###### Abstract

A multiwavelength study of galaxies is important to understand their formation
and evolution. Only in the recent past, thanks to the Atacama Large (Sub)
Millimeter Array (ALMA), were we able to study the far-infrared (IR)
properties of galaxies at high redshifts. In this article, we summarize recent
research highlights and their significance to our understanding of early
galaxy evolution from the ALPINE survey, a large program with ALMA to observe
the dust continuum and $158\,{\upmu\rm{m}}$ C+ emission of normal star-forming
galaxies at $z=$ 4–6. Combined with ancillary data at UV through near-IR
wavelengths, ALPINE provides the currently largest multiwavelength sample of
post-reionization galaxies and has advanced our understanding of (i) the
demographics of C+ emission; (ii) the relation of star formation and C+
emission; (iii) the gas content; (iv) outflows and enrichment of the
intergalactic medium; and (v) the kinematics, emergence of disks, and merger
rates in galaxies at $z>4$. ALPINE builds the basis for more detailed
measurements with the next generation of telescopes, and places itself as an
important post-reionization baseline sample to allow a continuous study of
galaxies over $13$ billion years of cosmic time.

###### keywords:

galaxies: evolution; galaxies: star formation; galaxies: formation; galaxies:
high-redshift; galaxies: ISM; submillimeter: galaxies; galaxies: kinematics
and dynamics

1 1 0 Academic Editor: Marc S. Seigar 2 May 2022 26 May 2022 https://doi.org/
ALPINE: A Large Survey to Understand Teenage Galaxies ALPINE: A Large Survey
to Understand Teenage Galaxies Andreas L. Faisst 1,∗, Lin Yan 2, Matthieu
Béthermin 3, Paolo Cassata 4,5, Miroslava Dessauges-Zavadsky 6, Yoshinobu
Fudamoto 6,7,8, Michele Ginolfi 9, Carlotta Gruppioni 10, Gareth Jones 11,12,
Yana Khusanova 13, Olivier LeFèvre 3, Francesca Pozzi 10,14, Michael Romano
15, Daniel Schaerer 6, John Silverman 16,17, and Brittany Vanderhoof 18 A.
Faisst, L. Yan, M. Bethermin, P. Cassata, M. Dessauges-Zavadsky, Y. Fudamoto,
M. Ginolfi, C. Gruppioni, G. Jones, Y. Khusanova, O. LeFevre, F. Pozzi, M.
Romano, D. Schaerer, J. Silverman, and B. Vanderhoof Faisst, A.; Yan, L.;
Béthermin, M.; Cassata, P.; Dessauges-Zavadsky, M.; Fudamoto, Y.; Ginolfi, M.;
Gruppioni, C.; Jones, G.; Khusanova, Y.; et al. Correspondence:
<EMAIL_ADDRESS>
##  1 Introduction

The Universe that we observe today is diverse, with a mix of star-forming and
quiescent galaxies with different internal (stellar mass, metallicity) and
external (structure, environment) properties. While most star-forming galaxies
(often called “spiral galaxies” due to their spiral structure) form stars at
low rates of a few solar masses per year, starbursts exhibiting multiples of
these rates are also observed. Quiescent galaxies on the other hand (called
“spheroids” due to their mostly symmetric and compact appearance with a smooth
light profile) had their star formation stopped in the past by a variety of
reasons (Ciotti and Ostriker, 1997; Ilbert et al., 2010; Cheung et al., 2016).
At earlier cosmic times, however, this picture changes; the sighting of
quiescent galaxies is rare, and star-forming galaxies (showing an irregular
and lumpy structure) form stars at rates higher than present-day starbursts.
Observing the evolution of galaxies across cosmic times starting from early
formation epochs and deriving a physical model of the evolutionary processes
that explain the diversity of galaxies is one of the main goals of the current
efforts in the astrophysical community.

From the combination of imaging and spectroscopic observations at ultraviolet
(UV), optical, and (far-) infrared (IR) wavelengths, a reasonably robust
picture of how galaxies evolve across the past 9–10 Gyrs of cosmic time
(corresponding to redshifts $z<3$) has been established. Similar to the local
universe, galaxies exhibit a tight relation between star-formation rate (SFR)
and stellar mass (the star-forming main-sequence; (Rodighiero et al., 2011;
Speagle et al., 2014)) as found by robust total SFR measurements from far-IR
observations. However, galaxies in the earlier universe are significantly more
star-forming on average and the fraction of quiescent galaxies is decreasing
strongly at redshifts higher than $\sim$$2$ (Bell et al., 2004; Ilbert et al.,
2010; Madau and Dickinson, 2014). This is also the epoch when the cosmic SFR
density reaches the peak over cosmic time (Madau and Dickinson, 2014). Along
with changing SFRs, the environment in which stars are being formed evolves
across cosmic time. Galaxies become more dust- and metal-enriched over time as
their stellar masses are being built up by galaxy–galaxy mergers and the
inflow of new gas to fuel star formation (Hopkins et al., 2006; Ho et al.,
2015). The rate of galaxy–galaxy major mergers (with a mass ratio smaller than
1:4) as well as the gas fractions of galaxies are observed to increase towards
earlier cosmic times (Tacconi et al., 2020). The overall increase in SFR as a
function of redshift is found to be coupled with increasingly large gas
reservoirs, while the vertical position on the main-sequence at a given
stellar mass and redshift is dominated by changes in star-formation efficiency
(Scoville et al., 2017; Silverman et al., 2015). Finally, high-resolution
space-based observations of the light distribution of galaxies at early times
show that they are significantly more irregular and dominated by clumps of
star-forming gas and minor mergers (Conselice, 2014; Bouwens et al., 2014;
Elmegreen et al., 2021). Spectroscopic observations of the H$\alpha$ emission
line of large samples of galaxies at $z$$\sim$$2$ have confirmed this picture
by revealing a significant amount of dispersion dominated and merging galaxies
(e.g., (Förster Schreiber et al., 2011)).

Large spectroscopic campaigns using 8–10 m-class telescopes over the past
decade have extended the study of statistical samples of galaxies beyond the
peak of cosmic SFR density towards the Epoch of Reionization at $z$$\sim$$6$.
The largest of these programs use the VIMOS spectrograph on the Very Large
Telescope (VLT) (Le Fèvre et al., 2003, 2015) and the DEIMOS spectrograph on
the Keck telescopes (Faber et al., 2003; Hasinger et al., 2018), and provide
robust redshifts for hundreds of galaxies at $z=$ 4–6. This redshift range,
the “Early Growth Phase” of galaxy evolution, represents a transition phase
between primordial galaxy formation in the Epoch of Reionization and mature
galaxy evolution at the peak of cosmic SFR density, and hence forms the
crucial link between early galaxies and modern galaxies (Figure 1). In
addition to spectroscopy, 10,000 s of galaxies have been identified
photometrically in this redshift range over many extragalactic fields observed
with the Hubble space telescope in multiple photometric bands (e.g., (Bouwens
et al., 2015)). Large programs using the Spitzer space telescope, covering
near-IR wavelengths, have imaged the rest-frame optical light (emitted by
older stars), which is crucial for estimating stellar masses of galaxies at
$z>4$ (Davidzon et al., 2017) and even allows the measurement of H$\alpha$, [O
II], and H$\beta$ emission lines (Shim et al., 2011; Faisst et al., 2016).

Figure 1: Cosmic SFR density as a function of cosmic time and redshift. The
global SFR density increases sharply during primordial galaxy assembly and
evolution to reach a peak at $z$$\sim$2–3 followed by a decline due to the
emergence of quiescent galaxies during the mature galaxy evolution. The ALPINE
survey (presented in Béthermin et al. (2020), Faisst et al. (2020), and Le
Fèvre et al. (2020)) studies galaxy evolution during the Early Growth Phase at
$z=$ 4–6, an important connection between primordial and mature galaxy
evolution, via a large multiwavelength sample. ALPINE builds the basis for
more detailed measurements with the next generation of telescopes, and places
itself as an important post-reionization baseline sample to allow a continuous
study of galaxies over $13$ billion years of cosmic time. The grayscale images
show the change in structure of the galaxies across cosmic time. Data points
from Madau and Dickinson (2014) and Bouwens et al. (2015).

While such large samples at these early cosmic times exist, they are mostly
selected at rest-frame UV (and sometimes optical) wavelengths. This means that
these samples are highly biased towards galaxies visible at these wavelengths,
i.e., not or only slightly attenuated by dust. As estimated in Bouwens et al.
(2009), at $z=$ 4–6, more than $40\%$ of the UV light is reprocessed by dust
and another $10\%$ is completely missed by UV studies. This significantly
limits our understanding of this galaxy population in UV light and, for
example, raises the question of how much dust-obscured star formation
contributes to the growth of these galaxies. Furthermore, the observation of
the spatial and kinematic structure of the colder gas (only observable at
submillimeter wavelengths) provides new insights into the physics of star-
formation and the conditions of the interstellar medium (ISM) in these
galaxies, complementary to what can be done at rest-frame UV and optical
wavelengths.

The high sensitivity of the Atacama Large (Sub-) Millimeter Array (ALMA)
enables such observations at sub-mm wavelengths. In combination with data in
the UV and optical, it enables us to study early galaxy evolution in more
detail than ever before. While bright sub-mm galaxies, including (Ultra)
Luminous Infrared Galaxies (ULIRGs), have been observed before with Herschel
(Lutz et al., 2011; Oliver et al., 2012), ALMA extends the analysis to normal
main-sequence galaxies at early cosmic times by targeting their far-IR dust
continuum together with emission lines, such as singly ionized carbon (C+, one
of the most dominant cooling lines) at rest-frame $158\,{\upmu\rm{m}}$.

The importance of such a multiwavelength approach was first demonstrated on a
sample of $10$ galaxies observed in C+ at $z$$\sim$5 in Capak et al. (2015)
(see also (Riechers et al., 2014; Barisic et al., 2017; Faisst et al., 2017)).
All galaxies reside on the Cosmic Evolution Survey (COSMOS, Scoville et al.
(2007)) field; thus, a wealth of data is available from UV to optical
wavelengths, including rest-frame UV spectroscopy from Keck/DEIMOS and
VLT/VIMOS (Hasinger et al., 2018; Le Fèvre et al., 2015). The coverage of the
field with Hubble/ACS imaging in F814W ($i$-band) (Koekemoer et al., 2007) as
well as partially in the near-IR from the CANDLES survey (Grogin et al., 2011;
Koekemoer et al., 2011), offers further high-resolution spatial information.
With $10$ out of $10$ C+ detections, the study suggested that C+ is abundant
in this galaxy population and a good tool to study these galaxies. In summary,
the study revealed large variations in the dust content (measured by sub-mm
continuum) and C+ emission in this small sample, and in particular highlighted
the kinematics of molecular gas and “UV-dark” dust-obscured major mergers,
which have been missed previously. However, without a large sample with
similar multiwavelength measurement, further conclusions on the galaxy
population as a whole are limited.

The ALMA Large Program to Investigate C+ at Early Times (ALPINE; Le Fèvre et
al. (2020), Béthermin et al. (2020), Faisst et al. (2020)) mitigates these
issues by providing similar far-IR dust continuum and C+ measurements for a
sample of $118$ main-sequence galaxies spectroscopically confirmed at
$4.4<z<5.9$ in the COSMOS field and the Extended Chandra Deep Field South
(ECDFS, Giacconi et al. (2002)). The ALPINE ALMA data (described in Béthermin
et al. (2020)) are taken by a $69\,{\rm hour}$ ALMA large program over cycles
5 and 6. All galaxies have a wealth of multiwavelength data and rest-UV
spectroscopy (described in Faisst et al. (2020)), which makes ALPINE the first
and largest multiwavelength survey of galaxies at these early cosmic times.
ALPINE has significantly advanced our understanding of post-reionization
galaxies during the Early Growth Phase at $z=$ 4–6 in several topics,
including

  * •

contribution of obscured star formation to the cosmic SFR density;

  * •

gas reservoirs and modes of star formation;

  * •

enrichment of the circumgalactic medium (CGM) via outflows from galaxies;

  * •

mixture of kinematic structure, emergence of rotators, and merger rates;

  * •

abundance of “UV-dark” sources detected serendipitously at high redshifts.

In this article, we summarize the research highlights from ALPINE and their
significance to our understanding of early galaxy evolution. Specifically, in
Section 2, we provide a brief introduction of ALPINE including its
multiwavelength data products. In Section 3, we present in detail the science
results and we discuss their significance in Section 4. We conclude in Section
5.

Throughout this work, we assume a $\Lambda$CDM cosmology with $H_{0}=70\,{\rm
km\,s^{-1}\,Mpc^{-1}}$, $\Omega_{\Lambda}=0.70$, and $\Omega_{\rm m}=0.30$.
All magnitudes are given in the AB system (Oke, 1974) and stellar masses and
SFRs are normalized to a Chabrier (2003) initial mass function (IMF) unless
noted otherwise.

##  2 ALPINE—The Largest Post-Reionization Multiwavelength Survey

The primary goal of ALPINE is to study the gas and dust properties of galaxies
shortly after the Epoch of Reionization at $z$$\sim$4–6 via the
$150\,{\upmu\rm{m}}$ dust-continuum and C+ line emission in combination with
rest-UV to optical observations. This epoch of cosmic time is of particular
interest as it connects primordial galaxy formation at $z>6$ with mature
galaxy evolution around the peak of cosmic SFR density ($z$$\sim$2–3). In this
section, we summarize the sample and observations as well as the most
important science goals. For more details on these topics, we refer the reader
to Béthermin et al. (2020) (ALMA observations) and Faisst et al. (2020)
(sample selection and non-ALMA ancillary data).

###  2.1 Sample and Observations

ALPINE is a $69\,{\rm hour}$ ALMA large program ($\\#$ 2017.1.00428.L) carried
out in Cycles 5 and 6 in Band 7 (0.8–1.1 mm or 275–373 GHz). The program is a
collaboration between several members of ALMA regional centers, including
Europe, North America, Chile, and Japan. Of the $118$ galaxies with
spectroscopic redshifts of 4.4–5.9, $105$ are located in the COSMOS field
(Scoville et al., 2007) and $13$ in the ECDFS (Giacconi et al., 2002). The
sample spans roughly two orders of magnitude in stellar mass and SFR on the
star-forming main-sequence, hence including a representative sample of typical
main-sequence galaxies at these cosmic times (Figure 2). The galaxies were
selected in two redshift windows at $4.40<z<4.65$ (67 galaxies) and
$5.05<z<5.90$ (51 galaxies) with median redshifts of $z$$\sim$$4.5$ and
$z$$\sim$$5.5$, respectively. The windows were chosen to avoid frequencies of
low atmospheric transmission and to optimize the observation efficiency. The
spectroscopic redshifts were gathered from two large spectroscopic surveys
carried out by Keck/DEIMOS (DEIMOS 10k Survey; (Hasinger et al., 2018)) and
VLT/VIMOS (VIMOS Ultra Deep Survey, VUDS; (Le Fèvre et al., 2015)). These
surveys combine redshifts of galaxies selected in a variety of ways, for
example, by narrowband Ly$\alpha$ emission, Spitzer $4.5\,{\upmu\rm{m}}$ flux
excess, Lyman Break color selection (LBGs), and photometric redshifts. This
variety is inherited in the final ALPINE sample, emphasizing the selection of
representative galaxies at these redshifts. Furthermore, the redshifts were
derived from Ly$\alpha$ emission as well as UV absorption lines, therefore
minimizing selection biases towards young, dusty-poor Ly$\alpha$ emitters. All
spectra have been consistently renormalized using the COSMOS2015 photometric
catalog (Laigle et al., 2016) or CANDELS photometry, using broadband and
narrowband data (see Faisst et al. (2020) for a full description). The ALPINE
galaxies have an absolute rest-UV magnitude of $M_{\rm 1500}>-20.2\,{\rm
mag}$, corresponding to an equivalent SFR of $10\,{\rm{M}_{\odot}\,yr^{-1}}$.
This cut was chosen to maximize the number of C+ line detections according to
the $L_{{\rm C^{+}}}$ vs. $M_{\rm 1500}$ relation found in Capak et al. (2015)
based on $10$ $z$$\sim$$5.5$ galaxies with similar observations.

Figure 2: ALPINE observed $118$ galaxies on the star-forming main-sequence at
redshifts $z~{}=~{}$4.4–5.9. The ALMA observations provide measurements of the
$158\,{\upmu\rm{m}}$ C+ line emission as well as the surrounding (rest-frame
$\sim$$150\,\upmu$m) dust continuum. Left Panels: Hubble ACS/F814W cutouts of
six ALPINE galaxies at different redshifts with a range of C+ and far-IR
emission morphologies. Contours show C+ emission (blue) and dust continuum
(red), target IDs, stellar masses, and redshifts are also indicated. Right
Panel: Distribution of the ALPINE galaxies (large symbols) and their parent
sample (blue dots) on the main-sequence (gray) at $z$$\sim$$5$. The color of
the symbols indicate the observed C+ line emission. Different symbols identify
mergers (stars) as well as galaxies whose Spitzer photometry is contaminated
by neighboring objects (squares); in which case, their stellar masses are
likely overestimated. Adapted from Ref. Faisst et al. (2020).

Most observations (102 galaxies) were carried out between May and August 2018
in Cycle 5 and the remaining ones were observed in January 2019 in Cycle 6.
The C+ lines of the targeted sources were covered by two contiguous spectral
windows of $1.875\,{\rm GHz}$ each. The remaining two windows were used to
observe the dust continuum around the C+ emission line. The compact array
configurations C43-1 and C43-2 were used to obtain a resolution
$>0.7^{\prime\prime}$ to avoid over-resolving of the flux, hence decreasing
the signal-to-noise (S/N). The final average synthesized beam full-width-at-
half-maximum (FWHM), depending on frequency and exact array configuration, is
$0.85^{\prime\prime}\times 1.13^{\prime\prime}$, corresponding to roughly 5–6
kpc at redshift $z=5$. The coarse spectral resolution is $\Delta v_{\rm
channel}~{}=~{}31.250\,{\rm MHz}$, which allows the resolution of the C+
emission line (typical FWHM of $235\,{\rm km\,s^{-1}}$). The integration times
per source vary from $10\,{\rm min}$ to $1\,{\rm h}\,20\,{\rm min}$, to
achieve an average root mean square (rms) line sensitivity of $0.14\,{\rm
Jy\,km\,s^{-1}}$ for C+ emissionThe C+ emission was estimated from the $\rm
L_{C^{+}}$ vs. $\rm M_{1500}$ relation from Capak et al. (2015).
(corresponding to $L_{{\rm C^{+}}}$$\sim$$0.4\times 10^{8}\,{\rm L}_{\odot}$)
and rms continuum sensitivity of $50\,\upmu{\rm Jy\,beam^{-1}}$ for continuum.
Out of the $118$ targeted galaxies, $23$ were detected in continuum at
>$3.5\sigma$ ($\sim$$20\%$) and $75$ were detected in C+ line emission at
>$3.5\sigma$ ($\sim$$64\%$). For a full description of line and continuum
measurements, we refer the reader to Béthermin et al. (2020). In addition,
ALPINE provides a blank-field survey of $\sim$$24\,{\rm arcmin^{2}}$, in which
$57$ sources were detected serendipitously in continuum at >$5\sigma$
(described in Béthermin et al. (2020)) and $14$ in line emission at >$3\sigma$
($8$ are confirmed C+ emissions at $z$$\sim$$5$ and two are confirmed CO
transitions at lower redshifts, see Loiacono et al. Loiacono et al. (2021)).

###  2.2 Overview of ALPINE’s Research Topics

ALPINE is the largest multiwavelength survey to study galaxies in the post-
reionization era at $z=$ 4–6. Specifically, the ALMA data are crucial to
mitigate common selection biases towards low-dust-attenuated, UV-bright
galaxies. It also extends earlier sub-mm samples focusing on intensely star-
forming (SFR $>1000\,{\rm M_{\odot}\,yr^{-1}}$) to main-sequence galaxies. In
combination with observations at higher frequencies, the ALPINE survey opens
the doors to study many different science topics, which we summarize in the
following.

The ALPINE observations focus on C+, which is an important cooling line and,
therefore, expected to be prevalent in star-forming galaxies. This is
especially the case at high redshifts where average SFRs are increased
compared to the local universe. Correspondingly, C+ is related to the SFR, as
demonstrated in large samples of low-redshift galaxies (e.g., (Carilli and
Walter, 2013; De Looze et al., 2014)). Starting in the early years of ALMA,
several studies have shown that it is possible to measure C+ out to high
redshifts, although such studies mostly focused on bright submillimeter
galaxies and only small samples of main-sequence galaxies (Willott et al.,
2015; Capak et al., 2015; Riechers et al., 2014; Maiolino et al., 2008). The
origin of C+ emission is complicated, which could affect its relation to star
formation especially at high redshifts, where star formation is taking place
in environments with different chemical and radiation properties compared to
low-$z$. While C+ is often emitted from photo-dissociation regions (PDRs) of
molecular clouds, it can also originate from the cold neutral medium and H II
regions (Herrera-Camus et al., 2015, 2017; Pineda et al., 2013; Vallini et
al., 2015) or traces the diffuse ionized gas (Pavesi et al., 2016, 2019).
Furthermore, some earlier studies suggested a C+-deficit (with respect to far-
IR luminosity) in high-redshift galaxies (e.g., (Maiolino et al., 2015;
Pentericci et al., 2016; Carniani et al., 2018)), which could be due to
absolutely lower Carbon levels, observations missing broad spatial components
of C+ emission, or simply selection effects. The multiwavelength information
(and especially the far-IR continuum emission) from ALPINE provides the first
verification of the relation between SFR and C+ emission at these redshifts.

By targeting a large sample of normal main-sequence galaxies, ALPINE studies,
for the first time, the statistical contribution of dust-obscured star
formation in this galaxy population. Serendipitously detected sources put
constraints on the remaining fraction of star formation that is not traced by
UV-detected galaxies. Further constraints on the dust mass can be placed by
the measurement of far-IR continuum emission, and the distribution of dust can
be studied by spatial distributions of UV, optical, far-IR continuum light,
and C+ emission or the relation between the $L_{{\rm IR}}$/$L_{{\rm UV}}$
continuum ratio (also denoted as IRX) and the UV continuum slope ($\beta$).
The latter IRX$-\beta$ diagnostic provides insight into the spatial
distribution of dust, dust grain properties, and metallicity (Reddy et al.,
2012; Faisst et al., 2017). In addition, the relation between IRX and stellar
mass provides insights into the buildup of dust at this critical epoch of
galaxy growth (e.g., (Graziani et al., 2020)).

At least out to $z$$\sim$2–3, increased gas fractions (i.e., larger gas
reservoirs) have been identified as the main reason for the higher SFRs of the
galaxies (Scoville et al., 2017; Tacconi et al., 2020). Commonly, CO lines are
good tracers of the molecular gas reservoirs in galaxies. At higher redshifts,
only high-$J$ CO transitions can be observed, which come with considerable
uncertainties due to necessary excitation corrections. At higher redshifts,
the gas content of main-sequence galaxies has therefore not been studied
statistically and robustly. C+ has been shown to be a reasonable empirical
predictor of the molecular gas content, which does not involve uncertainties
of excitation corrections associated with high-$J$ CO transitions (Hughes et
al., 2017; Zanella et al., 2018). The relation between C+ and gas mass is
likely due to the secondary causal connection with SFR. With ALPINE data, the
first statistical assessment of gas masses and fractions can be undertaken via
their estimation from C+. Together with a quantification of the contribution
of mergers (derived from close-pair counts in sub-mm data) a full picture of
mass growth in $z=$ 4–6 galaxies can be obtained.

C+ is an excellent dust-independent tracer of gas dynamics, which allows
studies similar to those undertaken at $z$$\sim$$2$ with H$\alpha$ (Förster
Schreiber et al., 2009; Epinat et al., 2012; Molina et al., 2017).
Specifically, sub-mm observations are sensitive to dust-obscured galaxy
mergers and starbursts. ALPINE provides the first morpho-kinematic
classification of mergers, rotators, and dispersion-dominated galaxies to
study the buildup of structure in galaxies as well as the emergence of “disk
galaxies” (i.e., smooth rotators). Furthermore, the high spectral resolution
of ALMA allows to put constraints on outflows and galactic winds via the width
and broad components of the C+ emission line. Such studies have an important
impact on our understanding of the baryon cycle (i.e., the outflow, inflow,
and recycling of gas) of galaxies at early cosmic times.

Finally, ALPINE provides the largest sample of C+-detections, making it
possible for the first time to study the demographics of C+-line emitters at
$z$$\sim$4–6 (Yan et al., 2020). More importantly, the calculated C+-line
luminosity functions (LF) allow us to compare with the volume density of
C+-emitters at $z$$\sim$$0$ (Hemmati et al., 2017). The C+-LF results provide
the quantitative constraints on the redshift evolution of C+-emitter as well
as the estimates of molecular gas density at $z$$\sim$4–6. We note the unique
aspect of ALPINE data, which is that the serendipitous C+-detections provide
the data to compute the incompleteness corrections to the C+-LF (Loiacono et
al., 2021).

In Section 3, we summarize the results of ALPINE on the topics above in more
detail.

##  3 Results

###  3.1 C+ and Far-Infrared Continuum Luminosity Function

The C+ line and far-IR continuum emission are the primary ALMA measurements
for the ALPINE galaxies. These measurements are obtained for the main ALPINE
targets as well as for the galaxies that are serendipitously detected in far-
IR continuum and C+ line emission in a total area of $24.92\,{\rm arcmin^{2}}$
(referred to as the ALPINE “blind survey”). In the following, we summarize the
results on the total far-IR and C+ luminosity functions obtained from these
basic measurements. For more detailed descriptions, we refer the reader to the
original ALPINE papers on these topics (Béthermin et al., 2020; Gruppioni et
al., 2020; Loiacono et al., 2021; Yan et al., 2020).

The average continuum and C+ line $1\sigma$ sensitivity reached by ALPINE are
$29\,\upmu{\rm Jy}$ and $0.14\,{\rm Jy\,km\,s^{-1}}$, respectively. At
$3.5\sigma$, this yields 23 detections in the continuum and 75 detections in
C+ emission, which correspond to $19.5\%$ and $63.5\%$, respectively, of the
total $118$ targeted galaxies (see (Béthermin et al., 2020)). Within the same
fields of the primary targets, $56$ continuum and $12$ C+ line emitters are
serendipitously detected. These detections are reported in Gruppioni et al.
(2020) and Loiacono et al. (2021).

The 56 serendipitous far-IR continuum sources are identified using the AstroPy
routine find_peaks in the signal-to-noise (S/N) ratio maps by applying a
threshold of ${\rm S/N}=5$ (resulting in a purity of $95\%$, (Béthermin et
al., 2020)). S/N maps are used to mitigate the issues of variable sensitivity
across the ALMA FoV. The redshifts of the $56$ sources are subsequently
constrained by matching their positions to ancillary catalogs as well as
fitting their SEDs with
LePharehttp://www.cfht.hawaii.edu/~arnouts/lephare.html, accessed on May 31,
2022 (Arnouts et al., 1999; Ilbert et al., 2006). Of the 56 serendipitous
continuum sources, at least 47 have photometric redshifts, 5 have
spectroscopic redshifts from C+ emission lines, and 4 have no redshifts. We
note that $6$ out of the $56$ sources are only detected in ALMA (hence, they
are “optically dark”) and their photometric redshifts are therefore highly
uncertain. The final redshift distribution of the $52$ sources ranges from
$z$$\sim$$0.5$ to $z$$\sim$$6$ with a peak at a median redshift of $\langle
z\rangle=2.84\pm 0.18$ (Gruppioni et al., 2020). Interestingly, 10 sources are
found at $z$$\sim$4–6, potentially due to physical overdensities around the
main ALPINE targets, suggesting abundant clustering of galaxies at
$z$$\sim$$5$.

The serendipitous C+ emitters are identified on the full three-dimensional
data cube using the find_clumps algorithm (Decarli et al., 2016; Walter et
al., 2016) by applying a threshold of ${\rm S/N}>6.3$, which corresponds to a
fidelity (proportional to the ratio of negative to positive peaks) of >$85\%$.
Two additional line emitters (at ${\rm S/N}$$\sim$$5.98$) with optical
counterparts are added due to their S/N being close to the threshold. In
total, $14$ serendipitous line emitters are subsequently matched to
photometric and spectroscopic catalogs. Out of these $14$ candidates, $8$ have
redshift confirming C+ emission at $4.3<z<5.4$. Specifically, $4$ of them have
spectroscopic redshifts and $4$ have photometric redshifts (consistent with C+
emission) based on the COSMOS multiwavelength photometry, including UV to
near-IR bands (with photo-z uncertainties $\Delta z<0.2$; (Laigle et al.,
2016)). Of the remaining candidates, two galaxies are identified as high-$J$
CO transition at $z=1.3$ and $z=0.9$, and the identification of $4$ lines is
ambiguous based on the available photometry.

####  3.1.1 The C+ Luminosity Function

The C+ luminosity function is derived by a $V_{\rm max}$ method (Schmidt,
1968) using the ALPINE main target galaxies as well as the serendipitously
detected C+ emitters. The inclusion of the latter is important to mitigate
selection biases in the main ALPINE target sample. Both luminosity functions
(Yan et al., 2020; Loiacono et al., 2021) are first corrected for
incompleteness. The serendipitous sample additionally includes a correction
factor based on the fidelity of the serendipitous detections. The completeness
correction of the target sample is based on the fact that the ALPINE sample
builds a subset of UV-detected galaxies (Yan et al., 2020). For the
serendipitous sample, the completeness has been computed using injection
simulations (Béthermin et al., 2020; Loiacono et al., 2021).

The left panel in Figure 3 shows the resulting luminosity function at
$z$$\sim$$5$ in comparison with the C+ LF at $z$$\sim$$0$ (solid gray line
from Hemmati et al. (2017)) as well as other literature measurements at higher
redshifts. It is important to note that the C+ LF at $z$$\sim$$5$ derived from
the ALPINE main sample is a lower limit, as it does not include
serendipitously detected C+ emitters, which can add to the number counts (see
(Loiacono et al., 2021)). The incompleteness correction of the LF is very
uncertain as it depends on the serendipitous sample, which is too small and
covers only a narrow luminosity interval (mostly high-luminosity end at
$L_{{\rm C^{+}}}>10^{8.5}\,L_{\odot}$). In addition, the serendipitous C+
emitters seem to be clustered with the main targets (see below); therefore,
they are not representative of the field population, which adds additional
uncertainty. Furthermore, the ALPINE data are not able to constrain the C+ LF
at $L_{{\rm C^{+}}}<10^{8}\,L_{\odot}$ due to the survey limits. Given these
caveats, the $z$$\sim$$5$ C+ LF (i.e., volume density of C+-emitters per
magnitude interval) seems to be comparable with that of $z$$\sim$$0$ at
$L_{{\rm C^{+}}}=10^{8.5}\text{--}10^{9.5}\,L_{\odot}$. This result is in
stark contrast with the strong evolution observed in the rest-frame UV LFs
(Ono et al., 2018; Bouwens et al., 2007). At the high-luminosity end
(>$10^{9.5}\,L_{\odot}$), a 1–2 $\sigma$ significant excess of C+ emitters
compared to the local C+ luminosity function (Hemmati et al., 2017) is found
(Figure 3). The excess compared to $z=0$ is amplified by the inclusion of “UV
dark” C+ emitters (serendipitously detected and missed by the ALPINE main
sample). Clustering of C+ emitters also plays a role in enhancing the number
density at bright luminosities. This is shown by the green symbols in the left
panel of Figure 3, which include serendipitous sources close to the main
targets.

The C+-LF result is also compared with that of CO LFs at $z$$\sim$3–5.8
derived by ASPECS (Decarli et al., 2019) and COLDz (Riechers et al., 2019)
using the CO($1-0$) to C+ conversion relation (see Equations (5) and (6) in
Yan et al. (2020)). The CO LFs confirm the excess of luminous C+-emitters that
were found in the ALPINE data, suggesting that at $\rm L_{{\rm
C^{+}}}>10^{9}\,L_{\odot}$ UV-faint but C+-bright sources likely make
significant contributions to the C+ emitter volume density. The derived
C+-LFs, in combination with far-IR and CO LFs, are also compared with current
available model predictions (Popping et al., 2016; Lagache et al., 2018),
which are found to significantly underestimate the number densities of C+
emitters at $z$$\sim$4–6.

Figure 3: C+ line emission and total far-IR LFs from ALPINE and literature.
Left Panel: C+ LF measured for the ALPINE main sample (blue squares,
$z$$\sim$$4.5$; red circles, $z$$\sim$$5.5$; Yan et al. Yan et al. (2020)) as
well as serendipitous sample (incl. clustered galaxies) from the ALPINE blind
survey (green open circles; (Loiacono et al., 2021)). Note that the counts of
serendipitous C+ emitters may be elevated due to clustering (see details in
(Loiacono et al., 2021)). Other results from the literature (Swinbank et al.,
2012; Capak et al., 2015; Yamaguchi et al., 2017; Cooke et al., 2018) at $z$ =
4.4, 4.5, 5.5, and $6$ are also shown with respective symbols (mostly limits).
For comparison, the $z$$\sim$$0$ C+ LF from Hemmati et al. (2017) is shown
(solid gray line) as well as predictions from semianalytical models (gray
dashed and dotted lines; (Lagache et al., 2018; Popping et al., 2019)). Note
that the ALPINE data become significantly incomplete and uncertain at $L_{{\rm
C^{+}}}<10^{8.5}\,L_{\odot}$ due to survey limits and the uncertain
incompleteness correction because of the lack of blindly detected C+ samples
(serving as incompleteness correction sample for the main targets). Hence, LF
is the lower limit. Figure adapted from Yan et al. (2020) and Loiacono et al.
(2021). Right Panel: Total far-IR LF from ALPINE continuum detections at $z$ =
4.5–5.9 (Gruppioni et al., 2020) excluding overdensities (black circles) and
including overdensities (open red squares). The solid, thick black line and
dotted red lines, respectively, show the best-fit Schechter functions. The
best fits to measurements from Herschel (thin solid lines; (Gruppioni et al.,
2013)) and SCUBA-2 S2CLS (thin dotted lines; (Koprowski et al., 2017)) for
different redshifts (from $z=1$ to $z=4$; from blue to red) are also shown.
Adapted from Ref. Gruppioni et al. (2020).

####  3.1.2 The Total Far-Infrared Luminosity Function

The computation of the total far-IR luminosity is less straightforward (see
details in (Gruppioni et al., 2020)). As ALMA only measures one continuum
point at rest-frame $\sim$$150\,\upmu{\rm m}$ for the ALPINE sample, a far-IR
SED shape has to be assumed in order to obtain the total far-IR luminosity
(integration between rest-frame 8–1000 $\upmu{\rm m}$). To this end, an
average far-IR SED is created by stacking Herschel measurements of several
hundred $z=$ 4–6 galaxies on the COSMOS field in the same stellar mass and SFR
range as the ALPINE sample (${\rm SFR_{UV}}>10\,{\rm M_{\odot}\,yr^{-1}}$)
(Béthermin et al., 2020). The obtained far-IR SED template is similar to a
modified black body with a luminosity-weighted dust temperature of $42\,{\rm
K}$, and is also in agreement with fits to $4$ ALPINE galaxies with multiple
far-IR continuum measurements (see Faisst et al. (2020)). This SED template
will also be used later to derive infrared-based SFRs of the ALPINE galaxies
from the total far-IR luminosity.

For the derivation of the total far-IR LF across cosmic time, the $56$
serendipitous far-IR continuum sources from the ALPINE blind survey are used
in order to mitigate potential selection biases towards strong C+ emitters.
Similar to the derivation of the C+ LF, a $V_{\rm max}$ method is used to
obtain the far-IR luminosity function. The resulting luminosity functions
(right panel of Figure 3) from $z$ = 0.5–6 (differentiated in colors) are
similar in shape with no significant decrease in their normalizations. The
results are also in good agreement with those derived from the CO luminosity
functions (Riechers et al., 2019; Decarli et al., 2016, 2019).

All in all, there is still a large uncertainty in the derived total far-IR LFs
due to small sample sizes and selection effects (for example, changes in
galaxy densities at small and large scales add significant uncertainties to
the number counts as shown by Loiacono et al. (2021) and Gruppioni et al.
(2020)). Large blind surveys would be a way to remedy these uncertainties;,
however, unless very deep, they are usually only sensitive to the most-
luminous sources and do not cover the full luminosity range.

###  3.2 Is C+ a Good Tracer of Star Formation at $z>4$?

A correlation between C+ emission and total SFR is expected from studies
crossing cosmic time from $z=0$ to $z$$\sim$$2$ (Pineda et al., 2014; Herrera-
Camus et al., 2015; De Looze et al., 2011, 2014). Such a relation is
fundamental as C+ is one of the strongest far-IR lines and is now widely
observed in high-$z$ galaxies. The far-IR continuum (a more-common SFR
indicator; (Kennicutt, 1998)) is significantly fainter; hence, it is much more
time-consuming to detect. While probed by large datasets at local redshifts,
the C+$-$SFR relation at higher redshifts is uncertain. Specifically, several
studies suggest a population of C+underluminous galaxies due to their observed
low C+/$L_{{\rm FIR}}$ ratios compared to lower redshifts (Maiolino et al.,
2015; Willott et al., 2015; Pentericci et al., 2016; Bradač et al., 2017;
Carniani et al., 2018; Capak et al., 2015; Riechers et al., 2014). The origin
of C+ from various regions in the galaxy (H II regions, diffuse neutral and
ionized ISM and PDRs; (Wolfire et al., 1995; Hollenbach and Tielens, 1999))
add additional complications.

One of the main goals of ALPINE is to revisit the C+$-$SFR relation at
$z$$\sim$$5$ using the largest sample of C+ emitters to date and compare it to
observations at lower redshifts as well as theoretical models. The full
analysis is detailed in Schaerer et al. (2020). Here, the most important
results are summarized.

As discussed in Section 3.1 and further elaborated in Section 3.3, a
significant population of dust-attenuated and -obscured galaxies has been
suggested even at $z>4$. As pointed out in Schaerer et al. (2020), an accurate
assessment of the total SFR (i.e., ${\rm SFR_{UV}}+{\rm SFR_{FIR}}$) and a
robust inclusion of limits in C+ and far-IR continuum is therefore crucial for
such an analysis. The total SFR of the ALPINE main targets are derived in
Schaerer et al. (2020) as follows. First, the dust uncorrected UV SFRs (${\rm
SFR_{UV}}$) are based on the rest-frame $L_{\rm 1500}$ luminosity derived from
SED fitting at $1500\,{\rm\text{\AA}}$ (see details in Faisst et al. (2020))
and by applying the Kennicutt (1998) relation, ${\rm SFR_{UV}}[{\rm
M_{\odot}\,yr^{-1}}]~{}=~{}1.59\times 10^{-10}\,L_{\rm 1500}/{\rm L_{\odot}}$
converted to a Chabrier (2003) IMF. For the calculation of the infrared SFR
(${\rm SFR_{FIR}}$), the conversion from ALMA-measured single-point photometry
at rest-frame $\sim$$150\,\upmu{\rm m}$ to total far-IR luminosity ($L_{\rm
IR}$) is crucial. The conversion depends strongly on the assumed shape of the
far-IR SED (itself depending on many parameters including the warm and cold
dust temperature), which is unknown as only one far-IR data point exists for
the ALPINE galaxies. To compute the conversion factor, an average empirical
far-IR template is created using the same approach as outlined in Section
3.1.2 (for details, see (Béthermin et al., 2020)). The far-IR SFRs for far-IR-
continuum-detected galaxies are derived via ${\rm SFR_{FIR}}[{\rm
M_{\odot}\,yr^{-1}}]=1.40\times 10^{-10}\,L_{\rm IR}/{\rm L_{\odot}}$
(Kennicutt, 1998), where the far-IR luminosity is again obtained by
integration of the far-IR SED at 8–1000 ${\upmu\rm{m}}$. For galaxies not
detected in far-IR continuum (i.e., ALMA sub-mm), $L_{\rm IR}$ is derived from
the stacked IRX$-\beta$ relationThe IRX$-\beta$ relation relates the rest-UV
continuum slope ($\beta$, described in Faisst et al. (2020)) to the $L_{\rm
IR}/L_{\rm UV}$ (IRX) luminosity ratio. presented in Fudamoto et al. (2020)
(see also Section 3.3).

Figure 4 shows the resulting relation between C+ and SFR as measured from the
ALPINE sample at $z=$ 4–6 from Schaerer et al. (2020). The best-fit relation
is shown as a solid black line and is derived using the Bayesian fitting
method described in Kelly (2007)The method is implemented in the Python
package linmix at https://github.com/jmeyers314/linmix, accessed on May 31,
2022., which properly treats errors and nondetections in astronomical data
during the fitting process. We also show the location of the stacked robust
nondetections from (purple empty star Romano et al. (2022)), which agrees well
with the C+ vs. SFR relation found by the stacked detections (purple filled
stars). In addition, the observed C+ vs. SFR relation of local galaxies (gray
line and region ($2\sigma$); (De Looze et al., 2014)) as well as theoretical
models (Lagache et al., 2018)Note that all of these relations have been
calibrated to the same IMF. are also shown. While other studies found C+ to be
underluminous (Maiolino et al., 2015; Willott et al., 2015; Pentericci et al.,
2016; Bradač et al., 2017; Carniani et al., 2018), the ALPINE sample shows a
very consistent relation between C+ and total star formation, similar to
findings at lower redshifts (De Looze et al., 2014). Even more so, the
comparison of ALPINE data with measurement from the literature at higher
redshifts (Matthee et al., 2019; Harikane et al., 2018) suggests only a slow
(if any) evolution of the C+$-$SFR relation out to higher redshifts.

Figure 4: C+ vs. total SFR (from UV + far-IR) relation derived from the ALPINE
sample from Schaerer et al. (2020). Galaxies detected in far-IR are shown as
red squares. For galaxies not detected in far-IR (blue circles), the far-IR
luminosity is derived from the IRX$-\beta$ relation from Fudamoto et al.
(2020). C+ non-detections at $3\sigma$ are shown as black upper limits. The
filled purple stars show stacked measurements (four bins of $L_{{\rm C^{+}}}$
and two bins in redshift). The empty purple star shows a stack from robust
nondetections from Romano et al. (2022). The best fit (${\rm
log(L_{C^{+}}/L_{\odot})}=\alpha+\beta\times{\rm
log(SFR/[M_{\odot}\,yr^{-1}])}$ with $\alpha=6.61\pm 0.20$ and $\beta=1.17\pm
0.12$) is shown as a thick black line. The $z=$ 4–6 relation from ALPINE is
consistent with the relation derived from local galaxies (gray dashed line
with shaded region ($2\sigma$); (De Looze et al., 2014)). The predictions from
the semianalytical model from Lagache et al. (2018) (green dashed line) and
the observations at $z>5$ from Harikane et al. (2018) (green dotted line) are
also shown. Adapted from Ref. Schaerer et al. (2020).

###  3.3 SFR Density, Main-Sequence, and Dust Abundance across Cosmic Time

The data presented Section 3.1 suggest that a significant fraction of the UV
light is obscured in main-sequence galaxies. In this section, we present more
detailed results on the dust abundance and the implication on the total cosmic
SFR density.

Figure 5: Dust obscuration and total SFR density from the ALPINE sample. Left
Panels: IRX$-\beta$ relation (top) and total obscured fraction of SFR as a
function of stellar mass (bottom) (Fudamoto et al., 2020). Individual ALPINE
galaxies at $z$$\sim$$4.5$ and $z$$\sim$$5.5$ are indicated in blue and red
circles (and limits). Stacked measurements in bins of $\beta$ and stellar
mass, respectively, are shown with filled squares. On the IRX$-\beta$ diagram,
we also show SMC-like dust (short-dashed line; (Prevot et al., 1984)), the
starburst relation (solid line; (Meurer et al., 1999)) and the updated local
relation (dotted line; (Overzier et al., 2011)), and the relation by Reddy et
al. (2018) for $\beta_{0}=-2.62$ (long-dashed line). On the obscured fraction
vs. stellar mass diagram, we also show the REBELS sample (only with ALMA
redshift, teal stars; (Inami et al., 2022)) and the $250\,{\upmu\rm{m}}$ data
from Whitaker et al. (2017) at $z$ = 0–2.5 using the far-IR template from Dale
and Helou (2002) (solid line) and Béthermin et al. (2015) or Magdis et al.
(2012) (dashed line) for the calculation of the total SFR. Figures adapted
from Fudamoto et al. (2020). Right Panel: Total SFR density as a function of
redshift derived from the ALPINE blind sample (black circles and red squares;
(Gruppioni et al., 2020)) and stacked far-IR measurements (red symbols;
(Khusanova et al., 2020)). We also include the result from serendipitous C+
detections that show a higher density because of clustering with the ALPINE
main targets (Loiacono et al., 2021). Measurements from the MORA 2mm ALMA
survey (far-IR SFRs only) from Casey et al. (2021) are shown as gray stars.
The predictions from Illustris TNG (green line (Pillepich et al., 2018)) and
Béthermin et al. (2017) (dashed line) are also shown. The total SFR density
fits for ${\rm SFR_{IR}}$ and ${\rm SFR_{UV+IR}}$ data from the Madau and
Dickinson (2014) review are shown as orange and blue swaths, respectively.
Adapted from Ref. Gruppioni et al. (2020).

The fraction of dust-attenuated and -obscured star formation in the ALPINE
sample is studied by Fudamoto et al. (2020) using two diagnostic diagrams,
namely, the IRX$-\beta$ and the IRX$-$M∗ relations. The measurements of the UV
continuum slope ($\beta$), UV luminosity, and stellar mass are described in
detail in Faisst et al. (2020). In brief, the quantities are determined from
the UV to optical best-fit SED to the broad and narrowband photometry of the
galaxies. The $\beta$ slope ($f_{\lambda}\propto\lambda^{\beta}$) is measured
between a rest-frame wavelength of $1300\,{\rm\text{\AA}}$ and
$2300\,{\rm\text{\AA}}$, consistent with previous studies (e.g., (Bouwens et
al., 2016; McLure et al., 2018)). The total far-IR luminosity was determined
from the ALMA continuum data by using the SED template derived in Béthermin et
al. (2020) (see also Section 3.2). The ALMA far-IR continuum images of the
ALPINE galaxies are then stacked in bins of $\beta$ and stellar mass to obtain
an average of the IRX$-\beta$ and IRX$-$M∗ relations.

The left panels of Figure 5 show the IRX$-\beta$ relation as well as a
slightly modified version of the IRX$-$M∗ relation, namely, the relation
between the fraction of dust-obscured SFR and stellar mass, for two different
redshifts ($z$$\sim$$4.5$ and $z$$\sim$$5.5$). This analysis shows that the
IRX$-\beta$ relation obtained from ALPINE is generally below the Meurer et al.
(1999) relation, which is based on local starburst galaxies, suggesting a
steepening of the attenuation curve. This confirms suspicions of earlier
studies based on samples that are a factor of $10$ and smaller (Capak et al.,
2015; Barisic et al., 2017). Furthermore, the obscured fraction of star
formation is significantly lower ($65\%$ and $45\%$ at $z$$\sim$$4.5$ and
$z$$\sim$$5.5$, respectively) compared to galaxies at $z<3$ ($80\%$) at high
masses of 1–3 $\times 10^{10}\,{\rm M_{\odot}}$. For lower stellar masses, the
obscured fractions are statistically consistent. Altogether, this suggests a
rapid evolution of dust attenuation and dust properties in massive
(>$10^{10}\,{\rm M_{\odot}}$) galaxies between $z$$\sim$$6$ and the peak of
cosmic SFR density at $z$$\sim$2–3. Specifically, a steeper dust attenuation
curve could be a sign of dust produced by supernovae (SNe) (Maiolino et al.,
2004; Hirashita et al., 2005; Stratta et al., 2007; Gallerani et al., 2010).
Such a scenario is favored in young, star-forming galaxies due to the lack of
time for other dust production mechanisms to work (e.g., dust production from
Asymptotic Giant Branch (AGB) stars or dust growth in the ISM (Asano et al.,
2013; Dwek and Cherchneff, 2011; Todini and Ferrara, 2001; Nozawa et al.,
2003; Schneider et al., 2004)). However, further investigations are crucial to
definitively decipher the dust production mechanisms at these cosmic times.
Further, it is interesting that there is a large range of dust attenuation
values at $z=5$. This suggests a wide range of dust production or geometrical
effects.

The total cosmic SFR density is an important tool to constrain the evolution
of galaxies. It has been measured robustly below $z$ = 2–3, where
multiwavelength data (especially in the far-IR) are available. At higher
redshifts, the evolution of the SFR density is more uncertain due to the lack
of far-IR data to measure the total SFR and to include dust-obscured galaxies.
Khusanova et al. (2020) derives the first robust measurement of the total
cosmic SFR density at $z=$ 4–6 based on UV$+$ALMA multiwavelength data from
ALPINE. The detailed procedure of this measurement is described in the
respective paper. In brief, the total SFR density is obtained by integrating
over the full SFR function, which was derived from two different proxy density
distribution functions: the absolute UV ($M_{\rm UV}$) LF and the stellar mass
function. The total SFR density is then obtained by integration from 0.03–100
${\rm L_{*}}$ or $\log(M/{M}_{\odot})$ = 6.0–12.4. The right panel in Figure 5
shows the resulting SFR density function derived for the ALPINE galaxies (red
symbols). The red boxes show the derived SFR density from serendipitous far-IR
detections from (Gruppioni et al., 2020). The green box shows the SFR density
when including an overdensity of serendipitously detected C+ emitters
(Loiacono et al., 2021). The ALPINE measurements are slightly higher than the
prediction from Illustris TNG (Pillepich et al., 2018) and measurements from
Madau and Dickinson (2014), but in line with the measurements from Béthermin
et al. (2017). The contribution of galaxies to the dust-obscured SFR density
from the MORA $2\,{\rm mm}$ survey (Casey et al., 2021) are also shown.

###  3.4 Gas Reservoirs and Baryon Cycle at $z>4$

The measurement of the molecular gas content (or gas fraction, $M_{\rm
molgas}/(M_{\rm molgas}+M_{*})$) of galaxies as a function of cosmic time is
crucial to understand their progress in forming stars. Specifically, the 5–10
times higher specific SFRs (sSFRs) at early cosmic times compared to local
galaxies (Madau and Dickinson, 2014) require either more substantial gas
reservoirs or a higher star-formation efficiency in these galaxies. At the
same time, vigorous star formation is connected with outflows that enrich the
surrounding intergalactic medium (IGM) with processed chemical elements.

Figure 6: Left Panel: Molecular gas density as a function of redshift
(following closely the cosmic SFR density, see Figure 5). The measurement from
ALPINE from Yan et al. Yan et al. (2020) is indicated by the red box. Other
measurements from COLDz (hatched boxes; (Riechers et al., 2019)) and ASPECS
(filled and empty gray boxes; (Decarli et al., 2016, 2019)), together with
empirical models from (Liu et al., 2019) (green solid), Scoville et al. (2017)
(orange long-dashed), and Tacconi et al. (2018) (pink dotted) are also shown.
The semi-analytical model from Popping et al. (2019) is shown as a short-
dashed blue line. Right Panel: Redshift evolution of molecular gas mass
fraction of galaxies from $z$ =0–6. The curves show the same empirical and
semianalytical models as indicated on the left panel. Measurements at $z=4.6$
from ALPINE (Dessauges-Zavadsky et al., 2020) are shown in red (distinguishing
from C+ detected, far-IR detected, and measurements with dynamical mass).
Literature CO data at $z<4$ are shown as gray points (see Dessauges-Zavadsky
et al. (2020) for references), together with the far-IR SED stacks from
(hatched region Béthermin et al. (2015)). Large black crosses show the median
(with error on the mean and scatter) in $7$ redshift bins.

####  3.4.1 Gas Fractions, Depletion Times, and Large Range in Gas Properties

The gas content of galaxies has been measured commonly via CO emission (a
tracer of H2) out to $z$$\sim$$3$ (Carilli and Walter, 2013) and it is found
to increase with redshift, reflecting the increase in sSFR (Madau and
Dickinson, 2014). The measurement of the gas content of galaxies out to higher
redshift is challenging and has not been measured for large samples of typical
galaxies prior to ALPINE. Low-$J$ CO emission becomes increasingly more
difficult to observe at high redshifts because of surface brightness dimming,
lower metal content of the galaxies, and redshift itself. Furthermore, the
increasing cosmic microwave background temperature with redshift decreases the
contrast of the line (da Cunha et al., 2013). On the other hand, the
conversion of high-$J$ CO transitions to CO(1-0) requires knowledge of the CO
excitation stage and the gas density. In addition, even with state-of-the-art
millimeter facilities such as VLA or NOEMA, a detection of high-$J$ CO
emission becomes unfeasible for a large sample of galaxies. For understanding
the molecular gas content of high redshift galaxies, other tracers of
molecular gas have to be explored. Among these are the dust mass inferred from
an SED fit to the far-IR emission (Dale and Helou, 2002; Sajina et al., 2006;
Casey, 2012), the cold dust continuum measured in the Rayleigh–Jeans (RJ) tail
regime at $\lambda_{\rm rest}\approx 850\,{\upmu\rm{m}}$ (Scoville et al.,
2014, 2017), and the empirically measured relation between C+ and molecular
gas mass (Zanella et al., 2018; Liu et al., 2019; Madden et al., 2020).
Furthermore, using an estimate of stellar, dust, and dark matter mass inside a
given radius, dynamical mass estimates from kinematics can be used to
constrain gas masses (Solomon and Vanden Bout, 2005; Genzel et al., 2015). The
ALPINE sample provides galaxies with the necessary far-IR continuum and C+
line luminosity measurements; C+ kinematics; and more importantly, far-IR and
C+-LFs, to undertake the first comprehensive measurement of the gas content of
main-sequence galaxies in the post-reionization phase at $z=$ 4–6.

To put the molecular gas masses in global context, Yan et al. (2020) computed
the cosmic molecular gas density using the cosmic-volume-averaged C+
luminosity density at $z$$\sim$$5$. For the computation of the latter, the
derived C+ LF (Yan et al., 2020) was integrated down to $7\times 10^{7}\,{\rm
L_{\odot}}$, yielding $L_{{\rm C^{+}}}$$\sim$$1.2\times 10^{6}\,{\rm
L_{\odot}}$. Several previous studies (Zanella et al., 2018; Liu et al., 2019)
and the study based on the ALPINE sample by (see below; Dessauges-Zavadsky et
al. (2020)) have derived a linear ratio $\rm M_{molgas}/L_{{\rm
C^{+}}}~{}=~{}\text{15--60}\,M_{\odot}/L_{\odot}$. Using this ratio, Yan et
al. (2020) derived the molecular gas mass density $\rho_{\rm
molgas}~{}=~{}\text{(2--7)}\times 10^{7}\,{\rm M_{\odot}\,pc^{-3}}$ at $z\sim$
4–6. At a $2\sigma$ and 95% confidence level, the estimated $\rho_{\rm
molgas}=\text{(1--14)}\times 10^{7}\,M_{\odot}\,{\rm Mpc^{-3}}$. The evolution
of the cosmic molecular gas mass density (left panel in Figure 6) closely
follows the evolution of the cosmic SFR density (see right panel of Figure 5).
Individual molecular gas masses of the ALPINE galaxies are calculated in
different ways using the abovementioned ingredients. Dessauges-Zavadsky et al.
(2020) show promisingly that molecular gas masses derived from the RJ dust
continuum, C+ emission, and dynamical mass agree well with each other within
the measurement uncertainties (approx. a factor of two). The RJ emission at
rest-frame $850\,{\upmu\rm{m}}$ was calculated using a far-IR SED template
with a temperature of $\sim$$40\,{\rm K}$ normalized to the ALPINE/ALMA
measurement at rest-frame $150\,{\upmu\rm{m}}$ (see Section 3.1.2 for more
details). The dynamical mass was calculated for a subset of $18$ nonmerger
galaxies classified by Le Fèvre et al. (2020) with C+ emission at S/N$>5$ and
with C+ halo size measurement from Fujimoto et al. (2020). Figure 6 shows the
gas fraction and depletion times at $z=$ 4–6 derived by Dessauges-Zavadsky et
al. (2020) in comparison to measurement from CO emission at lower redshifts
from the literature (Saintonge et al., 2011; Béthermin et al., 2015; Liu et
al., 2019). Overall, the rise of the molecular gas fraction traces the
evolution of the sSFR (e.g., (Faisst et al., 2016; Khusanova et al., 2020));
it increases with redshift up to $z$$\sim$3–4 (reaching a value of
$\sim$$63\%$ at $z$$\sim$$5$) and then flattens out at earlier cosmic times.
Individual measurement of gas masses for ALPINE galaxies show a large scatter,
which is likely the physical reason for the large range in the measurement of
the cosmic molecular gas mass density at $z$$\sim$$5$ (indicated by the
vertical size of the boxes in Figure 6, left panel). Furthermore, the study
finds a continuous decline in the molecular gas depletion time scale ($t_{\rm
depl}=M_{\rm gas}/{\rm SFR}$)with the total SFR derived from the infrared and
UV SFRs. of a factor of 2–3 from $z=0$ to $z=6$, suggesting a mild enhancement
of star-formation efficiency towards high redshifts. This trend is in
agreement with the extrapolation of the parametrization by Scoville et al.
(2017) based on $z<4$ as well as Tacconi et al. (2018), but significantly
shallower than $(1+z)^{-1.5}$, which is predicted by semianalytical and
cosmological simulations based on the framework of the bathtub model (e.g.,
(Davé et al., 2011, 2012; Genel et al., 2014; Lagos et al., 2015)). Dessauges-
Zavadsky et al. (2020) also show that the depletion time depends on the sSFR
(which has been shown to be true also at lower redshifts, e.g., (Saintonge et
al., 2011)), which may be the reason for the change of depletion time across
cosmic time. Still, compared to the upsizing of the gas reservoirs, the
increase in star-formation efficiency seems to play a minor role in reaching
the high average SFRs at high redshifts, in agreement with the study by
Scoville et al. (2017).

The interpopulation scatter in gas abundances (from $20\%$ to $90\%$) and
depletion times (from $10^{8}\,{\rm yr}$ to $10^{9}\,{\rm yr}$) may be a
result of the interconnection between gas abundance, depletion timescale, and
other physical properties, as well as the evolutionary stage of galaxies such
as the location on the star-forming main-sequence, metal and dust content, or
environment. Such a range of properties is also reflected in the dust
attenuation properties (see Section 3.3).

####  3.4.2 Enrichment of the IGM at $z$$\sim$4–6

The comparison of gas content and depletion time to models such as the bathtub
model indicates that, not surprisingly, galaxies are not closed boxes but,
instead, are governed by complex baryon cycles including inflows and outflows.
Constraining this cycle is important for understanding the evolution of
galaxies and, closely connected with this, the enrichment of the IGM
surrounding them. An extended dust continuum and C+ halo around high-redshift
galaxies indeed suggests chemical enrichment of the IGM. This was found in
multiple $z>4$ galaxies (Carniani et al., 2018; Fujimoto et al., 2019) and the
ALPINE sample allows for the first time a statistical study of extended C+
halos. As shown by Fujimoto et al. (2020), the C+ halo extent commonly exceeds
the UV size of the galaxies by factors of 2–3 or more for galaxies with
increasing stellar mass. Furthermore, about $30\%$ of (isolated) galaxies have
a C+ halo component extending more than $10\,{\rm kpc}$, at typical UV sizes
of 1–2 kpc (Fujimoto et al., 2019). The trend of increasing C+ to UV size
ratio with increasing stellar mass and SFR can be explained by star-formation-
driven outflows (cf. simulations by Maiolino et al. (2015)), although a
selection bias cannot be ruled out currently. Deeper observations with ALMA
will be needed to confirm this scenario.

On the other hand, Ginolfi et al. (2019) suggest direct evidence of star-
formation-driven outflows by carefully stacking the C+ spectra of isolated
ALPINE galaxies. This study shows an increase in broad wings ($\sim$500–700
km/s) of the C+ spectra for the most star-forming galaxies in the ALPINE
sample. This trend is strengthened by a bootstrapping analysis. The calculated
mass loading factor (close to unity) is similar to the one of local star-
forming galaxies but below the one expected from local AGN (which is
approximately $5$ times higher). This suggests that, compared to AGN feedback,
star-formation-driven outflows are likely a subdominant mechanism for rapid
quenching of normal galaxies in the early Universe. The contribution of AGN to
the physics of the most massive ALPINE galaxies is still an open question
(Barchiesi et al. in prep.).

From these studies, there is strong evidence that star-formation-driven
outflows may play an important role in the chemical enrichment of the IGM
surrounding the galaxies in the early Universe. In addition, galaxy
interactions can contribute to the enrichment, as shown by the triple-merger
galaxy system at $z$$\sim$$4.57$ presented in Ginolfi et al. (2020), showing
extended C+ emission covering the IGM between the merging components (see
Capak et al. (2015) for another example at $z$$\sim$$5.5$ of a triple-merger).
The IGM enrichment via outflows from stellar feedback and galaxy interactions
suggested from these observations is consistent with predictions from recent
simulations (see, e.g., (Oppenheimer and Davé, 2006; Oppenheimer et al., 2010;
Bournaud et al., 2011; Pallottini et al., 2014; Nelson et al., 2015; Anglés-
Alcázar et al., 2017; Hani et al., 2018; Graziani et al., 2020)); together
with galaxy–galaxy interactions, they are largely responsible for the chemical
enrichment of the IGM surrounding the galaxies in the early Universe. The
triple-merger galaxy system at $z$$\sim$$4.57$ presented in Ginolfi et al.
(2020) is only one example showcasing this scenario by exhibiting extended C+
emission covering the IGM between the merging components (see Capak et al.
(2015) for another example at $z$$\sim$$5.5$ of a triple-merger).

###  3.5 Contribution of Mergers to Mass Assembly and the Emergence of
Rotators

Understanding how galaxies grow at different cosmic times is one of the
current outstanding questions. Galaxies can increase their mass via various
processes such as internal star formation, the accretion of gas (usually also
including minor merging events), and major mergers. It is thought that,
specifically at lower redshift, gas accretion and in situ star formation are
the dominant avenues of mass assembly, with major mergers only playing a
subdominant role (Zepf et al., 2008; Conselice, 2014). On the other hand,
several studies suggest mergers to become more important for galaxy evolution
at higher redshifts (Kampczyk et al., 2013). This is in line with various
simulations suggesting an increase in merger rate towards the early universe
(Gottlöber et al., 2001; Rodriguez-Gomez et al., 2015).

The measurement of the number of major mergers is not trivial. Next to high-
resolution imaging, kinematic information (such as about the velocity
difference of the merging components) is necessary. Furthermore, approaches
focusing on the rest-frame UV or even optical may miss dust-obscured merging
components, which leads to an underestimation of the true merger rates. As
shown in the previous sections, dust obscuration may be significant even at
$z>4$. The triple-merger system examined in Ginolfi et al. (2020) is a prime
example of such a dust-obscured case that would be missed in UV/optical
imaging. The combination of ALMA and sub-kpc resolution HST imaging can
mitigate these issues. Importantly, C+ emission provides kinematic information
of UV and optically dust-obscured merger components (see e.g., (Jones et al.,
2021; Romano et al., 2021)).

The ALPINE sample allows for the first time a statistical analysis of the
merger fraction shortly after the Epoch of Reionization. The galaxies are
robustly categorized in mergers and nonmergers (e.g., rotators or dispersion-
dominated systems) using the full ALMA C+ cube in position–velocity space via
a morpho-kinematic approach similar to studies of H$\alpha$ at lower redshifts
(e.g., (Epinat et al., 2008; Law et al., 2009)) and by fitting a tilted ring
model (see also (Kamphuis et al., 2015; Jones et al., 2017)). The
classification procedures of both methods are detailed in Le Fèvre et al.
(2020) and Jones et al. (2021). Of the $75$ C+-detected ALPINE galaxies,
Romano et al. (2021) identified $23$ of them as major merger systems in the
mass range of $\log(M/{M}_{\odot})$ = 9–11 with a mass ratio less than $4$, a
velocity difference between the components of less than $500\,{\rm km/s}$, and
a physical distance of less than $20\,{\rm kpc}$. The authors computed the
fraction of major mergers in this sample ($\sim$$45\%$ and $\sim$$35\%$ for
$z$$\sim$$4.5$ and $z$$\sim$$5.5$, respectively). These values are a factor of
two higher than at $z$ = 2–3 ($\sim$$20\%$) and other studies at the same
redshift using only HST imaging (e.g., (Conselice and Arnold, 2009)). The
latter could highlight an incompleteness due to missing dust-obscured merger
components in the UV and optical data. The computed fraction of major mergers
is consistent with that predicted by the Evolution and Assembly of Galaxies
and their Environments (EAGLE) hydrodynamical simulation (Schaye et al.,
2015). The major merger fraction of 35–45% derived from the ALPINE sample by
Romano et al. (2021) suggests that major mergers could play a significant role
in galaxy evolution at these redshifts. To estimate the contribution to the
galaxy mass assembly, a merger timescale has to be assumed, which comes with
significant uncertainty. Assuming typical merger timescale representations by
Kitzbichler and White (2008), Jiang et al. (2014), and Snyder et al. (2017),
the contribution of major mergers to the SFR density at $z=$ 4–6 varies from
less than $5\%$ (for Kitzbichler et al.) to nearly $30\%$ (for Snyder et al.).

The recent studies by Le Fèvre et al. (2020) and Jones et al. (2021) picture
the morphological diversity of the ALPINE sample at $z=$ 4–6. Specifically,
next to the approximately $40\%$ interacting galaxies, about $30\%$ are
classified as dispersion-dominated systems and about $\sim$$15\%$ are found to
be rotators. The rotators are of special interest as they provide constraints
on the dark matter mass of galaxies and also suggest recent relatively smooth
mass growth in a cold-gas-accretion-dominated scenario. Rotators have been
characterized at $z<4$ mainly through Integral Field Unit (IFU) observations
of the H$\alpha$ emission line (e.g., (Epinat et al., 2008; Förster Schreiber
et al., 2009; Gnerucci et al., 2011)), but also via C+ emission for a handful
of bright starburst and quasars at higher redshifts (e.g., (Jones et al.,
2017; Pensabene et al., 2020; Tadaki et al., 2020; Fraternali et al., 2021;
Lelli et al., 2021; Rizzo et al., 2020, 2021)). Next to a main-sequence galaxy
at $z=4.2$ (Neeleman et al., 2020) and two galaxies at $z>6$ (Smit et al.,
2018; Bakx et al., 2020), the ALPINE sample complements these studies with
typical main-sequence galaxies at $z=$ 4–6. Within the ALPINE sample, Jones et
al. (2021) find rotators with rotational velocities between 50–250 km/s and
extended rotational structures commonly less than $7\,{\rm kpc}$ (although
some out to $\sim$$10\,{\rm kpc}$) (see also (Fujimoto et al., 2020)). The
flattening of the rotation curves at a radius of $\sim$1–2 kpc suggest
dominating baryon fractions over dark matter. However, strong conclusions
cannot be drawn because of insufficient spatial resolution of the ALMA
observations. A spatial resolution of at least $\sim$$1\,{\rm kpc}$ (or
0.1–0.2′′) at a high sensitivity out to large radii ($\sim$7–10 kpc) is
necessary for definite answers (see Figure 7 in (Jones et al., 2021)).

##  4 Discussion

ALPINE is a survey that is well-placed to study the ramp-up of galaxy
evolution at redshifts of $z=$ 4–6 and has led to many important science
results, as described in the previous sections. While past studies have
focused on bright sub-mm galaxies or quasars, mostly due to sensitivity
limitations, ALPINE has broadened the view to more typical main-sequence star-
forming galaxies in the post-reionization era.

The large sample size allowed the first statistical comparison of C+ emission
density of a post-reionization sample and the local Universe (Yan et al.,
2020). Compared to the currently best local comparison sample (Hemmati et al.,
2017), galaxies at $z=$ 4–6 show statistically an excess of C+ emission at the
luminous end of the C+ luminosity function (Yan et al., 2020). Since C+ is a
common cooling line in star-forming galaxies, the excess of luminous C+
emitters in high-redshift main-sequence galaxies is not surprising due to
their overall enhanced rates of (specific) star-formation compared to main-
sequence galaxies at lower redshifts. Loiacono et al. (2021) found that
clustering of C+ emitters adds a significant uncertainty to the measured C+
emission density. Specifically, it is intriguing that $7$ out of $8$
unambiguously identified serendipitous $z>4$ C+ emitters are within less than
$750\,{\rm km/s}$ ($\Delta z<0.015$) in velocity space and
<$17^{\prime\prime}$ in projected radiusRadius from phase center where primary
beam attenuation is <$90\%$. of the main target (Loiacono et al., 2021). This
suggests significant spatial clustering of C+ emitters in the early Universe
and may be used to inform cosmological structure formation models in the
future.

The excess of strong C+ emitters at high redshifts may be related to their
increased star formation. This is mainly motivated by the strong correlation
between C+ and star formation found in galaxy samples up to $z$$\sim$$2$
(e.g., (Pineda et al., 2013; Herrera-Camus et al., 2015; De Looze et al.,
2011, 2014)). Although verified at lower redshifts, it was far from clear how
well C+ traces star formation at early cosmic epochs. Several studies
suggested a C+ deficit in high-$z$ galaxies (e.g., (Maiolino et al., 2015;
Willott et al., 2015; Pentericci et al., 2016; Bradač et al., 2017; Carniani
et al., 2018)), resulting in a large scatter in the C+$-$SFR relation.
Furthermore, the different places of origin of C+ (from H II regions, the
diffuse neutral and ionized ISM, or photo-dissociation regions) could further
be relevant for its connection to physical properties of the galaxies. The
ALPINE sample emphasized the strong relation between C+ and total SFR (i.e.,
obscured and unobscured) and also verified its similarity to local galaxies
(Schaerer et al., 2020). However, there are still open questions. As mentioned
several times in this article, the ALPINE galaxies reside on the more massive
end of the star-forming main-sequence and are also suggested to be already
substantially metal-enriched (Faisst et al., 2020). Their ISM properties are
therefore not substantially different from their descendants at lower
redshifts (see also (Vanderhoof et al., 2022)). A way to remedy this is to
build up a statistical sample of low-mass (likely lensed) galaxies at
$z$$\sim$4–6 to study C+ physics in truly low-metallicity environments.
Furthermore, carrying out follow-up observations with ALMA of other far-IR
lines (such as [N II] at $122\,\upmu{\rm m}$ or $205\,\upmu{\rm m}$) would
allow to statistically pinpoint the dominant origin of C+ emission in these
galaxies (see observations and analyses by (Pavesi et al., 2016, 2019)).
Cospatial resolution-matched observations of optical emission (such as
H$\alpha$) from JWST and C+ from ALMA would further help to investigate this
issue.

As the ALPINE galaxies are rather mature in terms of their stellar mass and
ISM properties, it might not be very surprising to find a relatively large
dust attenuation in this population. The most massive galaxies in the sample
have a similar fraction of dust-obscured star formation as galaxies at the
peak of cosmic SFR density (Fudamoto et al., 2020). The measurement of dust
mass at this early epoch places constraints on the dust production mechanisms
and chemical evolution models. The analysis of ages and dust masses by Pozzi
et al. (2021) draws the picture that these galaxies are likely the progenitors
of bulge-dominated spiral or elliptical galaxies at lower redshifts. The dust
production has to occur quickly, in line with the evolution of proto-spheroids
(Calura et al., 2017). Dust production by supernovae on short time scales
provide the most likely scenario for the high dust masses of these $z=$ 4–6
galaxies (Gall and Hjorth, 2018; Burgarella et al., 2022). However, it is
interesting that current models have difficulties to reproduce the high dust-
mass to stellar-mass ratios ($\geq$$0.03$) of young $z$$\sim$5–6 galaxies with
high sSFRs ($\geq 40\,{\rm Gyr^{-1}}$) (Burgarella et al., 2022). This becomes
even more intriguing with the discovery of entirely optically dark galaxies at
$z$$\sim$$6.7$ and $z$$\sim$$7.4$ (Fudamoto et al., 2021; Inami et al., 2022)
from the REBELS sample (the $z>6$ continuation of ALPINE, see survey overview
described in Bouwens et al. (2021)), although there could be significant
uncertainties in the stellar masses (hence, the dust to stellar mass ratios)
of these galaxies (Sommogivo et al. in prep.). Such dust-obscured galaxies at
high redshifts challenge current dust formation models and at the same time
suggest that rest-UV observations are still missing a substantial amount
($\sim$10–25%) of galaxies contributing to the cosmic SFR density at $z>6$
(Fudamoto et al., 2021).

Several studies have consistently found a continuous increase in sSFR of
galaxies out to $z$$\sim$$3$, based on robust, optical, and infrared-based
total SFR measurements (Ilbert et al., 2015). This trend was found to continue
at $z>3$, although there was no consensus on the steepness of the sSFR
increase. While some studies suggested a flattening (Bouwens et al., 2012;
Tasca et al., 2015; Davidzon et al., 2018), others found a more significant
increase (Faisst et al., 2016; Stark et al., 2013; de Barros et al., 2014),
which could be due to the use of different SFR tracers. The study by Khusanova
et al. (2020) provided the first robust measurement of star formation at
$z$$\sim$$5$ from ALMA and supports a flattening of the sSFR evolution. The
apparent inconsistency in slope is likely due to the use of different star-
formation indicators. For example, the study by Faisst et al. (2016) used
H$\alpha$ (derived from Spitzer colors) as tracer for star formation (hence,
sSFR) on short timescales ($\sim$$10\,{\rm Myrs}$) and found a steeper slope
(i.e., higher sSFR at a given redshift) than other studies using continuum-
based, $100\,{\rm Myr}$-averaged SFR measurements (e.g., from SED fitting or
far-IR SFR as in (Khusanova et al., 2020)). Short-term SFR measurement may be
significantly increased due to burstiness in the star-formation process at
high redshifts as suggested in Faisst et al. (2019), and thus, could explain
the higher sSFRs.

A higher gas fraction or higher star-formation efficiency could both play a
role in increasing the star-formation activity of $z>4$ galaxies. The results
from Dessauges-Zavadsky et al. (2020) on $z>4$ galaxies show that, compared to
low-$z$ galaxies, on average the gas fractions are increased by a factor of
$6$ ($10\%$ vs. $60\%$), while the depletion times (i.e., inverse star-
formation efficiency) are shorter by a factor of two ($1\,{\rm Gyr}$ vs.
$0.5\,{\rm Gyrs}$). The gas fraction traces closely the sSFR evolution in
shape (including flattening at $z>3$). The decrease in depletion time is
significantly less than that predicted by the “bathtub” model, in which main-
sequence galaxies lie in a quasi-equilibrium state (Bouché et al., 2010; Davé
et al., 2012; Lilly et al., 2013; Dekel and Burkert, 2014), but is consistent
with extrapolated CO measurements from (Tacconi et al., 2018) and the relative
change in Scoville et al. (2017) derived from RJ dust-continuum gas masses.
This suggests that $z$$\sim$$5$ galaxies (on the main-sequence) are not
significantly more efficient in forming stars than present-day galaxies (a
conclusion also obtained by Scoville et al. (2017)). Most of the redshift
evolution of star formation on the main sequence is therefore due to increased
gas reservoirs rather than higher star-formation efficiency. The latter,
however, may be more important in pushing galaxies at a given stellar mass and
redshift above the main-sequence, and so creating the observed starburst
population (Scoville et al., 2017; Silverman et al., 2015). The high gas
fraction and the slowly changing depletion times suggest that a significant
amount of gas is expelled from galaxies via outflows. As shown by (Ginolfi et
al., 2019), outflows are ubiquitous in highly star-forming $z>4$ galaxies and
may also be responsible for extended C+ halos (Fujimoto et al., 2020).

The contribution of mergers to the mass growth of galaxies at $z>4$ is still
not clear. Although ALPINE provides currently the best constraints of the
merger fraction thanks to dust-independent measurements from far-IR continuum
and C+ emission, the translation to a merger rate and mass assembly due to
major mergers depends strongly on the assumption of merger timescales.
Assuming current state-of-the-art estimates of merger timescales, the
contribution of major mergers to galaxy mass growth can be up to $30\%$.
Clearly, there is more work to be done to understand the merging
process—either through more sophisticated simulation work or enhanced
statistics on the merger stages (early, late mergers) in the population.

##  5 Conclusions

ALPINE has progressed our understanding of galaxy evolution by measuring the
dust and gas properties of galaxies at $z=$ 4–6 through sub-mm observations.
Most previous observations were based on luminous sub-mm galaxies or only a
handful of main-sequence galaxies at these redshifts. Furthermore, rest-frame
UV-based surveys only provide a limited view on the total galaxy population as
they miss significant amounts of dust-obscured galaxies. Combined with UV to
optical imaging and spectroscopic data, ALPINE is currently the largest
multiwavelength sample of main-sequence galaxies in the post-reionization era
and builds a basis for future observations. The new findings enabled by ALPINE
can be summarized as follows:

  * •

The demographics of $z$$\sim$$5$ C+-emitters, i.e., LF, is quantified for the
first time by the ALPINE main and serendipitous samples. This study shows
evidence of a possible much higher volume density of luminous C+-emitters at
$z$$\sim$$5$ than that of $z$$\sim$$0$.

  * •

The C+ emission is a good tracer of total SFR for $\log(M/{M}_{\odot})>9$
main-sequence galaxies at $z$$\sim$$5$. The relation is consistent with what
was found at lower redshifts (including local galaxies). This suggests no
significant evolution of the C+$-$SFR relation across cosmic time up to $z=6$
for main-sequence galaxies at this stellar mass.

  * •

Significant dust attenuation (45–65%) is found in the most massive
($\log(M/{M}_{\odot})>10$) galaxies, together with a significant number of
“UV/optical-dark” galaxies at $z=$ 4–6. This shows that UV-selected samples
miss a dusty population of galaxies even at $z>4$. The most massive galaxies
still challenge current models of dust production.

  * •

The gas fraction of main-sequence galaxies increases out to $z=6$ and follows
in shape the evolution of the sSFR. While the gas fraction evolves
significantly, the star-formation efficiency does not; hence, it is suggested
to contribute little to the increased star-formation activity in high-$z$
galaxies.

  * •

Outflows are ubiquitous in highly star-forming main-sequence galaxies and may
contribute to enriching the IGM with metals. Enriched IGM is also suggested by
extended C+ emission halos around the galaxies.

  * •

The morpho-kinematic selection of major mergers suggests an increase of galaxy
interactions at $z=$ 4–6. Adopting state-of-the-art estimates of merger
timescales, major mergers contribute at most $30\%$ to the galaxy mass
assembly at that epoch.

Despite these advances, future research is important to understand better the
details of this galaxy population and to connect it with galaxies in the Epoch
of Reionization. While the above results contribute to our understanding of
relatively massive and mature main-sequence galaxies, conclusions about the
fainter end of the population cannot be made with the current sample.
Extending the sample to lower stellar masses and (likely) less mature galaxies
(in terms of chemical enrichment) would provide an important comparison. For
example, does the C+$-$SFR relations still hold for such galaxies? Is star
formation more dominated by cold gas accretion or mergers in fainter galaxies?
A large sample of lensed galaxies at $z=$ 4–6 would serve as a promising
avenue to answer such questions. With enough magnification, ALMA observations
of the low-mass end of the main-sequence would not require significantly more
time. ALPINE builds a basis sample at this epoch, which can serve as “anchor”
for other studies at lower and higher redshifts. An important study to mention
in this context is REBELS, a high-redshift extension of ALPINE to measure C+
and far-IR continuum at $z>6.5$ using a spectral scan of galaxies with
photometric redshifts (Bouwens et al., 2021). A careful comparison between
REBELS and ALPINE would inform us about possible different galaxy evolution in
the Epoch of Reionization as well as shortly thereafter (see, e.g., (Sommovigo
et al., 2022)). In addition to existing surveys, a higher-resolution C+ and
dust-continuum follow-up with ALMA would further help us understand this
important epoch in galaxy evolution. Sub-kpc resolution observations would
reveal the location of star-formation as well as their gas velocity
dispersion. The comparison to studies at lower redshifts (Dessauges-Zavadsky
et al., 2019) would help us constrain star formation in general as well as the
role of feedback from stellar winds, SNe, and AGN on smaller spatial scales
than currently possible. The combination of deep high-resolution and shallow
low-resolution observations with ALMA would also significantly improve the
measurement of velocity curves to pin down the dark matter content of these
galaxies. The spatial sampling of current observations is not fine enough to
unambiguously determine between a flat or declining velocity curve out to
large radii (Jones et al., 2021). Finally, JWST will be the workhorse for
optical exploration of the galaxies, by providing, for example, resolved
metallicity measurements or stellar mass and optical dust maps. The paper by
Vanderhoof et al. (2022) already provides a taste of the possibilities that
arise by combining optical emission lines with UV and sub-mm measurements.

Project administration, Olivier LeFèvre; Writing – original draft preparation,
Andreas Faisst and Lin Yan; Writing – review and editing, Matthieu Béthermin,
Paolo Cassata, Miroslava Dessauges-Zavadsky, Yoshinobu Fudamoto, Michele
Ginolfi, Carlotta Gruppioni, Gareth Jones, Yana Khusanova, Francesca Pozzi,
Michael Romano, Daniel Schaerer, John Silverman and Brittany Vanderhoof. All
authors have read and agreed to the published version of the manuscript.

This research received no external funding. Not applicable.

Not applicable.

The data used in this article are available online at
https://cesam.lam.fr/a2c2s/data_release.php, accessed on May 31, 2022.

###### Acknowledgements.

We thank the reviewers for their useful comments, which greatly improved this
article. M.R. acknowledges support from the Narodowe Centrum Nauki
(UMO-2020/38/E/ST9/00077). G.C.J. acknowledges ERC Advanced Grant 695671
“QUENCH” and support by the Science and Technology Facilities Council (STFC).
YK acknowledges the support by funding from the European Research Council
Advanced Grant ERC–2010–AdG–268107–EARLY. This paper makes use of the
following ALMA data: ADS/JAO.ALMA#2017.1.00428.L. ALMA is a partnership of ESO
(representing its member states), NSF (USA) and NINS (Japan), together with
NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in
cooperation with the Republic of Chile. The Joint ALMA Observatory is operated
by ESO, AUI/NRAO and NAOJ. This research made use of Astropy
(http://www.astropy.org, accessed on May 31, 2022), a community-developed core
Python package for Astronomy (Astropy Collaboration et al., 2013, 2018). We
would also like to recognize the contributions from all of the members of the
COSMOS Team who helped in obtaining and reducing the large amount of
multiwavelength data that are now publicly available through IRSA at
http://irsa.ipac.caltech.edu/Missions/cosmos.html, accessed on May 31, 2022.
This article is dedicated to the memory of Olivier Le Fèvre, PI of the ALPINE
survey. The authors declare no conflict of interest. [custom] References

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