# The first fireworks: A roadmap to Population III stars during the Epoch of
Reionization through Pair-Instability Supernovae

Alessandra Venditti1,2,3,4,5; Volker Bromm5,6; Steven L. Finkelstein5; Luca
Graziani1,2,3; Raffaella Schneider1,2,3
1Dipartimento di Fisica, Sapienza, Universit$\grave{a}$ di Roma, Piazzale Aldo
Moro 5, 00185, Roma, Italy
2INFN, Sezione di Roma I, Piazzale Aldo Moro 2, 00185, Roma, Italy
3INAF-Osservatorio Astronomico di Roma, Via di Frascati 33, 00078, Monte
Porzio Catone, Italy
4Dipartimento di Fisica, Tor Vergata, Universit$\grave{a}$ di Roma, Via
Cracovia 50, 00133, Roma, Italy
5Department of Astronomy, University of Texas at Austin, 2515 Speedway, Stop
C1400, Austin, TX 78712, USA
6Weinberg Institute for Theoretical Physics, University of Texas at Austin,
Austin, TX 78712, USA<EMAIL_ADDRESS>
###### Abstract

With the launch of JWST and other scheduled missions aimed at probing the
distant Universe, we are entering a new promising era for high-$z$ astronomy.
One of our main goals is the detection of the first population of stars
(Population III or Pop III stars), and models suggest that Pop III star
formation is allowed well into the Epoch of Reionization (EoR), rendering this
an attainable achievement. In this paper, we focus on our chance of detecting
massive Pop IIIs at the moment of their death as Pair-Instability Supernovae
(PISNe). We estimate the probability of discovering PISNe during the EoR in
galaxies with different stellar masses
($7.5\leq\mathrm{Log}(M_{\star}/$\mathrm{M}_{\odot}$)\leq 10.5$) from six
dustyGadget simulations of $50h^{-1}$ cMpc per side. We further assess the
expected number of PISNe in surveys with JWST/NIRCam and Roman/WFI. On
average, less than one PISN is expected in all examined JWST fields, while
$\simeq 1.5\,\eta_{\mathrm{III}}$ PISNe may be found in a $\sim 1$ deg2 Roman
field, with potential for increased discoveries when considering more
optimistic choices for the Pop III initial mass function and formation
efficiency $\eta_{\mathrm{III}}$, and when including the contribution of
coarsely-resolved environments. JWST/NIRCam and Roman/WFI allow the detection
of massive-progenitor ($\sim 250~{}$\mathrm{M}_{\odot}$$) PISNe throughout all
the optimal F200W-F356W, F277W-F444W, and F158-F213 colors. PISNe are also
predominantly located at the outskirts of their hosting haloes, facilitating
the disentangling of underlying stellar emission thanks to the spatial-
resolution capabilities of the instruments.

###### keywords:

supernovae: pair-instability supernovae - stars: Population III - galaxies:
star formation – galaxies: high-redshift – dark ages, reionization, first
stars – cosmology: theory.

††pagerange: The first fireworks: A roadmap to Population III stars during the
Epoch of Reionization through Pair-Instability Supernovae–References††pubyear:
2022

##  1 Introduction

Pair-instability supernovae (PISNe) are a type of supernova (SN) that occurs
when a massive star, with a mass between 140 $\mathrm{M}_{\odot}$ and 260
$\mathrm{M}_{\odot}$, undergoes a thermonuclear explosion due to the
production and subsequent annihilation of electron-positron pairs in its hot
core. These reactions lead to a rapid loss of radiation pressure support
causing the core to collapse, and thus igniting explosive oxygen and silicon
burning that ultimately results in the complete disruption of the star (Rakavy
& Shaviv, 1967; Barkat et al., 1967; Fraley, 1968; Bond et al., 1984; Fryer et
al., 2001). PISNe are particularly interesting because they provide valuable
insights on the first generation of stars, known as Population III (Pop III)
stars.

Pop III stars formed from pristine gas, almost entirely composed of hydrogen
and helium. Because of the absence of heavy elements, they are expected to
have very different properties compared to second-generation (Pop II) stars,
that formed from the gas pre-enriched by Pop III. Most notably, they are
expected to be predominantly massive, with masses ranging from $\sim$10s
$\mathrm{M}_{\odot}$ to $\sim$100s $\mathrm{M}_{\odot}$ or even $\sim$1000s
$\mathrm{M}_{\odot}$ (Abel et al., 2002; Bromm et al., 2002; Hosokawa et al.,
2011; Hirano et al., 2014, 2015a, 2015b; Susa et al., 2014; Stacy et al.,
2016; Hosokawa et al., 2016; Sugimura et al., 2020; Latif et al., 2022),
implying that some of the most massive Pop III stars may be able to produce
PISNe. When a PISN explodes, large amounts of metals are released into the
surrounding medium (Heger & Woosley, 2002). Hence, PISNe arising from Pop III
stars are thought to be one of the main sources of heavy elements in the early
Universe, and are therefore key to understand the process of early chemical
enrichment (e.g. Salvadori et al., 2007, 2008; Karlsson et al., 2013; de
Bennassuti et al., 2017; Aguado et al., 2023a).

The properties of PISNe, such as their explosive energy output and light
curve, can provide important constraints on the characteristics of the
progenitor stars (Mackey et al., 2003; Scannapieco et al., 2005; Whalen et
al., 2013; Pan & Loeb, 2013; de Souza et al., 2014; Wang et al., 2017).
Several simulations have been carried out to model the distinctive light curve
and afterglow emission of PISNe arising from Pop III (Scannapieco et al.,
2005; Woosley et al., 2007; Pan et al., 2012; Chen et al., 2014; Whalen et
al., 2014; Jerkstrand et al., 2016; Kozyreva et al., 2017; Gilmer et al.,
2017; Hartwig et al., 2018). Simulations suggest that they are very energetic,
with total energy produced up to $10^{53}$ erg, and have an extended light
curve duration, $\sim$ 1 yr in the source frame (Kasen et al., 2011).

The detection of PISNe is especially challenging due to their rarity. Pop III
stars are expected to have formed at high redshifts ($z\sim 20-30$; Bromm
2013; Graziani et al. 2015; Graziani et al. 2017; Klessen & Glover 2023), when
the Universe was only a few hundred million years old, and their rate of
formation is expected to have declined rapidly as the Universe became more
metal-enriched - although recent simulations suggest a late Pop III star
formation, down to the Epoch of Reionization (EoR, $z\sim 6$), is also
possible (Xu et al., 2016; Jaacks et al., 2019; Liu & Bromm, 2020; Sarmento et
al., 2018; Sarmento & Scannapieco, 2022; Skinner & Wise, 2020; Visbal et al.,
2020; Venditti et al., 2023). The exact rate of PISNe across cosmic time is
however highly uncertain (Miralda-Escudé & Rees, 1997; Wise & Abel, 2005;
Hummel et al., 2012; Pan et al., 2012; Johnson et al., 2013; Tanaka et al.,
2013; Magg et al., 2016), as it depends on the details of the metal enrichment
process, as well as other factors such as the Pop III initial mass function
(IMF). A more top-heavy Pop III IMF, for example, would yield a higher rate of
PISNe, as a large fraction of the stars would be massive enough to undergo
pair instability (Lazar & Bromm, 2022). However, the exact shape of the Pop
III IMF is unconstrained. The typical metallicity of the gas in which Pop III
stars formed is also uncertain, as it depends on the details of the primordial
star-formation process and the efficiency of metal mixing. Simulations suggest
that Pop III stars formed in very low-metallicity environments, with
metallicity not higher than $10^{-4}-10^{-6}~{}$\mathrm{Z}_{\odot}$$ (Bromm et
al., 2001a; Omukai et al., 2005; Maio et al., 2010; Schneider et al., 2012a;
Schneider et al., 2012b; Chiaki et al., 2016; Chiaki & Yoshida, 2022),
although a massive stellar component in excess of what predicted by a present-
day IMF may persist up to metallicity $\lesssim
10^{-2}~{}$\mathrm{Z}_{\odot}$$ (Chon et al., 2021; Chon et al., 2022).

Despite the challenges, several efforts have been made to detect PISNe in the
past. One of the most promising candidates proposed is SN 2007bi, a super-
luminous SN (SLSN), discovered in 2007 in a nearby dwarf galaxy (Gal-Yam et
al., 2009). SN 2007bi has several properties that are consistent with a PISN,
including its high energy output, long duration, measured yield of radioactive
nickel and elemental composition of the ejecta. However, its exact nature is
still a matter of debate, and other explanations have been proposed in the
literature (see e.g. Moriya et al. 2010; Dessart et al. 2012). Other examples
of SLSNe with slowly evolving light curves at high redshift ($z=2.05$ and
$z=3.90$) have been found with Keck I follow-up, late-time spectroscopy of two
objects first identified in archival data from the Canada-France-Hawaii
Telescope Legacy Survey Deep Fields (Cooke et al., 2012). Possible survey
strategies dedicated to the search of PISNe during the EoR with JWST and with
the Nancy Grace Roman Space Telescope have been discussed in Hartwig et al.
(2018), Regős et al. (2020) and Moriya et al. (2022b), while the possibility
of detecting PISNe in the Euclid Deep Survey (EDS, Laureijs et al. 2011;
Euclid Collaboration et al. 2022) at $z\lesssim 2.5$ is studied in Moriya et
al. (2022a).

Stellar archaeology can provide a complementary probe to constrain the
properties of the first stars - particularly their IMF - and their SN
outcomes, by looking at the atmospheres of old and metal-poor stars in our
galaxy. Notably, the detection of a peculiar chemical abundance pattern in a
star with [Fe/H$]=-2.5$, possibly indicative of a PISN nucleosynthetic yield
(Aoki et al., 2014), presents evidence that very high masses are indeed
allowed for Pop III stars (de Bennassuti et al., 2017). Salvadori et al.
(2019) and Aguado et al. (2023a) reported other instances of metal-poor stars
with suggested PISN signatures in their atmosphere. A contribution of PISNe
from massive Pop III was also suggested to explain the unusual abundance
feature of Fe and Mg in the broad-line region of a quasar at $z=7.54$ (Yoshii
et al., 2022). Simulations of early chemical enrichment (e.g. Jeon et al.,
2015) have suggested that PISN-produced material predominantly resides in the
intergalactic medium (IGM), raising the possibility of using the ultra-
luminous afterglows of high-redshift gamma ray bursts (GRBs) to probe this IGM
signature with deep absorption spectroscopy (Wang et al., 2012).

An important factor in the detectability of PISNe is their host environment.
Pop III stars are expected to have formed predominantly in low-mass, faint
haloes. However, some models also suggest that Pop III could still form in
more massive and luminous haloes (Liu & Bromm, 2020; Bennett & Sijacki, 2020;
Riaz et al., 2022; Venditti et al., 2023). Although massive galaxies are
generally easier to detect, their higher luminosity might even hinder our
ability to clearly identify a PISN in such hosts. This is especially true if
the SN is observed at late times, when the emission has faded considerably
(Kasen et al., 2011). An extensive study of the expected rate of PISNe as a
function of their host environments is currently missing.

This work is aimed at assessing the probability of observing PISNe arising
from Pop III stars during the EoR, in galaxies with different stellar masses.
We rely on a suite of six
$50h^{-1}~{}$\mathrm{c}\mathrm{M}\mathrm{p}\mathrm{c}$$ simulations already
introduced in Di Cesare et al. (2023) and Venditti et al. (2023), carried out
with the hydrodynamical code dustyGadget (Graziani et al., 2020). Our findings
can guide the design of optimal strategies to search for potential PISN-
hosting candidates, both from archival data and from dedicated surveys. While
achieving the first clear detection of a PISN would be a remarkable
accomplishment in and of itself, finding PISNe at high redshifts would also
have deeper implications for the search of the first stars. As PISNe are in
fact the natural outcome of very massive stars, hardly attainable for normal
Pop II/I stars, they can be used as markers to identify potential Pop III
hosts. Hence, the synergy between wide-field PISNe searches and spatially
resolved observations of their host galaxies (possibly enhanced by
gravitational lensing) may offer one of our finest tools to directly probe Pop
III stars and test our predictions on primordial star-formation.

The paper is organised as follows. Section 2 presents our methodology: Section
2.1 describes our simulation suite, while Section 2.2 outlines our strategy
for evaluating the probability of finding PISNe during the EoR from the
simulations. Our results are presented in Section 3. Specifically, in Section
3.1 we compute the expected number of PISNe in galaxies of different stellar
mass per unit halo and volume, and we predict the expected number of PISNe
within JWST and Roman fields. In Section 3.2 we discuss our capability of
observing PISNe and discriminating from the stellar emission of their host
galaxies, by considering their integrated emission (Section 3.2.1) and
possibly resolved observations (Section 3.2.2). A critical discussion is
presented in Section 4, including a number of caveats in our modelling
(Section 4.1), and a discussion on the implication of either future detections
or non-detections of PISNe (Section 4.2), and on the advantages and
disadvantages of many possible detection strategies (Section 4.3). Finally, we
summarize and offer conclusions in Section 5.

##  2 Methodology

###  2.1 Simulating the cosmological environment

Our study is based on a suite of eight cosmological simulations carried out
with the hydrodynamical code dustyGadget. The code is extensively described in
Graziani et al. (2020), especially regarding its most novel feature, i.e. the
implementation of a self-consistent model for dust production and evolution,
while our simulations (hereafter named as U6 - U13) are introduced in Di
Cesare et al. (2023) and Venditti et al. (2023). More specifically, Di Cesare
et al. (2023) studied the main scaling relations in the context of available
observations and model predictions, while Venditti et al. (2023) focused on
the properties of galaxies hosting Pop III star formation during the EoR,
which are of particular interest for the present work. We briefly describe
relevant aspects of the simulations here, and refer to the aforementioned
papers for further details.

All the simulated volumes have a (comoving) size of
$50h^{-1}~{}$\mathrm{c}\mathrm{M}\mathrm{p}\mathrm{c}$$, a total number of
$2\times 672^{3}$ particles and a mass resolution for dark matter/gas
particles of $3.53\times 10^{7}h^{-1}~{}$\mathrm{M}_{\odot}$$/$5.56\times
10^{6}h^{-1}~{}$\mathrm{M}_{\odot}$$. They assume a $\mathrm{\Lambda}$CDM
cosmology, consistent with Planck Collaboration et al. (2016) parameters
($\Omega_{\mathrm{m,0}}=0.3089$, $\Omega_{\mathrm{b,0}}=0.0486$,
$\Omega_{\mathrm{\Lambda},0}=0.6911$, $h=0.6774$), and share a common feedback
setup based on Graziani et al. (2020). A cold gas phase density threshold for
star formation of $n_{\mathrm{th}}\simeq 300~{}$\mathrm{c}\mathrm{m}^{-3}$$ is
adopted. When this threshold is reached, stellar populations represented by
stellar particles of mass $\sim 2\times 10^{6}~{}$\mathrm{M}_{\odot}$$ are
generated in a single, instantaneous burst. Their IMF/metal yields (following
C, O, Mg, S, Si and Fe) are assigned according to their metallicity
$Z_{\star}$, given a critical metallicity
$Z_{\mathrm{crit}}=10^{-4}~{}$\mathrm{Z}_{\odot}$$111We assume
$Z_{\mathrm{\odot}}=0.02$ (Anders & Grevesse, 1989). (Tornatore et al., 2007;
Maio et al., 2010; Graziani et al., 2020), specifically:

  1. 1.

a Salpeter-like IMF in the mass range [100, 500] $\mathrm{M}_{\odot}$ for Pop
III stars ($Z_{\star}<Z_{\mathrm{crit}}$), with mass-dependent yields
describing the metal pollution from stars in the PISN range [140, 260]
$\mathrm{M}_{\odot}$ (Heger & Woosley, 2002);

  2. 2.

a standard Salpeter IMF (Salpeter, 1955) in the mass range [0.1, 100]
$\mathrm{M}_{\odot}$ for Pop II stars ($Z_{\star}\geq Z_{\mathrm{crit}}$),
with mass and metallicity-dependent yields describing the metal pollution from
long-lived, low/intermediate-mass stars (van den Hoek & Groenewegen, 1997),
high mass stars (> 8 $\mathrm{M}_{\odot}$), dying as core-collapse SNe
(Woosley & Weaver, 1995), and SNeIa (Thielemann et al., 2003).

Pop II/I stars with masses $\geq 40\;$\mathrm{M}_{\odot}$$ and Pop III stars
outside the PISN mass range do not contribute to the metal enrichment, as they
are assumed to directly collapse into black holes (not followed explicitly
here). The impact of our choice of the Pop III IMF, and hence of neglecting
the contribution of traditional core-collapse SNe from Pop IIIs, is discussed
in Section 4.

The identification of dark matter haloes and their substructures is performed
in post-processing with the AMIGA halo finder (Knollmann & Knebe, 2009).
Finally, the simulations are carried out from $z\simeq 100$ down to $z\simeq
4$, while this work only focuses on the redshift range $6\lesssim z\lesssim
8$. Indeed, the number of well-resolved Pop III-hosting haloes (with a stellar
mass $\mathrm{log}(M_{\star}/$\mathrm{M}_{\odot}$)\gtrsim 7.5$, corresponding
to a number of stellar particles $\gtrsim 20$) decreases significantly at
higher redshifts, while a drop in Pop III star formation is expected at lower
redshifts due to the joint effect of cosmic metal enrichment and ultraviolet
(UV)/Lyman-Werner (LW) radiative feedback. A more extensive discussion can be
found in Venditti et al. (2023).

###  2.2 Computing the probability of finding PISNe

The average number of PISNe, $\overline{N}_{\mathrm{PISN}}$, produced by a Pop
III stellar population per unit Pop III mass $M_{\mathrm{III}}$, with our
assumed IMF $\phi(m)$ (whose lower and upper limits are $m_{\mathrm{low}}$ and
$m_{\mathrm{up}}$, respectively), is given by:

$\frac{\overline{N}_{\mathrm{PISN}}}{M_{\mathrm{III}}}=\frac{\int_{140~{}$\mathrm{M}_{\odot}$}^{260~{}$\mathrm{M}_{\odot}$}\phi(m)\differential{m}}{\int_{m_{\mathrm{low}}}^{m_{\mathrm{up}}}m\phi(m)\differential{m}}\simeq
0.0022~{}$\mathrm{M}_{\odot}^{-1}\mathrm{,}$$ (1)

indicating an average of one PISN event per 460 $\mathrm{M}_{\odot}$. For Pop
III stellar populations with mass $\sim 2\times
10^{6}~{}$\mathrm{M}_{\odot}$$, this would result in more than 4000 PISNe
produced on average by each stellar population (but see the discussion below
on more realistic outcomes).

Figure 1: Compilation of various theoretical models for the Pop III IMF, $\phi(m)$, normalised to a total mass of $2\times 10^{6}$ $\mathrm{M}_{\odot}$ (i.e. approximately our Pop III stellar particle mass resolution). The models shown here are from Schauer et al. (2022) (blue), Hartwig et al. (2018) (orange), Jaacks et al. (2018) (pink), and they can all be expressed through the general expression in the top-right corner (Equation 2), with parameters specified in Table 1. Our Salpeter-like IMF (Graziani et al., 2020; Di Cesare et al., 2023; Venditti et al., 2023) is shown as a black, solid line. The gray shaded region indicates the stellar progenitor mass range of PISNe. Table 1: Values of the average number of PISNe produced per unit Pop III mass $\overline{N}_{\mathrm{PISN}}/M_{\mathrm{III}}$ computed for a compilation of Pop III IMFs, expressed through the general form of Equation 2, with parameters $\alpha$, $\beta$, $m_{\mathrm{cut}}$ and mass range $m_{\mathrm{range}}$ as specified. The IMF adopted in this work is highlighted in bold. See Figure 1 for references. | $\alpha$ | $\beta$ | $m_{\mathrm{cut}}$ | $m_{\mathrm{range}}$ | $\overline{N}_{\mathrm{PISN}}/M_{\mathrm{III}}$
---|---|---|---|---|---
|  |  | [$\mathrm{M}_{\odot}$] | [$\mathrm{M}_{\odot}$] | [$\mathrm{1}\mathrm{0}^{-3}~{}\mathrm{M}_{\odot}^{-1}$]
Larson | 2.35 | 1 | 10 | [1,500] | 0.62
Log-flat | 1 | 0 | 0 | [1,500] | 1.24
Log-flat | 1 | 0 | 0 | [3,300] | 2.08
Salpeter-like | 2.35 | 0 | 0 | [100,500] | 2.17
pow-law | 0.17 | 0 | 0 | [1,150] | 9.32
mod-Larson | 0.17 | 2 | 4.47 | [1,150] | 9.40
flat | 0 | 0 | 0 | [1,150] | 10.67
pow-law | -0.17 | 0 | 0 | [1,150] | 12.13

We note that $\overline{N}_{\mathrm{PISN}}/M_{\mathrm{III}}$ can vary
depending on the adopted IMF. As both the shape and mass range of the Pop III
IMF are still largely uncertain, in Table 1 we evaluate this quantity for a
compilation of IMFs that have been adopted in the literature to describe Pop
III stellar populations (see Figure 1). The shape of all these IMFs can be
expressed in the general form (Lazar & Bromm, 2022):

$\phi(m)\propto m^{-\alpha}\exp[-(m_{\mathrm{cut}}/m)^{\beta}],$ (2)

i.e. a modified-Larson IMF (Larson, 1998), with various parameters describing
the slope ($\alpha$) and the exponential cut-off at low stellar masses
($m_{\mathrm{cut}}$, $\beta$). We note that
$\overline{N}_{\mathrm{PISN}}/M_{\mathrm{III}}$ can vary in the range
$\sim[0.6-12]\times 10^{-3}~{}$\mathrm{M}_{\odot}^{-1}$$ over all the included
IMFs.

Another source of uncertainty comes from our Pop III stellar mass resolution
element $M_{\mathrm{III,res}}\sim 2\times 10^{6}~{}$\mathrm{M}_{\odot}$$.
Indeed, since the expected number of PISNe is directly proportional to the
total Pop III mass $M_{\mathrm{III}}$, it is important to carefully estimate
the amount of stellar mass produced in a single star-formation event. In
principle, this could be lower than $M_{\mathrm{III,res}}$, which should more
accurately be interpreted as the amount of extremely metal-poor gas above our
density threshold that is available for star formation. We can formally
express this through an efficiency factor $\eta_{\mathrm{III}}<1$:

$M_{\mathrm{III}}=\eta_{\mathrm{III}}M_{\mathrm{III,res}},$ (3)

and place a lower limit on $\eta_{\mathrm{III}}\sim 0.01$ from a wealth of
simulation data describing the first sites of Pop III star formation in mini-
haloes (see Bromm 2013 and references therein). However, mini-haloes at the
Rees-Ostriker cooling threshold (Rees & Ostriker, 1977) are known to be very
inefficient hosts for star formation, given their shallow potential well. We
can thus argue that $\eta_{\mathrm{III}}$ could be larger in more massive
haloes at later times, and explore our results for a range of different values
of $\eta_{\mathrm{III}}\geq 0.01$. An empirical hint that higher values of
$\eta_{\mathrm{III}}$ (even up to $\eta_{\mathrm{III}}\simeq 1$) might be
allowed at least in some cases is offered by the tentative detection of HeII
emission at $\simeq 2.5~{}$\mathrm{k}\mathrm{p}\mathrm{c}$$ from an
exceptionally luminous galaxy at $z=10.6$, that might indicate the presence of
a Pop III cluster with a top-heavy IMF and a total Pop III mass of $6-7\times
10^{5}~{}$\mathrm{M}_{\odot}$$ (Maiolino et al., 2023). With this caveat in
mind, the average number of PISNe produced by a single Pop III stellar
population is reduced to $\sim 4000\,\eta_{\mathrm{III}}$, for our adopted
IMF.

Figure 2: Pop III main-sequence lifetimes $\tau$ as a function of the initial
mass $m$ of the stars, from Schaerer (2002), in the mass range of our assumed
IMF. The black, solid line refers to the model assuming no mass loss (see
table 4 of the original paper), while the black, dotted line refers to the
model assuming strong mass loss (see their table 5). The interpolated
lifetimes at the limits of the PISN progenitors mass range [140, 260]
$\mathrm{M}_{\odot}$ (grey, shaded area) are indicated for the two models. The
average lifetimes $\overline{\tau}$ of Pop III stellar populations for the two
models with our assumed IMF are also shown, on top of the horizontal,
solid/dotted, black lines.

Since Pop III stellar particles in our simulations are formed in an
instantaneous burst, and Pop IIIs with initial masses $m$ in the range [140,
260] $\mathrm{M}_{\odot}$ explode as PISNe over a time span $\Delta
t_{\mathrm{PISN}}=\tau(140~{}$\mathrm{M}_{\odot}$)-\tau(260~{}$\mathrm{M}_{\odot}$)$,
where $\tau(m)$ is the lifetime of a star with initial mass $m$, we can
approximately compute the average number of PISNe expected to be seen at a
given time $t$ within $\Delta t_{\mathrm{PISN}}$ as:

$\overline{N}_{\mathrm{PISN,t}}\simeq\overline{N}_{\mathrm{PISN}}\times\frac{\Delta
t_{\mathrm{prompt}}}{\Delta t_{\mathrm{PISN}}},$ (4)

where $\Delta t_{\mathrm{prompt}}\simeq$ 1 yr is the rest-frame time interval
over which the prompt PISN emission is expected to be bright (Kasen et al.,
2011).

The Pop III lifetimes $\tau(m)$ as a function of initial stellar mass $m$ are
taken from the models of Schaerer (2002)222Note that these are in fact main-
sequence lifetimes. However, Marigo et al. (2001) show that the He burning
lifetime is $\lesssim 10\%$ of the main sequence phase.. Given the
uncertainties for existing Pop III evolution models, they reported results for
models assuming strong mass loss333As hot-star winds are mainly driven by
photon momentum transfer through metal absorption, any mass loss arising from
metal-poor stars is in fact expected to be sub-dominant. This is confirmed by
observations of wind velocities and average momenta in the Magellanic clouds
(Kudritzki & Puls, 2000) and by theoretical studies (Baraffe et al., 2001).
Nonetheless, e.g. Regős et al. (2020) considered models for Pop IIIs that have
lost their outer envelope due to rotationally-induced mixing before exploding
as PISNe. arising from high-mass Pop III stars and models assuming no mass
loss at all (see their tables 5 and 4 respectively). In Figure 2, we show
$\tau(m)$ for both models over the mass range of our assumed Pop III IMF, to
emphasize the existing differences, indicating that mass loss can result in
longer lifetimes by up to a factor of $\simeq 1.3$, and even in an inversion
of the trend for masses $m\gtrsim 300~{}$\mathrm{M}_{\odot}$$, with $\tau$
increasing rather than decreasing for larger stellar masses. The lifetimes of
stars with masses 140 $\mathrm{M}_{\odot}$ and 260 $\mathrm{M}_{\odot}$ are
also shown in the plots. With these lifetimes, $\Delta t_{\mathrm{PISN}}\simeq
0.65/0.33$ Myr respectively for the models assuming strong/no mass loss. This
results in an average number of PISNe from our stellar populations of the
order of $\sim 10^{-2}\,\eta_{\mathrm{III}}$ at a given time444Note that for
the strong-mass-loss case this is likely an upper limit, as a fraction of the
stars will not explode as PISN if they experience strong mass loss due to
rotation. (Equation 4).

To compute the average number of PISNe that we expect to find in haloes with
stellar mass in the range [$M_{\star}$, $M_{\star}+\Delta M_{\star}$] of a
given simulated volume $V$ and simulation snapshot, i.e. at a given time $t$,
we sum over all Pop III particles with age
$\tau(260~{}$\mathrm{M}_{\odot}$)\leq
t_{\mathrm{III}}\leq\tau(140~{}$\mathrm{M}_{\odot}$)$ in these haloes to
recover the total mass $M_{\mathrm{III,PISN}}(M_{\star})$ of Pop III stellar
populations that can produce PISNe within a time $\Delta t_{\mathrm{PISN}}$.
The average number of PISNe as a function of $M_{\star}$ is then:

$\overline{N}_{\mathrm{PISN,t}}(M_{\star})\simeq
M_{\mathrm{III,PISN}}(M_{\star})\times\frac{\overline{N}_{\mathrm{PISN}}}{M_{\mathrm{III}}}\times\frac{\Delta
t_{\mathrm{prompt}}}{\Delta t_{\mathrm{PISN}}}.$ (5)

If we assume the actual number of PISNe $k$ found in a fixed volume $V$ at
time $t$ follows a Poisson distribution
$P(k;\lambda)=\lambda^{k}e^{-\lambda}/k!$ with parameter
$\lambda\equiv\overline{N}_{\mathrm{PISN,t}}(M_{\star})$, we can estimate the
probability of finding at least 1 PISN in haloes with stellar mass within
[$M_{\star}$, $M_{\star}+\Delta M_{\star}$] as:

$P(\geq\mathrm{1~{}PISN})=1-P(0;\lambda)=1-e^{-\lambda},$ (6)

and if the average number of PISNe that we find in the volume is indeed very
small - as we would expect - we will have
$P(\geq\mathrm{1~{}PISN})\simeq\lambda\equiv\overline{N}_{\mathrm{PISN,t}}(M_{\star})$.

##  3 Results

###  3.1 Expected number of PISNe in galaxies of different mass

Figure 3: Top/middle panels: Average number of PISNe per halo
($\overline{N}_{\mathrm{PISN,t}}/N_{\mathrm{haloes}}$)/per unit volume
($\overline{n}_{\mathrm{PISN,t}}$) that we expect to find at a given redshift
$z$ in haloes within a given range of stellar mass $M_{\star}$ as a function
of $M_{\star}$, computed in six bins of $M_{\star}$ (with a spacing of 0.5 dex
in the range $7.5\leq\mathrm{Log}M_{\star}/$\mathrm{M}_{\odot}$<10.5$). The
various colours in the top panels refer to different values of the efficiency
$\eta_{\mathrm{III}}$ of a single star-formation episode;
$\eta_{\mathrm{III}}=0.01$ (gold), $\eta_{\mathrm{III}}=0.1$ (black), and
$\eta_{\mathrm{III}}=1$ (brown). The solid lines refer to the model assuming
no mass loss, while the dotted line refers to the model assuming strong mass
loss for the case $\eta_{\mathrm{III}}=0.1$ (Figure 2). The shaded area also
demonstrates the expected scatter around the model assuming no mass loss and
$\eta_{\mathrm{III}}=0.1$ for different assumed IMFs (see Figure 2 and Table
1). Bottom panels: comoving number density $n_{\mathrm{haloes}}$ of haloes
found in each $M_{\star}$ bin. The total number of haloes found in each bin is
also indicated on top of the bin. Results are shown for the combined simulated
volumes U6, U7, U8, U10, U12, and U13 at redshifts $z=8.1$ (left panels),
$z=7.3$ (middle panels) and $z=6.7$ (right panels).

We compute the average number of PISNe at a given redshift $z$ as a function
of the stellar mass $M_{\star}$ of the halo in which they are found, using the
method outlined in Section 2.2 (see Equation 4). We consider Pop III stellar
particles within all the simulated volumes U6, U7, U8, U10, U12, and U13 to
provide the largest possible statistics555Data from U9 and U11 is not included
as the snapshot dumps for these cubes are not aligned with the others.,
meaning we are virtually probing a total volume
$V_{\mathrm{eff}}=6\times(50h^{-1}~{}$\mathrm{c}\mathrm{M}\mathrm{p}\mathrm{c}$)^{3}$.
We also focused on six bins of $M_{\star}$ spaced by 0.5 dex in the range
$7.5\leq\mathrm{Log}M_{\star}/$\mathrm{M}_{\odot}$<10.5$, for three different
redshift points, $z=8.1,\,7.3$ and 6.7.

The results are shown in the top and middle panels of Figure 3, for the models
assuming no/strong mass loss (solid/dotted, black lines). In the plots, the
average number of PISNe is normalised by the total number of haloes
$N_{\mathrm{haloes}}$ in each bin (top panels) and by the total volume
$V_{\mathrm{eff}}$ (middle panels), to recover the expected number of PISNe
per halo/per unit volume; these numbers provide an indication respectively on
the number of galaxies one should be looking at to have a reasonable chance of
observing PISNe at a given redshift and on the average comoving number density
of PISNe expected in a blind survey. Different assumptions on the efficiency
$\eta_{\mathrm{III}}$ (see Equation 3) and on the IMF $\phi(m)$ (see Equation
1) are explored. The total number and comoving number density of haloes are
also shown in the bottom panels to demonstrate our explored statistics, and we
refer to Di Cesare et al. (2023) for a detailed comparison of the dustyGadget
galaxy stellar mass functions at various redshifts with observations and with
other models and simulations.

We see that the probability of finding PISNe in our simulated volumes is small
but non-negligible: in our reference model for Pop III (Salpeter-like IMF in
the range [100, 500] $\mathrm{M}_{\odot}$, Pop III star formation efficiency
of $\eta_{\mathrm{III}}=0.1$ and no mass loss), the comoving number density of
PISNe can reach values $\sim
10^{-1}~{}$\mathrm{c}\mathrm{M}\mathrm{p}\mathrm{c}^{-3}$$, while the average
number of PISNe per halo can be up to $\sim 5\times 10^{-6}$, meaning we would
expect about 1 PISN every two hundred thousand haloes, on average (if we take
into account the contributions of all the considered stellar mass bins). These
numbers depend however on the considered redshift, on the assumed Pop III
model and on the halo stellar mass. Particularly, high-mass haloes
($10^{9.5}~{}$\mathrm{M}_{\odot}$\lesssim M_{\star}\lesssim
10^{10}~{}$\mathrm{M}_{\odot}$$) at $z=6.7$ seem to be the most favourable for
the search of PISNe at high redshifts
($\overline{N}_{\mathrm{PISN}}/N_{\mathrm{haloes}}\gtrsim 3\times 10^{-5}$ in
our reference model, see top panels). In general, the probability of finding
PISNe in a given halo increases with $M_{\star}$, dropping to zero at the
highest masses ($M_{\star}\gtrsim 10^{9.5}~{}$\mathrm{M}_{\odot}$$ at $z=8.1$,
$M_{\star}\gtrsim 10^{10}~{}$\mathrm{M}_{\odot}$$ at $z=7.3/6.7$). On the
other hand, given the higher number of haloes at the low-mass end, the
expected number density of PISNe in lower-mass galaxies is generally higher,
even though the fraction of low-mass galaxies hosting PISNe is lower; the
highest number density is found in haloes with $M_{\star}\lesssim
10^{8}~{}$\mathrm{M}_{\odot}$$ at $z=6.7$ ($\overline{n}_{\mathrm{PISN}}\sim
2\times 10^{-8}~{}$\mathrm{c}\mathrm{M}\mathrm{p}\mathrm{c}^{-3}$$ in our
reference model, see middle panels). We emphasize that the statistics for the
highest stellar mass bins is very limited, as no more than a few/a few tens of
haloes are found in these bins (see bottom panels), and hence our results are
very sensitive to the adopted selection criterion, see e.g. the difference
between the no/strong mass loss cases.

While the discrepancies due to the assumption of no/strong mass loss in our
estimate of Pop III lifetimes are mostly sub-dominant (apart from the rare
massive haloes), a more significant variation is expected when considering
different IMFs and/or different values of $\eta_{\mathrm{III}}$. In
particular, a factor of ten in the assumed $\eta_{\mathrm{III}}$ yields a
difference of $\sim 1$ dex in the number of PISNe. The scatter resulting from
different assumptions on the IMF (covering all the cases explored in Table 1
and shown as a shaded region for the reference case
$\eta_{\mathrm{III}}=0.1$), is instead slightly higher than 1 dex.

Figure 4: Average number of PISNe $\overline{N}_{\mathrm{PISN,t}}$ (normalised
to the Pop III formation efficiency $\eta_{\mathrm{III}}$) as a function of
the effective survey volume $V_{\mathrm{eff}}$ at $z=8.1$. Vertical, dashed
lines indicate the effective volume of selected JWST surveys and their
cumulative volume at $z\simeq 8$, with $\Delta z=1$ (filled circles, see text
for details), and the comoving volume of an equivalent $\sim 1$ deg2 survey
with the Roman Space Telescope (RST, filled triangles); the average number of
PISNe found in our six dustyGadget cubes is also indicated in the plot (DG,
empty squares). A horizontal, dashed line further indicates the reference
value of 1 PISN per volume. The black line refers to the average number of
PISNe found in all haloes with
$7.5<\mathrm{Log}(M_{\star}/$\mathrm{M}_{\odot}$)\leq 9.5$, while the coloured
lines refer to the average number found in haloes of different stellar mass
bins (see Figure 3). Solid lines refer to our reference model for Pop III
stars, i.e. a Salpeter-like IMF in the range [100, 500] $\mathrm{M}_{\odot}$
with no mass loss, while dotted lines refer to the corresponding model
assuming strong mass loss; the shaded area shows the expected scatter for
different assumed IMFs (see Figure 1 and Table 1). As a reference, the purple
pentagon indicates the cumulative number of PISNe at $z>8$ expected in a
survey of $\sim$1 deg2 in one year, computed by integrating over the observed
PISN rate as a function of redshift from Jaacks et al. (2019, see their figure
15) in this redshift range, and re-normalizing by the considered survey area.

Figure 4 shows the average number of PISNe at $z=8.1$ that we expect as a
function of effective survey volume in our reference model. We multiply the
values of $\overline{n}_{\mathrm{PISN}}$ in our simulations by the comoving
volume of selected JWST surveys at $z\simeq 8$, with $\Delta z=1$:

  1. 1.

the Next Generation Deep Extragalactic Exploratory Public (NGDEEP) Survey
(Finkelstein et al., 2021; Pirzkal et al., 2023; Bagley et al., 2023);

  2. 2.

the Grism Lens-Amplified Survey from Space
(GLASS666https://glass.astro.ucla.edu/ers/, Treu et al. 2017, 2022; Castellano
et al. 2022);

  3. 3.

the Ultradeep NIRSpec and NIRCam ObserVations before the Epoch of Reionization
(UNCOVER777https://jwst-uncover.github.io/, Bezanson et al. 2022; Furtak et
al. 2022; Weaver et al. 2023);

  4. 4.

the Cosmic Evolution Early Release Science Survey
(CEERS888https://ceers.github.io/ceers-first-images-release, Finkelstein et
al. 2017, 2022, 2023);

  5. 5.

the Public Release IMaging for Extragalactic Research
(PRIMER999https://primer-jwst.github.io/) survey (Dunlop et al., 2021);

  6. 6.

the PANORAMIC survey (Williams et al., 2021);

  7. 7.

the Cosmic Evolution Survey (COSMOS-
Web101010https://cosmos.astro.caltech.edu/, Casey et al. 2022).

In our reference model, we expect less than 1 PISN on average in all the
examined JWST surveys, even when considering all fields together. However,
more than one PISN per volume can be found in the COSMOS-Web and PANORAMIC
fields in some of the most optimistic scenarios, i.e. with
$\eta_{\mathrm{III}}=1$ and assuming the highest values of
$\overline{N}_{\mathrm{PISN}}/M_{\mathrm{III}}$. We also consider a possible
$\sim 1$ deg2 survey with the Wide Field Instrument (WFI) of the Nancy Grace
Roman Space Telescope111111https://roman.gsfc.nasa.gov/ in the same redshift
range: we see that the expected number of PISNe in this volume in our
reference model is $\simeq 1.5\,\eta_{\mathrm{III}}$, and it can go up to
$\sim 10\,\eta_{\mathrm{III}}$ in the most optimistic cases. Even higher
survey volumes with Roman have been proposed in the literature: Moriya et al.
(2022b), for example, suggested a 10 deg2 transient survey with a limiting
magnitude of 27.0 mag and 26.5 mag in the F158 and F213 filters respectively,
to be conducted for five years with a cadence of one year with the aim of
looking for PISNe candidates during the EoR (also see Section 3.2.1). This
would further increase the expected number of PISNe by a factor ten.

We emphasize that in this paper we investigate the possibility of detecting
PISNe during the EoR and using them as a marker for Pop III stars. Hence, we
focus on galaxies that are potentially observable with JWST and Roman, so that
we can also study the underlying stellar populations in details. However,
mini-haloes are the most favourable environments for Pop III star formation at
high redshifts, meaning we expect a higher number of PISNe occurring in low-
mass halos closer to Cosmic Dawn (also refer to the first caveat of Section
4.1). We can compute the cumulative observed PISN rate per unit time per unit
solid angle at $z>8$ as:

$\frac{\differential\overline{N}_{\mathrm{PISN}}}{\differential
t\differential\Omega}(z>8)\simeq\frac{\overline{N}_{\mathrm{PISN}}}{M_{\mathrm{III}}}\int_{z=8}^{\infty}\frac{\Psi_{\mathrm{III}}(z)}{1+z}r^{2}(z)\diff{r}{z}\differential
z,$ (7)

where $\Psi_{\mathrm{III}}(t)$ is the Pop III cosmic star formation rate
density (SFRD) at redshift $z$, and $r(z)$ is the comoving distance to
redshift $z$ (see e.g. Hummel et al. 2012; Jaacks et al. 2019). In Figure 4,
we show the total number of PISNe up to Cosmic Dawn that would be found in 1
yr in a survey area of $\sim$1 deg2 (purple pentagon), computed by integrating
over the observed PISN rate as a function of redshift shown in figure 15 of
Jaacks et al. (2019)121212Their model is able to better resolve star formation
in low-mass halos at high redshifts ($z\gtrsim 13$), that we tend to
underestimate systematically due to our coarse resolution. See e.g. figure A1
of Venditti et al. 2023 for a comparison with the Pop III SFRD of various
high-resolution models and simulations on smaller boxes (box side $\lesssim
4h^{-1}$ cMpc).. We see that $\simeq 26$ PISNe/yr can be found on average at
$z>8$ from their model131313Note that the total mass of Pop III stellar
populations in this simulation is $\sim 1000~{}$\mathrm{M}_{\odot}$$, much
smaller than our stellar populations of $\sim 10^{6}~{}$\mathrm{M}_{\odot}$$.
Hence, this number should not be rescaled by the efficiency
$\eta_{\mathrm{III}}$ (i.e. a value of $\eta_{\mathrm{III}}=1$ should be
considered). We also re-normalize by our considered survey area..

###  3.2 Detecting PISNe and discriminating against stellar emission

####  3.2.1 Integrated emission

To estimate the chance of observing PISNe against the stellar emission of
their hosting galaxies, in Figure 5 we compare the predicted bolometric light
curves of representative PISNe with the bolometric luminosity arising from the
stellar populations in galaxies of given stellar mass.

Figure 5: Total bolometric luminosity $L_{\mathrm{bol}}$ of galaxies with
various stellar masses $M_{\star}$ (horizontal, dashed, light-grey lines),
compared with the light curve of PISNe with different RSG/BSG progenitors as a
function of rest-frame time (see text for details); the left-hand side of the
plot (before the vertical, dashed line) shows the brief, “shock-breakout”
phase (from figure 3 of Kasen et al. 2011), expanded to display the time
evolution in units of hours, while the right-hand side shows the long-term
emission in day units (from figure 5 of Kasen et al. 2011). The
$L_{\mathrm{bol}}$ of galaxies with given $M_{\star}$ is computed assuming all
the stellar mass consists of Pop II/I stellar populations following a Salpeter
IMF in the range [0.1, 100] $\mathrm{M}_{\odot}$, and that all stars obey
standard mass-luminosity relations (Equation 10, valid for stars at solar
metallicity on the ZAMS, with
$C=10^{2.68}~{}$\mathrm{L}_{\odot}\,\mathrm{M}_{\odot}^{-1}$$). The magenta,
shaded region also shows a comparison with the average stellar luminosity of
haloes with virial mass $\sim 10^{11}~{}$\mathrm{M}_{\odot}$$ at $6\lesssim
z\lesssim 30$, corresponding to $M_{\star}\sim
10^{8.2}-10^{8.9}~{}$\mathrm{M}_{\odot}$$, from Riaz et al. (2022, see their
figures 1 and 2).

We consider PISNe with five different progenitor stars from Kasen et al.
(2011), particularly two zero-metallicity stars dying as compact blue super-
giants (BSGs, i.e. B250 and B200, respectively with initial masses of 250
$\mathrm{M}_{\odot}$ and 200 $\mathrm{M}_{\odot}$) and three
$10^{-4}~{}$\mathrm{Z}_{\odot}$$ stars dying as red super-giants141414The
authors argued that the difference between the two expected outcomes also
relies on the choice of other uncertain parameters such as primary nitrogen
production and mixing, and that with typical values most zero-metallicity
stars would also end their life as RSGs. (RSGs, i.e. R250, R200 and R150, with
250 $\mathrm{M}_{\odot}$, 200 $\mathrm{M}_{\odot}$ and 150
$\mathrm{M}_{\odot}$ respectively), with radii 10-50 times larger. The highest
luminosities are reached during the “shock-breakout” phase of the explosion,
when the radiation-dominated shock, resulting from the expansion of the
exploded He core into the hydrogen envelope, approaches the surface of the
star and escapes in a luminous X-ray/UV burst. The peak luminosity for each SN
can reach values higher than $10^{12}~{}$\mathrm{L}_{\odot}$$ (see table 2 of
Kasen et al. 2011). However, this phase only lasts a few hours. We are instead
more interested in the longer-lasting emission following the breakout, as
radiation continues to diffuse out of the expanding, cooling ejecta and it may
be visible at rest-frame optical wavelengths for several weeks, and even
longer in the IR (see e.g. figure 7 of Kasen et al. 2011). The initial phase
of the light-curve is powered by the diffusion of thermal energy deposited by
the shock and it is dimmer for the BSG models due to the relatively small
radii of the progenitors; the secondary peak results from the radioactive
decay of synthesized 56Ni.

To roughly estimate the luminosity arising from the stellar populations in
galaxies of given stellar mass, we assume the luminosity of a given star of
mass $m$ in the range $[m_{i},~{}m_{i+1}]$ can be inferred from a simple mass-
luminosity relation of the form

$L^{(i)}(m)=a_{i}m^{b_{i}},$ (8)

(see, e.g. Riaz et al., 2022)151515The spread between the average stellar
luminosities of the most massive haloes in Riaz et al. (2022) is also shown as
a reference in Figure 5.. The luminosity arising from all stars within this
mass range in a given stellar population can then be obtained by integrating
over our assumed IMF:

$L_{\star}^{(i)}=M_{\star}\frac{\int_{m_{i}}^{m_{i+1}}L^{(i)}(m)\phi(m)\differential
m}{\int_{m_{\mathrm{low}}}^{m_{\mathrm{up}}}m\phi(m)\differential m}.$ (9)

Hence, we find a simple relation between the total stellar mass of the haloes
$M_{\star}$ and their luminosity $L_{\star}$:

$L_{\star}=\sum_{i}L_{\star}^{(i)}=C\times M_{\star},$ (10)

with $C=\left[\sum_{i}\int_{m_{i}}^{m_{i+1}}L^{(i)}(m)\phi(m)\differential
m\right]/\left[\int_{m_{\mathrm{low}}}^{m_{\mathrm{up}}}m\phi(m)\differential
m\right]$. Since we are interested in the total emission, as a first
approximation we assume all the stellar mass consists of Pop II/I stars and
neglect the contribution of Pop III161616Note that this is a reasonable
approximation only when considering the total bolometric emission, while the
contribution of massive Pop IIIs to the detailed spectral energy distribution,
especially in the ionising bands, may be non-negligible (Tumlinson & Shull,
2000; Tumlinson et al., 2001; Bromm et al., 2001b; Schaerer, 2002, 2003;
Raiter et al., 2010)., making up less than 5% of the total stellar mass (see
e.g. figure 3 of Venditti et al. 2023 and the lower curves of figure 3 in Riaz
et al. 2022). We use standard mass-luminosity relations171717The average mass-
luminosity relation for stars with masses $1\,$\mathrm{M}_{\odot}$\lesssim
m\lesssim 50\,$\mathrm{M}_{\odot}$$ is taken from Kippenhahn et al. (2013, p.
253). The relation at low stellar masses, for which convection is the dominant
energy transport process, is taken from Duric (2003, p. 19), as inferred from
observations of stars in the Hyades cluster (Torres et al., 1997). At high
masses, as the stars approach the Eddington limit and become unstable, quickly
losing mass by intense stellar winds due to the increasing radiation pressure
(Kudritzki & Puls, 2000), the relation becomes progressively flatter,
approximated as linear in the limit $m\gtrsim 50~{}$\mathrm{M}_{\odot}$$. for
Pop II/I stars (in Eq. 8):

$L(m)\simeq\begin{cases}L_{50}(m/50~{}$\mathrm{M}_{\odot}$)&m\gtrsim
50~{}$\mathrm{M}_{\odot}$,\\\
$\mathrm{L}_{\odot}$(m/$\mathrm{M}_{\odot}$)^{3.35}&1~{}$\mathrm{M}_{\odot}$\lesssim
m\lesssim 50~{}$\mathrm{M}_{\odot}$,\\\
$\mathrm{L}_{\odot}$(m/$\mathrm{M}_{\odot}$)^{4.0}&0.4~{}$\mathrm{M}_{\odot}$\lesssim
m\lesssim 1~{}$\mathrm{M}_{\odot}$,\\\
L_{0.4}(m/0.4~{}$\mathrm{M}_{\odot}$)^{2.3}&m\lesssim
0.4~{}$\mathrm{M}_{\odot}$,\end{cases}$ (11)

where $L_{50}$ and $L_{0.4}$ are, respectively, the luminosity of a star with
50 $\mathrm{M}_{\odot}$ and 0.4 $\mathrm{M}_{\odot}$. By integrating these
relations over our assumed Salpeter IMF in the range [0.1, 100]
$\mathrm{M}_{\odot}$, we find
$C=10^{2.68}~{}$\mathrm{L}_{\odot}\,\mathrm{M}_{\odot}^{-1}$$ (Equation 10).

Figure 6: Expected observed light curve of PISNe from the different RSG
progenitors of Figure 5 in the same F356W and F200W filters (thick, yellow
lines and thick, cyan lines), in the F444W and F277W filters (thin, red lines
and thin, dark-green lines), and in the F213 and F158 filters of the Roman
Space Telescope (thick, orange lines and thick, aquamarine lines), at $z\simeq
6$, as a function of observer-frame time (from figure 4 of Hartwig et al. 2018
and figure 6 of Moriya et al. 2022b). The sensitivity limits of selected JWST
surveys and the limiting sensitivity necessary to separate SNeIa and SNeII at
$z>1.5$ from PISNe and SLSNe at $z>6$ with Roman (see text for details) are
indicated as horizontal, dashed lines, with the same colour legend used for
the filters.

Note that the relations in Equation 11 are only valid for the bolometric
luminosities of stars on the Zero Age Main Sequence (ZAMS), while older stars
would be found at progressively lower luminosities. Therefore, these results
should be strictly interpreted as upper limits. Keeping this caveat in mind,
we see from Figure 5 that the peak emission from most PISNe would easily
outshine the stellar emission of their hosting haloes, at least for
$M_{\star}\lesssim 10^{9}~{}$\mathrm{M}_{\odot}$$, especially when considering
the most likely RSG-scenarios. However, as previously emphasised, this
emission is short-lived with respect to the total light curve, and our chance
of catching the event close to its peak is of the order of $\sim 1$ hour/1
yr$\sim 10^{-4}$. Considering the long-term evolution, when the luminosity can
drop by more than two orders of magnitude, we have a much less favourable
scenario, with only the extreme R250 PISN clearly rising above the stellar
emission from $M_{\star}\lesssim 10^{8}~{}$\mathrm{M}_{\odot}$$ haloes.

Figure 6 shows the observed PISN light curves for the RSG-progenitor models at
$z\simeq 6$, in four JWST/NIRCam filters (F444W, F356W, F277W and F200W), as
well as in two filters of the Nancy Grace Roman Space Telescope (F213 and
F158). The combination of F356W and F200W was suggested by Hartwig et al.
(2018) as the optimal 2-filter diagnostic to detect the prompt emission of
PISNe at $6\lesssim z\lesssim 12$ with JWST, thus identifying possible
candidates to be confirmed as transients through follow-up observations. This
choice of filters maximizes the visibility time (i.e. the fraction of the
light curve that we are able to observe) and thus the probability of finding a
PISN, with an optimal exposure time of $\sim 600$ s (see figure 6 of Hartwig
et al. 2018). Similarly, Moriya et al. (2022b) determined that F158-F213 is
the best two-filter combination to discriminate between the classical
SNeIa/SNeII at $z>1.5$ and PISNe/SLSNe at $z>6$ with Roman, by comparing the
color-magnitude diagrams of SNe at all phases.

The sensitivity limits181818The sensitivity limits are from (i) table 1 of
Casey et al. (2022) for COSMOS-Web; (ii) https://ceers.github.io/obs.html for
CEERS; (iii) table 1 of Bagley et al. (2023) for NGDEEP. in the reference
filters of CEERS and of the shallowest/deepest JWST surveys (COSMOS-
Web/NGDEEP) included in Figure 4 are indicated as horizontal, dashed lines in
the plot; for COSMOS-Web, as the optimal filters F356W and F200W are not
available, we report the limits of the closest filters in terms of wavelength
coverage, i.e. F444W and F277W191919Note however that these filters cannot be
exposed simultaneously. The only two-filter diagnostics available for COSMOS-
Web would be F150W-F277W and F150W-F444W, but these would be among the least
efficient combinations (see figure 6 of Hartwig et al. 2018).. We see that the
PISNe arising from the most massive progenitors would be visible from a time
$\lesssim 2$ months (in the case of R200 in the COSMOS-Web/F277W filter) up to
a time $\sim 9$ yr (in the case of R250 in the NGDEEP/F356W filter). The
least-massive-progenitor PISN (R150) would also be visible for almost one year
in NGDEEP/F200W and almost two years in NGDEEP/F356W. The limiting sensitivity
necessary to separate SNeIa and SNeII at $z>1.5$ from PISNe and SLSNe at $z>6$
with Roman (see Moriya et al. 2022b) is also indicated: with these
sensitivities, the most massive PISN would be observable for about three years
in F213 and for about a year and a half in F158.

####  3.2.2 Resolved observations

Figure 7: Ratio between the Pop III distance from the centre of mass of the
hosting halo $r_{\mathrm{III}}$ and the stellar mass-weighted radius
$r_{\star}$ of the halo, for each Pop III stellar particle that could
potentially produce PISNe (gold stars, i.e. Pop III particles with age
$\tau_{\mathrm{noML}}(260~{}$\mathrm{M}_{\odot}$)\leq
t_{\mathrm{III}}\leq\tau_{\mathrm{strongML}}(140~{}$\mathrm{M}_{\odot}$)$).
The mean and standard deviation computed in five bins of $M_{\star}$ (with a
spacing of 0.5 dex in the range
$7.5\leq\mathrm{Log}M_{\star}/$\mathrm{M}_{\odot}$<10$) is also shown as a
gold, thick, solid line. Results are reported at $z=8.1$ (top panel), $z=7.3$
(middle panel) and $z=6.7$ (bottom panel). The black, dashed lines indicate
where $r_{\mathrm{III}}=r_{\star}$ or $r_{\mathrm{III}}=2r_{\star}$; Pop IIIs
with $r_{\mathrm{III}}$ above these thresholds (depending on the strictness of
the adopted criterion) are considered “external”. The mean and standard
deviation of $r_{\star}$ normalized to the PSF of selected JWST/NIRCam and
Roman/WFI filters (F200W/F356W and F158/F213 respectively) are also shown in
the plots as thin, coloured lines, with same colour legend of Figure 6. The
segments at the top-left corners indicate the relative size of the filters PSF
(coloured segments) compared to the average value of $r_{\star}$ over the
considered sample (gold segments); the absolute size is also indicated next to
each segment.

In Figure 5 we considered the integrated emission arising from all stellar
populations in the galaxies, but in reality it is unlikely that this emission
would be concentrated in a small region near their centre. In Venditti et al.
(2023) we discussed the complex and irregular morphology of early galaxies in
dustyGadget simulations in terms of their gas, dust and stellar components, as
they are mostly still in an assembly phase. Moreover, given the low
metallicity required for their formation, many Pop IIIs will be found either
at the periphery of Pop II clusters or in pristine satellites of their hosting
haloes. This could result in lower levels of contamination from higher-
metallicity stellar populations to the signal of Pop IIIs and of their PISNe,
provided that we are able to observe these galaxies with enough spatial
resolution.

In Figure 7 we show the ratio between the distance of Pop III
particles202020Note that in this figure we consider the largest sample of
potential candidates, i.e. Pop III particles with age
$\tau_{\mathrm{noML}}(260~{}$\mathrm{M}_{\odot}$)\leq
t_{\mathrm{III}}\leq\tau_{\mathrm{strongML}}(140~{}$\mathrm{M}_{\odot}$)$,
with $\tau_{\mathrm{noML}}(260~{}$\mathrm{M}_{\odot}$)=2.10$ Myr the lifetime
of a $260~{}$\mathrm{M}_{\odot}$$ Pop III star assuming no mass loss and
$\tau_{\mathrm{strongML}}(140~{}$\mathrm{M}_{\odot}$)=3.06$ Myr the lifetime
of a $140~{}$\mathrm{M}_{\odot}$$ Pop III star assuming strong mass loss. that
may produce PISNe at a given redshift ($z=8.1$, 7.3 and 6.7) from the centre
of mass of their hosting halo and the stellar-mass-weighted radius
$r_{\star}$, as a function of the halo stellar mass $M_{\star}$. We see that
there is a large scatter in the values, and that Pop IIIs can be found at a
distance up to twenty-five times $r_{\star}$, in the most extreme case. To
highlight the trend of $r_{\mathrm{III}}/r_{\star}$ as a function of
$M_{\star}$, we also plot the mean and standard deviation in the same
$M_{\star}$ bins of Figure 3. Most particles have an $r_{\mathrm{III}}$
slightly higher than $r_{\star}$, although if we consider a stricter criterion
to indicate “external” PISNe (i.e. $r_{\mathrm{III}}>2r_{\star}$), only
particles in haloes higher than $10^{8.5}~{}$\mathrm{M}_{\odot}$$ satisfy this
requirement on average, and only particles in haloes higher than
$10^{9.5}~{}$\mathrm{M}_{\odot}$$ at $z=6.7$. Note, however, that low-mass
galaxies also have a generally lower luminosity, and therefore they are less
likely to outshine their hosted PISN (see Figure 5). Despite the large
scatter, there is indeed a slightly growing trend of
$r_{\mathrm{III}}/r_{\star}$ with increasing $M_{\star}$.

We compare the physical size of our galaxies to the resolution element of the
selected JWST/NIRCam and Roman/WFI filters discussed in Section 3.2.1. The
physical size of the Point Spread Function (PSF) at given redshift is
$s(z)=\theta D_{\mathrm{A}}(z)$, with $D_{\mathrm{A}}(z)$ the angular diameter
distance at redshift $z$ and $\theta$ the angular size212121The PSF of
NIRCam/F200W and NIRCam/F356W is taken from https://jwst-docs.stsci.edu/jwst-
near-infrared-camera/nircam-performance/nircam-point-spread-functions, while
the PSF of WFI/F158 and WFI/F213 is taken from
https://roman.gsfc.nasa.gov/science/WFI_technical.html. of the PSF. In Figure
7, we show the mean and standard deviation of $r_{\star}$ normalized to the
PSF in the same bins of $M_{\star}$. For reference, we also show the size of
the various PSFs relative to the average $r_{\star}$ of our PISN-hosting
galaxies at each redshift. We see that, on average, the bulk of our galaxies
is resolved with more than one pixel in all the considered filters.
Particularly, they are best resolved in NIRCam/F200W, while WFI/F213 has the
coarsest spatial resolution. High-mass galaxies up to
$10^{9.5}~{}$\mathrm{M}_{\odot}$$ are also generally better resolved than
their lower-mass counterparts.

##  4 Discussion

###  4.1 Main caveats

The following caveats should be kept in mind:

  1. 1.

the statistics for high-mass, well-resolved haloes in our simulations is quite
scarce. More reliable results for the highest-stellar-mass bins in Figure 3
would require even larger simulated volumes. We also did not take into account
the contribution of galaxies with $M_{\star}<10^{7.5}~{}$\mathrm{M}_{\odot}$$,
that are not well resolved in our simulations due to our mass resolution
limits, and that would also be the most affected by radiative feedback (see
point (v)). Neglecting this halo population, that hosts a significant portion
of the total Pop III mass ($\gtrsim 60\%$ at the considered redshifts, see
Venditti et al. 2023), will result in an underestimation of the total number
of expected PISNe, at least by a factor 1.5. However, we remark that we are
mainly interested in PISN hosts in which we can potentially study the
underlying stellar populations in details, to look for candidate Pop III stars
during the EoR. A full picture on all the PISNe produced in our cubes
regardless of their environment is beyond the scopes of the present work.

  2. 2.

In Equation 4, we are assuming for simplicity that PISNe have uniform
probability of occurring within $\Delta t_{\mathrm{PISN}}$ for a given stellar
population. However, in reality this probability depends on the assumed IMF;
in particular, with our IMF, lower-mass Pop III stars are more likely to form,
therefore we should expect more PISNe arising from stars closer to the lower-
mass threshold for PISN progenitors, and hence having longer lifetimes.
Moreover, a random sampling of the IMF would be required for a more realistic
estimate of the average number of PISNe produced per stellar population.

  3. 3.

We have explored two different models with different assumptions for the
stellar mass loss arising from Pop IIIs, however, many other uncertainties
exist. For example, we have not explored different choices for the value of
$Z_{\mathrm{crit}}$, although the chosen assumptions may change the results
for Pop III star formation at cosmological scales considerably (see e.g. Maio
et al. 2010). We did consider the impact of choosing different IMFs in the
estimate of the average number of PISNe produced per unit Pop III mass
(Equation 1). Nonetheless, we emphasize that a full exploration of the impact
of IMF variations would require a self-consistent approach.

  4. 4.

Our chosen Pop III IMF covers the mass range [100, 500] $\mathrm{M}_{\odot}$.
On the other hand, studies on the properties of carbon-enhanced extremely
metal-poor stars show that they are best matched by the nucleosynthetic yield
of traditional core-collapse SNe222222However, some level of contamination of
enrichment from Pop II stars is also possible (Ji et al., 2015; Vanni et al.,
2023). (Ishigaki et al., 2014; de Bennassuti et al., 2014, 2017; Fraser et
al., 2017; Magg et al., 2022; Aguado et al., 2023b), suggesting that Pop III
progenitors with masses $\sim 10-40~{}M_{\odot}$ are indeed more prevalent.
Here, we are not interested in the detailed nucleosynthetic pattern, hence our
conclusions should not be significantly affected by this assumption. We also
note that, while considering an IMF more biased towards massive stars might
cause in principle an overproduction of PISNe, the reality is more complex. In
fact, given the exceptionally high metal yield of PISNe, this choice may
actually lead in the opposite direction, as a faster enrichment might induce
an earlier transition to the Pop II mode of star formation. The effect of the
Pop III IMF on cosmic star formation history is debated (Maio et al., 2010,
2016; Pallottini et al., 2014). In Venditti et al. (2023), we found that our
Pop III SFRD is in line with other models and simulations, although large
uncertainties are involved.

  5. 5.

Even though the simulation includes an homogeneous UV background as in Haardt
& Madau (1996), this does not have feedback on cosmic star formation at $z>6$,
i.e. in the epoch considered in the present work. The lack of a proper
treatment of radiative feedback, - especially in the UV and LW bands -
certainly affects the late Pop III star formation. This limitation is
extensively discussed in Venditti et al. (2023), in which our Pop III star
formation rate density is also carefully compared with the results of other
small-scale simulations modelling the local/global effects of UV and LW
radiation.

  6. 6.

We have not discussed our ability to discriminate PISNe from other theoretical
red sources such as dark stars (Spolyar et al., 2008; Freese et al., 2008,
2010; Yoon et al., 2008; Natarajan et al., 2009; Hirano et al., 2011; Banik et
al., 2019) and direct-collapse black holes (Haemmerlé et al., 2020). We note,
however, that we should be able to distinguish these sources through follow-up
observations after a few years, due to the time variability of PISNe.

###  4.2 Implications of future detections

In light of our results, we wish to discuss the implications of future
detections/non-detections of PISNe with both JWST and Roman. In our model, we
predict that we should be able to see some PISNe at high-redshift at least
through wide surveys with the Roman Space Telescope. Hence, the following
questions arise: what if we do not find any PISN at high redshift? What if,
conversely, we find a surprisingly high number of PISNe?

A higher number of PISNe than allowed by our models may be explained if a
substantial fraction of Pop II stars is also able to reach sufficiently high
masses. The JWST capabilities for discovering PISNe from 0.14–0.43
$\mathrm{Z}_{\odot}$ stars at $z<10$ have been discussed e.g. in Regős et al.
(2020). Although the general consensus is that Pop II/I stars usually follow a
standard Salpeter IMF, with masses $\sim 0.1-100~{}$\mathrm{M}_{\odot}$$, our
constraints on the IMF are mainly derived from observations of the local
Universe. On the other hand, more top-heavy IMFs might actually be more common
at high redshifts (see e.g. Chon et al. 2022). The prevalence of a top-heavy
IMF has been suggested to alleviate the tension between JWST observations and
existing models and simulations, which seem to systematically under-produce
massive, bright galaxies at high redshifts ($z\gtrsim 10$, Yung et al. 2023;
Harikane et al. 2023; Trinca et al. 2023). Olivier et al. (2022) also
demonstrated that a high-temperature black-body spectrum
($T_{\mathrm{eff}}\sim 80000$ K, associated to very massive stars) is
necessary to explain the ionization level of low-$z$, extreme-emission-line
galaxies that are considered analogues to EoR galaxies. We further note that
we focused on our chance of observing PISNe through their prompt emission over
a time $\Delta t_{\mathrm{prompt}}\sim$ 1 yr, hence neglecting the possibility
that PISNe may be observable through their afterglow on much longer
timescales. Hartwig et al. (2018) predict that the PISN afterglow is not
accessible through current observational facilities, although observatories
and telescopes with stronger capabilities may be able to detect it in the
future. However, more accurate modelling may find that this signal is actually
brighter than these predictions, implying that the $\Delta
t_{\mathrm{prompt}}\longrightarrow\Delta t_{\mathrm{afterglow}}$ in Equation 4
\- and hence the expected number of PISNe - can be boosted up to a hundred
times.

Not finding any PISNe during the EoR with either JWST or Roman would also be
surprising, and it would require a revision of our models for Pop III stars.
Maybe Pop IIIs do not reach high enough masses to produce a significant number
of PISNe, either because the physics of star-forming clouds only allows
stellar masses lower than $\sim 140~{}$\mathrm{M}_{\odot}$$, or because the
stars lose most of their mass before dying. An alternative explanation is that
Pop III star formation is suppressed much earlier than $z\sim 10$. As most
models and simulation currently predict that the inhomogeneous metal
enrichment should allow a late Pop III star formation, our models for chemical
and radiative feedback may also need to be reconsidered in this scenario.

###  4.3 Detection strategies: archaeology vs. direct detections at high $z$

In the introduction of this paper we listed many possible strategies to study
PISNe and their Pop III progenitors. These include direct detection,
especially at high redshift where massive Pop III stars may still be actively
forming, and cosmic archaeology (Aoki et al., 2014; Salvadori et al., 2007;
Yoshii et al., 2022; Aguado et al., 2023a). Both techniques present unique
advantages and challenges.

The first obvious advantage of cosmic archaeology is that it makes the study
of PISNe accessible through observations in the local Universe. However, the
nucleosynthetic footprint of low-metallicity gas may result from a complex
stratification of multiple sources of metal pollution, that can be hard to
disentangle (e.g. Ji et al., 2015; Vanni et al., 2023). Moreover, an inherent
issue lies in the selection of candidate PISN descendants: in fact, given its
significant metal yields, a single PISN may cause its environment to
“overshoot” and suddenly reach a relatively high metallicity of order $\sim
10^{-3}~{}$\mathrm{Z}_{\odot}$$ (Karlsson et al., 2008; Greif et al., 2010;
Wise et al., 2012). This means we should not only look at the most metal-poor
stars/environments, rendering the identification and interpretation of
potential candidates even more difficult (see also de Bennassuti et al. 2017).
We certainly need improved selection strategies (Aguado et al., 2023a),
possibly relying on photometry rather than costly spectroscopy on each source.

Throughout this paper, we demonstrated that a direct detection of PISNe during
the EoR is not beyond hope. The identification of PISNe in this case is
probably more straightforward and it has been already discussed in the
literature (Kasen et al., 2011; Hartwig et al., 2018; Moriya et al., 2022b).
We also note that no SN of any kind has yet been found at $z\gtrsim 3$ (e.g.
Cooke et al., 2012; Jones et al., 2013). Due to our sensitivity limits, it is
actually more likely that if we do find SNe at high redshifts, these will be
either PISNe or other kinds of SLSNe. The main obstacle is the fundamentally
transient nature of SNe: although PISNe light curves can be stretched up to
$\sim 10$ yr in the observer frame, this transient nature, combined with their
rarity, make their detection less likely. A longer visibility time might be
attained through their afterglow (see e.g. the discussion in Section 4.2). The
direct imprints of SN feedback may also be studied as a fossil record for
longer time scales after the explosion. If we consider for example a galaxy
with $M_{\star}\sim 10^{7}~{}$\mathrm{M}_{\odot}$$, of which $\sim
10^{4}~{}$\mathrm{M}_{\odot}$$ in Pop IIIs, $\sim 40\%$ of the Pop III mass
would end up as PISNe with our assumed IMF, while $\sim 10\%$ of the Pop II
mass would end up as a traditional core-collapse SNe. By assuming a return
fraction of $\sim 0.1$ for core-collapse progenitors and $\sim 0.5$ for PISN
progenitors (Karlsson et al., 2013), the ratio of metals from PISNe vs core-
collapse would be of the order of $2\times 10^{-2}$, i.e. non negligible. This
means we may be able to reliably tell apart the chemical signature of PISNe
outflows. A thorough investigation of such matters is left to future works.

Looking for PISNe at even higher redshifts ($z\gtrsim 10$) may also be
feasible thanks to the efficient Pop III formation in low-mass, pristine halos
towards Cosmic Dawn (see e.g. the discussion at the end of Section 3.2). We
did not investigate such possibility in depth as the galaxies hosting these
PISNe are less likely to be observable, while in the current work we were
mainly interested in using PISNe as tracers for Pop III stars. Nonetheless,
the tentative detection of HeII emission in the vicinity of a luminous
$z=10.6$ galaxy (Maiolino et al., 2023) might already indicate the presence of
observable Pop III clusters at these redshifts. Dedicated surveys aimed at
finding PISNe at very high redshifts may reveal even more of these fascinating
events.

Ultimately, the combination of all the proposed diagnostics of PISNe will
serve our purposes, as they can provide independent constraints on the rate of
PISNe at high-$z$ and on the properties of their Pop III progenitors.

##  5 Summary and Conclusions

In this paper we studied the probability of finding PISNe arising from Pop III
stars during the EoR. Starting from a suite of six $50h^{-1}$ cMpc dustyGadget
simulations, we provided indications on the most promising galaxy candidates
with $M_{\star}>10^{7.5}~{}$\mathrm{M}_{\odot}$$ to look for PISNe at
$6\lesssim z\lesssim 8$. We also provided predictions on the expected number
of PISNe in selected JWST surveys and in a future $\sim 1$ deg2 survey with
the Nancy Grace Roman Space Telescope. Finally, we discussed the observability
of PISNe within their hosting galaxies in these surveys, in terms of both
their integrated and resolved stellar emission. We considered many possible
sources of uncertainties in our results, including the effect of mass loss on
Pop III lifetimes, the impact of choosing different IMFs on the expected
number of PISNe per unit Pop III mass, and the possibility of a reduced Pop
III star formation efficiency with respect to the nominal efficiency of the
simulation.

We find that, although the probability of observing PISNe is indeed small, it
is non-negliglible. In our reference model for Pop III (Salpeter-like IMF in
the range [100, 500] $\mathrm{M}_{\odot}$, Pop III star formation efficiency
of $\eta_{\mathrm{III}}=0.1$ and no mass loss), the comoving number density of
PISNe and the average number of PISNe per halo can be up to $\sim
10^{-1}~{}$\mathrm{c}\mathrm{M}\mathrm{p}\mathrm{c}^{-3}$$ and $\sim 5\times
10^{-6}$ (i.e. about 1 PISN every two hundred thousand haloes, on average)
respectively. A higher number density of PISNe is generally found in haloes
with decreasing stellar mass, given the higher absolute number density of low-
mass haloes at all the considered redshifts. However, the relative fraction of
low-mass haloes hosting PISNe is smaller with respect to higher-mass haloes,
and hence the probability of finding PISNe in a given halo increases with
$M_{\star}$, and it is highest in haloes with
$10^{9.5}~{}$\mathrm{M}_{\odot}$\lesssim M_{\star}\lesssim
10^{10}~{}$\mathrm{M}_{\odot}$$ at $z=6.7$. Therefore, different observing
strategies may be considered: either targeted follow-up observations of
candidate high-mass galaxies - with a higher PISNe-hosting fraction -, or
blind wide-field surveys - also including the numerous low-mass galaxies that
can also potentially host PISNe.

PISNe from progenitors with masses higher than 200 $\mathrm{M}_{\odot}$ would
be observable for a variable time range (from $\sim$ 2 months up to $\sim$ 9
yr) through all the considered JWST/NIRCam filters, particularly the F356W and
F200W filters that have been indicated by Hartwig et al. 2018 as the best two-
filter diagnostic to identify possible PISNe candidates, and the F444W and
F277W filters available for the largest considered JWST survey (COSMOS-Web).
The 150 $\mathrm{M}_{\odot}$-progenitor PISN would also be visible for almost
one/two years in the F200W/F356W filters of the deepest considered JWST survey
(NGDEEP). However, detecting PISNe with JWST may still be challenging due to
their rarity: in our reference model, we expect on average less than 1 PISN in
all the examined JWST surveys.

A higher potential might be obtained through the WFI instrument on board of
Roman, thanks to its large field-of-view. By considering an example $\sim 1$
deg2 survey, we see that $\simeq 1.5\,\eta_{\mathrm{III}}$ PISNe are expected
in our reference model. An even higher survey volume would further increase
the number of expected PISNe. For example, the $\sim 10$ deg2 survey suggested
by Moriya et al. 2022b with limiting magnitudes of 27.0 mag and 26.5 mag in
the F158 and F213 filters (low enough to see at least the 250
$\mathrm{M}_{\odot}$-progenitor PISN for about a year and a half/three years
in F158/F213) would further increase this number by a factor ten. More
favourable scenarios are also obtained when considering different Pop III IMFs
and/or higher Pop III formation efficiencies, and when including the
contribution of coarsely-resolved environments that have not been specifically
targeted in this study.

While the integrated flux of the underlying galaxies might exceed the flux of
PISNe in the considered filters, Pop III stars - and hence PISNe - are usually
found at the periphery of their hosting haloes. This should mitigate the
contamination of the signal arising from stars, especially for the most
massive galaxies in which the stellar emission is more likely to outshine
PISNe. The bulk of most PISN-hosting galaxies would also be resolved in
JWST/NIRCam and Roman/WFI at these redshifts.

We remark once again that if we do find a galaxy hosting a PISN at high
redshifts, this incredible accomplishment may also pave the way for an even
more incredible discovery. Indeed, by observing the target galaxy again after
some years, when the SN has faded considerably, we might even be able to
discern an active underlying Pop III stellar population. This would possibly
lead to the first clear detection of Pop III stars in the history of
astronomy.

## Acknowledgments

LG and RS acknowledge support from the Amaldi Research Center funded by the
Italian Ministry for Education, Universities and Research (MIUR) program
"Dipartimento di Eccellenza" (CUP:B81I18001170001). We have benefited from the
publicly available programming language Python, including the numpy,
matplotlib and scipy packages.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

## References

  * Abel et al. (2002) Abel T., Bryan G. L., Norman M. L., 2002, http://dx.doi.org/10.1126/science.295.5552.93 Science, https://ui.adsabs.harvard.edu/abs/2002Sci…295…93A 295, 93
  * Aguado et al. (2023a) Aguado D. S., et al., 2023a, http://dx.doi.org/10.1093/mnras/stad164 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.520..866A 520, 866
  * Aguado et al. (2023b) Aguado D. S., et al., 2023b, http://dx.doi.org/10.1051/0004-6361/202245392 , https://ui.adsabs.harvard.edu/abs/2023A&A…669L…4A 669, L4
  * Anders & Grevesse (1989) Anders E., Grevesse N., 1989, http://dx.doi.org/10.1016/0016-7037(89)90286-X , https://ui.adsabs.harvard.edu/abs/1989GeCoA..53..197A 53, 197
  * Aoki et al. (2014) Aoki W., Tominaga N., Beers T. C., Honda S., Lee Y. S., 2014, http://dx.doi.org/10.1126/science.1252633 Science, https://ui.adsabs.harvard.edu/abs/2014Sci…345..912A 345, 912
  * Bagley et al. (2023) Bagley M. B., et al., 2023, http://dx.doi.org/10.48550/arXiv.2302.05466 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2023arXiv230205466B p. arXiv:2302.05466
  * Banik et al. (2019) Banik N., Tan J. C., Monaco P., 2019, http://dx.doi.org/10.1093/mnras/sty3298 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.483.3592B 483, 3592
  * Baraffe et al. (2001) Baraffe I., Heger A., Woosley S. E., 2001, http://dx.doi.org/10.1086/319808 , https://ui.adsabs.harvard.edu/abs/2001ApJ…550..890B 550, 890
  * Barkat et al. (1967) Barkat Z., Rakavy G., Sack N., 1967, http://dx.doi.org/10.1103/PhysRevLett.18.379 , https://ui.adsabs.harvard.edu/abs/1967PhRvL..18..379B 18, 379
  * Bennett & Sijacki (2020) Bennett J. S., Sijacki D., 2020, http://dx.doi.org/10.1093/mnras/staa2835 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.499..597B 499, 597
  * Bezanson et al. (2022) Bezanson R., et al., 2022, http://dx.doi.org/10.48550/arXiv.2212.04026 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2022arXiv221204026B p. arXiv:2212.04026
  * Bond et al. (1984) Bond J. R., Arnett W. D., Carr B. J., 1984, http://dx.doi.org/10.1086/162057 , https://ui.adsabs.harvard.edu/abs/1984ApJ…280..825B 280, 825
  * Bromm (2013) Bromm V., 2013, http://dx.doi.org/10.1088/0034-4885/76/11/112901 Reports on Progress in Physics, https://ui.adsabs.harvard.edu/abs/2013RPPh…76k2901B 76, 112901
  * Bromm et al. (2001a) Bromm V., Ferrara A., Coppi P. S., Larson R. B., 2001a, http://dx.doi.org/10.1046/j.1365-8711.2001.04915.x , https://ui.adsabs.harvard.edu/abs/2001MNRAS.328..969B 328, 969
  * Bromm et al. (2001b) Bromm V., Kudritzki R. P., Loeb A., 2001b, http://dx.doi.org/10.1086/320549 , https://ui.adsabs.harvard.edu/abs/2001ApJ…552..464B 552, 464
  * Bromm et al. (2002) Bromm V., Coppi P. S., Larson R. B., 2002, http://dx.doi.org/10.1086/323947 , https://ui.adsabs.harvard.edu/abs/2002ApJ…564…23B 564, 23
  * Casey et al. (2022) Casey C. M., et al., 2022, http://dx.doi.org/10.48550/arXiv.2211.07865 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2022arXiv221107865C p. arXiv:2211.07865
  * Castellano et al. (2022) Castellano M., et al., 2022, http://dx.doi.org/10.3847/2041-8213/ac94d0 , https://ui.adsabs.harvard.edu/abs/2022ApJ…938L..15C 938, L15
  * Chen et al. (2014) Chen K.-J., Heger A., Woosley S., Almgren A., Whalen D. J., 2014, http://dx.doi.org/10.1088/0004-637X/792/1/44 , https://ui.adsabs.harvard.edu/abs/2014ApJ…792…44C 792, 44
  * Chiaki & Yoshida (2022) Chiaki G., Yoshida N., 2022, http://dx.doi.org/10.1093/mnras/stab2799 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.510.5199C 510, 5199
  * Chiaki et al. (2016) Chiaki G., Yoshida N., Hirano S., 2016, http://dx.doi.org/10.1093/mnras/stw2120 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.463.2781C 463, 2781
  * Chon et al. (2021) Chon S., Omukai K., Schneider R., 2021, http://dx.doi.org/10.1093/mnras/stab2497 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.508.4175C 508, 4175
  * Chon et al. (2022) Chon S., Ono H., Omukai K., Schneider R., 2022, http://dx.doi.org/10.1093/mnras/stac1549 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.514.4639C 514, 4639
  * Cooke et al. (2012) Cooke J., et al., 2012, http://dx.doi.org/10.1038/nature11521 , https://ui.adsabs.harvard.edu/abs/2012Natur.491..228C 491, 228
  * Dessart et al. (2012) Dessart L., Hillier D. J., Waldman R., Livne E., Blondin S., 2012, http://dx.doi.org/10.1111/j.1745-3933.2012.01329.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.426L..76D 426, L76
  * Di Cesare et al. (2023) Di Cesare C., Graziani L., Schneider R., Ginolfi M., Venditti A., Santini P., Hunt L. K., 2023, http://dx.doi.org/10.1093/mnras/stac370210.48550/arXiv.2209.05496 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.519.4632D 519, 4632
  * Dunlop et al. (2021) Dunlop J. S., et al., 2021, PRIMER: Public Release IMaging for Extragalactic Research, JWST Proposal. Cycle 1, ID. #1837
  * Duric (2003) Duric N., 2003, Advanced Astrophysics
  * Euclid Collaboration et al. (2022) Euclid Collaboration et al., 2022, http://dx.doi.org/10.1051/0004-6361/202142897 , https://ui.adsabs.harvard.edu/abs/2022A&A…662A..92E 662, A92
  * Finkelstein et al. (2017) Finkelstein S. L., et al., 2017, The Cosmic Evolution Early Release Science (CEERS) Survey, JWST Proposal ID 1345. Cycle 0 Early Release Science
  * Finkelstein et al. (2021) Finkelstein S. L., et al., 2021, The Next Generation Deep Extragalactic Exploratory Public (NGDEEP) Survey: Feedback in Low-Mass Galaxies from Cosmic Dawn to Dusk, JWST Proposal. Cycle 1, ID. #2079
  * Finkelstein et al. (2022) Finkelstein S. L., et al., 2022, http://dx.doi.org/10.3847/2041-8213/ac966e , https://ui.adsabs.harvard.edu/abs/2022ApJ…940L..55F 940, L55
  * Finkelstein et al. (2023) Finkelstein S. L., et al., 2023, http://dx.doi.org/10.3847/2041-8213/acade4 , https://ui.adsabs.harvard.edu/abs/2023ApJ…946L..13F 946, L13
  * Fraley (1968) Fraley G. S., 1968, http://dx.doi.org/10.1007/BF00651498 , https://ui.adsabs.harvard.edu/abs/1968Ap&SS…2…96F 2, 96
  * Fraser et al. (2017) Fraser M., Casey A. R., Gilmore G., Heger A., Chan C., 2017, http://dx.doi.org/10.1093/mnras/stx480 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.468..418F 468, 418
  * Freese et al. (2008) Freese K., Bodenheimer P., Spolyar D., Gondolo P., 2008, http://dx.doi.org/10.1086/592685 , https://ui.adsabs.harvard.edu/abs/2008ApJ…685L.101F 685, L101
  * Freese et al. (2010) Freese K., Ilie C., Spolyar D., Valluri M., Bodenheimer P., 2010, http://dx.doi.org/10.1088/0004-637X/716/2/1397 , https://ui.adsabs.harvard.edu/abs/2010ApJ…716.1397F 716, 1397
  * Fryer et al. (2001) Fryer C. L., Woosley S. E., Heger A., 2001, http://dx.doi.org/10.1086/319719 , https://ui.adsabs.harvard.edu/abs/2001ApJ…550..372F 550, 372
  * Furtak et al. (2022) Furtak L. J., et al., 2022, http://dx.doi.org/10.48550/arXiv.2212.04381 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2022arXiv221204381F p. arXiv:2212.04381
  * Gal-Yam et al. (2009) Gal-Yam A., et al., 2009, http://dx.doi.org/10.1038/nature08579 , https://ui.adsabs.harvard.edu/abs/2009Natur.462..624G 462, 624
  * Gilmer et al. (2017) Gilmer M. S., Kozyreva A., Hirschi R., Fröhlich C., Yusof N., 2017, http://dx.doi.org/10.3847/1538-4357/aa8461 , https://ui.adsabs.harvard.edu/abs/2017ApJ…846..100G 846, 100
  * Graziani et al. (2015) Graziani L., Salvadori S., Schneider R., Kawata D., de Bennassuti M., Maselli A., 2015, http://dx.doi.org/10.1093/mnras/stv494 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.449.3137G 449, 3137
  * Graziani et al. (2017) Graziani L., de Bennassuti M., Schneider R., Kawata D., Salvadori S., 2017, http://dx.doi.org/10.1093/mnras/stx900 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.469.1101G 469, 1101
  * Graziani et al. (2020) Graziani L., Schneider R., Ginolfi M., Hunt L. K., Maio U., Glatzle M., Ciardi B., 2020, http://dx.doi.org/10.1093/mnras/staa79610.48550/arXiv.1909.07388 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.494.1071G 494, 1071
  * Greif et al. (2010) Greif T. H., Glover S. C. O., Bromm V., Klessen R. S., 2010, http://dx.doi.org/10.1088/0004-637X/716/1/510 , https://ui.adsabs.harvard.edu/abs/2010ApJ…716..510G 716, 510
  * Haardt & Madau (1996) Haardt F., Madau P., 1996, http://dx.doi.org/10.1086/177035 , https://ui.adsabs.harvard.edu/abs/1996ApJ…461…20H 461, 20
  * Haemmerlé et al. (2020) Haemmerlé L., Mayer L., Klessen R. S., Hosokawa T., Madau P., Bromm V., 2020, http://dx.doi.org/10.1007/s11214-020-00673-y , https://ui.adsabs.harvard.edu/abs/2020SSRv..216…48H 216, 48
  * Harikane et al. (2023) Harikane Y., Nakajima K., Ouchi M., Umeda H., Isobe Y., Ono Y., Xu Y., Zhang Y., 2023, http://dx.doi.org/10.48550/arXiv.2304.06658 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2023arXiv230406658H p. arXiv:2304.06658
  * Hartwig et al. (2018) Hartwig T., et al., 2018, http://dx.doi.org/10.1093/mnras/sty1176 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.478.1795H 478, 1795
  * Heger & Woosley (2002) Heger A., Woosley S. E., 2002, http://dx.doi.org/10.1086/338487 , https://ui.adsabs.harvard.edu/abs/2002ApJ…567..532H 567, 532
  * Hirano et al. (2011) Hirano S., Umeda H., Yoshida N., 2011, http://dx.doi.org/10.1088/0004-637X/736/1/58 , https://ui.adsabs.harvard.edu/abs/2011ApJ…736…58H 736, 58
  * Hirano et al. (2014) Hirano S., Hosokawa T., Yoshida N., Umeda H., Omukai K., Chiaki G., Yorke H. W., 2014, http://dx.doi.org/10.1088/0004-637X/781/2/60 , https://ui.adsabs.harvard.edu/abs/2014ApJ…781…60H 781, 60
  * Hirano et al. (2015a) Hirano S., Hosokawa T., Yoshida N., Omukai K., Yorke H. W., 2015a, http://dx.doi.org/10.1093/mnras/stv044 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.448..568H 448, 568
  * Hirano et al. (2015b) Hirano S., Zhu N., Yoshida N., Spergel D., Yorke H. W., 2015b, http://dx.doi.org/10.1088/0004-637X/814/1/18 , https://ui.adsabs.harvard.edu/abs/2015ApJ…814…18H 814, 18
  * Hosokawa et al. (2011) Hosokawa T., Omukai K., Yoshida N., Yorke H. W., 2011, http://dx.doi.org/10.1126/science.1207433 Science, https://ui.adsabs.harvard.edu/abs/2011Sci…334.1250H 334, 1250
  * Hosokawa et al. (2016) Hosokawa T., Hirano S., Kuiper R., Yorke H. W., Omukai K., Yoshida N., 2016, http://dx.doi.org/10.3847/0004-637X/824/2/119 , https://ui.adsabs.harvard.edu/abs/2016ApJ…824..119H 824, 119
  * Hummel et al. (2012) Hummel J. A., Pawlik A. H., Milosavljević M., Bromm V., 2012, http://dx.doi.org/10.1088/0004-637X/755/1/72 , https://ui.adsabs.harvard.edu/abs/2012ApJ…755…72H 755, 72
  * Ishigaki et al. (2014) Ishigaki M. N., Tominaga N., Kobayashi C., Nomoto K., 2014, http://dx.doi.org/10.1088/2041-8205/792/2/L32 , https://ui.adsabs.harvard.edu/abs/2014ApJ…792L..32I 792, L32
  * Jaacks et al. (2018) Jaacks J., Thompson R., Finkelstein S. L., Bromm V., 2018, http://dx.doi.org/10.1093/mnras/sty062 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.475.4396J 475, 4396
  * Jaacks et al. (2019) Jaacks J., Finkelstein S. L., Bromm V., 2019, http://dx.doi.org/10.1093/mnras/stz1529 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.488.2202J 488, 2202
  * Jeon et al. (2015) Jeon M., Bromm V., Pawlik A. H., Milosavljević M., 2015, http://dx.doi.org/10.1093/mnras/stv1353 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.452.1152J 452, 1152
  * Jerkstrand et al. (2016) Jerkstrand A., Smartt S. J., Heger A., 2016, http://dx.doi.org/10.1093/mnras/stv2369 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.455.3207J 455, 3207
  * Ji et al. (2015) Ji A. P., Frebel A., Bromm V., 2015, http://dx.doi.org/10.1093/mnras/stv2052 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.454..659J 454, 659
  * Johnson et al. (2013) Johnson J. L., Dalla Vecchia C., Khochfar S., 2013, http://dx.doi.org/10.1093/mnras/sts011 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.428.1857J 428, 1857
  * Jones et al. (2013) Jones D. O., et al., 2013, http://dx.doi.org/10.1088/0004-637X/768/2/166 , https://ui.adsabs.harvard.edu/abs/2013ApJ…768..166J 768, 166
  * Karlsson et al. (2008) Karlsson T., Johnson J. L., Bromm V., 2008, http://dx.doi.org/10.1086/533520 , https://ui.adsabs.harvard.edu/abs/2008ApJ…679….6K 679, 6
  * Karlsson et al. (2013) Karlsson T., Bromm V., Bland-Hawthorn J., 2013, http://dx.doi.org/10.1103/RevModPhys.85.809 Reviews of Modern Physics, https://ui.adsabs.harvard.edu/abs/2013RvMP…85..809K 85, 809
  * Kasen et al. (2011) Kasen D., Woosley S. E., Heger A., 2011, http://dx.doi.org/10.1088/0004-637X/734/2/102 , https://ui.adsabs.harvard.edu/abs/2011ApJ…734..102K 734, 102
  * Kippenhahn et al. (2013) Kippenhahn R., Weigert A., Weiss A., 2013, Stellar Structure and Evolution, http://dx.doi.org/10.1007/978-3-642-30304-3. doi:10.1007/978-3-642-30304-3.
  * Klessen & Glover (2023) Klessen R. S., Glover S. C. O., 2023, http://dx.doi.org/10.48550/arXiv.2303.12500 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2023arXiv230312500K p. arXiv:2303.12500
  * Knollmann & Knebe (2009) Knollmann S. R., Knebe A., 2009, http://dx.doi.org/10.1088/0067-0049/182/2/608 , https://ui.adsabs.harvard.edu/abs/2009ApJS..182..608K 182, 608
  * Kozyreva et al. (2017) Kozyreva A., et al., 2017, http://dx.doi.org/10.1093/mnras/stw2562 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.464.2854K 464, 2854
  * Kudritzki & Puls (2000) Kudritzki R.-P., Puls J., 2000, http://dx.doi.org/10.1146/annurev.astro.38.1.613 , https://ui.adsabs.harvard.edu/abs/2000ARA&A..38..613K 38, 613
  * Larson (1998) Larson R. B., 1998, http://dx.doi.org/10.1046/j.1365-8711.1998.02045.x10.48550/arXiv.astro-ph/9808145 , https://ui.adsabs.harvard.edu/abs/1998MNRAS.301..569L 301, 569
  * Latif et al. (2022) Latif M. A., Whalen D., Khochfar S., 2022, http://dx.doi.org/10.3847/1538-4357/ac3916 , https://ui.adsabs.harvard.edu/abs/2022ApJ…925…28L 925, 28
  * Laureijs et al. (2011) Laureijs R., et al., 2011, http://dx.doi.org/10.48550/arXiv.1110.3193 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2011arXiv1110.3193L p. arXiv:1110.3193
  * Lazar & Bromm (2022) Lazar A., Bromm V., 2022, http://dx.doi.org/10.1093/mnras/stac176 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.511.2505L 511, 2505
  * Liu & Bromm (2020) Liu B., Bromm V., 2020, http://dx.doi.org/10.1093/mnras/staa2143 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.497.2839L 497, 2839
  * Mackey et al. (2003) Mackey J., Bromm V., Hernquist L., 2003, http://dx.doi.org/10.1086/367613 , https://ui.adsabs.harvard.edu/abs/2003ApJ…586….1M 586, 1
  * Magg et al. (2016) Magg M., Hartwig T., Glover S. C. O., Klessen R. S., Whalen D. J., 2016, http://dx.doi.org/10.1093/mnras/stw1882 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.462.3591M 462, 3591
  * Magg et al. (2022) Magg M., Schauer A. T. P., Klessen R. S., Glover S. C. O., Tress R. G., Jaura O., 2022, http://dx.doi.org/10.3847/1538-4357/ac5aac , https://ui.adsabs.harvard.edu/abs/2022ApJ…929..119M 929, 119
  * Maio et al. (2010) Maio U., Ciardi B., Dolag K., Tornatore L., Khochfar S., 2010, http://dx.doi.org/10.1111/j.1365-2966.2010.17003.x , https://ui.adsabs.harvard.edu/abs/2010MNRAS.407.1003M 407, 1003
  * Maio et al. (2016) Maio U., Petkova M., De Lucia G., Borgani S., 2016, http://dx.doi.org/10.1093/mnras/stw1196 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.460.3733M 460, 3733
  * Maiolino et al. (2023) Maiolino R., et al., 2023, http://dx.doi.org/10.48550/arXiv.2306.00953 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2023arXiv230600953M p. arXiv:2306.00953
  * Marigo et al. (2001) Marigo P., Girardi L., Chiosi C., Wood P. R., 2001, http://dx.doi.org/10.1051/0004-6361:20010309 , https://ui.adsabs.harvard.edu/abs/2001A&A…371..152M 371, 152
  * Miralda-Escudé & Rees (1997) Miralda-Escudé J., Rees M. J., 1997, http://dx.doi.org/10.1086/310550 , https://ui.adsabs.harvard.edu/abs/1997ApJ…478L..57M 478, L57
  * Moriya et al. (2010) Moriya T., Tominaga N., Tanaka M., Maeda K., Nomoto K., 2010, http://dx.doi.org/10.1088/2041-8205/717/2/L83 , https://ui.adsabs.harvard.edu/abs/2010ApJ…717L..83M 717, L83
  * Moriya et al. (2022a) Moriya T. J., et al., 2022a, http://dx.doi.org/10.1051/0004-6361/202243810 , https://ui.adsabs.harvard.edu/abs/2022A&A…666A.157M 666, A157
  * Moriya et al. (2022b) Moriya T. J., Quimby R. M., Robertson B. E., 2022b, http://dx.doi.org/10.3847/1538-4357/ac415e , https://ui.adsabs.harvard.edu/abs/2022ApJ…925..211M 925, 211
  * Natarajan et al. (2009) Natarajan A., Tan J. C., O’Shea B. W., 2009, http://dx.doi.org/10.1088/0004-637X/692/1/574 , https://ui.adsabs.harvard.edu/abs/2009ApJ…692..574N 692, 574
  * Olivier et al. (2022) Olivier G. M., Berg D. A., Chisholm J., Erb D. K., Pogge R. W., Skillman E. D., 2022, http://dx.doi.org/10.3847/1538-4357/ac8f2c , https://ui.adsabs.harvard.edu/abs/2022ApJ…938…16O 938, 16
  * Omukai et al. (2005) Omukai K., Tsuribe T., Schneider R., Ferrara A., 2005, http://dx.doi.org/10.1086/429955 , https://ui.adsabs.harvard.edu/abs/2005ApJ…626..627O 626, 627
  * Pallottini et al. (2014) Pallottini A., Ferrara A., Gallerani S., Salvadori S., D’Odorico V., 2014, http://dx.doi.org/10.1093/mnras/stu451 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.440.2498P 440, 2498
  * Pan & Loeb (2013) Pan T., Loeb A., 2013, http://dx.doi.org/10.1093/mnrasl/slt089 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.435L..33P 435, L33
  * Pan et al. (2012) Pan T., Kasen D., Loeb A., 2012, http://dx.doi.org/10.1111/j.1365-2966.2012.20837.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.422.2701P 422, 2701
  * Pirzkal et al. (2023) Pirzkal N., Finkelstein S., Papovich C., Ngdeep Team 2023, in American Astronomical Society Meeting Abstracts. p. 455.04
  * Planck Collaboration et al. (2016) Planck Collaboration et al., 2016, http://dx.doi.org/10.1051/0004-6361/201525830 , https://ui.adsabs.harvard.edu/abs/2016A&A…594A..13P 594, A13
  * Raiter et al. (2010) Raiter A., Schaerer D., Fosbury R. A. E., 2010, http://dx.doi.org/10.1051/0004-6361/201015236 , https://ui.adsabs.harvard.edu/abs/2010A&A…523A..64R 523, A64
  * Rakavy & Shaviv (1967) Rakavy G., Shaviv G., 1967, http://dx.doi.org/10.1086/149204 , https://ui.adsabs.harvard.edu/abs/1967ApJ…148..803R 148, 803
  * Rees & Ostriker (1977) Rees M. J., Ostriker J. P., 1977, , https://ui.adsabs.harvard.edu/abs/1977MNRAS.179..541R 179, 541
  * Regős et al. (2020) Regős E., Vinkó J., Ziegler B. L., 2020, http://dx.doi.org/10.3847/1538-4357/ab8636 , https://ui.adsabs.harvard.edu/abs/2020ApJ…894…94R 894, 94
  * Riaz et al. (2022) Riaz S., Hartwig T., Latif M. A., 2022, http://dx.doi.org/10.3847/2041-8213/ac8ea6 , https://ui.adsabs.harvard.edu/abs/2022ApJ…937L…6R 937, L6
  * Salpeter (1955) Salpeter E. E., 1955, http://dx.doi.org/10.1086/145971 , https://ui.adsabs.harvard.edu/abs/1955ApJ…121..161S 121, 161
  * Salvadori et al. (2007) Salvadori S., Schneider R., Ferrara A., 2007, http://dx.doi.org/10.1111/j.1365-2966.2007.12133.x , https://ui.adsabs.harvard.edu/abs/2007MNRAS.381..647S 381, 647
  * Salvadori et al. (2008) Salvadori S., Ferrara A., Schneider R., 2008, http://dx.doi.org/10.1111/j.1365-2966.2008.13035.x , https://ui.adsabs.harvard.edu/abs/2008MNRAS.386..348S 386, 348
  * Salvadori et al. (2019) Salvadori S., Bonifacio P., Caffau E., Korotin S., Andreevsky S., Spite M., Skúladóttir Á., 2019, http://dx.doi.org/10.1093/mnras/stz1464 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.4261S 487, 4261
  * Sarmento & Scannapieco (2022) Sarmento R., Scannapieco E., 2022, http://dx.doi.org/10.3847/1538-4357/ac815c , https://ui.adsabs.harvard.edu/abs/2022ApJ…935..174S 935, 174
  * Sarmento et al. (2018) Sarmento R., Scannapieco E., Cohen S., 2018, http://dx.doi.org/10.3847/1538-4357/aa989a , https://ui.adsabs.harvard.edu/abs/2018ApJ…854…75S 854, 75
  * Scannapieco et al. (2005) Scannapieco E., Madau P., Woosley S., Heger A., Ferrara A., 2005, http://dx.doi.org/10.1086/444450 , https://ui.adsabs.harvard.edu/abs/2005ApJ…633.1031S 633, 1031
  * Schaerer (2002) Schaerer D., 2002, http://dx.doi.org/10.1051/0004-6361:20011619 , https://ui.adsabs.harvard.edu/abs/2002A&A…382…28S 382, 28
  * Schaerer (2003) Schaerer D., 2003, http://dx.doi.org/10.1051/0004-6361:20021525 , https://ui.adsabs.harvard.edu/abs/2003A&A…397..527S 397, 527
  * Schauer et al. (2022) Schauer A. T. P., Bromm V., Drory N., Boylan-Kolchin M., 2022, http://dx.doi.org/10.3847/2041-8213/ac7f9a , https://ui.adsabs.harvard.edu/abs/2022ApJ…934L…6S 934, L6
  * Schneider et al. (2012a) Schneider R., Omukai K., Bianchi S., Valiante R., 2012a, http://dx.doi.org/10.1111/j.1365-2966.2011.19818.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.419.1566S 419, 1566
  * Schneider et al. (2012b) Schneider R., Omukai K., Limongi M., Ferrara A., Salvaterra R., Chieffi A., Bianchi S., 2012b, http://dx.doi.org/10.1111/j.1745-3933.2012.01257.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.423L..60S 423, L60
  * Skinner & Wise (2020) Skinner D., Wise J. H., 2020, http://dx.doi.org/10.1093/mnras/staa139 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.492.4386S 492, 4386
  * Spolyar et al. (2008) Spolyar D., Freese K., Gondolo P., 2008, http://dx.doi.org/10.1103/PhysRevLett.100.051101 , https://ui.adsabs.harvard.edu/abs/2008PhRvL.100e1101S 100, 051101
  * Stacy et al. (2016) Stacy A., Bromm V., Lee A. T., 2016, http://dx.doi.org/10.1093/mnras/stw1728 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.462.1307S 462, 1307
  * Sugimura et al. (2020) Sugimura K., Matsumoto T., Hosokawa T., Hirano S., Omukai K., 2020, http://dx.doi.org/10.3847/2041-8213/ab7d37 , https://ui.adsabs.harvard.edu/abs/2020ApJ…892L..14S 892, L14
  * Susa et al. (2014) Susa H., Hasegawa K., Tominaga N., 2014, http://dx.doi.org/10.1088/0004-637X/792/1/32 , https://ui.adsabs.harvard.edu/abs/2014ApJ…792…32S 792, 32
  * Tanaka et al. (2013) Tanaka M., Moriya T. J., Yoshida N., 2013, http://dx.doi.org/10.1093/mnras/stt1469 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.435.2483T 435, 2483
  * Thielemann et al. (2003) Thielemann F. K., et al., 2003, http://dx.doi.org/10.1016/S0375-9474(03)00704-8 , https://ui.adsabs.harvard.edu/abs/2003NuPhA.718..139T 718, 139
  * Tornatore et al. (2007) Tornatore L., Ferrara A., Schneider R., 2007, http://dx.doi.org/10.1111/j.1365-2966.2007.12215.x , https://ui.adsabs.harvard.edu/abs/2007MNRAS.382..945T 382, 945
  * Torres et al. (1997) Torres G., Stefanik R. P., Latham D. W., 1997, http://dx.doi.org/10.1086/304422 , https://ui.adsabs.harvard.edu/abs/1997ApJ…485..167T 485, 167
  * Treu et al. (2017) Treu T. L., et al., 2017, Through the Looking GLASS: A JWST Exploration of Galaxy Formation and Evolution from Cosmic Dawn to Present Day, JWST Proposal ID 1324. Cycle 0 Early Release Science
  * Treu et al. (2022) Treu T., et al., 2022, http://dx.doi.org/10.3847/1538-4357/ac8158 , https://ui.adsabs.harvard.edu/abs/2022ApJ…935..110T 935, 110
  * Trinca et al. (2023) Trinca A., Schneider R., Valiante R., Graziani L., Ferrotti A., Omukai K., Chon S., 2023, http://dx.doi.org/10.48550/arXiv.2305.04944 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2023arXiv230504944T p. arXiv:2305.04944
  * Tumlinson & Shull (2000) Tumlinson J., Shull J. M., 2000, http://dx.doi.org/10.1086/312432 , https://ui.adsabs.harvard.edu/abs/2000ApJ…528L..65T 528, L65
  * Tumlinson et al. (2001) Tumlinson J., Giroux M. L., Shull J. M., 2001, http://dx.doi.org/10.1086/319477 , https://ui.adsabs.harvard.edu/abs/2001ApJ…550L…1T 550, L1
  * Vanni et al. (2023) Vanni I., Salvadori S., Skúladóttir Á., 2023, http://dx.doi.org/10.48550/arXiv.2305.02358 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2023arXiv230502358V p. arXiv:2305.02358
  * Venditti et al. (2023) Venditti A., Graziani L., Schneider R., Pentericci L., Di Cesare C., Maio U., Omukai K., 2023, http://dx.doi.org/10.1093/mnras/stad1201 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.522.3809V 522, 3809
  * Visbal et al. (2020) Visbal E., Bryan G. L., Haiman Z., 2020, http://dx.doi.org/10.3847/1538-4357/ab994e , https://ui.adsabs.harvard.edu/abs/2020ApJ…897…95V 897, 95
  * Wang et al. (2012) Wang F. Y., Bromm V., Greif T. H., Stacy A., Dai Z. G., Loeb A., Cheng K. S., 2012, http://dx.doi.org/10.1088/0004-637X/760/1/27 , https://ui.adsabs.harvard.edu/abs/2012ApJ…760…27W 760, 27
  * Wang et al. (2017) Wang L., et al., 2017, http://dx.doi.org/10.48550/arXiv.1710.07005 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2017arXiv171007005W p. arXiv:1710.07005
  * Weaver et al. (2023) Weaver J. R., et al., 2023, http://dx.doi.org/10.48550/arXiv.2301.02671 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2023arXiv230102671W p. arXiv:2301.02671
  * Whalen et al. (2013) Whalen D. J., et al., 2013, http://dx.doi.org/10.1088/0004-637X/777/2/110 , https://ui.adsabs.harvard.edu/abs/2013ApJ…777..110W 777, 110
  * Whalen et al. (2014) Whalen D. J., et al., 2014, http://dx.doi.org/10.1088/0004-637X/797/1/9 , https://ui.adsabs.harvard.edu/abs/2014ApJ…797….9W 797, 9
  * Williams et al. (2021) Williams C. C., et al., 2021, PANORAMIC - A Pure Parallel Wide Area Legacy Imaging Survey at 1-5 Micron, JWST Proposal. Cycle 1, ID. #2514
  * Wise & Abel (2005) Wise J. H., Abel T., 2005, http://dx.doi.org/10.1086/430434 , https://ui.adsabs.harvard.edu/abs/2005ApJ…629..615W 629, 615
  * Wise et al. (2012) Wise J. H., Turk M. J., Norman M. L., Abel T., 2012, http://dx.doi.org/10.1088/0004-637X/745/1/50 , https://ui.adsabs.harvard.edu/abs/2012ApJ…745…50W 745, 50
  * Woosley & Weaver (1995) Woosley S. E., Weaver T. A., 1995, http://dx.doi.org/10.1086/192237 , https://ui.adsabs.harvard.edu/abs/1995ApJS..101..181W 101, 181
  * Woosley et al. (2007) Woosley S. E., Blinnikov S., Heger A., 2007, http://dx.doi.org/10.1038/nature06333 , https://ui.adsabs.harvard.edu/abs/2007Natur.450..390W 450, 390
  * Xu et al. (2016) Xu H., Norman M. L., O’Shea B. W., Wise J. H., 2016, http://dx.doi.org/10.3847/0004-637X/823/2/140 , https://ui.adsabs.harvard.edu/abs/2016ApJ…823..140X 823, 140
  * Yoon et al. (2008) Yoon S.-C., Iocco F., Akiyama S., 2008, http://dx.doi.org/10.1086/593976 , https://ui.adsabs.harvard.edu/abs/2008ApJ…688L…1Y 688, L1
  * Yoshii et al. (2022) Yoshii Y., Sameshima H., Tsujimoto T., Shigeyama T., Beers T. C., Peterson B. A., 2022, http://dx.doi.org/10.3847/1538-4357/ac8163 , https://ui.adsabs.harvard.edu/abs/2022ApJ…937…61Y 937, 61
  * Yung et al. (2023) Yung L. Y. A., Somerville R. S., Finkelstein S. L., Wilkins S. M., Gardner J. P., 2023, http://dx.doi.org/10.48550/arXiv.2304.04348 arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2023arXiv230404348Y p. arXiv:2304.04348
  * de Bennassuti et al. (2014) de Bennassuti M., Schneider R., Valiante R., Salvadori S., 2014, http://dx.doi.org/10.1093/mnras/stu1962 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.445.3039D 445, 3039
  * de Bennassuti et al. (2017) de Bennassuti M., Salvadori S., Schneider R., Valiante R., Omukai K., 2017, http://dx.doi.org/10.1093/mnras/stw2687 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.465..926D 465, 926
  * de Souza et al. (2014) de Souza R. S., Ishida E. E. O., Whalen D. J., Johnson J. L., Ferrara A., 2014, http://dx.doi.org/10.1093/mnras/stu984 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.442.1640D 442, 1640
  * van den Hoek & Groenewegen (1997) van den Hoek L. B., Groenewegen M. A. T., 1997, http://dx.doi.org/10.1051/aas:1997162 , https://ui.adsabs.harvard.edu/abs/1997A&AS..123..305V 123, 305