11institutetext: Departamento de Fisica Teorica, Modulo 8, Facultad de
Ciencias, Universidad Autonoma de Madrid, 28049 Madrid, Spain
11email<EMAIL_ADDRESS>22institutetext: CIAFF, Facultad de Ciencias,
Universidad Autonoma de Madrid, 28049 Madrid, Spain 33institutetext:
Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo
113-0033, Japan 44institutetext: Kavli Institute for the Physics and
Mathematics of the Universe (WPI), UT Institute for Advanced Study, The
University of Tokyo, Kashiwa, Chiba 277-8583, Japan 55institutetext: Research
Center for the Early Universe, School of Science, The University of Tokyo,
7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan 66institutetext: Universität
Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik,
Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany 77institutetext: Universität
Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, INF
205, 69120, Heidelberg, Germany

# Redshift-dependent galaxy formation efficiency at z=5-13 in the FirstLight
Simulations

D. Ceverino 1122 Y. Nakazato 33 N. Yoshida 334455 R. S. Klessen 6677 S. C. O.
Glover 66

(Received Month day, year; accepted Month day, year)

###### Abstract

Context. Current models of the formation of first galaxies predict low masses
and faint objects at extremely high redshifts, $z\simeq 9-15$. However, the
first observations of this epoch indicate a higher-than-expected number of
bright (sometimes massive) galaxies.

Aims. Numerical simulations can help to elucidate the mild evolution of the
bright end of the UV luminosity function and they can provide the link between
the evolution of bright galaxies and variations of the galaxy formation
efficiency across different redshifts.

Methods. We use the FirstLight database of 377 zoom-in cosmological
simulations of a mass-complete sample of galaxies. Mock luminosities are
estimated by a dust model constrained by current observations of an evolution
of the $\beta$-MUV relation at high-z.

Results. FirstLight contains a high number of bright galaxies, M${}_{\rm
UV}\leq-20$, consistent with current data at $z=6-13$. The evolution of the UV
cosmic density is driven by the evolution of the galaxy efficiency and the
relation between MUV and halo mass. The efficiency of galaxy formation
increases significantly with redshift at a fixed halo mass because galactic
halos at extremely high redshifts convert gas into stars at a higher rate than
at lower redshifts. The high gas densities in galaxies at $z\geq 9$ enable
these high efficiencies. Our simulations predict higher number densities of
massive galaxies, $M_{*}\simeq 10^{9}\ M_{\odot}$, than other models with
constant efficiency.

Conclusions. Cosmological simulations of galaxy formation with self-consistent
models of star formation and feedback can reproduce the different regimes of
galaxy formation across cosmic history.

###### Key Words.:

Galaxies: formation – Galaxies: evolution – Galaxies: high-redshift

##  1 Introduction

The formation of the first galaxies marks the end of the cosmic dark ages and
the beginning of cosmic dawn. The Universe during this first-light epoch was
dense, mostly neutral and pristine. The conditions for galaxy and star
formation were very different than at later times (Abel et al., 2002; Bromm et
al., 2002; Yoshida et al., 2008; Klessen & Glover, 2023). Thanks to the brand
new James Webb Space Telescope (JWST), we are now getting a first glimpse of
this epoch.

The most surprising result from JWST is the higher-than-expected number of
bright (sometimes massive) galaxies observed at extremely high redshifts,
$z=9-15$ (Naidu et al., 2022; Castellano et al., 2022; Adams et al., 2023;
Atek et al., 2023; Donnan et al., 2023; Harikane et al., 2023; Pérez-González
et al., 2023; Leung et al., 2023; Hainline et al., 2023; Casey et al., 2023;
Finkelstein et al., 2023; Yan et al., 2023). These galaxies are bright in the
rest-frame UV, M${}_{\rm UV}<-20$, and they are relatively massive,
$M_{*}=10^{8}-10^{9}\ M_{\odot}$, for that early epoch. As a result, both
cosmic UV and mass density decrease gently with redshift and this pushes the
formation of first galaxies to even higher redshifts. These observations,
although uncertain, challenge our understanding of the growth of galaxies at
these early times.

Several solutions have been proposed. For example, UV variability due to
bursts of star formation (SF) could impact the bright-end of the UV luminosity
function (UVLF) at these high redshifts (Shen et al., 2023; Sun et al.,
2023a). However, it is not clear whether the necessary degree of burstiness is
consistent with the SF histories of these galaxies. Mason et al. (2023)
similarly argue that current observations are biased towards the most extreme
star-forming galaxies for a given halo mass. This highlights the need for
deeper observations of galaxies at $z>9$. If dust attenuation is negligible at
high-z, UV bright galaxies can be more abundant than expected (Ferrara et al.,
2023; Tsuna et al., 2023). A related solution involves the evolution of the
initial mass function (IMF). A top-heavy IMF due to Pop III stars can boost
the UV luminosities by a factor of a few (Yung et al., 2023, 2024). However,
metallicity increases quickly after the first supernovae (SN) explosions and
these SN shells produce dust in short time-scales (Leśniewska & Michałowski,
2019). Therefore, the relatively massive galaxies observed by JWST should also
host significant amounts of metals and dust. Some of these stellar mass
estimates show a 3-$\sigma$ tension with the $\Lambda$CDM scenario, but this
does not necessarily falsify the current paradigm (Lovell et al., 2023).
Instead, better mass estimates from photometry fitting are needed to constrain
complex SF histories and total stellar masses.

The intrinsic UV luminosities of these galaxies are related to their star
formation rates (SFRs) and galaxy growth. The fuel for SF is provided mainly
by gas accretion into galaxies (Dekel et al., 2009). At a first approximation,
this mass accretion is regulated by the halo growth (Bouché et al., 2010;
Lilly et al., 2013; Dekel et al., 2013). We can therefore define a galaxy
formation efficiency as the ratio between stellar and halo growth. This
definition excludes the growth of the gaseous component (Dekel et al., 2013),
as these UV luminosities mostly trace stellar light. In principle this
efficiency may vary with mass and redshift, depending on the particular
conditions of the galaxy/halo assembly. A higher efficiency at extremely high
redshifts could explain the excess of UV-bright galaxies at $z\geq 9$. Dekel
et al. (2023) propose a scenario in which stellar feedback from massive stars
is not able to regulate the SF process in massive galaxies at high-z. In the
Feedback Free Bursts (FFB) model, the SF efficiency is higher than in
starbursts at lower redshifts. Li et al. (2023) provides predictions that can
be compared with current observations.

Cosmological simulations that predict self-consistently the efficiency of
feedback need to resolve the small scales where mass, energy and momentum are
injected into the interstellar medium (Ceverino & Klypin, 2009; Fichtner et
al., 2024). Only zoom-in simulations resolve the expansion of over-pressured
bubbles that merge into galactic-scale outflows. However, most of these
simulations only sample a few regions (O’Shea et al., 2015; Ma et al., 2018;
Katz et al., 2019; Pallottini et al., 2019) and therefore it is difficult to
make predictions of the overall galaxy population. The FirstLight database
(Ceverino et al., 2017a, 2018) is a mass-complete sample of zoom-in
simulations that allows population-averaged statistics with 10-20 pc
resolution. For example, Ceverino et al. (2018) characterise the typical SF
bursts at these high redshifts, using more than 1000 individual starbursts.

A subsample of the FirstLight simulations shows that the stellar-to-halo mass
relation evolves by a factor 3 between $z=6$ and $z=10$ for a fixed halo mass
around $M_{\rm vir}\sim 10^{10}{\rm M}_{\odot}$ (Ceverino et al., 2017a). This
evolution is related to the galaxy formation efficiency. In this paper we
extend that relation to higher masses and redshifts. We investigate whether
the FirstLight simulations with a diverse feedback model
(thermal+radiative+kinetic) is able to reproduce the JWST observations of
bright galaxies at $z\geq 9$ as well as previous HST observations at lower
redshifts, $z\simeq 6$. This paper also links the origin of the evolution of
the UVLF with a redshift-dependent galaxy formation efficiency. The outline of
this paper is as follows. Section §2 summarises the FirstLight simulations.
Section §3 computes the UV luminosity, taking into account a redshift-
dependent dust attenuation model. Section §4 provides the main findings,
Section §5 discusses the results and Section §6 provides a summary and a
general conclusion.

Figure 1: Constrained relations between the UV continuum slope, $\beta$, and
the absolute UV magnitude at $z=6$ (left) and $z=9$ (right). Small crosses
represent intrinsic values. Points represent dust-attenuated values. The solid
black lines fit observations by Bouwens et al. (2014) at $z=6$ and by Atek et
al. (2023) at $z\geq 9$. Grey dashed and dash-dotted lines show models by
Vijayan et al. (2021) and Kannan et al. (2022) that fail to reproduce these
observations.

##  2 The FirstLight Simulations

The FirstLight simulations are multi-object, zoom-in cosmological simulations
of a mass-complete sample of galaxies. The initial conditions are first
described in Ceverino et al. (2017a). The suite is composed by three
cosmological boxes. The 10-Mpc and 20-Mpc samples contain all halos within
these volumes with a maximum circular velocity, V${}_{\rm max}>50\,{\rm
km}\,{\rm s}^{-1}$ and V${}_{\rm max}>100\,{\rm km}\,{\rm s}^{-1}$
respectively at $z=5$. Similarly, the 40-Mpc box contains galaxies with
V${}_{\rm max}>180\,{\rm km}\,{\rm s}^{-1}$. Overall, the FirstLight database
includes 377 galaxies.

The simulations are performed with the $N$-body+Hydro ART code (Kravtsov et
al., 1997; Kravtsov, 2003; Ceverino & Klypin, 2009; Ceverino et al., 2014,
2017a). Gravity and hydrodynamics are solved by an Eulerian, adaptive mesh
refinement (AMR) approach. The code includes astrophysical processes relevant
for galaxy formation, such as gas cooling by hydrogen, helium and metals.
Photoionization heating uses a redshift-dependent cosmological UV background
with partial self-shielding.

Star formation and feedback (thermal+kinetic+radiative) models are described
in Ceverino et al. (2017a). In short, star formation is assumed to occur at
densities above a threshold of 1 cm-3 and at temperatures below $10^{4}$ K.
The code implements a stochastic star formation model that scales with the gas
free-fall time (Schmidt, 1959; Kennicutt, 1998). In addition to thermal energy
feedback, the simulations use radiative feedback, as a local approximation of
radiation pressure. This model adds non-thermal pressure to the total gas
pressure in regions where ionizing photons from massive stars are produced and
trapped. The model of radiative feedback is named RadPre_IR in Ceverino et al.
(2014) and it uses a moderate trapping of infrared photons. The kinetic
feedback model also includes the injection of momentum coming from the
(unresolved) expansion of gaseous shells from supernovae and stellar winds
(Ostriker & Shetty, 2011). More details can be found in Ceverino et al.
(2017a), Ceverino et al. (2014), Ceverino et al. (2010), and Ceverino & Klypin
(2009).

For the 10 and 20 Mpc boxes, the DM particle mass resolution is
$m_{\mathrm{DM}}=10^{4}\ {\rm M}_{\odot}$ and the minimum mass of star
particles is $10^{2}\ {\rm M}_{\odot}$. The maximum spatial resolution is
between 8.7 and 17 proper pc (a comoving resolution of 109 pc after $z<11$).
For the 40-Mpc box, the spatial and mass resolution are two and eight times
lower respectively.

Previous papers using this database predict rest-frame spectral energy
distributions (SEDs), and emission from visible (Ceverino et al., 2019, 2021)
and far-infrared (Nakazato et al., 2023) lines. In addition, FirstLight
predicts a weak evolution of the mass-metallicity relation at $z\geq 5$
(Langan et al., 2020), consistent with current findings (Curti et al., 2023;
Venturi et al., 2024).

##  3 Dust attenuation and evolution of the $\beta$-MUV relation

Figure 2: Evolution of the UV luminosity function from $z=6$ to $z=13$ (blue
regions). JWST observations are marked by blue circles (Harikane et al.,
2023), blue squares (Finkelstein et al., 2023), red circles (Bouwens et al.,
2022), and red squares (Yan et al., 2023). Pre-JWST observations are shown by
black lines (Bouwens et al., 2021). The fiducial models by Yung et al. (2023)
(dashed lines) and Mauerhofer & Dayal (2023) (dash-dotted lines) fail to
reproduce JWST observations at $z\geq 9$.

The rest-frame UV luminosities can be affected by dust attenuation. This
reduces the observed flux but also modifies the UV slope, $\beta$. In order to
compare to observations, we include a dust attenuation model constrained by
current observations that show an evolution of $\beta$ with redshift (Bouwens
et al., 2014; Atek et al., 2023; Roberts-Borsani et al., 2024). They generally
suggest that dust attenuation is lower at higher redshifts.

The intrinsic SEDs of FirstLight galaxies are described in Ceverino et al.
(2019). The stellar spectrum from 1 to 100 000 Å coming from each star
particle uses the templates of single stellar populations (SSP) from the
Binary Population and Spectral Synthesis (BPASS) model (Eldridge et al., 2017)
including nebular emission (Xiao et al., 2018). BPASS v2.1 assumes a Kroupa-
like initial mass function with power slopes $\alpha=-1.3$ for star masses
$m=0.1-0.5\ {\rm M}_{\odot}$ and $\alpha_{2}=2.35$ for star masses $m=0.5-100\
{\rm M}_{\odot}$. From these SEDs, we compute the dust-free values of MUV,0
and $\beta_{\rm 0}$. The UV absolute magnitude is defined at 1500 Å with a
bandwidth of 300 Å. The UV slope is computed between 1700 and 2200 Å (Bouwens
et al., 2014).

In Ceverino et al. (2019), we compare these intrinsic values with the observed
relation at $z\sim 6$ by Bouwens et al. (2014). At magnitudes brighter than
M${}_{\rm UV,0}=-19$, there is a mismatch between observed and intrinsic
values due to dust attenuation. We fit these observed values with a mean
relation $\langle\beta\rangle=f(M_{\rm UV})$ following the observations at
$z\sim 6$ by Bouwens et al. (2014) and by Atek et al. (2023) at $z\geq 9$
(Figure 1).

For galaxies with M${}_{\rm UV,0}<-19$, we compute the ($\beta$, MUV) pair
needed to follow these observed relations, starting with the intrinsic values
($\beta_{0}$, MUV,0). First, we compute the average intrinsic slope,
$\langle\beta_{0}\rangle=-2.37$, for all galaxies brighter than M${}_{\rm
UV,0}=-19$. For each galaxy, we compute the deviation from this average,
$\Delta\beta_{0}=\beta_{0}\ -\langle\beta_{0}\rangle$. This scatter is kept
invariant because it is due to the intrinsic differences in the age of the
stellar populations. Then, a first guess of the attenuated value is

$\beta=f(x)+\ \Delta\beta_{0},$ (1)

where $x={\rm M}_{\rm UV,0}$, the intrinsic magnitude. The dust attenuation,
AUV, is computed using the definition of the UV slope and the relation between
intrinsic and attenuated values:

$\beta=\beta_{0}-C\ {\rm A}_{\rm UV},$ (2)

where $C=-0.55$ assuming a Calzetti attenuation law (Calzetti et al., 2000).
Therefore, the attenuated magnitude is MUV=M${}_{\rm UV,0}+$AUV. Using this
value, we recompute $\beta$ using Eq. (1) with $x={\rm M}_{\rm UV}$. The new
$\beta$ is now consistent with the dust attenuated magnitude.

Figure 1 shows the $\beta$-MUV relations from FirstLight galaxies, constrained
by observations. Other attempts to compute dust attenuation using radiative
transfer calculations (Vijayan et al., 2021; Kannan et al., 2022) are not able
to reproduce relatively red slopes, $\beta>-1.8$, which are very common in
bright sources, M${}_{\rm UV}<-20$ at $z\simeq 6$ (Bouwens et al., 2014). Our
approach to dust attenuation reproduces these red slopes by construction.
Future attempts using radiative transfer calculations will compute dust
attenuation self-consistently from galaxy properties. This requires high-
resolution simulations that resolve the dust-star mixture accurately (Mushtaq
et al., 2023; Esmerian & Gnedin, 2023), as well as the holes and clumps in the
dust distribution.

At higher redshifts, $z\geq 9$, JWST observations indicate lower attenuations
at a fixed UV magnitude (Atek et al., 2023; Franco et al., 2023). This could
be due to a lower dust or metal content in these first galaxies. Our
estimation of dust attenuation is constrained by these observations but larger
samples of galaxies with accurately values of $\beta$ at $z\geq 9$ are needed
to confirm these trends.

##  4 Results

###  4.1 Evolution of the UV luminosity function

Using the dust-attenuated rest-frame UV absolute magnitudes constrained by the
observed evolution of the $\beta$-MUV relation between $z=6$ and $z\geq 9$, we
can generate the UV luminosity functions at different redshifts and compare
with pre-JWST and JWST observations (Figure 2). At $z=6$, FirstLight galaxies
are consistent with the compilation of pre-JWST observations by Bouwens et al.
(2021), although the faint end falls slightly below observations by about 0.1
dex.

At $z=9$, The FirstLight simulations are consistent with new JWST observations
(Harikane et al., 2023; Finkelstein et al., 2023). The number densities for
bright sources, M${}_{\rm UV}<-20$, are higher than in pre-JWST data. This
trend continues at higher redshifts, $z=11$ and 13, where FirstLight number
densities are remarkably similar to the observed JWST estimates (Bouwens et
al., 2022; Yan et al., 2023), although the uncertainties are high for these
relatively small samples. FirstLight predictions are higher than other recents
models that assume a constant galaxy efficiency (e.g. Yung et al., 2023;
Mauerhofer & Dayal, 2023), especially for bright galaxies.

Bright galaxies form earlier and faster than fainter galaxies at $z\geq 9$ and
therefore, their number density increases slowly at later times. For example,
the number density of galaxies with M${}_{\rm UV}=-19$ increases by two orders
of magnitudes from $z=13$ to $z=6$. During the same period of time, the number
density of galaxies with M${}_{\rm UV}=-20$ increases only by a factor of 60.
For a better understanding of this galaxy growth, we need to link these UV
magnitudes with the virial mass of the halos hosting these galaxies. According
to gas-regulator models (Bouché et al., 2010; Lilly et al., 2013; Dekel et
al., 2013; Dekel & Mandelker, 2014), the halo mass at a given redshift sets
the amount of gas accreted into the galaxy and regulates the subsequent star
formation at the central galaxy. Then, we can look at the galaxy growth at
different halo masses and redshifts.

###  4.2 Scaling relations: $M_{\rm vir}$ vs MUV

Figure 3: Virial mass versus MUV at $z\simeq 6$, 9 and 12 in FirstLight
galaxies. The coloured regions cover the 25 and 75% quantiles. As redshift
increases, the UV luminosity increases at a fixed virial mass.

The relation between the UV magnitude and the stellar (or halo) mass evolves
with redshift (Ceverino et al., 2019). This is due to the evolution of the
specific star-formation rate (sSFR), partially driven by the specific halo
mass growth, $\dot{M}_{\rm vir}/M_{\rm vir}\propto(1+z)^{5/2}$ (Dekel et al.,
2013; Dekel & Mandelker, 2014; Ceverino et al., 2018). Figure 3 shows the
evolution of the relation between the UV magnitude and the virial mass,
$M_{\rm vir}$ (Bryan & Norman, 1998). A bright galaxy with M${}_{\rm UV}=-20$
at $z\simeq 6$, corresponding to an Universe age of $t_{\rm U}\simeq 1\ {\rm
Gyr}$, typically lives in a halo of mass ${\rm log}(M_{\rm vir}/{\rm
M}_{\odot})=10.8\pm 0.1$. A second galaxy with the same rest-frame UV
magnitude but at $z=12$ ($t_{\rm U}\simeq 0.4\ {\rm Gyr}$) has a halo of mass
${\rm log}(M_{\rm vir}/{\rm M}_{\odot})\simeq 10.4$, a factor three lower than
in the first case. At $z=12$, galaxies with this second halo mass are
therefore more abundant than galaxies with the first halo mass. As a result,
the bright sources have higher number densities at $z=12$ than in the case of
no evolution in the MUV-$M_{\rm vir}$ relation.

For brighter objects, M${}_{\rm UV}<-20$, there is a change in the slope of
the relation due to dust attenuation at $z=6$. This increase the difference
described above between galaxies with M${}_{\rm UV}<-20$ at different
redshifts. Unfortunately, there are no objects with M${}_{\rm UV}<-21$ at
higher redshifts within the simulated volume and we cannot compare their
virial masses at the brightest end. Therefore, most of the evolution seen in
Figure 3 is insensitive to the dust attenuation model.

For a fixed virial mass, a halo with ${\rm log}(M_{\rm vir}/{\rm
M}_{\odot})=10.6$ at $z\simeq 6$ typically hosts a relatively low luminosity
galaxy with M${}_{\rm UV}\simeq-19$. Another halo of the same mass at $z\simeq
12$ contains a galaxy two magnitudes brighter, M${}_{\rm UV}\simeq-21$. This
can be explained if the halo at the higher redshift has a higher halo growth.
In that case, it can host a galaxy with higher sSFR than its low-z
counterpart. Using the Einstein-de Sitter approximation, the sSFR evolves by a
factor of five between $z=6$ and 12 (Ceverino et al., 2018). Is this
sufficient to explain the evolution of the MUV-$M_{\rm vir}$ relation? If the
answer is positive, then this evolution could be a direct consequence of the
higher specific mass accretion into halos at earlier times. As a consequence,
the galaxy growth would be just a fixed fraction of the halo growth at all
times.

###  4.3 Instantaneous galaxy formation efficiency

Figure 4: Instantaneous galaxy formation efficiency,
$\epsilon=\dot{M}_{\rm*}/(\dot{M}_{vir}f_{B})$, at different redshifts. The
coloured regions cover the 25 and 75% quantiles. The efficiency increases with
mass and redshift.  Figure 5: Integrated galaxy formation efficiency,
$\epsilon_{*}=M_{\rm*}/(M_{vir}f_{B})$, at different redshifts. The lines are
the same as in Fig. 4. Blue points represent the VELA-6 simulations (Ceverino
et al., 2023) at $z=4$ and the blue star represents a $z=0$ galaxy from
Ceverino et al. (2017b). As redshift increases, the efficiency increases at a
fixed virial mass.  Figure 6: Evolution of the galaxy stellar mass function
from z=6 to z=13. FirstLight is consistent with pre-JWST observations
(Stefanon et al., 2021) at $z=6$ but it shows higher numbers of massive
galaxies at $z=9$, in agreement with JWST results (Harvey et al., 2024; Weibel
et al., 2024). Simulations by Lovell et al. (2021) and semi-analytical models
by Yung et al. (2023) and Mauerhofer & Dayal (2023) show lower values at high
masses.

The instantaneous galaxy formation efficiency can be defined as the ratio
between the stellar and halo mass growth,

$\epsilon=\frac{\dot{M}_{\rm*}}{\dot{M}_{\rm vir}f_{B}},$ (3)

normalized to the universal baryonic fraction, $f_{B}$. This ratio removes the
explicit redshift dependence, $(1+z)^{5/2}$, described above. It mainly
depends on the ability of accreted baryons to contribute to the galaxy stellar
mass growth: the penetration of gas streams into the halo center and the
regulation of the gas-stars cycle by feedback. These processes depend on halo
mass. For example, feedback regulates strongly the formation of stars in low-
mass halos with shallow potential wells (Dekel & Silk, 1986). At a fixed halo
mass, this efficiency may increase with redshift due to an increase in the
penetration factor or due to a decrease in the mass-loading factor of galactic
outflows (Dekel & Mandelker, 2014; Dekel et al., 2023). Therefore, the galaxy
efficiency can vary with redshift due to alterations in these processes.

We compute the instantaneous efficiency using all snapshots stored every 10
Myr. Mass variations, $\Delta M_{*}$ and $\Delta M_{\rm vir}$ between
consecutive snapshots of the same galaxy can be compared within a given
redshift bin. Figure 4 shows the evolution of this efficiency from $z\simeq 6$
to 12. There is a significant increase of this efficiency with redshift. At a
fixed halo mass, $M_{\rm vir}\simeq 10^{11}{\rm M}_{\odot}$, the efficiency
increases a factor 3 between 10% at $z\simeq 6$ and $\sim$30% at $z\simeq 12$.
They are similar to the values required for reconciling UV and halo mass
functions at $z\geq 10$ (Inayoshi et al., 2022). For more massive galaxies,
$M_{\rm vir}\simeq 10^{11.5}{\rm M}_{\odot}$, the values can be higher,
although there is a flattening of the efficiency, with maximum values of
$\sim$40% at $z\simeq 6$ on average. These massive galaxies are absent within
the limited volume of these simulations at redshift higher than 7 and we
cannot constrain the evolution at this massive end.

###  4.4 Integrated galaxy formation efficiency

The integrated galaxy formation efficiency differs from the instantaneous
efficiency because it involves time-integrated values:

$\epsilon_{*}=\frac{M_{*}}{M_{\rm vir}f_{B}},$ (4)

where $M_{*}$ is the stellar mass of the galaxy. Figure 5 shows the evolution
of this efficiency with redshift. It has a similar dependence with virial mass
than the instantaneous efficiency although its redshift evolution is milder.
At a fixed virial mass, $M_{\rm vir}\simeq 10^{11}{\rm M}_{\odot}$, the
integrated efficiency doubles its value from $\epsilon_{*}\simeq 0.1$ at
$z\simeq 6$ to $\epsilon_{*}\simeq 0.2$ at $z\simeq 10$. At lower masses, the
evolution is below a factor 2 and the efficiency remains at lower values,
$\epsilon_{*}<0.1$, because feedback regulates efficiently the SF process at
low masses.

This redshift dependency continues towards lower redshifts. Other simulations
with the same feedback model show lower efficiencies at $z<5$. This is
especially relevant at low masses, $M_{\rm vir}<10^{11}{\rm M}_{\odot}$, where
feedback is most efficient. For example, the VELA-6 simulations (Ceverino et
al., 2023) have a factor 3-4 lower efficiency at $z=4$ than FirstLight
galaxies with the same virial mass, $M_{\rm vir}\simeq 10^{10.5}{\rm
M}_{\odot}$, at $z=12$. On the other hand, the AGORA galaxy at $z\simeq 0$
(Ceverino et al., 2017b) has a more massive halo, $M_{\rm vir}\simeq
10^{11.2}{\rm M}_{\odot}$ and it reaches the same efficiency,
$\epsilon_{*}\simeq 0.1$, than FirstLight galaxies of similar mass at $z\simeq
6$. There are no counterparts at higher redshift and therefore we cannot see
if the efficiency is higher at the high-mass end but the extrapolation from
lower masses hints to that possibility. We conclude that the integrated
efficiency evolves with time, but this evolution depends on halo mass.
Ultimately, it is related to the competition between the penetration of gas
flows into galaxies and the outflows driven by feedback.

###  4.5 Galaxy stellar mass function

The evolution in the integrated galaxy formation efficiency drives a non-
homogeneous evolution of the galaxy stellar mass function (Figure 6). This is
consistent with recent JWST results at $z\simeq 9$ (Harvey et al., 2024;
Weibel et al., 2024) within observational uncertainties. Low-mass galaxies,
$M_{*}=10^{8.5}\ {\rm M}_{\odot}$, grow in numbers by a factor 5 between
$z=11$ and $z=9$. Slightly more massive galaxies, $M_{*}=10^{9}\ {\rm
M}_{\odot}$, grow by a factor 10 within the same period. As a result, they are
more abundant than in other models (Lovell et al., 2021; Yung et al., 2023;
Mauerhofer & Dayal, 2023) with lower efficiencies at $z\geq 10$.

Galaxies more massive than $10^{9}\ {\rm M}_{\odot}$ at $z>11$ are absent
within these cosmological volumes. Larger volumes are needed to simulate these
massive and relatively rare halos. FirstLight also predicts higher number
densities than pre-JWST observations (Stefanon et al., 2021) at $z\simeq 9$,
even after different assumptions on IMF and cosmology are corrected. However,
this excess almost disappears at $z\simeq 6$, as the integrated efficiency
decreases with time.

The lower numbers found at low masses indicate some incompleteness in the
small and intermediate boxes at the lowest redshifts, $z\simeq 6$ (Ceverino et
al., 2018). However, the agreement between observations and FirstLight at high
masses, $M_{*}>10^{10}{\rm M}_{\odot}$, is good within uncertainties. There
are ways to correct for incompleteness (Ma et al., 2018; Lovell et al., 2021)
but they are not used here, as we are focusing on high masses and redshifts,
where FirstLight includes all halos available within the simulated volumes.

##  5 Discussion

###  5.1 Comparison of integrated efficiency from observations and other
models

Figure 7: Comparison of the integrated efficiency at $z=6$ (top) and $z\simeq
9$ (bottom) between FirstLight (solid black lines, as in Figure 5), pre-JWST
observations by Stefanon et al. (2021) (points with error bars), SPHINX
(dashed) and FIRE-2 (solid) simulations, and semi-empirical models by Behroozi
& Silk (2015) (red contour), Tacchella et al. (2018) (dot-dashed), Behroozi et
al. (2019) (dotted), and Li et al. (2023) models with $\epsilon_{\rm max}=0.2$
and 1 (solid cyan).

The integrated efficiency, eq. (4), has been computed in different works but
there is no consensus on whether it is time dependent or independent. Figure 7
shows a comparison between FirstLight results and other works at two different
redshifts. Stefanon et al. (2021) use the deepest Spitzer and HST observations
and show that the integrated efficiency increases with mass but there is no
significant evolution from $z\simeq 10$ to $z\simeq 6$. FirstLight is
consistent with their results at $z=6$ but it is significantly higher at
$z\simeq 9$ by a factor 2-4. Their low values are mostly driven by the
accelerated evolution of the galaxy stellar mass function between $z\simeq 9$
and $z\simeq 6$ (Figure 6), inconsistent with the FirstLight results. The
semi-empirical model by Tacchella et al. (2018) combine UVLF from HST
observations at $z=5-10$ and dark-matter halo accretion rates from N-body
simulations. They also conclude that the integrated efficiency is redshift-
independent in that redshift range. Therefore, they agree with FirstLight at
$z=6$ but they are significantly lower at $z=9$, in agreement with the
previous observations. A similar approach is used in others abundance-matching
models (e.g. Behroozi et al., 2019) that use pre-JWST observations to infer
relatively low efficiencies at high redshifts.

Other cosmological simulations, like SPHINX (Rosdahl et al., 2018; Katz et
al., 2023), have a high efficiency. It therefore over-predicts the values at
low redshifts, $z=6$, where observational estimates are more robust. On the
other hand, the FIRE-2 simulations (Ma et al., 2018) under-predict the
efficiency at the same redshift. Both simulations have roughly constant values
with time because feedback is either too strong (FIRE) or too weak (SPHINX) to
self-regulate the combined cycle of SF and feedback.

Other models consider a redshift-dependent efficiency, which is qualitatively
consistent with FirstLight. For example, Behroozi & Silk (2015) use a variable
ratio between the sSFR and the halo specific mass accretion rate to predict
the galaxy efficiency to $z\simeq 15$. Although their estimates are higher
than in previous redshift-independent models, they are consistent with
FirstLight at $z=6$. At $z\simeq 10$, their uncertainties are higher and these
predictions are also above FirstLight by a factor of a few. In the FFB
scenario (Dekel et al., 2023), the efficiency is a function of mass and
redshift, assuming a maximum value, $\epsilon_{\rm max}$, above a mass
threshold that declines with redshift (Li et al., 2023). Their minimum model
with $\epsilon_{\rm max}=0.2$ is both consistent with JWST observations and
FirstLight at $z=10$. Order-unity efficiencies, $\epsilon_{\rm max}\simeq 1$,
are excluded within the mass range explored by these simulations. At $z=6$,
the maximum efficiency in FirstLight is closer to $\epsilon_{\rm max}\simeq
0.3$, consistent with the cumulative values estimated using MIRI photometry of
massive galaxies (Wang et al., 2024). These efficiencies are higher than in
the FFB scenario at a fixed mass. In particular, the maximum efficiency in
FirstLight is reached at lower masses, $M_{\rm vir}(\epsilon_{\rm max})\simeq
10^{11.5}\ {\rm M}_{\odot}$. A maximum value of around unity at $z=10$ could
only be reached at very massive halos, $M_{\rm vir}\simeq 10^{12}\ {\rm
M}_{\odot}$, not explored in FirstLight.

###  5.2 Evolution of the cosmic UV and stellar mass density

Figure 8: Evolution of the cosmic UV density for galaxies with $M_{UV}<-17$.
FirstLight values are above the redshift-independent models of efficiency by
Harikane et al. (2022) and Tacchella et al. (2018), as well as other pre-JWST
observations at $z\geq 10$ (Oesch et al., 2018). JWST values (Harikane et al.,
2023; McLeod et al., 2023; Chemerynska et al., 2023; Donnan et al., 2024) are
consistent with FirstLight within the estimated uncertainties.

The integration of the UVLF (Figure 2) to M${}_{\rm UV}<-17$ at different
redshifts gives an estimate of the comoving cosmic UV density (Figure 8),
which can we compared with other works. Due to the increase of the efficiency
at $z\geq 9$, the values are above the redshift-independent models (Tacchella
et al., 2018; Harikane et al., 2022). There is no sign of accelerated
evolution between $z=10$ and $z=8$, as seen in pre-JWST observations (Oesch et
al., 2018). In fact, a gentle evolution, approximately fitted by
log($\rho_{\rm UV})\propto-0.7(1+z)$, is consistent with most JWST
observations up to $z\simeq 13$. FirstLight results are only slightly below
observations by 0.2-0.3 dex at $z\geq 11$, still in between the estimated
uncertainties. Larger samples of galaxies with robust redshift estimations are
necessary for more accurate constrains.

Figure 9: Evolution of the cosmic stellar mass density for galaxies with
$M_{*}>10^{8}{\rm M}_{\odot}$. FirstLight-derived densities are higher than
pre-JWST values at $z>9$ (Stefanon et al., 2021) and previous models with a
redshift-independent efficiency (Tacchella et al., 2018).

The comoving cosmic stellar mass density, for all galaxies more massive than
$10^{8}{\rm M}_{\odot}$, provides another overall comparison with previous
works (Figure 9). At $z\simeq 6$, FirstLight values are slightly lower than
other models. This is due to the slight incompleteness at low masses discussed
above. At higher redshifts, $z>9$, models that assume a constant efficiency
(Tacchella et al., 2018) and pre-JWST observations (Stefanon et al., 2021)
show a much more drastic drop due to the lack of massive galaxies. However,
FirstLight values show a smooth evolution, log($\rho_{*})\propto-(1+z)$, due
to the high efficiency at these high redshifts. Future JWST observations are
needed to confirm the gentle rise of the stellar mass density at these early
times.

###  5.3 What determines galaxy efficiency?

Figure 10: Example of a highly efficient galaxy at $z=9$ (top) and a galaxy at
$z=6$ with the same halo mass of $M_{\rm vir}\simeq 10^{11}{\rm M}_{\odot}$
but lower efficiency (bottom). Left panels show the star formation rate
surface density and right panels depict the gas density, averaged along the
line of sight.

Different galaxy conditions determine different efficiencies in the galaxy
growth with respect to halo growth, eq. (3). For example, the baryonic inflow
from the halo to the galaxy depends on the cycle from the circumgalactic
medium to the star-forming interstellar medium. Variations in this cycle could
modify the rate of galaxy growth even at a fixed halo mass growth (Dekel et
al., 2013). Feedback regulates the SF process by driving galactic outflows or
by decreasing the fraction of cold and dense, star-forming gas (Ceverino et
al., 2014). However, feedback depends on gas conditions, particularly on its
density (Dekel & Silk, 1986; Dekel et al., 2023). Therefore, galaxy efficiency
can vary with redshift as gas within galaxies evolves with time. A more in-
depth study to identify the main driver of this evolution is beyond the scope
of this paper, but we can provide some hints.

In Figure 10 we compare two examples of galaxies with a similar halo mass,
$M_{\rm vir}\simeq 10^{11}{\rm M}_{\odot}$, but different galaxy efficiencies
at different redshifts. The first galaxy at $z=9$ has a high efficiency,
$\epsilon\simeq 0.3$ and $\epsilon_{*}\simeq 0.6$. A significant fraction of
the galaxy, especially the center and off-center clumps, has very high
densities, $n\geq 3000\ {\rm cm}^{-3}$. The corresponding free-fall time is
lower than 1 Myr and the effect of feedback drastically decreases at these
high densities, according to the FFB scenario (Dekel et al., 2023). Therefore,
the SFR surface density reaches extreme values, $\Sigma_{\rm SFR}\geq
10^{3}{\rm M}_{\odot}{\rm yr}^{-1}\,{\rm kpc}^{-2}$, similar to the
observational estimates in a very dense star-forming environment of a $z=12$
galaxy (Calabro et al., 2024).

The second example at $z=6$ has a lower efficiency, $\epsilon\simeq 0.1$ and
$\epsilon_{*}\simeq 0.09$. Both the gas density and the SFR surface density
are much lower than in the previous example, although consistent with
observations that spatially resolve the Kennicutt-Schmidt relation at $z=7$
(Vallini et al., 2024). This galaxy has the same amount of gas within the
virial radius as in the previous case ($M_{\rm gas,halo}=2\times 10^{10}\ {\rm
M}_{\odot}$), but only 7% of this mass is forming stars. This fraction
increases to 30% in the first galaxy at $z=9$. As a result, the star-formation
rate of this highly efficient galaxy is ten times higher than the other
example at lower redshift. This also translates into a factor-of-two shorter
gas depletion time, $t_{\rm D}=M_{\rm gas,galaxy}/{\rm SFR}=60\,{\rm Myr}$.
This value is close to the average at $z=10$ (Ceverino et al., 2018), but it
is a factor 30 shorter than in local galaxies (Leroy et al., 2008; Saintonge &
Catinella, 2022; Sun et al., 2023b). We conclude that the gas densities in SF
bursts at extremely high redshifts, $z\geq 9$, facilitates very high galaxy
efficiencies, $\epsilon_{\rm max}\simeq 0.3-0.4$, at moderate halo masses,
$M_{\rm vir}\simeq 10^{11}\ {\rm M}_{\odot}$. Future simulations of bigger
volumes will explore higher masses and possible higher efficiencies in more
extreme and rare halos at high redshifts.

##  6 Conclusions

We use the FirstLight database of 377 zoom-in cosmological simulations of a
mass-complete sample of galaxies with a spatial resolution of 10-20 parsecs,
to understand galaxy growth at extremely high redshifts, $z=9-13$.

The main highlights of this paper are the following:

  1. 1.

FirstLight contains a high number of bright galaxies, M${}_{\rm UV}\simeq-20$,
consistent with JWST data.

  2. 2.

The relation between MUV and halo mass evolves with redshift, independently of
the dust attenuation model.

  3. 3.

The galaxy formation efficiency, eqs. (3) and (4), increases significantly
with redshift at a fixed halo mass.

  4. 4.

Galactic halos at extremely high redshifts convert gas into stars at a higher
rate than at lower redshifts.

  5. 5.

The number density of massive galaxies, $M_{*}\simeq 10^{9}\ {\rm M}_{\odot}$
at $z\geq 9$, are higher than in other models with a constant star-formation
efficiency.

  6. 6.

The high gas densities in these SF bursts at $z\geq 9$ enable these high
efficiencies.

In spite of this success in reproducing current JWST observations, FirstLight
simulations also have some caveats. For example, they do not include the
radiative transfer of ionizing photons, instead assuming that these photons
are mostly absorbed in the immediate vicinity of the massive stars producing
them. Therefore, radiative feedback only affects gas close to massive stars;
the effects of the leakage of this radiation into the interstellar medium is
not included. This could modify the gas conditions further away from the star-
forming regions (Emerick et al., 2019). The maximum resolution achieved in
FirstLight (10-20 parsecs) also imposes some limitations. Future models of
feedback at this scale can be improved thanks to insights from high-resolution
simulations of the formation of individual massive clusters (e.g. Kim et al.,
2016; Fukushima & Yajima, 2021; Calura et al., 2022; Polak et al., 2023).
Indeed, the high star-formation efficiencies found in these high-density
clouds are consistent with FirstLight findings at galaxy-scales at high-z.

We conclude that cosmological simulations of galaxy formation with self-
consistent models of star formation and feedback can reproduce different
conditions of galaxy formation across cosmic history. Relatively massive
galaxies at extremely high redshifts have a low efficiency of feedback and
therefore star formation and galaxy growth can proceed faster than at later
times. Other modern cosmological simulations with phenomenological feedback
models (Pillepich et al., 2018; Davé et al., 2019) include a decrease of the
mass in galactic outflows with increasing galaxy mass. However, these models
are calibrated on observations at lower redshifts and they may fail at much
early times, when gas densities are much higher. Future observations by JWST
will utilize multi-line diagnostics to infer the gas density in star-forming
regions at these high-z and they can validate the redshift evolution advocated
here. The next generation of cosmological simulations must reproduce the
galaxy conditions across different redshifts, from the local Universe at $z=0$
well into the dark epoch, $z=10-20$, before the reionization of the Universe.

###### Acknowledgements.

The authors gratefully acknowledge the Gauss Center for Supercomputing for
funding this project by providing computing time on the GCS Supercomputer
SuperMUC at Leibniz Supercomputing Centre (Project ID: pr92za). The authors
thankfully acknowledge the computer resources at MareNostrum and the technical
support provided by the Barcelona Supercomputing Center (RES-
AECT-2020-3-0019). This work used the v2.1 of the Binary Population and
Spectral Synthesis (BPASS) models as last described in Eldridge et al. (2017).
DC is a Ramon-Cajal Researcher and is supported by the Ministerio de Ciencia,
Innovación y Universidades (MICIU/FEDER) under research grant
PID2021-122603NB-C21. YN acknowledges funding from JSPS KAKENHI Grant Number
23KJ0728 and a JSR fellowship. RSK and SCOG acknowledge funding from the ERC
via Synergy Grant ”ECOGAL” (project ID 855130), from the German Excellence
Strategy via the Heidelberg Cluster of Excellence (EXC 2181 - 390900948)
”STRUCTURES”, and from the German Ministry for Economic Affairs and Climate
Action in project “MAINN” (funding ID 50OO2206). RSK and SCOG also thank for
computing resources provided by the Ministry of Science, Research and the Arts
(MWK) of the State of Baden-Württemberg through bwHPC and DFG through grant
INST 35/1134-1 FUGG and for data storage at SDS@hd through grant INST
35/1314-1 FUGG.

## References

  * Abel et al. (2002) Abel, T., Bryan, G. L., & Norman, M. L. 2002, Science, 295, 93
  * Adams et al. (2023) Adams, N. J., Conselice, C. J., Ferreira, L., et al. 2023, MNRAS, 518, 4755
  * Atek et al. (2023) Atek, H., Chemerynska, I., Wang, B., et al. 2023, MNRAS, 524, 5486
  * Behroozi et al. (2019) Behroozi, P., Wechsler, R. H., Hearin, A. P., & Conroy, C. 2019, MNRAS, 488, 3143
  * Behroozi & Silk (2015) Behroozi, P. S. & Silk, J. 2015, ApJ, 799, 32
  * Bouché et al. (2010) Bouché, N., Dekel, A., Genzel, R., et al. 2010, ApJ, 718, 1001
  * Bouwens et al. (2022) Bouwens, R. J., Illingworth, G., Ellis, R. S., Oesch, P., & Stefanon, M. 2022, ApJ, 940, 55
  * Bouwens et al. (2014) Bouwens, R. J., Illingworth, G. D., Oesch, P. A., et al. 2014, ApJ, 793, 115
  * Bouwens et al. (2021) Bouwens, R. J., Oesch, P. A., Stefanon, M., et al. 2021, AJ, 162, 47
  * Bromm et al. (2002) Bromm, V., Coppi, P. S., & Larson, R. B. 2002, ApJ, 564, 23
  * Bryan & Norman (1998) Bryan, G. L. & Norman, M. L. 1998, ApJ, 495, 80
  * Calabro et al. (2024) Calabro, A., Castellano, M., Zavala, J. A., et al. 2024, arXiv e-prints, arXiv:2403.12683
  * Calura et al. (2022) Calura, F., Lupi, A., Rosdahl, J., et al. 2022, MNRAS, 516, 5914
  * Calzetti et al. (2000) Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682
  * Casey et al. (2023) Casey, C. M., Akins, H. B., Shuntov, M., et al. 2023, arXiv e-prints, arXiv:2308.10932
  * Castellano et al. (2022) Castellano, M., Fontana, A., Treu, T., et al. 2022, ApJ, 938, L15
  * Ceverino et al. (2010) Ceverino, D., Dekel, A., & Bournaud, F. 2010, MNRAS, 404, 2151
  * Ceverino et al. (2017a) Ceverino, D., Glover, S. C. O., & Klessen, R. S. 2017a, MNRAS, 470, 2791
  * Ceverino et al. (2021) Ceverino, D., Hirschmann, M., Klessen, R. S., et al. 2021, MNRAS, 504, 4472
  * Ceverino et al. (2018) Ceverino, D., Klessen, R. S., & Glover, S. C. O. 2018, MNRAS, 480, 4842
  * Ceverino et al. (2019) Ceverino, D., Klessen, R. S., & Glover, S. C. O. 2019, MNRAS, 484, 1366
  * Ceverino & Klypin (2009) Ceverino, D. & Klypin, A. 2009, ApJ, 695, 292
  * Ceverino et al. (2014) Ceverino, D., Klypin, A., Klimek, E. S., et al. 2014, MNRAS, 442, 1545
  * Ceverino et al. (2023) Ceverino, D., Mandelker, N., Snyder, G. F., et al. 2023, MNRAS, 522, 3912
  * Ceverino et al. (2017b) Ceverino, D., Primack, J., Dekel, A., & Kassin, S. A. 2017b, MNRAS, 467, 2664
  * Chemerynska et al. (2023) Chemerynska, I., Atek, H., Furtak, L. J., et al. 2023, arXiv e-prints, arXiv:2312.05030
  * Curti et al. (2023) Curti, M., D’Eugenio, F., Carniani, S., et al. 2023, MNRAS, 518, 425
  * Davé et al. (2019) Davé, R., Anglés-Alcázar, D., Narayanan, D., et al. 2019, MNRAS, 486, 2827
  * Dekel et al. (2009) Dekel, A., Birnboim, Y., Engel, G., et al. 2009, Nature, 457, 451
  * Dekel & Mandelker (2014) Dekel, A. & Mandelker, N. 2014, MNRAS, 444, 2071
  * Dekel et al. (2023) Dekel, A., Sarkar, K. C., Birnboim, Y., Mandelker, N., & Li, Z. 2023, MNRAS, 523, 3201
  * Dekel & Silk (1986) Dekel, A. & Silk, J. 1986, ApJ, 303, 39
  * Dekel et al. (2013) Dekel, A., Zolotov, A., Tweed, D., et al. 2013, MNRAS, 435, 999
  * Donnan et al. (2023) Donnan, C. T., McLeod, D. J., Dunlop, J. S., et al. 2023, MNRAS, 518, 6011
  * Donnan et al. (2024) Donnan, C. T., McLure, R. J., Dunlop, J. S., et al. 2024, arXiv e-prints, arXiv:2403.03171
  * Eldridge et al. (2017) Eldridge, J. J., Stanway, E. R., Xiao, L., et al. 2017, PASA, 34, e058
  * Emerick et al. (2019) Emerick, A., Bryan, G. L., & Mac Low, M.-M. 2019, MNRAS, 482, 1304
  * Esmerian & Gnedin (2023) Esmerian, C. J. & Gnedin, N. Y. 2023, arXiv e-prints, arXiv:2308.11723
  * Ferrara et al. (2023) Ferrara, A., Pallottini, A., & Dayal, P. 2023, MNRAS, 522, 3986
  * Fichtner et al. (2024) Fichtner, Y. A., Mackey, J., Grassitelli, L., Romano-Díaz, E., & Porciani, C. 2024, arXiv e-prints, arXiv:2402.11008
  * Finkelstein et al. (2023) Finkelstein, S. L., Leung, G. C. K., Bagley, M. B., et al. 2023, arXiv e-prints, arXiv:2311.04279
  * Franco et al. (2023) Franco, M., Akins, H. B., Casey, C. M., et al. 2023, arXiv e-prints, arXiv:2308.00751
  * Fukushima & Yajima (2021) Fukushima, H. & Yajima, H. 2021, MNRAS, 506, 5512
  * Hainline et al. (2023) Hainline, K. N., Johnson, B. D., Robertson, B., et al. 2023, arXiv e-prints, arXiv:2306.02468
  * Harikane et al. (2022) Harikane, Y., Ono, Y., Ouchi, M., et al. 2022, ApJS, 259, 20
  * Harikane et al. (2023) Harikane, Y., Ouchi, M., Oguri, M., et al. 2023, ApJS, 265, 5
  * Harvey et al. (2024) Harvey, T., Conselice, C., Adams, N. J., et al. 2024, arXiv e-prints, arXiv:2403.03908
  * Inayoshi et al. (2022) Inayoshi, K., Harikane, Y., Inoue, A. K., Li, W., & Ho, L. C. 2022, ApJ, 938, L10
  * Kannan et al. (2022) Kannan, R., Smith, A., Garaldi, E., et al. 2022, MNRAS, 514, 3857
  * Katz et al. (2019) Katz, H., Galligan, T. P., Kimm, T., et al. 2019, MNRAS, 487, 5902
  * Katz et al. (2023) Katz, H., Rosdahl, J., Kimm, T., et al. 2023, The Open Journal of Astrophysics, 6, 44
  * Kennicutt (1998) Kennicutt, Jr., R. C. 1998, ApJ, 498, 541
  * Kim et al. (2016) Kim, J.-G., Kim, W.-T., & Ostriker, E. C. 2016, ApJ, 819, 137
  * Klessen & Glover (2023) Klessen, R. S. & Glover, S. C. O. 2023, ARA&A, 61, 65
  * Kravtsov (2003) Kravtsov, A. V. 2003, ApJ, 590, L1
  * Kravtsov et al. (1997) Kravtsov, A. V., Klypin, A. A., & Khokhlov, A. M. 1997, ApJS, 111, 73
  * Langan et al. (2020) Langan, I., Ceverino, D., & Finlator, K. 2020, MNRAS, 494, 1988
  * Leroy et al. (2008) Leroy, A. K., Walter, F., Brinks, E., et al. 2008, AJ, 136, 2782
  * Leśniewska & Michałowski (2019) Leśniewska, A. & Michałowski, M. J. 2019, A&A, 624, L13
  * Leung et al. (2023) Leung, G. C. K., Bagley, M. B., Finkelstein, S. L., et al. 2023, ApJ, 954, L46
  * Li et al. (2023) Li, Z., Dekel, A., Sarkar, K. C., et al. 2023, arXiv e-prints, arXiv:2311.14662
  * Lilly et al. (2013) Lilly, S. J., Carollo, C. M., Pipino, A., Renzini, A., & Peng, Y. 2013, ApJ, 772, 119
  * Lovell et al. (2023) Lovell, C. C., Harrison, I., Harikane, Y., Tacchella, S., & Wilkins, S. M. 2023, MNRAS, 518, 2511
  * Lovell et al. (2021) Lovell, C. C., Vijayan, A. P., Thomas, P. A., et al. 2021, MNRAS, 500, 2127
  * Ma et al. (2018) Ma, X., Hopkins, P. F., Garrison-Kimmel, S., et al. 2018, MNRAS, 478, 1694
  * Mason et al. (2023) Mason, C. A., Trenti, M., & Treu, T. 2023, MNRAS, 521, 497
  * Mauerhofer & Dayal (2023) Mauerhofer, V. & Dayal, P. 2023, MNRAS, 526, 2196
  * McLeod et al. (2023) McLeod, D. J., Donnan, C. T., McLure, R. J., et al. 2023, arXiv e-prints, arXiv:2304.14469
  * Mushtaq et al. (2023) Mushtaq, M., Ceverino, D., Klessen, R. S., Reissl, S., & Puttasiddappa, P. H. 2023, MNRAS, 525, 4976
  * Naidu et al. (2022) Naidu, R. P., Oesch, P. A., van Dokkum, P., et al. 2022, ApJ, 940, L14
  * Nakazato et al. (2023) Nakazato, Y., Yoshida, N., & Ceverino, D. 2023, ApJ, 953, 140
  * Oesch et al. (2018) Oesch, P. A., Bouwens, R. J., Illingworth, G. D., Labbé, I., & Stefanon, M. 2018, ApJ, 855, 105
  * O’Shea et al. (2015) O’Shea, B. W., Wise, J. H., Xu, H., & Norman, M. L. 2015, ApJ, 807, L12
  * Ostriker & Shetty (2011) Ostriker, E. C. & Shetty, R. 2011, ApJ, 731, 41
  * Pallottini et al. (2019) Pallottini, A., Ferrara, A., Decataldo, D., et al. 2019, MNRAS, 487, 1689
  * Pérez-González et al. (2023) Pérez-González, P. G., Costantin, L., Langeroodi, D., et al. 2023, ApJ, 951, L1
  * Pillepich et al. (2018) Pillepich, A., Springel, V., Nelson, D., et al. 2018, MNRAS, 473, 4077
  * Polak et al. (2023) Polak, B., Mac Low, M.-M., Klessen, R. S., et al. 2023, arXiv e-prints, arXiv:2312.06509
  * Roberts-Borsani et al. (2024) Roberts-Borsani, G., Treu, T., Shapley, A., et al. 2024, arXiv e-prints, arXiv:2403.07103
  * Rosdahl et al. (2018) Rosdahl, J., Katz, H., Blaizot, J., et al. 2018, MNRAS, 479, 994
  * Saintonge & Catinella (2022) Saintonge, A. & Catinella, B. 2022, ARA&A, 60, 319
  * Schmidt (1959) Schmidt, M. 1959, ApJ, 129, 243
  * Shen et al. (2023) Shen, X., Vogelsberger, M., Boylan-Kolchin, M., Tacchella, S., & Kannan, R. 2023, MNRAS, 525, 3254
  * Stefanon et al. (2021) Stefanon, M., Bouwens, R. J., Labbé, I., et al. 2021, ApJ, 922, 29
  * Sun et al. (2023a) Sun, G., Faucher-Giguère, C.-A., Hayward, C. C., et al. 2023a, ApJ, 955, L35
  * Sun et al. (2023b) Sun, J., Leroy, A. K., Ostriker, E. C., et al. 2023b, ApJ, 945, L19
  * Tacchella et al. (2018) Tacchella, S., Bose, S., Conroy, C., Eisenstein, D. J., & Johnson, B. D. 2018, ApJ, 868, 92
  * Tsuna et al. (2023) Tsuna, D., Nakazato, Y., & Hartwig, T. 2023, MNRAS, 526, 4801
  * Vallini et al. (2024) Vallini, L., Witstok, J., Sommovigo, L., et al. 2024, MNRAS, 527, 10
  * Venturi et al. (2024) Venturi, G., Carniani, S., Parlanti, E., et al. 2024, arXiv e-prints, arXiv:2403.03977
  * Vijayan et al. (2021) Vijayan, A. P., Lovell, C. C., Wilkins, S. M., et al. 2021, MNRAS, 501, 3289
  * Wang et al. (2024) Wang, T., Sun, H., Zhou, L., et al. 2024, arXiv e-prints, arXiv:2403.02399
  * Weibel et al. (2024) Weibel, A., Oesch, P. A., Barrufet, L., et al. 2024, arXiv e-prints, arXiv:2403.08872
  * Xiao et al. (2018) Xiao, L., Stanway, E. R., & Eldridge, J. J. 2018, MNRAS, 477, 904
  * Yan et al. (2023) Yan, H., Sun, B., Ma, Z., & Ling, C. 2023, arXiv e-prints, arXiv:2311.15121
  * Yoshida et al. (2008) Yoshida, N., Omukai, K., & Hernquist, L. 2008, Science, 321, 669
  * Yung et al. (2023) Yung, L. Y. A., Somerville, R. S., Finkelstein, S. L., et al. 2023, MNRAS, 519, 1578
  * Yung et al. (2024) Yung, L. Y. A., Somerville, R. S., Finkelstein, S. L., Wilkins, S. M., & Gardner, J. P. 2024, MNRAS, 527, 5929


* [124] J. Joshi, A. Dhall, R. Goecke, M. Breakspear, G. Parker, Neural-net classification for spatio-temporal descriptor based depression analysis, in: Proceedings of the 21st International Conference on Pattern Recognition (ICPR2012), IEEE, 2012, pp. 2634–2638.
  * [125] J. Joshi, A. Dhall, R. Goecke, J. F. Cohn, Relative body parts movement for automatic depression analysis, in: 2013 Humaine Association Conference on Affective Computing and Intelligent Interaction, IEEE, 2013, pp. 492–497.
  * [126] B. Hosseinifard, M. H. Moradi, R. Rostami, Classifying depression patients and normal subjects using machine learning techniques and nonlinear features from eeg signal, Computer methods and programs in biomedicine 109 (3) (2013) 339–345.
  * [127] R. Adorni, A. Gatti, A. Brugnera, K. Sakatani, A. Compare, Could fnirs promote neuroscience approach in clinical psychology?, Frontiers in psychology 7 (2016) 456.
  * [128] C. S. Ho, L. J. Lim, A. Lim, N. H. Chan, R. Tan, S. Lee, R. Ho, Diagnostic and predictive applications of functional near-infrared spectroscopy for major depressive disorder: A systematic review, Frontiers in Psychiatry 11 (2020) 378\.
  * [129] T. Suto, M. Fukuda, M. Ito, T. Uehara, M. Mikuni, Multichannel near-infrared spectroscopy in depression and schizophrenia: cognitive brain activation study, Biological psychiatry 55 (5) (2004) 501–511.
  * [130] S. Scherer, G. M. Lucas, J. Gratch, A. S. Rizzo, L.-P. Morency, Self-reported symptoms of depression and ptsd are associated with reduced vowel space in screening interviews, IEEE Transactions on Affective Computing 7 (1) (2015) 59–73.
  * [131] J. T. Becker, F. Boiler, O. L. Lopez, J. Saxton, K. L. McGonigle, The natural history of cognitive decline in alzheimer’s disease, Archives of Neurology 51 (6) (1994) 585–594.
  * [132] H. Stassen, S. Kuny, D. Hell, The speech analysis approach to determining onset of improvement under antidepressants, European Neuropsychopharmacology 8 (4) (1998) 303–310.
  * [133] D. J. France, R. G. Shiavi, S. Silverman, M. Silverman, M. Wilkes, Acoustical properties of speech as indicators of depression and suicidal risk, IEEE Transactions on Biomedical Engineering 47 (7) (2000) 829–837.
  * [134] M. Alpert, E. R. Pouget, R. R. Silva, Reflections of depression in acoustic measures of the patient’s speech, Journal of Affective Disorders 66 (1) (2001) 59–69.
  * [135] E. Moore, M. Clements, J. Peifer, L. Weisser, Comparing objective feature statistics of speech for classifying clinical depression, in: Engineering in Medicine and Biology Society, 2004. IEMBS’04. 26th Annual International Conference of the IEEE, Vol. 1, IEEE, IEEE, San Francisco, CA, USA, 2004, pp. 17–20.
  * [136] T. Yingthawornsuk, H. K. Keskinpala, D. France, D. M. Wilkes, R. G. Shiavi, R. M. Salomon, Objective estimation of suicidal risk using vocal output characteristics, in: Ninth International Conference on Spoken Language Processing, ISCA, Pittsburgh, Pennsylvania, 2006, pp. 649–652.
  * [137] N. C. Maddage, R. Senaratne, L.-S. A. Low, M. Lech, N. Allen, Video-based detection of the clinical depression in adolescents, in: Engineering in Medicine and Biology Society, 2009. EMBC 2009. Annual International Conference of the IEEE, IEEE, IEEE, Minneapolis, MN, USA, 2009, pp. 3723–3726.
  * [138] S. Alghowinem, R. Goecke, M. Wagner, J. Epps, M. Breakspear, G. Parker, From joyous to clinically depressed: Mood detection using spontaneous speech, in: Proceedings of the Twenty-Fifth International Florida Artificial Intelligence Research Society Conference, AAAI, Marco Island, Florida, 2012, pp. 141–146.
  * [139] K. Ooi, L. Low, M. Lech, N. Allen, Prediction of clinical depression in adolescents using facial image analysis, in: WIAMIS 2011: 12th International Workshop on Image Analysis for Multimedia Interactive Services, WIAMIS, WIAMIS, Delft, The Netherlands, 2011, pp. 1–4.
  * [140] J. C. Mundt, A. P. Vogel, D. E. Feltner, W. R. Lenderking, Vocal acoustic biomarkers of depression severity and treatment response, Biological Psychiatry 72 (7) (2012) 580–587.
  * [141] M. Valstar, B. Schuller, K. Smith, T. Almaev, F. Eyben, J. Krajewski, R. Cowie, M. Pantic, AVEC 2014: 3D dimensional affect and depression recognition challenge, in: Proceedings of the 4th International Workshop on Audio/Visual Emotion Challenge, ACM, ACM, Orlando, Florida, USA, 2014, pp. 3–10.
  * [142] G. G. J. Chen, Visualizations for mental health topic models (2014) 1–54.
  * [143] K.-Y. Huang, C.-H. Wu, Y.-T. Kuo, F.-L. Jang, Unipolar depression vs. bipolar disorder: An elicitation-based approach to short-term detection of mood disorder., in: INTERSPEECH, 2016, pp. 1452–1456.
  * [144] H. Dibeklioğlu, Z. Hammal, J. F. Cohn, Dynamic multimodal measurement of depression severity using deep autoencoding, IEEE Journal of Biomedical and Health Informatics 22 (2) (2018) 525–536.
  * [145] E. Çiftçi, H. Kaya, H. Güleç, A. A. Salah, The turkish audio-visual bipolar disorder corpus, in: 2018 First Asian Conference on Affective Computing and Intelligent Interaction (ACII Asia), IEEE, 2018, pp. 1–6.
  * [146] H. Cai, Y. Gao, S. Sun, N. Li, F. Tian, H. Xiao, J. Li, Z. Yang, X. Li, Q. Zhao, et al., Modma dataset: a multi-model open dataset for mental-disorder analysis, arXiv preprint arXiv:2002.09283 (2020).
  * [147] S. Alghowinem, R. Goecke, M. Wagner, J. Epps, M. Hyett, G. Parker, M. Breakspear, Multimodal depression detection: fusion analysis of paralinguistic, head pose and eye gaze behaviors, IEEE Transactions on Affective Computing 9 (4) (2016) 478–490.
  * [148] E. Moore, M. Clements, J. Peifer, L. Weisser, Analysis of prosodic variation in speech for clinical depression, in: Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat. No. 03CH37439), Vol. 3, IEEE, 2003, pp. 2925–2928.
  * [149] H. Meng, D. Huang, H. Wang, H. Yang, M. Ai-Shuraifi, Y. Wang, Depression recognition based on dynamic facial and vocal expression features using partial least square regression, in: Proceedings of the 3rd ACM international workshop on Audio/visual emotion challenge, 2013, pp. 21–30.
  * [150] N. Cummins, J. Joshi, A. Dhall, V. Sethu, R. Goecke, J. Epps, Diagnosis of depression by behavioural signals: a multimodal approach, in: Proceedings of the 3rd ACM international workshop on Audio/visual emotion challenge, 2013, pp. 11–20.
  * [151] K. Ooi, Early prediction of clinical depression in adolescents using single-channel and multi-channel classification approach (2014).
  * [152] M. Sidorov, W. Minker, Emotion recognition and depression diagnosis by acoustic and visual features: A multimodal approach, in: Proceedings of the 4th International Workshop on Audio/Visual Emotion Challenge, 2014, pp. 81–86.
  * [153] M. Kächele, M. Schels, F. Schwenker, Inferring depression and affect from application dependent meta knowledge, in: Proceedings of the 4th International Workshop on Audio/Visual Emotion Challenge, 2014, pp. 41–48.
  * [154] I. T. Meftah, N. Le Thanh, C. B. Amar, Detecting depression using multimodal approach of emotion recognition, in: 2012 IEEE International Conference on Complex Systems (ICCS), IEEE, 2012, pp. 1–6.
  * [155] U. R. Acharya, S. L. Oh, Y. Hagiwara, J. H. Tan, H. Adeli, D. P. Subha, Automated eeg-based screening of depression using deep convolutional neural network, Computer Methods and Programs in Biomedicine 161 (2018) 103–113.
  * [156] A. Zandvakili, N. S. Philip, S. R. Jones, A. R. Tyrka, B. D. Greenberg, L. L. Carpenter, Use of machine learning in predicting clinical response to transcranial magnetic stimulation in comorbid posttraumatic stress disorder and major depression: A resting state electroencephalography study, Journal of Affective Disorders 252 (2019) 47–54.
  * [157] D. Kan, P. Lee, Decrease alpha waves in depression: An electroencephalogram (eeg) study, in: 2015 International Conference on BioSignal Analysis, Processing and Systems (ICBAPS), IEEE, 2015, pp. 156–161.
  * [158] X. Zhang, J. Shen, Z. ud Din, J. Liu, G. Wang, B. Hu, Multimodal depression detection: Fusion of electroencephalography and paralinguistic behaviors using a novel strategy for classifier ensemble, IEEE Journal of Biomedical and Health Informatics 23 (6) (2019) 2265–2275.
  * [159] H. Cai, X. Zhang, Y. Zhang, Z. Wang, B. Hu, A case-based reasoning model for depression based on three-electrode eeg data, IEEE Transactions on Affective Computing (2018) 1–1.
  * [160] D. Zhi, X. Ma, L. Lv, Q. Ke, Y. Yang, X. Yang, M. Pan, S. Qi, R. Jiang, Y. Du, et al., Abnormal dynamic functional network connectivity and graph theoretical analysis in major depressive disorder, in: 2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), IEEE, 2018, pp. 558–561.
  * [161] J. J. Maller, S. S. George, R. P. Viswanathan, P. B. Fitzgerald, P. Junor, Using thermographic cameras to investigate eye temperature and clinical severity in depression, Journal of biomedical optics 21 (2) (2016) 026001.
  * [162] M. Hamilton, Arating scalefordepression. journalofneurology, Neurosurgery, and Psychiatry 23 (1960) 5642.
  * [163] M. Niu, J. Tao, B. Liu, J. Huang, Z. Lian, Multimodal spatiotemporal representation for automatic depression level detection, IEEE Transactions on Affective Computing (2020).
  * [164] P. Viola, M. J. Jones, Robust real-time face detection, International journal of computer vision 57 (2) (2004) 137–154.
  * [165] T. Baltrušaitis, P. Robinson, L.-P. Morency, Openface: an open source facial behavior analysis toolkit, in: 2016 IEEE Winter Conference on Applications of Computer Vision (WACV), IEEE, 2016, pp. 1–10.
  * [166] G. Littlewort, J. Whitehill, T. Wu, I. Fasel, M. Frank, J. Movellan, M. Bartlett, The computer expression recognition toolbox (cert), in: Face and gesture 2011, IEEE, 2011, pp. 298–305.
  * [167] M. Cannizzaro, B. Harel, N. Reilly, P. Chappell, P. J. Snyder, Voice acoustical measurement of the severity of major depression, Brain and cognition 56 (1) (2004) 30–35.
  * [168] E. Moore II, M. A. Clements, J. W. Peifer, L. Weisser, Critical analysis of the impact of glottal features in the classification of clinical depression in speech, IEEE transactions on biomedical engineering 55 (1) (2007) 96–107.
  * [169] B. J. Shannon, K. K. Paliwal, A comparative study of filter bank spacing for speech recognition, in: Microelectronic engineering research conference, Vol. 41, Citeseer, 2003, pp. 310–12.
  * [170] F. Eyben, B. Schuller, opensmile:) the munich open-source large-scale multimedia feature extractor, ACM SIGMultimedia Records 6 (4) (2015) 4–13.
  * [171] L. Yang, D. Jiang, H. Sahli, Feature augmenting networks for improving depression severity estimation from speech signals, IEEE Access 8 (2020) 24033–24045.
  * [172] M. Niu, B. Liu, J. Tao, Q. Li, A time-frequency channel attention and vectorization network for automatic depression level prediction, Neurocomputing (2021).  doi:https://doi.org/10.1016/j.neucom.2021.04.056.
URL https://www.sciencedirect.com/science/article/pii/S0925231221005981

  * [173] Y. Dong, X. Yang, A hierarchical depression detection model based on vocal and emotional cues, Neurocomputing 441 (2021) 279–290.
  * [174] D. Yi, Z. Lei, S. Liao, S. Z. Li, Learning face representation from scratch, arXiv preprint arXiv:1411.7923 (2014).
  * [175] X. Zhou, K. Jin, Y. Shang, G. Guo, Visually interpretable representation learning for depression recognition from facial images, IEEE Transactions on Affective Computing 11 (3) (2020) 542–552.  doi:10.1109/TAFFC.2018.2828819.
  * [176] W. C. de Meto, E. Granger, M. B. Lopez, Encoding temporal information for automatic depression recognition from facial analysis, in: ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2020, pp. 1080–1084.
  * [177] L. He, J. C.-W. Chan, Z. Wang, Automatic depression recognition using cnn with attention mechanism from videos, Neurocomputing 422 165–175.
  * [178] M. Niu, J. Tao, B. Liu, C. Fan, Automatic depression level detection via lp-norm pooling., in: INTERSPEECH, 2019, pp. 4559–4563.
  * [179] Z. Zhao, Q. Li, N. Cummins, B. Liu, H. Wang, J. Tao, B. W. Schuller, Hybrid network feature extraction for depression assessment from speech, Proc. Interspeech 2020 (2020) 4956–4960.
  * [180] T. Al Hanai, M. M. Ghassemi, J. R. Glass, Detecting depression with audio/text sequence modeling of interviews., in: Interspeech, 2018, pp. 1716–1720.
  * [181] W. C. de Melo, E. Granger, A. Hadid, A deep multiscale spatiotemporal network for assessing depression from facial dynamics, IEEE Transactions on Affective Computing (2020).
  * [182] L. He, C. Guo, P. Tiwari, H. M. Pandey, W. Dang, Intelligent system for depression scale estimation with facial expressions and case study in industrial intelligence, International Journal of Intelligent Systems (2021).
  * [183] W. Carneiro de Melo, E. Granger, M. Bordallo Lopez, Mdn: A deep maximization-differentiation network for spatio-temporal depression detection, IEEE Transactions on Affective Computing (2021) 1–1doi:10.1109/TAFFC.2021.3072579.
  * [184] L. Yang, D. Jiang, W. Han, H. Sahli, Dcnn and dnn based multi-modal depression recognition, in: 2017 Seventh International Conference on Affective Computing and Intelligent Interaction (ACII), IEEE, 2017, pp. 484–489.
  * [185] Z. Zhao, Z. Bao, Z. Zhang, J. Deng, N. Cummins, H. Wang, J. Tao, B. Schuller, Automatic assessment of depression from speech via a hierarchical attention transfer network and attention autoencoders, IEEE Journal of Selected Topics in Signal Processing 14 (2) (2020) 423–434.  doi:10.1109/JSTSP.2019.2955012.
  * [186] L. Yang, D. Jiang, X. Xia, E. Pei, M. C. Oveneke, H. Sahli, Multimodal measurement of depression using deep learning models, in: Proceedings of the 7th Annual Workshop on Audio/Visual Emotion Challenge, 2017, pp. 53–59.
  * [187] S. Yin, C. Liang, H. Ding, S. Wang, A multi-modal hierarchical recurrent neural network for depression detection, in: Proceedings of the 9th International on Audio/Visual Emotion Challenge and Workshop, 2019, pp. 65–71.
  * [188] M. Rodrigues Makiuchi, T. Warnita, K. Uto, K. Shinoda, Multimodal fusion of bert-cnn and gated cnn representations for depression detection, in: Proceedings of the 9th International on Audio/Visual Emotion Challenge and Workshop, 2019, pp. 55–63.
  * [189] W. Fan, Z. He, X. Xing, B. Cai, W. Lu, Multi-modality depression detection via multi-scale temporal dilated cnns, in: Proceedings of the 9th International on Audio/Visual Emotion Challenge and Workshop, 2019, pp. 73–80.
  * [190] L. Zhang, J. Driscol, X. Chen, R. Hosseini Ghomi, Evaluating acoustic and linguistic features of detecting depression sub-challenge dataset, in: Proceedings of the 9th International on Audio/Visual Emotion Challenge and Workshop, 2019, pp. 47–53.
  * [191] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, I. Polosukhin, Attention is all you need, Advances in neural information processing systems 30 (2017) 5998–6008.
  * [192] K. Hara, H. Kataoka, Y. Satoh, Can spatiotemporal 3d cnns retrace the history of 2d cnns and imagenet?, in: Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, 2018, pp. 6546–6555.
  * [193] L. Yang, Y. Li, H. Chen, D. Jiang, M. C. Oveneke, H. Sahli, Bipolar disorder recognition with histogram features of arousal and body gestures, in: Proceedings of the 2018 on Audio/Visual Emotion Challenge and Workshop, 2018, pp. 15–21.
  * [194] Z. Du, W. Li, D. Huang, Y. Wang, Bipolar disorder recognition via multi-scale discriminative audio temporal representation, in: Proceedings of the 2018 on Audio/Visual Emotion Challenge and Workshop, 2018, pp. 23–30.
  * [195] Z. S. Syed, K. Sidorov, D. Marshall, Automated screening for bipolar disorder from audio/visual modalities, in: Proceedings of the 2018 on Audio/Visual Emotion Challenge and Workshop, 2018, pp. 39–45.
  * [196] X. Xing, B. Cai, Y. Zhao, S. Li, Z. He, W. Fan, Multi-modality hierarchical recall based on gbdts for bipolar disorder classification, in: Proceedings of the 2018 on Audio/Visual Emotion Challenge and Workshop, 2018, pp. 31–37.
  * [197] Z. Huang, J. Epps, D. Joachim, Investigation of speech landmark patterns for depression detection, IEEE Transactions on Affective Computing (2019) 1–1doi:10.1109/TAFFC.2019.2944380.
  * [198] K. Anis, H. Zakia, D. Mohamed, C. Jeffrey, Detecting depression severity by interpretable representations of motion dynamics, in: 2018 13th IEEE International Conference on Automatic Face & Gesture Recognition (FG 2018), IEEE, 2018, pp. 739–745.
  * [199] S. M. Alghowinem, T. Gedeon, R. Goecke, J. Cohn, G. Parker, Interpretation of depression detection models via feature selection methods, IEEE Transaction on Affective Computing (01) (2020) 1–1.
  * [200] S. Jayawardena, J. Epps, E. Ambikairajah, Ordinal logistic regression with partial proportional odds for depression prediction, IEEE Transactions on Affective Computing (2020).
  * [201] L. He, D. Jiang, H. Sahli, Automatic depression analysis using dynamic facial appearance descriptor and dirichlet process fisher encoding, IEEE Transactions on Multimedia 21 (6) (2018) 1476–1486.
  * [202] S. Jayawardena, J. Epps, E. Ambikairajah, Evaluation measures for depression prediction and affective computing, in: ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019, pp. 6610–6614.  doi:10.1109/ICASSP.2019.8682956.
  * [203] S. Amiriparian, A. Awad, M. Gerczuk, L. Stappen, A. Baird, S. Ottl, B. Schuller, Audio-based recognition of bipolar disorder utilising capsule networks, in: 2019 International Joint Conference on Neural Networks (IJCNN), IEEE, 2019, pp. 1–7.
  * [204] Y. Li, L. Yang, H. Chen, D. Jiang, H. Sahli, Audio visual multimodal classification of bipolar disorder episodes, in: 2019 8th International Conference on Affective Computing and Intelligent Interaction Workshops and Demos (ACIIW), IEEE, 2019, pp. 115–120.
  * [205] Z. Ren, J. Han, N. Cummins, Q. Kong, M. D. Plumbley, B. W. Schuller, Multi-instance learning for bipolar disorder diagnosis using weakly labelled speech data, in: Proceedings of the 9th International Conference on Digital Public Health, 2019, pp. 79–83.
  * [206] N. Abaei, H. Al Osman, A hybrid model for bipolar disorder classification from visual information, in: ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2020, pp. 4107–4111.
  * [207] H. He, E. A. Garcia, Learning from imbalanced data, IEEE Transactions on knowledge and data engineering 21 (9) (2009) 1263–1284.
  * [208] L. A. Jeni, J. F. Cohn, F. De La Torre, Facing imbalanced data–recommendations for the use of performance metrics, in: 2013 Humaine association conference on affective computing and intelligent interaction, IEEE, 2013, pp. 245–251.

  *[HAMD]: Hamilton Rating Scale for Depression
  *[ADE]: Automatic Depression Estimation
  *[DL]: Deep Learning
  *[BDI]: Beck Depression Index
  *[DCNN]: Deep Convolutional Neural Network