stellar mass and dust
luminosity uncertainties, sample selection effects, etc.), it could have a
profound meaning: that galaxies in the epoch of reionization already have
significant amounts of dust, and indeed perhaps more dust than we were
expecting to observe in such young galaxies. This in turn might challenge our
understanding of how metals and dust evolve in the interstellar medium of
early galaxies, as I discuss in the next section.

##  4 Can we explain so much dust at early times?

Having large amounts of dust in early galaxies, when the Universe was less
than a billion years old, could be a challenge for our current understanding
of how dust forms and evolves. The lifecycle of dust in intimately related
with the lifecycle of stars (Fig. 5). In the local Universe, one of the main
environments for stardust formation is the cool envelope of AGB stars,
however, the timescales for these stars to evolve are of the order of 1
billion years or more (i.e., longer than the Hubble time at $z>6$). Based on
stellar evolution timescales, at early ages, the main channel for stardust
production has to be supernova dust, however the effective dust yields in
supernova are still uncertain even in the local Universe. After being formed
in stellar envelopes/supernova remnants, dust grows through coagulation and
mantle accretion in dense molecular clouds, and although the timescale and
efficiency for this process is still debated, models predict that this ISM
growth is only efficient once the gas reaches a ‘critical metallicity’
($Z_{\mathrm{crit}}\sim 0.05-0.3\,Z_{\odot}$; e.g., Asano et al. 2013a, see
also Galliano et al. 2018 for a review). For all these reasons, in galaxies at
the epoch of reionization (which presumably have young ages and low
metallicities), the main source of dust should be supernova stardust (e.g.,
Gall et al. 2011).

Figure 5: A schematic representation of the lifecycle of dust in galaxies
(after, e.g., Dwek 1998; Zhukovska et al. 2008; Dwek & Cherchneff 2011; Asano
et al. 2013a; Zhukovska 2014).

The different channels of dust production and growth also affect the grain
size distributions, which in turn affect the dust extinction curves in
galaxies (e.g., Asano et al. 2013b; Aoyama et al. 2020). This could explain
the location of high-redshift galaxies in the IRX-$\beta$ diagram. Mancini et
al. (2016) post-processed a hydrodynamical galaxy simulation with a detailed
chemical and dust evolution model and find that lower stellar mass galaxies at
high redshift, which are less chemically evolved, follow a steep SMC-like
attenuation curve because their dust is mostly contributed by stellar sources,
with less efficient ISM growth than in more metal-rich massive galaxies (see
also, Graziani et al. 2020).

Regarding the production of the large dust masses found at high-redshift
(REBELS and other ALMA observations find dust masses $M_{\mathrm{dust}}\gtrsim
10^{7}\,M_{\odot}$ at $z\simeq 7$), models have not reached a consensus yet.
Some models find that the dust masses can be explained by high supernova rates
and/or yields, or efficient ISM dust growth (e.g., Popping et al. 2017), while
others find that efficient ISM growth is needed (e.g., Mancini et al. 2015).
The need for efficient ISM dust growth in early galaxies may be problematic:
Ferrara et al. (2016) point out that at high-redshifts, icy dust grain mantles
formed in the cold ISM do not survive in the hot diffuse ISM. Recently, Dayal
et al. (2022) showed that the DELPHI semi-analytic model can reproduce the
dust masses of REBELS sources with minimal ISM dust growth, coupling metal and
dust enrichment, and using new stellar yields from Kobayashi et al. (2020).

This is not a resolved issue. There are still large uncertainties in modelling
ISM dust growth and stellar yields. On the observational side, the dust mass
measurements of most sources are still uncertain as they rely on limited ALMA
continuum measurements. The stellar masses, gas-phase metallicities, and star
formation histories of these sources are also critical ingredients in the dust
formation and evolution modelling, but so far these measurements are either
non-existent (in the case of metallicities) or very uncertain (in the case of
the stellar masses and star formation histories; Topping et al. 2022). Future
observations of the rest-frame optical emission of EoR galaxies with the JWST
will be critical to constrain these properties (e.g., Schaerer et al. 2022;
Katz et al. 2022).

##  5 A few surprises/challenges from recent ALMA observations

###  5.1 A hidden population of dusty galaxies in the EoR?

A surprising result to come out of the REBELS survey was the serendipitous
detection of two dust-obscured galaxies at $z\simeq 7$ that have no optical
counterparts in deep HST imaging (Fudamoto et al., 2021) – this implies SEDs
and dust attenuations similar to those of the dustiest known galaxies, sub-
millimetre galaxies, but in galaxies at much higher redshifts and lower
stellar masses than typical SMGs. ALMA observations are not only revealing
that there is a variety of dust obscuration at high-redshifts, but that there
might be a hidden population of dusty galaxies at the EoR that we did not know
about before (similar to optically-dark galaxies seen at lower redshifts;
e.g., Wang et al. 2019; Smail et al. 2021). Fudamoto et al. (2021) estimate
that these dusty galaxies could contribute 10 to 25% of the total cosmic SFR
density at $z>6$. This intriguing population needs further study, and these
sources are prime targets for JWST follow-up.

###  5.2 Spatial offsets between UV/optical and infrared emission

Some of the REBELS sources show large spatial offsets between the observed
ultraviolet and infrared emission – up to 1.5 arcsec (or 7.6 kpc; Inami et al.
2022). Similar offsets have also been observed in high-resolution observations
of star-forming galaxies at lower redshifts (e.g., Hodge et al. 2019; Cochrane
et al. 2021). These offsets could be a result of the multi-phase ISM – dust
and stars are not homogeneously distributed, with opaque star-forming clumps
and a more transparent diffuse component. This could be a challenge for SED
fitting methods that assume energy balance (e.g., da Cunha et al. 2008), as
well as for modelling the IRX-$\beta$ relation (Ferrara et al., 2022). More
high-resolution follow-up of the dust (with ALMA) and stellar (with JWST)
emissions in these sources will be key to better understand these offsets.

##  6 Summary & Open Questions

Thanks to ALMA we can now detect the dust emission of galaxies all the way
into the epoch of reionization. Dust at those early times seems to have
different properties than dust in star-forming galaxies at lower redshifts,
with some indication of steeper attenuation curves, resembling dust in the SMC
rather than in the Milky Way. However, this result depends on assumptions on
the dust temperature (used to extrapolate single-band continuum measurements
to obtain the total infrared luminosity). Dust in high-redshift galaxies seems
to be warmer than dust in lower-redshift galaxies, but not enough to reconcile
their infrared excesses with a Milky Way-like attenuation curve, and not as
hot as predicted by theoretical models or by extrapolating the temperature-
redshift relation calibrated at lower redshift. More direct measurements of
the dust emission SEDs in multiple bands for larger samples of galaxies are
needed to confirm this result.

The contribution of dust-obscured star formation rate to the cosmic SFR
density at $z\gtrsim 6$ is non-negligible, and it could be as high as 30%
based on recent REBELS results. This however needs to be confirmed with
larger, preferably, blind surveys of dust emission at those redshifts.

ALMA observations show that many $z>6$ UV-selected galaxies have copious
amounts of dust. The production of high dust masses in the early Universe
still pose a challenge to models. For now there seems to be a consensus in the
literature that high supernova yields and/or significant ISM dust growth are
needed, but the exact contribution of each process is still debated. Going
forward, we need to improve the measurements of the main stellar and dust
parameters that need to be compared with models, which at the moment have
large uncertainties. JWST will yield more robust stellar masses, star
formation histories, and metallicities; ALMA multi-band observations will
constrain the dust masses more accurately.

The REBELS survey also finds a new population of dust-obscured galaxies in the
epoch of reionization with no optical counterparts – how significant is this
population and what are the properties of these galaxies? Searches for larger
samples of these sources with ALMA, and JWST follow-up to observe their
stellar emission are needed to address these questions.

Finally, REBELS also provides the first opportunity to compare the UV and IR
emission in early galaxies in a systematic way. This shows that spatial
offsets between these two emissions are common, which begs the question: how
should we deal with decoupled stellar and dust emissions? This may involve
revising how we model the SEDs of galaxies. High-resolution ALMA and JWST
follow-up of these sources will be crucial to further characterise their ISM
and stellar morphologies and study the impact of these offsets.

###### Acknowledgements.

I would like to thank the organizers of this symposium for the invitation to
present this talk and my colleagues from the REBELS team for their excellent
work in producing the results I reviewed. I also gratefully acknowledge the
Australian Research Council as the recipient of a Future Fellowship (project
FT150100079) and the ARC Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D; project CE170100013). I acknowledge that this paper was
written on Noongar land, and pay my respects to its traditional custodians and
elders, past and present.

## References

  * Algera et al. (2022) Algera, H., Inami, H., Oesch, P., et al. 2022, arXiv e-prints, arXiv:2208.08243
  * Aoyama et al. (2020) Aoyama, S., Hirashita, H., & Nagamine, K. 2020, MNRAS, 491, 3844
  * Asano et al. (2013a) Asano, R. S., Takeuchi, T. T., Hirashita, H., & Inoue, A. K. 2013a, Earth, Planets, and Space, 65, 213
  * Asano et al. (2013b) Asano, R. S., Takeuchi, T. T., Hirashita, H., & Nozawa, T. 2013b, MNRAS, 432, 637
  * Bakx et al. (2021) Bakx, T. J. L. C., Sommovigo, L., Carniani, S., et al. 2021, MNRAS, 508, L58
  * Barisic et al. (2017) Barisic, I., Faisst, A. L., Capak, P. L., et al. 2017, ApJ, 845, 41
  * Behrens et al. (2018) Behrens, C., Pallottini, A., Ferrara, A., Gallerani, S., & Vallini, L. 2018, MNRAS, 477, 552
  * Bertoldi et al. (2003) Bertoldi, F., Carilli, C. L., Cox, P., et al. 2003, A&A, 406, L55
  * Bouwens et al. (2016) Bouwens, R. J., Aravena, M., Decarli, R., et al. 2016, ApJ, 833, 72
  * Bouwens et al. (2022) Bouwens, R. J., Smit, R., Schouws, S., et al. 2022, ApJ, 931, 160
  * Bowler et al. (2018) Bowler, R. A. A., Bourne, N., Dunlop, J. S., McLure, R. J., & McLeod, D. J. 2018, MNRAS, 481, 1631
  * Calzetti et al. (1994) Calzetti, D., Kinney, A. L., & Storchi-Bergmann, T. 1994, ApJ, 429, 582
  * Capak et al. (2015) Capak, P. L., Carilli, C., Jones, G., et al. 2015, Nature, 522, 455
  * Casey et al. (2014) Casey, C. M., Narayanan, D., & Cooray, A. 2014, Physics Reports, 541, 45
  * Cochrane et al. (2021) Cochrane, R. K., Best, P. N., Smail, I., et al. 2021, MNRAS, 503, 2622
  * da Cunha et al. (2008) da Cunha, E., Charlot, S., & Elbaz, D. 2008, MNRAS, 388, 1595
  * da Cunha et al. (2021) da Cunha, E., Hodge, J. A., Casey, C. M., et al. 2021, ApJ, 919, 30
  * Dayal et al. (2022) Dayal, P., Ferrara, A., Sommovigo, L., et al. 2022, MNRAS, 512, 989
  * Dole et al. (2006) Dole, H., Lagache, G., Puget, J. L., et al. 2006, A&A, 451, 417
  * Dudzevičiūtė et al. (2020) Dudzevičiūtė, U., Smail, I., Swinbank, A. M., et al. 2020, MNRAS, 494, 3828
  * Dwek (1998) Dwek, E. 1998, ApJ, 501, 643
  * Dwek & Cherchneff (2011) Dwek, E., & Cherchneff, I. 2011, ApJ, 727, 63
  * Faisst et al. (2020) Faisst, A. L., Fudamoto, Y., Oesch, P. A., et al. 2020, MNRAS, 498, 4192
  * Faisst et al. (2017) Faisst, A. L., Capak, P. L., Yan, L., et al. 2017, ApJ, 847, 21
  * Ferrara et al. (2016) Ferrara, A., Viti, S., & Ceccarelli, C. 2016, MNRAS, 463, L112
  * Ferrara et al. (2022) Ferrara, A., Sommovigo, L., Dayal, P., et al. 2022, MNRAS, 512, 58
  * Fudamoto et al. (2017) Fudamoto, Y., Oesch, P. A., Schinnerer, E., et al. 2017, MNRAS, 472, 483
  * Fudamoto et al. (2020) Fudamoto, Y., Oesch, P. A., Magnelli, B., et al. 2020, MNRAS, 491, 4724
  * Fudamoto et al. (2021) Fudamoto, Y., Oesch, P. A., Schouws, S., et al. 2021, Nature, 597, 489
  * Gall et al. (2011) Gall, C., Andersen, A. C., & Hjorth, J. 2011, A&A, 528, A13
  * Galliano et al. (2018) Galliano, F., Galametz, M., & Jones, A. P. 2018, ARA&A, 56, 673
  * Graziani et al. (2020) Graziani, L., Schneider, R., Ginolfi, M., et al. 2020, MNRAS, 494, 1071
  * Hirashita & Ferrara (2002) Hirashita, H., & Ferrara, A. 2002, MNRAS, 337, 921
  * Hodge & da Cunha (2020) Hodge, J. A., & da Cunha, E. 2020, Royal Society Open Science, 7, 200556
  * Hodge et al. (2019) Hodge, J. A., Smail, I., Walter, F., et al. 2019, ApJ, 876, 130
  * Inami et al. (2022) Inami, H., Algera, H. S. B., Schouws, S., et al. 2022, MNRAS, 515, 3126
  * Jin et al. (2018) Jin, S., Daddi, E., Liu, D., et al. 2018, ApJ, 864, 56
  * Jin et al. (2022) Jin, S., Daddi, E., Magdis, G. E., et al. 2022, A&A, 665, A3
  * Katz et al. (2022) Katz, H., Saxena, A., Cameron, A. J., et al. 2022, MNRAS
  * Kobayashi et al. (2020) Kobayashi, C., Karakas, A. I., & Lugaro, M. 2020, ApJ, 900, 179
  * Liang et al. (2019) Liang, L., Feldmann, R., Kereš, D., et al. 2019, MNRAS, 489, 1397
  * Liu et al. (2018) Liu, D., Daddi, E., Dickinson, M., et al. 2018, ApJ, 853, 172
  * Ma et al. (2019) Ma, X., Hayward, C. C., Casey, C. M., et al. 2019, MNRAS, 487, 1844
  * Madau & Dickinson (2014) Madau, P., & Dickinson, M. 2014, ARA&A, 52, 415
  * Mancini et al. (2016) Mancini, M., Schneider, R., Graziani, L., et al. 2016, MNRAS, 462, 3130
  * Mancini et al. (2015) —. 2015, MNRAS, 451, L70
  * McAlpine et al. (2019) McAlpine, S., Smail, I., Bower, R. G., et al. 2019, MNRAS, 488, 2440
  * Meurer et al. (1999) Meurer, G. R., Heckman, T. M., & Calzetti, D. 1999, ApJ, 521, 64
  * Narayanan et al. (2018) Narayanan, D., Davé, R., Johnson, B. D., et al. 2018, MNRAS, 474, 1718
  * Popping et al. (2017) Popping, G., Somerville, R. S., & Galametz, M. 2017, MNRAS, 471, 3152
  * Riechers et al. (2013) Riechers, D. A., Bradford, C. M., Clements, D. L., et al. 2013, Nature, 496, 329
  * Schaerer et al. (2022) Schaerer, D., Marques-Chaves, R., Barrufet, L., et al. 2022, A&A, 665, L4
  * Schouws et al. (2022) Schouws, S., Stefanon, M., Bouwens, R., et al. 2022, ApJ, 928, 31
  * Schreiber et al. (2018) Schreiber, C., Elbaz, D., Pannella, M., et al. 2018, A&A, 609, A30
  * Schreiber et al. (2015) Schreiber, C., Pannella, M., Elbaz, D., et al. 2015, A&A, 575, A74
  * Smail et al. (2021) Smail, I., Dudzevičiūtė, U., Stach, S. M., et al. 2021, MNRAS, 502, 3426
  * Sommovigo et al. (2021) Sommovigo, L., Ferrara, A., Carniani, S., et al. 2021, MNRAS, 503, 4878
  * Sommovigo et al. (2020) Sommovigo, L., Ferrara, A., Pallottini, A., et al. 2020, arXiv e-prints, arXiv:2004.09528
  * Sommovigo et al. (2022) —. 2022, MNRAS, 513, 3122
  * Topping et al. (2022) Topping, M. W., Stark, D. P., Endsley, R., et al. 2022, MNRAS, 516, 975
  * Walter et al. (2012) Walter, F., Decarli, R., Carilli, C., et al. 2012, Nature, 486, 233
  * Wang et al. (2019) Wang, T., Schreiber, C., Elbaz, D., et al. 2019, Nature, 572, 211
  * Whitaker et al. (2017) Whitaker, K. E., Pope, A., Cybulski, R., et al. 2017, ApJ, 850, 208
  * Witstok et al. (2022) Witstok, J., Smit, R., Maiolino, R., et al. 2022, MNRAS, 515, 1751
  * Zavala et al. (2021) Zavala, J. A., Casey, C. M., Manning, S. M., et al. 2021, ApJ, 909, 165
  * Zhukovska (2014) Zhukovska, S. 2014, A&A, 562, A76
  * Zhukovska et al. (2008) Zhukovska, S., Gail, H. P., & Trieloff, M. 2008, A&A, 479, 453