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Recent discoveries of a significant population of bright galaxies at cosmic dawn (z10)\left(z \gtrsim 10\right) have enabled critical tests of cosmological galaxy formation models. In particular, the bright end of the galaxy UV luminosity function (UVLF) appears higher than predicted by many models. Using approximately 25,000 galaxy snapshots at 8z128 \leq z \leq 12 in a suite of FIRE-2 cosmological "zoom-in'' simulations from the Feedback in Realistic Environments (FIRE) project, we show that the observed abundance of UV-bright galaxies at cosmic dawn is reproduced in these simulations with a multi-channel implementation of standard stellar feedback processes, without any fine-tuning. Notably, we find no need to invoke previously suggested modifications such as a non-standard cosmology, a top-heavy stellar initial mass function, or a strongly enhanced star formation efficiency. We contrast the UVLFs predicted by bursty star formation in these original simulations to those derived from star formation histories (SFHs) smoothed over prescribed timescales (e.g., 100 Myr). The comparison demonstrates that the strongly time-variable SFHs predicted by the FIRE simulations play a key role in correctly reproducing the observed, bright-end UVLFs at cosmic dawn: the bursty SFHs induce order-or-magnitude changes in the abundance of UV-bright (MUV20M_\mathrm{UV} \lesssim -20) galaxies at z10z \gtrsim 10. The predicted bright-end UVLFs are consistent with both the spectroscopically confirmed population and the photometrically selected candidates. We also find good agreement between the predicted and observationally inferred integrated UV luminosity densities, which evolve more weakly with redshift in FIRE than suggested by some other models.
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Bursty Star Formation Naturally Explains the Abundance of Bright Galaxies at Cosmic Dawn
Guochao Sun,1Claude-Andr´
e Faucher-Gigu`
ere,1Christopher C. Hayward,2Xuejian Shen,3, 4 Andrew Wetzel,5
and Rachel K. Cochrane2
1CIERA and Department of Physics and Astronomy, Northwestern University, 1800 Sherman Ave, Evanston, IL 60201, USA
2Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA
3TAPIR, California Institute of Technology, Pasadena, CA, 91125
4Department of Physics & Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA
02139, USA
5Department of Physics & Astronomy, University of California, Davis, CA 95616
Submitted to ApJL
ABSTRACT
Recent discoveries of a significant population of bright galaxies at cosmic dawn (z10) have enabled
critical tests of cosmological galaxy formation models. In particular, the bright end of the galaxy UV
luminosity function (UVLF) appears higher than predicted by many models. Using approximately
25,000 galaxy snapshots at 8 z12 in a suite of FIRE-2 cosmological “zoom-in” simulations from
the Feedback in Realistic Environments (FIRE) project, we show that the observed abundance of UV-
bright galaxies at cosmic dawn is reproduced in these simulations with a multi-channel implementation
of standard stellar feedback processes, without any fine-tuning. Notably, we find no need to invoke
previously suggested modifications such as a non-standard cosmology, a top-heavy stellar initial mass
function, or a strongly enhanced star formation efficiency. We contrast the UVLFs predicted by bursty
star formation in these original simulations to those derived from star formation histories (SFHs)
smoothed over prescribed timescales (e.g., 100 Myr). The comparison demonstrates that the strongly
time-variable SFHs predicted by the FIRE simulations play a key role in correctly reproducing the
observed, bright-end UVLFs at cosmic dawn: the bursty SFHs induce order-or-magnitude changes
in the abundance of UV-bright (MUV 20) galaxies at z10. The predicted bright-end UVLFs
are consistent with both the spectroscopically confirmed population and the photometrically selected
candidates. We also find good agreement between the predicted and observationally inferred integrated
UV luminosity densities, which evolve more weakly with redshift in FIRE than suggested by some other
models.
Keywords: galaxies: formation galaxies: evolution galaxies: star formation galaxies: high-redshift
1. INTRODUCTION
For the first time, the James Webb Space Telescope
(JWST) has unlocked the door to a population-level
analysis of galaxies well into the era of cosmic dawn (for
a review of key high-redshift science themes of JWST,
see Robertson 2022). Following its discovery of an unex-
pectedly high abundance of UV-bright, massive galaxy
candidates at redshift z10 (e.g., Finkelstein et al.
Corresponding author: Guochao Sun
guochao.sun@northwestern.edu
2022;Naidu et al. 2022a;Donnan et al. 2023;Harikane
et al. 2023b;Yan et al. 2023), there is a long list of
intriguing questions to be answered about how to in-
terpret these observations. What is the true nature
(redshift, mass, metallicity, age, etc.) of these bright
galaxies? If they are truly massive galaxies at cosmic
dawn, what makes it possible for them to have formed
so early? Are these observations in significant tension
with the standard ΛCDM cosmological model? Obser-
vational and theoretical investigations into these ques-
tions are being actively pursued in a large body of recent
literature from different perspectives, including the pu-
arXiv:2307.15305v1 [astro-ph.GA] 28 Jul 2023
2Sun et al.
rity of high-zcandidates (Naidu et al. 2022b;Arrabal
Haro et al. 2023;Curtis-Lake et al. 2023;Furlanetto &
Mirocha 2023;Zavala et al. 2023), the physics of star for-
mation in high-zgalaxies (Dekel et al. 2023;Mirocha &
Furlanetto 2023;Robertson et al. 2023;Qin et al. 2023;
Sipple & Lidz 2023;Trinca et al. 2023), the implica-
tions of high-zobservations for the cosmological model
(Boylan-Kolchin 2023;Hassan et al. 2023;Melia 2023),
and so forth.
While spectroscopic follow-up studies for many of
the galaxy candidates are still ongoing, conservative
lower limits on the bright end of UV luminosity func-
tion (UVLF) and the integrated UV luminosity den-
sity at z10 derived from the existing, spectroscop-
ically confirmed samples have already suggested milder
redshift evolution towards z > 10 than expected by
many theoretical models (e.g., Harikane et al. 2023a).
Such a higher-than-expected abundance of bright galax-
ies based on secure redshifts is consistent with earlier
studies based on photometrically selected samples, thus
calling for a re-examination of the theoretical landscape
of galaxy formation at cosmic dawn. Several physi-
cal mechanisms have been considered to explain a high
abundance of bright galaxies at high redshifts. For ex-
ample, a higher star formation efficiency (SFE) resulting
from less efficient feedback regulation could boost the
UV-bright galaxy abundance by forming more stars per
unit baryon (Dekel et al. 2023;Harikane et al. 2023b),
whereas a more top-heavy initial mass function (IMF)
of the stellar population could similarly lead to more
bright galaxies by creating more UV photons per unit
stellar mass formed (Inayoshi et al. 2022;Yung et al.
2023). A conspiracy between the redshift evolution of
dust attenuation and the abundance of massive halos at
high zcould also potentially allow the bright-end UVLF
and UV luminosity density to evolve relatively mildly
(Ferrara et al. 2023;Mirocha & Furlanetto 2023), al-
though such a coincidence would not by itself explain
the correct absolute abundance of bright galaxies. A
number of studies have also examined the possibility
that the high abundance of early massive galaxies im-
plies physics beyond the standard ΛCDM cosmology,
such as a modified primordial power spectrum (Hirano
& Yoshida 2023;Padmanabhan & Loeb 2023;Parashari
& Laha 2023; though see Sabti et al. 2023), primor-
dial non-Gaussianity (Biagetti et al. 2023), or alterna-
tive dark matter models (Bird et al. 2023;Dayal & Giri
2023;Gong et al. 2023).
Another promising avenue to elevate the abundance
of bright galaxies is the strong time variability (“bursti-
ness”) of star formation. In recent years, several dif-
ferent galaxy formation simulations have predicted that
the star formation rate (SFR) is highly time variable in
low-mass galaxies (e.g., Hopkins et al. 2014;Dom´ınguez
et al. 2015;Muratov et al. 2015;Sparre et al. 2017;
Pallottini & Ferrara 2023). The prediction of bursty
star formation appears generic to codes that resolve
the clustering of supernovae in the interstellar medium
(Hu et al. 2023). The simulations predict that bursty
star formation is especially common in low-mass galax-
ies, likely due to the shallow potential wells which al-
low clumpy, cold inflows and outflows to drive repeated
inflow-star formation-outflow cycles (Stern et al. 2021;
Gurvich et al. 2023;Byrne et al. 2023;Hopkins et al.
2023). Since low-mass galaxies dominate at high red-
shift, we expect the implications of bursty star forma-
tion on the UVLF to be particularly important in this
regime (e.g., Furlanetto & Mirocha 2022). Indeed, ev-
idence for an increased level of bursty star formation
has emerged from recent JWST observations of cos-
mic dawn galaxies (e.g., Dressler et al. 2023;Endsley
et al. 2023;Looser et al. 2023a,b). As pointed out in
recent theoretical studies (Mason et al. 2023;Mirocha
& Furlanetto 2023;Shen et al. 2023;Mu˜noz et al. 2023),
an increased level of UV variability sourced by bursty
star formation can give rise to more UV-bright galax-
ies due to the Eddington bias, which flattens the bright
end of the UVLF. In this case, the observed UVLFs
at z10 could potentially be explained by bursty star
formation combined with “normal” SFE and production
efficiency of UV photons. While bursty star formation
can in principle enhance the abundance of bright galax-
ies, it remains to be shown whether the enhancement
is sufficient to reproduce the observed bright-end of the
UVLF in a self-consistent galaxy formation model, such
as those provided by hydrodynamic simulations.
In this Letter, we use a suite of cosmological “zoom-
in” simulations from the Feedback in Realistic Envi-
ronments (FIRE) project1to investigate the effects of
bursty star formation on the UVLF at 8 z12.
In these simulations, the SFR variability arises self-
consistently from the modeling of standard stellar feed-
back processes. It is noteworthy that these simulations
generated before the launch of JWST were in par-
ticular not in any way tuned to match recent observa-
tions. Moreover, the simulations use exactly the same
FIRE-2 code (Hopkins et al. 2018) that has been used
to evolve large sets of simulated galaxies all the way to
z= 0 and demonstrated to produce broadly realistic
galaxy properties down to the present time (e.g. Wetzel
et al. 2023, and references therein). This is in contrast
1See the FIRE project website: http://fire.northwestern.edu.
Bursty Star Formation and High-zGalaxy LFs 3
with many other simulations of cosmic dawn galaxies,
in which the simulations are stopped at high redshift
and for which we therefore do not know how the feed-
back model performs at lower redshifts. We show that
the FIRE-2 simulations produce an excellent match to
the UVLF recently measured by JWST during cosmic
dawn, and that the time variability of star formation
plays an important role in explaining the observations
at the bright end. These results constitute an impor-
tant test of the feedback model and highlight the im-
portance of considering the variability of star formation
when modeling high-zobservations.
Throughout the Letter, we adopt a flat ΛCDM cos-
mology consistent with Planck Collaboration et al.
(2020), and all magnitudes are quoted in the AB sys-
tem (Oke & Gunn 1983).
2. SIMULATIONS AND ANALYSIS METHODS
2.1. The Simulations
In this Letter, we analyze the same set of simulations
as recently studied by Sun et al. (2023a), which is a sub-
set of the High-Redshift suite (Ma et al. 2018a,b,2019) of
the FIRE-2 cosmological zoom-in simulations (Hopkins
et al. 2018). The FIRE-2 simulations use the GIZMO
code with its meshless-finite mass (MFM) hydro solver
(Hopkins 2015), and include multiple channels of stel-
lar feedback to regulate star formation. Star formation
occurs in dense molecular gas (nH>1000 cm3) that
is self-gravitating and self-shielding. The stellar feed-
back mechanisms implemented include: (1) energy, mo-
mentum, mass, and metal injection from core collapse
and Type Ia supernovae and winds from OB and AGB
stars, (2) photoionization and photoelectric heating, and
(3) radiation pressure. A redshift-dependent but homo-
geneous ionizing background is also included following
Faucher-Gigu`ere et al. (2009).2The baryonic (dark mat-
ter) mass resolution of the set of simulations considered
in this work is mb= 7 ×103M(mDM = 4 ×104M),
except for the simulations z5m11a and z5m11b, which
2The version of the ionizing background used in these simulations
reionizes the universe at zreion 10, which is earlier than the
mid-point of reionization of zreion 8 favored by more recent
observational constraints (e.g., Planck Collaboration et al. 2020;
Faucher-Gigu`ere 2020). However, our main results focus on the
bright end of the UVLF, which arises from relatively massive
halos, whereas the suppression of galaxy formation due to heat-
ing by the ionizing background primarily affects low-mass halos
(Mh109M; e.g. Gnedin 2000;Noh & McQuinn 2014). More-
over, an earlier reionization redshift implies that in the present
simulations, galaxy formation is suppressed starting earlier in the
small halos, so adopting a more up-to-date reionization model
would (if anything) enhance the predicted UV luminosity den-
sity. Similar arguments apply to other IGM heating processes.
have mb1×103M(mDM = 5 ×103M). The
gravitational softenings are fixed in physical units to
ϵDM = 42 pc for the dark matter and ϵstar = 2.1 pc for
stars. The gravitational softenings are adaptive for gas,
with a minimum of ϵb= 0.42 pc. This is, again, with
the exception of z5m11a and z5m11b (see Figure 4for
a list of simulation IDs considered in this work), which
have ϵDM = 21 pc, ϵstar = 1.4 pc, and ϵb= 0.28 pc.
Part of the High-Redshift suite of simulations were
presented and analyzed in detail by Ma et al. (2018a,b)
for the predicted properties of the simulated galaxy
population at 5 z12, including sizes, morpholo-
gies, scaling relations, and number statistics measured
by the stellar mass and luminosity functions. In this
follow-up analysis of Ma et al. (2018b) motivated by re-
cent JWST observations of the abundance of galaxies
at z10, we follow closely the methodology adopted in
Ma et al. (2018b) for fair comparisons, but the sample
size of high-z, massive galaxies has been substantially
increased to better determine the bright-end behavior
of galaxy UVLFs at cosmic dawn. Below, we will only
briefly summarize the key information about the sample
of simulated galaxies pertinent to the analysis presented
here. We refer interested readers to the aforementioned
papers for further details about the FIRE-2 simulations
and the High-Redshift suite.
For a robust analysis of UVLFs at their bright end, we
build a maximum possible sample size of massive galax-
ies by making use of all the zoom-in simulations available
at each redshift above the ending redshift zend. In each
zoom-in region, we consider all the well-resolved halos3
that host a central galaxy, rather than the one hosting
just the most massive, primary galaxy (typically near
the center of the zoom-in region). Following Ma et al.
(2018b), we define galaxies based on catalogs of halos
identified with the Amiga Halo Finder (AHF; Knoll-
mann & Knebe 2009). The radius Rmax at which the
halo rotation curve reaches maximum is used to define
a galaxy by incorporating star particles within Rmax/3
and excluding the contamination from subhalos outside
Rmax/5. We restrict the scope of our UVLF analysis
to halos with mass Mh>107.5Min snapshots at
8z12 because most of the recent UVLF measure-
ments at z < 8 with JWST can be well explained by
previous theoretical predictions and a sufficiently con-
straining sample of spectroscopically-confirmed galax-
ies is not available at z > 12 (Harikane et al. 2023a).
In Appendix A, we illustrate how the halo/galaxy sam-
3Halos containing at least 104particles in total and uncontami-
nated by low-resolution particles are considered “well-resolved”.
4Sun et al.
ple is constructed with (snapshots of) the 26 individual
zoom-in simulations, which build up a total sample of
25,000 galaxy snapshots over 8 z12.
2.2. Processing of the Simulations
We process the simulated galaxy sample in order to
arrive at their 1600 ˚
A UV magnitudes MUV, following
Sun et al. (2023a). Templates of binary, single-stellar-
population (SSP) spectra from BPASS v2.1 (Eldridge
et al. 2017) are interpolated and applied to star particles
according to their stellar age and metallicity, assuming
a Kroupa IMF (Kroupa 2001). Including nebular (con-
tinuum) emission can in principle augment both the UV
emissivity and variability (Byler et al. 2017), although
we opt to ignore it here as nebular emission is not ex-
pected to strongly affect the measurement of MUV, es-
pecially when compared with effects of SFR variations.
Two notable differences from Sun et al. (2023a) exist,
though, for the treatment of (1) the connection between
MUV and the SFH and (2) dust attenuation, on which
we elaborate below.
2.2.1. Bursty vs Smoothed Star Formation Histories
At cosmic dawn, an increased SFR variability can
strongly modulate the observed number statistics of
galaxies. To assess the impact of bursty star forma-
tion on the MUVMhrelation and thus the UVLF, we
consider two contrasting scenarios to model MUV .
The baseline scenario, which we refer to as “bursty”,
assumes that the SFH of each galaxy in our sample is
exactly as predicted by the simulations and thus MUV
can be derived by summing up the spectral emissivities
of all star particles of the galaxy at a given snapshot
according to their age and metallicity, as in Sun et al.
(2023a). This is the approach most faithful to the SFHs
predicted by the simulations. In this approach, MUV
naturally inherits the burstiness predicted by the simu-
lations as the SFR varies, the UV 1600˚
A luminosity
of the galaxy also fluctuates accordingly because most
of FUV continuum emission is sourced by the massive,
short-lived stars formed. As a result, a bursty SFH im-
prints significant stochasticity in MUV at a fixed stellar
or halo mass.
In the contrasting scenario, which we refer to as
“smoothed”, we artificially reduce the impact of bursty
SFH on the evaluation of MUV by redistributing the
ages of star particles (while retaining their metallici-
ties). Specifically, we first define a smoothing kernel
of duration τSF Myr and bin star particles using their
star formation times into time bins of width τSF. We
then redistribute the ages of the star particles in indi-
vidual bins such that the stellar mass forms at a nearly
constant rate by enforcing evenly-distributed star for-
mation times within each bin. This redistribution of
stellar ages effectively smooths the SFH and reduces
to the “bursty” case for a sufficiently small τSF. No-
tably, unlike some previous work where effects of vary-
ing the UV variability on UVLFs are studied assuming
a fixed mean/median LUVMhrelation (e.g., Mirocha
& Furlanetto 2023;Shen et al. 2023), our method by its
nature conserves the total amount of cosmic star forma-
tion such that the two scenarios differ only in terms of
the short-timescale SFR variability and its impact on
the UV emissivity.
2.2.2. Dust Attenuation
Observations have shown compelling evidence of
early chemical enrichment and the production of non-
negligible dust in galaxies at z7 (Tamura et al. 2019;
Fudamoto et al. 2021;Witstok et al. 2023). A reason-
able treatment of dust attenuation is therefore needed
for our predictions of the UVLF at cosmic dawn, espe-
cially at the bright end because massive (intrinsically
UV-bright) galaxies generally contain more dust.
To estimate the effect of dust attenuation on MUV, we
employ an empirical model motivated by an up-to-date
measurement of the βUVMUV (color–magnitude) rela-
tion at z > 8byCullen et al. (2023) using a combination
of JWST and ground-based observations4. We combine
the best-fit relation βUV =0.17MUV + 5.40 with the
attenuation–UV slope relation, AUV = 0.48(βUV +2.62),
determined from z5.5 galaxies observed in the
ALPINE survey (Fudamoto et al. 2020; see also Reddy
et al. 2018). While an extrapolation in redshift is in-
volved, this best-fit relation from ALMA observations
represents a state-of-the-art empirical baseline for es-
timating dust attenuation properties at cosmic dawn,
which should suffice for the purpose of this work. We
neglect the scatter around these mean relations given
its small impact on MUV and caution that results with
dust attenuation included that follow should be taken
as rough estimates only. The validity of these simplistic
treatments can be tested with simulations with detailed
dust radiative transfer (Cochrane et al. 2019,2022;Ma
et al. 2019;Vogelsberger et al. 2020;Shen et al. 2022)
and multi-wavelength observations (Akins et al. 2023;
Bakx et al. 2023), which are left for future work. We
note, though, that at z > 10 the difference between
UVLFs with and without dust attenuation is predicted
to be very small in our model (see Figure 2), such that
4See also Topping et al. (2023), who find slightly steeper βUV that
steepens with increasing redshift from z6–12.
Bursty Star Formation and High-zGalaxy LFs 5
uncertainties in the treatment of dust should not affect
our results significantly.
2.3. Estimating the UVLF from Zoom-in Simulations
Using UV magnitudes derived for the sample of sim-
ulated galaxies binned into redshift bins of width z=
±0.5, we calculate the UVLF through a convolution with
the halo mass function (HMF) following the “HMF-
weighting” method introduced by Ma et al. (2018b).
This method has been verified to provide robust esti-
mates of the UVLF from galaxy samples drawn from
zoom-in simulations, so we only summarize briefly here.
First, in narrow halo mass and redshift bins, we count
the number of simulated halos NSfrom the sample and
compute the expected number of halos NE, which scales
with the HMF, dn/d log Mh, calculated using the hmf
code (Murray et al. 2013) for the fitting function from
Behroozi et al. (2013). A common weight w=NE/NS
is assigned to all the halos in the same bin, such that
a summation of halo weights in a given mass bin yields
the expected number of halos in the universe. These
weights are then applied to sample galaxies binned in
MUV to obtain the UVLF, which is essentially a con-
volution between the HMF and MUVMhrelation in-
cluding the full, Mh-dependent distribution (see Section
2.4 of Ma et al. 2018b). Finally, we stress that, com-
pared with Ma et al. (2018b) where only a subset of
the High-Redshift suite was analyzed, we substantially
increase the number of samples of massive halos/bright
galaxies in this work (a factor 8 increase of halos with
Mh>1010 Mat z= 10) by considering the full High-
Redshift suite as in Ma et al. (2019), thereby extending
the magnitude down to which the UVLF at z > 10 can
be reliably determined to MUV <20, overlapping with
the bright-end UVLF probed by JWST.
3. RESULTS
3.1. The MUVMhRelation and the UVLF
Following the methods outlined in Sections 2.2 and
2.3, we first use our samples of simulated galaxies
to quantify the MUVMhrelation in different redshift
regimes, assuming either “bursty” or “smoothed” SFH.
A comparison of the MUVMhrelations at z= 8, 10,
and 12 from our simulations is shown in the top row of
Figure 1. Overall, galaxies become more UV-bright at
higher Mhand, at a given Mh,MUV decreases modestly
with increasing redshift as a result of more rapid halo
growth at higher redshift. A significant scatter in MUV
around the median relation that gradually increases to-
wards lower masses exists, which is a sign of increas-
ing star formation burstiness at low masses, given the
proportionality between LUV and the SFR. From the
comparison between the “bursty” and “smoothed” cases
shown by the 5–95th percentiles (especially in the top
middle panel where three “smoothed” cases with vary-
ing τSF are shown), it can be seen that evaluating MUV
from a smoothed SFH leads to a shallower MUVMhre-
lation with a reduced scatter in MUV at higher masses,
which effectively suppresses the population of UV-bright
galaxies at a given Mh.
In the bottom row of Figure 1, we show the UVLF
at z= 8–12 implied by the MUVMhrelation. From
the comparisons against recent observational constraints
and between the two SFH cases, several key results are
immediately apparent. First, in the fiducial, “bursty”
SFH scenario, the predicted UVLFs agree remarkably
well with the observational constraints available. In
particular, our z10 predictions lie safely above
the firm lower bounds set by the dust-uncorrected,
spectroscopically-confirmed samples recently compiled
by Harikane et al. (2023a), and they are also broadly
consistent with the variety of measurements based on
photometrically selected candidates (see the caption for
details)5. Unlike some other theoretical predictions
(e.g., Mason et al. 2023;Yung et al. 2023), for which a
clear tension with the spec-zlower bounds exists with-
out modifications, our bursty-case predictions do not
require any additional tuning of UV variability or pro-
duction efficiency to match observations. Despite un-
certainties associated with the treatment of dust, this
good agreement implies that the UVLFs observed by
JWST at z10 are consistent with generally “nor-
mal” SFE and UV production efficiency as predicted by
the FIRE-2 simulations. As demonstrated in Ma et al.
(2018b), the relation between Mand Mhin these sim-
ulations is broadly consistent with extrapolations from
lower zwhere empirical analyses show that the SFE is
strongly suppressed by stellar feedback in low-mass ha-
los (Behroozi et al. 2013;Tacchella et al. 2018).
Second, in the contrasting, “smoothed” SFH scenario,
a clear deficit of UV-bright galaxies is seen as a result
of suppressed up-scattering in MUV of low-mass halos
when the SFR is averaged over a long timescale τSF. The
underestimated abundance of UV-bright galaxies reveals
the important role played by the burstiness of star for-
mation in determining the number statistics of galaxies
at cosmic dawn. As also shown by the comparison of
5We have verified by bootstrapping 1000 times the simulated
galaxy samples that the statistical uncertainty on the UVLF,
especially at the bright end, is small enough that it does not
affect the bright-end comparisons of interest to this study. In
the brightest bin, the 1σstatistical uncertainties in log ϕesti-
mated from bootstrapping are approximately 0.15 dex, 0.15 dex,
and 0.3 dex at z= 8, 10, and 12, respectively.
6Sun et al.
Figure 1. Top: UV magnitude–halo mass relations at z= 8–12. Data for individual galaxies are denoted by the grey dots (no
smoothing applied to the SFH). The thick solid curves indicate the range of the 5th and 95th percentiles in the “bursty” and
“smoothed” cases, from which the suppression of bright galaxy number counts due to smoothing is apparent. Bottom: UVLFs
at z= 8–12 derived from the convolution between the UV magnitude–halo mass relation and the HMF. Dust-free predictions
are shown as solid for both “bursty” and “smoothed” cases, whereas the dust-attenuated scenario is shown as dashed for only
the “bursty” case (Section 2.2.2) for visual clarity. Constraints from observations are shown by the data points in black for
the spectroscopically-confirmed-only samples (Harikane et al. 2023a) and in grey for data sets involving photometric candidates
(Oesch et al. 2018;Bowler et al. 2020;Rojas-Ruiz et al. 2020;Bouwens et al. 2021,2023;Finkelstein et al. 2022;Leethochawalit
et al. 2022;Castellano et al. 2023;Donnan et al. 2023;Harikane et al. 2023a;P´erez-Gonz´alez et al. 2023). Cases with larger
and smaller smoothing timescale τSF values than the fiducial one (100 Myr) are shown at z= 10 to illustrate the impact of SFH
smoothing on the UVLF.
Table 1. Dust-free UVLFs at z= 8, 10, and 12 from the
simulated galaxies.
MUV log ϕ MUV log ϕ MUV log ϕ
z= 8 z= 10 z= 12
10.50.085 10.25 0.207 9.75 0.234
12.50.570 12.25 0.677 11.75 0.971
14.51.206 14.25 1.242 13.75 1.576
16.51.926 16.25 2.124 15.75 2.200
18.52.815 18.25 3.072 17.75 3.282
20.53.872 20.25 4.344 19.75 4.500
22.55.158 22.25 5.902
Notes.
ϕvalues are quoted in units of mag1Mpc3. See Equa-
tion (1) for analytic fits to the UVLF over 8 < z < 12.
For reference, in the two brightest bins, ϕis extracted
from a sample of (39, 17), (39, 13), (93, 17) galaxies at
z= 8, 10, and 12, respectively.
different τSF values at z= 10, smoothed SFHs with
τSF 100 Myr result in bright-end UVLFs that are too
steep compared with observations, especially the pho-
tometrically selected samples, for which the bright-end
UVLF can be underpredicted at >2σlevel in some cases
(Castellano et al. 2023;Donnan et al. 2023). At z= 12,
predictions of the smoothed SFH are in tension with
even the most conservative lower limits derived from
only the spectroscopically confirmed samples (Harikane
et al. 2023a). It is therefore clear that the UVLF serves
as a useful probe of the burstiness in the SFH, as been
noted in e.g., Furlanetto & Mirocha (2022) and Shen
et al. (2023), although in practice it can be challeng-
ing to extract the burstiness information from only the
UVLF measurements (see Section 4). The overall shal-
lower MUVMhrelation when the SFH is smoothed also
leads to slightly steeper slope at the faint end, although
Bursty Star Formation and High-zGalaxy LFs 7
8 10 12 14 16 18 20 22 24
M
UV
7
6
5
4
3
2
1
0
1
log [Number/mag/Mpc3]
z = 8
z = 10
z = 12
This work
Best-fit model (Eq. 1)
MillenniumTNG (Kannan+23)
FLARES (Vijayan+21/Wilkins+23)
CoDa II (Ocvirk+20/Dawoodbhoy+23)
Figure 2. Dust-free UVLFs at z= 8, 10, and 12 predicted
by the FIRE-2 simulations and from the literature. The
binned and the best-fit, double-power law UVLFs are de-
noted by the crosses and solid curves, as specified in Table 1
and Equation (1), respectively. Several example dust-free
predictions from other cosmological hydrodynamical simu-
lations, including MillenniumTNG (dashed, Kannan et al.
2023), FLARES (dotted, Vijayan et al. 2021;Wilkins et al.
2023), and CoDa II (dotted and only at z= 8 and 10, Ocvirk
et al. 2020;Dawoodbhoy et al. 2023) are also plotted for com-
parison.
the effect is much smaller than the suppression at the
bright end.
The binned UVLFs without dust attenuation ex-
tracted from our simulations at z= 8, 10, and 12 are
summarized in Table 1. The binning scheme is chosen
such that the brightest MUV bin contains more than
ten simulated galaxies for robust statistics. Meanwhile,
we fit the dust-free UVLF at 8 z12 assuming a
universal double-power law (DPL) in MUV ,
Φ(MUV) = 0.4(ln 10) 10ϕ
100.4(α+1)(M
UVMUV )+ 100.4(β+1)(M
UVMUV ).
(1)
We specify the redshift-dependent DPL parameters ϕ,
M
UV,α, and βin the form of a single power law as
ϕ(z) = ϕ,0[(1 + z)/10]ϕ,1,M
UV(z) = M,0
UV[(1 +
z)/10]M,1
UV ,α(z) = α,0[(1 + z)/10]α,1, and β(z) =
β,0[(1 + z)/10]β,1, where the best-fit parameters are
found to be ϕ,0=2.01, ϕ,1= 0.68, M,0
UV =17.26,
M,1
UV =0.08, α,0=0.31, α,1=0.93, β,0= 0.68,
and α,1= 0.93. Figure 2shows a comparison between
the binned and best-fit UVLFs predicted by our sim-
ulations and other theoretical predictions in the litera-
ture based on cosmological hydrodynamical simulations
(Ocvirk et al. 2020;Vijayan et al. 2021;Dawoodbhoy
et al. 2023;Kannan et al. 2023;Wilkins et al. 2023).
Overall, our predicted UVLFs show a weaker redshift
evolution beyond z= 8 compared with the predic-
tions from the MillenniumTNG (Kannan et al. 2023)
and CoDa II (Ocvirk et al. 2020;Dawoodbhoy et al.
2023) simulations, which results in a higher abundance
of bright (MUV 20) galaxies at z10. Our bright-
end predictions are generally comparable to those from
the FLARES simulations (Vijayan et al. 2021;Wilkins
et al. 2023) in both normalization and slope, despite the
vastly different nature of the simulations and methods
to evaluate the UVLF. It is noteworthy, though, that
the FIRE-2 simulations analyzed in this work have sig-
nificantly higher resolution (mb7×103Min FIRE-2
vs. mb2×106Min FLARES), which allows us to
predict the UVLFs at 8 z12 down to MUV 10
vs. the FLARES predictions down to MUV 18. We
have also verified that UVLFs in this work and from
Ma et al. (2018b,2019) are in good agreement in the
overlapping regime.
3.2. UV Luminosity Density
By integrating the predicted UVLFs, we can de-
rive the UV luminosity density, ρUV, as a function of
time, which traces the cosmic star formation rate den-
sity (SFRD). Since at z10 only the brightest end
(MUV MUV,) of the UVLF has been probed, we
follow Harikane et al. (2023a) to compare the UV lu-
minosity density contributed by galaxies brighter than
MUV =18, namely ρUV,bright =ρUV(MUV <18),
which corresponds to the contribution from halos with
Mh1010 Mat z= 10. The unconstrained contri-
bution by fainter, lower-mass galaxies is highly sensitive
to the faint-end slope of the UVLF and might even out-
weigh ρUV,bright (Sun & Furlanetto 2016), but the com-
parison restricted to MUV <18 galaxies still serves as
a useful test of the overall abundance of bright, massive
galaxies and their SFE at cosmic dawn6.
Figure 3shows a comparison of the cumulative UV
luminosity density between the dust-attenuated predic-
tions from our simulations and a compilation of con-
straints from observations and theoretical forecasts in
the literature. Throughout, dust-attenuated predictions
from models/simulations (curves) are compared with
observations (data points), which are dust-uncorrected.
Over 8 z12, dust-attenuated luminosity den-
6Results from this work, Harikane et al. (2018,2023b), and
Bouwens et al. (2023) are integrated down to MUV,lim =18,
whereas the rest are down to MUV,lim =17. Figure 3thus
shows conservatively that our simulations without smoothing pre-
dict enough total UV emission compared with observations, re-
gardless of the modest difference in MUV,lim .
8Sun et al.
8 9 10 11 12 13 14
z
23.0
23.5
24.0
24.5
25.0
25.5
26.0
26.5
27.0
log( UV/erg s 1Hz 1Mpc 3)
M
UV 18
bursty
smoothed
Harikane+18
Mason+15
McLeod+23
Donnan+23
Bouwens+23
Harikane+23
Figure 3. The cumulative UV luminosity density ρUV (<
MUV,lim) integrated down to MUV,lim 18 with dust at-
tenuation included (see Section 2.2.2). At z10, some the-
oretical models (e.g., Mason et al. 2015;Harikane et al. 2018)
underestimate ρUV compared with observational constraints
based on photometric galaxy candidates (e.g., Bouwens et al.
2023;Donnan et al. 2023;McLeod et al. 2023;erez-
Gonz´alez et al. 2023) and/or spectroscopically-confirmed
galaxies as firm lower limits (Harikane et al. 2023a). Predic-
tions from our “bursty” case are broadly consistent with both
photometric and spectroscopic samples and show a slightly
weaker redshift evolution ρUV (1 + z)0.3over 8 z12.
sities predicted by our simulations without smoothing
the SFH are fully consistent with observations of both
photometric galaxy candidates and spectroscopically-
confirmed galaxies that provide firm lower limits. Due to
the integrated nature of ρUV, the “smoothed” case ap-
pears more consistent with the spec-z-only lower limits
here than at the bright end of the UVLF as shown in Fig-
ure 2. In both cases with dust attenuation, a power-law
evolution of ρUV (1+z)0.3over 8 z12 is implied,
which appears more gradual compared with the predic-
tions by some previously proposed semi-analytic/semi-
empirical models, such as in Mason et al. (2015) and
Harikane et al. (2018).
4. DISCUSSION AND CONCLUSIONS
We have demonstrated that the FIRE-2 simulations
with a multi-channel implementation of standard stel-
lar feedback processes can reproduce well the observed
abundance of UV-bright galaxies at z10, including
both the photometrically selected candidates and the
spectroscopically confirmed sources recently discovered
by JWST. We further showed that the bursty SFH pre-
dicted to be common in galaxies at cosmic dawn is im-
portant for explaining the bright-end of the UVLF. With
burstiness included, the simulations demonstrate that a
boosted UV emissivity due to, e.g., an enhanced SFE,
a top-heavy IMF, AGN contributions, or Population III
stars (see e.g., Harikane et al. 2023b,c), is not necessary
to explain the bright-end UVLF at z10. (This is of
course not to say that none of these other effects could
be present in the real universe, so it certainly remains in-
teresting to investigate these other possibilities!) Com-
pared to semi-analytic/empirical models (Mason et al.
2023;Mirocha & Furlanetto 2023;Shen et al. 2023;Yung
et al. 2023), our predictions based on the FIRE-2 simu-
lations avoid ad hoc fine-tuning of the MUVMhrelation
to match observations.
We note that Pallottini & Ferrara (2023) also re-
cently used a set of cosmological zoom-in simulations
(SERRA; Pallottini et al. 2022) to investigate implica-
tions of stochastic star formation in early galaxies for
the abundance of z10 galaxies observed by JWST. By
characterizing the distribution of time-dependent varia-
tions in the SFR of individual galaxies, they concluded
that the predicted SFR variability cannot account for
the required boost suggested by some recent literature
to match the observed UVLF at z10 (Mirocha &
Furlanetto 2023;Shen et al. 2023). However, Pallot-
tini & Ferrara (2023) did not self-consistently derive the
UVLF from their simulations. Since other physical fac-
tors such as the SFE also impact the UVLF, in addition
to burstiness (Mirocha & Furlanetto 2023;Mu˜noz et al.
2023), in order to unambiguously gauge the importance
of bursty star formation it is desirable to perform a self-
consistent, end-to-end study of the UVLF as we do in
this work.
Looking ahead, a detailed characterization of the SFR
variability on different timescales will shed light on the
physical processes at play in the build-up of galaxies at
early times, as has been demonstrated in recent work
using periodogram (Pallottini & Ferrara 2023) or more
generally power spectral density (PSD) analysis (Iyer
et al. 2020;Tacchella et al. 2020). Moreover, various
implications of bursty star formation should be explic-
itly considered when interpreting observations of high-z
galaxies. For example, Sun et al. (2023a) showed that
SFR variability introduces important selection effects in
rest UV-selected samples. Since most galaxies at cosmic
dawn may form stars in a highly bursty manner, the
impact of burstiness on galaxy number statistics also
raises questions about how to reliably constrain cosmol-
ogy with high-zgalaxy observations (Sabti et al. 2023).
At the same time, it is of great interest to investigate
how to observationally characterize the time variability
of star formation, e.g. using SFR indicators sensitive to
different timescales (Sparre et al. 2017;Flores Vel´azquez
Bursty Star Formation and High-zGalaxy LFs 9
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
log(
M
h/
M
)
1
10
100
Number of haloes at
z
= 10 ± 0.5
z5m12a
z5m12b
z5m12c
z5m12d
z5m12e
z5m11a
z5m11b
z5m11c
z5m11d
z5m11e
z5m11f
z5m11g
z5m11h
z5m11i
z7m11a
z7m11b
z7m11c
z7m12a
z7m12b
z7m12c
z9m11a
z9m11b
z9m11c
z9m11d
z9m11e
z9m12a
Figure 4. The number of galaxies sampled in each halo
mass bin for the 26 simulations inspected for evaluating the
UVLF at z= 10 ±0.5. This amounts to a total of 9000
galaxies sampled from snapshots of the 26 zoom-in regions
over 9.5< z < 10.5. Simulation IDs are listed in the legend
(c.f., Sun et al. 2023a).
et al. 2021;Sun et al. 2023b) or the spatial clustering
of galaxies (Mu˜noz et al. 2023). Quantifying the effects
of bursty star formation on statistics such as galaxy
clustering is a critical stepping stone towards the usage
of high-zgalaxies as robust cosmological probes.
The authors thank Pratik Gandhi, Yuichi Harikane,
and Julian Mu˜noz for helpful discussion. GS was sup-
ported by a CIERA Postdoctoral Fellowship. CAFG
was supported by NSF through grants AST-2108230
and CAREER award AST-1652522; by NASA through
grants 17-ATP17-0067 and 21-ATP21-0036; by STScI
through grant HST-GO-16730.016-A; and by CXO
through grant TM2-23005X. The Flatiron Institute
is supported by the Simons Foundation. AW re-
ceived support from: NSF via CAREER award AST-
2045928 and grant AST-2107772; NASA ATP grant
80NSSC20K0513; HST grants AR-15809, GO-15902,
GO-16273 from STScI.
Software: BPASS (Eldridge et al. 2017), Giz-
moAnalysis (Wetzel & Garrison-Kimmel 2020), hmf
(Murray et al. 2013)
APPENDIX
A. FORMING THE HALO/GALAXY SAMPLE
Throughout, we analyze snapshots of a galaxy in a
z= 0.5 bin multiple times per the cadence at which
snapshots are stored (every 10–20 Myr). While the same
galaxy from neighbouring snapshots are not strictly in-
dependent as far as MUV is considered, this method is
useful because the highly time-variable SFR limits the
temporal correlation between consecutive snapshots. It
yields a large statistical sample appropriate for UVLF
analysis (see Figure 4) and the sampling cadence does
not bias the results, as have been shown by analyses
that randomly exclude approximately half of the sam-
ples (Ma et al. 2018b). At z= 8, 10, and 12, the UVLF
is evaluated from a sample of approximately 12,000,
9,000, and 4,000 galaxies, respectively. Summing over
the three redshift bins, this yields 25,000 galaxy sam-
ples in total.
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Understanding the star formation rate (SFR) variability and how it depends on physical properties of galaxies is important for developing and testing the theory of galaxy formation. We investigate how statistical measurements of the extragalactic background light (EBL) can shed light on this topic and complement traditional methods based on observations of individual galaxies. Using semi-empirical models of galaxy evolution and SFR indicators sensitive to different star formation timescales (e.g., Hα and UV continuum luminosities), we show that the SFR variability, quantified by the joint probability distribution of the SFR indicators (i.e., the bivariate conditional luminosity function), can be characterized as a function of galaxy mass and redshift through the cross-correlation between deep, near-infrared maps of the EBL and galaxy distributions. As an example, we consider combining upcoming SPHEREx maps of the EBL with galaxy samples from Rubin/LSST. We demonstrate that their cross-correlation over a sky fraction of fsky ∼ 0.5 can constrain the joint SFR indicator distribution at high significance up to z ∼ 2.5 for mass-complete samples of galaxies down to M* ∼ 109 M⊙. These constraints not only allow models of different SFR variability to be distinguished, but also provide unique opportunities to investigate physical mechanisms that require large number statistics such as environmental effects. The cross-correlations investigated illustrate the power of combining cosmological surveys to extract information inaccessible from each data set alone, while the large galaxy populations probed capture ensemble-averaged properties beyond the reach of targeted observations towards individual galaxies.
Article
JWST observations indicate a surprising excess of luminous galaxies at z ∼ 10 and above, consistent with efficient conversion of the accreted gas into stars, unlike the suppression of star formation by feedback at later times. We show that the high densities and low metallicities at this epoch guarantee a high star-formation efficiency (SFE) in the most massive dark-matter haloes. Feedback-free starbursts (FFBs) occur when the free-fall time is shorter than ∼1 Myr, below the time for low-metallicity massive stars to develop winds and supernovae. This corresponds to a characteristic density of ∼3 × 103 cm−3. A comparable threshold density permits a starburst by allowing cooling to star-forming temperatures in a free-fall time. The galaxies within ∼1011M⊙ haloes at z ∼ 10 are expected to have FFB densities. The halo masses allow efficient gas supply by cold streams in a halo crossing time ∼80 Myr. The FFBs gradually turn all the accreted gas into stars in clusters of ∼104 − 7M⊙ within galaxies that are rotating discs or shells. The starbursting clouds are insensitive to radiative feedback and are shielded against feedback from earlier stars. We predict high SFE above thresholds in redshift and halo mass, where the density is 103 − 4 cm−3. The z ∼ 10 haloes of ∼1010.8M⊙ are predicted to host galaxies of ∼1010M⊙ with SFR ∼65M⊙ − 1, blue colors, and sub-kpc sizes. The metallicity is ≤0.1Z⊙ with little dust, gas, outflows and hot circum-galactic gas, allowing a top-heavy IMF but not requiring it. The compact galaxies with thousands of young FFB clusters may have implications on reionization, black-hole growth and globular clusters.
Article
The earliest JWST observations have revealed an unexpected abundance of super-early (z > 10), massive (M109MM_*\, \approx 10^9 {\rm M}_{\odot } ) galaxies at the bright-end (MUV ≈ −21) of the ultraviolet luminosity function (UV LF). We present a minimal physical model that explains the observed galaxy abundance at z = 10–14. The model primarily combines (i) the halo mass function, with (ii) an obscured star formation fraction prescription that is consistent with findings of the ALMA REBELS dusty galaxy survey. It has been successfully tested on well-known UV LFs up to z = 7. We argue that the weak evolution from z = 7 to z ≈ 14 of the LF bright-end can arise from a conspiracy between a decreasing dust attenuation, making galaxies brighter, that almost exactly compensates for the increasing shortage of their host halos. Our minimal model naturally reproduces the z = 10–14 LF if galaxies at z\lower.5ex\rm{\,\, \buildrel\gt \over \sim \,\,}11 contain a negligible amounts of dust. We speculate that dust could have been efficiently ejected during the very first phases of galaxy build-up.
Article
We present the first constraints on the prevalence of z > 10 galaxies in the Hubble Ultra Deep Field (HUDF) leveraging new NIRCam observations from JEMS (JWST Extragalactic Medium-band Survey). These NIRCam observations probe redward of 1.6μm, beyond the wavelength limit of HST, allowing us to search for galaxies to z > 10. These observations indicate that the highest redshift candidate identified in the HUDF09 data with HST, UDFj-39546284, has a redshift of z > 11.5, as had been suggested in analyses of the HUDF12/XDF data. This has now been confirmed with JWST NIRSpec. This source is thus the most distant galaxy discovered by HST in its >30 years of operation. Additionally, we identify nine other z ∼ 8-13 candidate galaxies over the HUDF, two of which are new discoveries that appear to lie at z ∼ 11-12. We use these results to characterize the evolution of the UV luminosity function (LF) from z ∼ 15 to z ∼ 8.7. While our LF results at z ∼ 8.7 and z ∼ 10.5 are consistent with previous findings over the HUDF, our new LF estimates at z ∼ 12.6 are higher than other results in the literature, potentially pointing to a milder evolution in the UV luminosity density from z ∼ 12.6. We emphasize that our LF results are uncertain given the small number of z ∼ 12.6 sources and limited volume probed. The new NIRCam data also indicate that the faint z ∼ 8-13 galaxies in the HUDF/XDF show blue UV-continuum slopes β ∼−2.7, high specific star formation rates ∼24.5 Gyr−1, and high EW (∼1300Å) [OIII]+Hβ emission, with two z ∼ 8.5 sources showing [OIII]+Hβ EWs of ∼2300Å.