# Hypernova signatures of the first stars in dwarf galaxies in the Local Group

Teayong Lee1, Myoungwon Jeon1,2 and Volker Bromm3,4
1School of Space Research, Kyung Hee University, 1732 Deogyeong-daero, Yongin-
si, Gyeonggi-do 17104, Korea
2Department of Astronomy & Space Science, Kyung Hee University, 1732
Deogyeong-daero, Yongin-si, Gyeonggi-do 17104, Korea
3Department of Astronomy, University of Texas, Austin, TX 78712, USA
4Weinberg Institute for Theoretical Physics, University of Texas at Austin,
Austin, TX 78712, USA<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Observing the first generation of stars, Population III (Pop III), is still a
challenge even with the James Webb Space Telescope (JWST) due to their
faintness. Instead, searching for fossil records of Pop III stars in nearby
dwarf galaxies provides an alternative method for studying their physical
properties. It is intriguing that a star recently discovered in the Sculptor
dwarf galaxy, named AS0039, is considered to show the unique signature of a
Pop III star. The detailed abundance patterns of AS0039 are well-matched with
those predicted by nucleosynthesis models for Pop III exploding as an
energetic hypernova (HN), confirming its potential to provide insight into the
properties of the first stars. This study aims to explore the environmental
conditions required for the formation of such a unique star using cosmological
hydrodynamic zoom-in simulations on dwarf galaxies with a mass of $M_{\rm
vir}\approx 10^{8}{\,M_{\odot}}$ at $z=0$ while varying the fraction of Pop
III stars that undergo HNe. Our simulations identify rapid gas inflow
($\dot{M}_{\rm gas}\sim 0.08{\,M_{\odot}}$ $\rm yr^{-1}$) as a possible factor
in facilitating the formation of stars similar to AS0039. Alternatively, the
delayed formation of subsequent Pop II stars in the gas-enriched environment
may lead to low-metallicity stars like AS0039. Additionally, using the A-SLOTH
code, we investigate the probability of finding remnants of Pop II stars with
HN signatures in nearby dwarf satellite galaxies. We suggest that the most
likely dwarf galaxies to contain HN signatures are massive satellites with a
probability of 40% in the range of $M_{\rm peak}\approx
10^{10}-10^{11}{\,M_{\odot}}$ and $M_{\ast}\approx
10^{7}-10^{8}{\,M_{\odot}}$, considering observational limitations.

###### keywords:

galaxies: formation – galaxies: dwarf – galaxies: star formation – methods:
numerical – cosmology: dark ages, reionization, first stars

††pubyear: 2021††pagerange: Hypernova signatures of the first stars in dwarf
galaxies in the Local Group–B

##  1 Introduction

Understanding the physical characteristics of the first generation of stars,
known as Population III (Pop III) stars, and the first galaxies is crucial for
gaining a comprehensive understanding of the entire Universe (reviewed in
Bromm et al., 2009; Bromm, 2013; Klessen & Glover, 2023). Recent breakthroughs
in observing distant galaxies born at $z\gtrsim 10$ by the James Webb Space
Telescope (JWST) have opened up new previously inaccessible territories of the
early Universe (e.g., Atek et al., 2022; Donnan et al., 2022; Whitler et al.,
2022; Bouwens et al., 2023; Finkelstein et al., 2023). The discovery of
unexpectedly bright high-$z$ galaxies has prompted the investigation of the
possible existence of massive Pop III stars in these galaxies (e.g., Kannan et
al., 2023; Boylan-Kolchin, 2023; Inayoshi et al., 2022; Haslbauer et al.,
2022). As a result, understanding the characteristics of the first stars has
become even more important. While JWST could possibly directly observe the
first stars, if Pop III were making up most of the stellar mass in early
galaxies or globular clusters (e.g., Mowla et al., 2022), detecting individual
Pop III stars remains challenging and requires larger telescopes (e.g.,
Schauer et al., 2020; Woods et al., 2021; Katz et al., 2023; Larkin et al.,
2023; Venditti et al., 2023), except for the cases where the brightness is
significantly increased by gravitational lensing effects (e.g., Schauer et
al., 2022; Welch et al., 2022).

Although direct detection of the first stars remains elusive, extensive
theoretical studies have been conducted to infer their physical properties
(see, e.g., Bromm, 2013 for a review). It is widely accepted that Pop III
stars were massive stars, with masses larger than a few tens of solar masses,
formed from primordial gas in minihaloes with virial masses of $M_{\rm
vir}\approx 10^{5-6}{\,M_{\odot}}$ at $z\gtrsim 15$ (e.g., Haiman et al.,
1997; Tegmark et al., 1997; Bromm et al., 1999; Abel et al., 2002; Yoshida et
al., 2003). Pop III stars, depending primarily on their initial masses, are
expected to undergo supernovae (SNe) explosions, ejecting metals synthesized
in their cores and polluting the surrounding interstellar medium (ISM) (e.g.,
Wise & Abel, 2008; Greif et al., 2010; Wise et al., 2012; Jeon et al., 2014).
This contaminated medium eventually gives rise to the second generation of
stars, Population II (Pop II) stars, which tend to have lower masses and
longer lifespans than their Pop III predecessors (e.g., Omukai, 2000; Bromm et
al., 2001; Schneider et al., 2002). Consequently, such Pop II stars ($m_{\rm
PopII}\lesssim 0.8{\,M_{\odot}}$) may still exist in the Local Universe,
displaying the distinctive characteristics of Pop III stars. The search for
such traces of ancient stars that existed in the Local Universe is known as
“stellar archaeology." Furthermore, if these Pop II stars belong to local
dwarf galaxies, it is possible to infer information not only about the stars
themselves but also about the environment in which they formed by
reconstructing the star formation histories (SFHs) of these galaxies. This
approach is known as “galaxy archaeology" (e.g., Bovill & Ricotti, 2011;
Frebel & Norris, 2015)

What unique characteristics of the first generation of stars have been
preserved in local dwarf galaxies? One possible answer lies in carbon-enhanced
metal-poor stars (CEMPs) (e.g., Beers & Christlieb, 2005; Aoki et al., 2007),
which have been thought to be associated with Pop III stars due to their
commonness in observed dwarf galaxies such that the fraction of CEMPs
increases as decreasing metallicities, reaching $\sim$92% below $\rm[Fe/H]<-4$
(e.g., Lee et al., 2013; Placco et al., 2014; Placco et al., 2021).
Specifically, these stars are defined by $\rm[C/Fe]\gtrsim$ 0.7 and
$\rm[Fe/H]\lesssim-2$. One possible explanation for this is the weak supernova
explosion of Pop III stars, which can expel light elements such as carbon and
oxygen from the outer layers of the star while heavy elements like iron fall
back onto the core (e.g., Norris et al., 2013; Jeon et al., 2021).

Recently, in the Sculptor dwarf spheroidal (dSph), Skúladóttir et al. (2021)
have identified a potential remnant of Pop III stars by discovering AS0039,
the most metal-poor star with $\rm[Fe/H]=-4.11$, among the observed local
dwarf galaxies. According to the nucleosynthesis model for metal-free stars
proposed by Heger & Woosley (2002, 2010), the chemical abundance patterns of
AS0039 appear to be consistent with those of a Pop III star with a mass of
$m_{\rm PopIII}\approx 20\pm 2{\,M_{\odot}}$ that ended its life as a
hypernova (HN) explosion with an SN energy of $E_{\rm SN}=10^{52}$ erg.
Notably, AS0039 is a peculiar carbon-poor star with $\rm[C/Fe]_{LTE}\sim-0.75$
and has distinct $\alpha$-element patterns, which sets it apart from normal-
carbon stars. According to Hartwig2023, there is a 77% chance that the
enrichment of AS0039 is due to a single Pop III SN event. Furthermore, Placco
et al. (2021) have reported another potential HN signature associated with Pop
III stars. They have identified a star in Stripe 82 called SPLUS J2104-0049,
whose chemical composition appears to be consistent with that of a Pop II star
formed from gas polluted by a Pop III star with a mass of $30{\,M_{\odot}}$.
This Pop III star would have exploded as an HN with an energy of $E_{\rm
SN}=10^{52}$ erg as well.

The aim of this study is to offer a theoretical interpretation of the observed
stars and gain insights into the era of the first and second generations of
stars. In particular, the goal is to reproduce stars such as AS0039, which are
rare and could potentially offer clues about Pop III HN events as a component
of the stellar population in a nearby dwarf galaxy. To be specific, we
investigate how the signatures of Pop III HN events might appear in subsequent
Pop II stars. Moreover, we examine the circumstances under which a star like
the observed AS0039 can form. To achieve this goal, we conduct a series of
cosmological zoom-in simulations on a local dwarf analog, which is comparable
to the ultra-faint dwarf galaxy (UFD) with a mass of $M_{\rm vir}\lesssim
10^{8}~{}\mbox{M}_{\odot}$ at $z=0$. UFDs are the smallest and most metal-poor
galaxies in the Universe, and they are considered an excellent laboratory for
studying the earliest stars since they preserve traces of them. (For a review,
see Simon, 2019, and also see Tolstoy et al., 2009; Brown et al., 2014;
McConnachie, 2012.)

The exact mechanism for the explosion of highly energetic HN is still unclear.
However, there is widespread agreement that it may be connected to massive
stars exhibiting high angular momentum (e.g., Nomoto et al., 2006; Burrows et
al., 2007). Several studies have been conducted on the level of rotation in
metal-free stars (e.g., Stacy et al., 2011; Hirano & Bromm, 2018). One such
study by Stacy et al. (2011) estimates the rotational velocity of Pop III
stars by tracking the evolution of primordial gas up to densities of $n_{\rm
H}=10^{12}\rm cm^{-3}$ in minihaloes. This suggests that the rotational
velocity of stars larger than $30{\,M_{\odot}}$ may potentially exceed 1000 km
$\rm s^{-1}$. Consequently, these stars may experience chemically homogeneous
evolution (CHE) (Sibony et al., 2022), creating a reservoir of rotational
energy sufficient to initiate an HN explosion. Another study by Choplin et al.
(2019) investigated the abundance patterns of carbon-enhanced extremely metal-
poor (EMP) stars ($\rm-4<[Fe/H]<-3$), comparing them to massive stellar models
that consider rotation. The findings suggest a higher fraction of fast
rotators at low metallicity, with the velocity distribution of star models
reaching equatorial velocities of 550-640 km $\rm s^{-1}$. As such, whether or
not Pop III stars undergo HN explosions are determined by their initial masses
as well as by their degree of rotation (e.g., Marigo et al., 2003; Ekström et
al., 2008; Heger & Woosley, 2010; Chatzopoulos & Wheeler, 2012; Choplin et
al., 2019; Murphy et al., 2021). For instance, Yoon et al. (2012), where they
take into account magnetic fields and the rotation of metal-free stars,
suggest that zero-age main sequence stars with masses between
$13{\,M_{\odot}}$ and $84{\,M_{\odot}}$ may undergo HN explosions if they
experience CHE.

In this work, we have conducted cosmological simulations on a dwarf galaxy
analog, where we vary the fraction of Pop III stars that end their lives as
HNe as a free parameter, covering the full range of possibilities. To further
understand the observed frequency of HN signatures, we have also utilized a
semi-analytic model of galaxy formation called A-SLOTH (Hartwig et al., 2023).
This model enables us to connect the formation of early Pop III stars with
their fossil remnants in nearby galaxy analogs, providing an estimate of the
probability of discovering satellite galaxies that contain Pop III HN
signatures based on the fraction of Pop III stars exploding as HNe in the
early Universe.

The paper is structured as follows: Section 2 outlines the numerical
methodology employed in this research. Section 3 presents and analyzes the
simulation results, including the growth of simulated galaxies over cosmic
time, the prevalence of minihaloes and Pop II stars exhibiting Pop III HN
signatures, and the chemical imprints left on the remaining Pop II stars. In
Section 4, we discuss the likelihood of finding satellite galaxies that harbor
Pop III HN signatures using a semi-analytic galaxy formation model. The key
discoveries of this study are summarized in Section 5. Unless otherwise
indicated, all distances are provided in physical (proper) units to maintain
consistency.

##  2 Numerical methodology

###  2.1 Simulation Setup

We have conducted cosmological hydrodynamic zoom-in simulations on dwarf
galaxies using a modified version of the parallel N-body/smoothed particle
hydrodynamics code, GADGET3 (e.g., Springel et al., 2001; Springel, 2005;
Schaye et al., 2010). We utilize cosmological parameters with a fraction of
dark energy of $\Omega_{\rm\Lambda}=0.73$, dark matter of $\Omega_{\rm
m}=0.26$, baryons of $\Omega_{\rm b}=0.04$, and a Hubble constant of $\rm
H_{0}=0.71$ km $\rm s^{-1}Mpc^{-1}$, respectively (Planck Collaboration,
2016). We employ the code MUSIC (Hahn & Abel, 2011) to generate initial
conditions for a cosmological simulation box with a linear size of 3.125
comoving Mpc. In the first step, we conducted a dark-matter-only simulation to
$z=0$ using $128^{3}$ particles to represent this box and then identify a
target galaxy with a mass of $M_{\rm vir}\approx 10^{8}{\,M_{\odot}}$ at $z=0$
using a halo-finder code called ROCKSTAR (Behroozi et al., 2013). As a second
step, we performed three consecutive refinements for the Lagrangian volume
that encompasses particles within $R=2.5R_{\rm vir}$ at $z=0$. This results in
the most refined region where the masses of dark matter and gas particles are
$m_{\rm DM}\sim 500{\,M_{\odot}}$ and $m_{\rm gas}\sim 63{\,M_{\odot}}$,
respectively.

At each time step, we solve the rate equations for primordial species such as
$\rm H,H^{+},H^{-},H_{2},H^{+}2,He,He^{+},He^{++},e^{-},D,D^{+}$, and HD,
considering all the relevant cooling processes such as H and He collisional
ionization, excitation and recombination cooling, bremsstrahlung, inverse
Compton cooling, and collisional excitation cooling of $\rm H{2}$ and HD. We
also account for the cooling of gas by metal species such as carbon, oxygen,
silicon, magnesium, neon, nitrogen, and iron, using cooling rates from the
photoionization package CLOUDY (Ferland et al., 1998). To mimic the effect of
reionization, we introduce a cosmic UV background (Haardt & Madau, 2012) at
$z=7$ and linearly increase its strength until $z=6$, which is when cosmic
reionization is believed to have completed (e.g., Gunn & Peterson, 1965; Fan
et al., 2006).

###  2.2 Star formation

As gas densities increase, stars are allowed to form as collisionless
particles when the density surpasses a threshold of $n_{\rm H}=100$ $\rm
cm^{-3}$, according to the Schmidt law (Schmidt, 1959). The star formation
rate is governed by the equation $\dot{\rho}{\ast}=\rho_{\rm th}/\tau_{\ast}$,
where $\tau_{\ast}=\tau_{\rm ff}/\epsilon_{\rm ff}$ is the star formation time
scale. Here, $\tau_{\rm ff}=[3\pi/(32G\rho_{\rm th})]^{1/2}$ is the free-fall
time at the threshold $\rho_{\rm th}$, and $\epsilon_{\rm ff}$ is the star
formation efficiency per free-fall time. We set the star formation efficiency
to $\epsilon_{\rm ff}\sim 0.01$ for both Pop III and Pop II stars in this
study, which is a typical value in the local Universe (e.g., Leroy et al.,
2008).

The timescale for star formation is determined as follows:

$\tau_{\ast}=\frac{\tau_{\rm ff}(n_{\rm H,th})}{\epsilon_{\rm ff}}\sim 400{\rm
Myr}\left(\frac{n_{\rm H,th}}{100~{}\mbox{cm}^{-3}}\right)^{-1/2}.$ (1)

####  2.2.1 Pop III stars

While the exact mass of metal-free stars in the early Universe remains
uncertain, it is widely accepted that they were likely to be highly massive,
as efficient cooling mechanisms were scarce at that time, with molecular
hydrogen (H2) being the primary coolant available (e.g., Bromm, 2013; Whalen
et al., 2013; Hirano et al., 2014; Stacy et al., 2016; Lazar & Bromm, 2022).
Therefore, we adopt a top-heavy initial mass function (IMF) over a mass range
of $[1-260]{\,M_{\odot}}$ for Pop III stars to extract an individual star. The
functional form of the IMF is expressed as follows:

$\phi=\frac{dN_{\rm PopIII}}{d\ln m}\propto
m^{-1.3}\exp{\left[-\left(\frac{m_{\rm char}}{m}\right)^{1.6}\right]}\mbox{\
,}$ (2)

where $m_{\rm char}=60{\,M_{\odot}}$ is the characteristic mass.

####  2.2.2 Pop II stars

Pop II stars form in gas clouds that have been contaminated by metals expelled
by previous Pop III SN. The threshold density for Pop II star formation is the
same as that for Pop III stars, but there is an additional requirement that
the gas metallicity should be higher than a critical metallicity value of
$Z_{\rm crit}=10^{-5.5}{\rm\,Z_{\odot}}$, which is motivated by dust-continuum
cooling. Since the resolution of the gas mass is not high enough to directly
convert a gas particle into an individual Pop II star with a mass of around 1
${\,M_{\odot}}$, the assumption is made that Pop II stars form as a cluster
with a total mass of 500 ${\,M_{\odot}}$, following the Salpeter initial mass
function with a slope of $\alpha=1.35$ over the mass range of
$[0.1-100]{\,M_{\odot}}$. Once a gas particle meets the two conditions of
$n_{\rm th}$ and $Z_{\rm crit}$, it is replaced by a sink particle that
accretes surrounding gas until it attains a mass of $M_{\rm
PopII}=500{\,M_{\odot}}$.

###  2.3 Supernova feedback

The fate of individual Pop III stars depends on their initial masses, with
stars in the $10-40{\,M_{\odot}}$ range undergoing core-collapse supernovae
(CCSNe) with typical energies of $10^{51}$ erg and stars in the
$140-260{\,M_{\odot}}$ range dying in pair-instability supernovae (PISNe) with
energies of $10^{52}$ erg. We transfer the resulting SN energy as thermal
energy to neighboring SPH particles, increasing their temperature and ejecting
metals based on the properties of the SN progenitor. Pop III metal yields
provided by Heger & Woosley (2010) and Heger & Woosley (2002) are adopted for
CCSNe/HNe, and PISNe, respectively, with seven metal species (C, N, O, Si, Mg,
Ne, Fe) tracked for normal CCSNe and PISNe, and 16 metals tracked by adding
nine species (Na, Al, Ca, Sc, Cr, Mn, Co, Ni, Zn) for HNe.

The mass range at which Pop III stars produce an HN is not yet fully
understood (e.g., Karlsson et al., 2013). In this study, we aim to investigate
the environmental conditions required for producing a star resembling AS0039
in a dwarf galaxy. For simplicity, whenever an HN event occurs, we assume a
fixed metal yield from a $21{\,M_{\odot}}$ Pop III progenitor (Heger &
Woosley, 2010), which is considered as a progenitor mass of AS0039. Varying
metal yields based on progenitor mass would make it difficult to distinguish
unique HN signatures. This, in turn, would hinder our ability to examine the
conditions necessary for Pop II stars to display HN signatures comparable to
the observed AS0039. We note that each HN event releases $E_{\rm SN}=10^{52}$
erg of energy. For Pop II stars, possible metal yields associated with various
evolutionary phases, such as AGB, TypeII, and Type I a SNe, are considered.
Jeon et al. (2017) provides a detailed description of the models adopted for
each event.

Metals expelled by SNe are spread among approximately 32 neighboring gas
particles, $N_{\rm Ngb}\approx 32$, located around the explosion site. This
initial distribution results in the metallicity of $Z_{\rm i}$, which is
determined by the metal mass divided by the number of neighboring gas
particles and a spline kernel function $W(r)$, dependent on the distance from
the metal ejection site. Afterward, the metals diffuse from the original gas
particle to its surrounding particles through a diffusion process described by
a diffusion equation.

$\frac{dc}{dt}=\frac{1}{\rho}\nabla\cdot(D\nabla c)\mbox{\ ,}$ (3)

, where $c$ is the concentration of a contaminant fluid per unit mass, and $D$
is the diffusion coefficient. To incorporate the diffusion process into SPH
simulations, Greif et al. (2009) has discretized the equation for an particle
$i$ as follows,

$\frac{dc_{i}}{dt}=\Sigma_{j}K_{ij}(c_{i}-c_{j})\mbox{\ ,}$ (4)

where

$K_{ij}=\frac{m_{j}}{\rho_{i}\rho_{j}}\frac{4D_{i}D_{j}}{(D_{i}+D_{j})}\frac{r_{ij}\cdot\nabla_{i}W_{ij}}{r^{2}_{ij}}.$
(5)

Here, the index $j$ indicates surrounding gas particles, $W_{ij}$ is the
kernel, and $r_{ij}$ is the distance between particle $i$ and j.

Name | ${Z_{\rm crit}}[{Z_{\odot}}]$ | $f_{\rm HN}$
---|---|---
Z35-F50 | $10^{-3.5}$ | 50%
Z55-F50 | $10^{-5.5}$ | 50%
Z55-F100 | $10^{-5.5}$ | 100%
Z55-Early | $10^{-5.5}$ | early 1 star
Z55-Late | $10^{-5.5}$ | late 1 star
Z55-Mass | $10^{-5.5}$ | mass range $25-40~{}\mbox{M}_{\odot}$
Table 1: Summary of the simulations. Column (1): Run name. Column (2):
Critical metallicity for Pop II star formation. Column (3): Fraction of Pop
III stars exploding as HNe. Figure 1: The metal species of individual elements
observed (represented by the red pentagon) are compared with the best-fit
values provided by STARFIT (shown as the blue line). This comparison suggests
that the progenitor of the Pop III star responsible for the observed metal
abundances had a mass of $m_{\rm PopIII}\approx 21{\,M_{\odot}}$, and it
exploded as an HN explosion with an energy of $E_{\rm SN}=10^{\rm 52}$ erg.
The abundance patterns produced by the HN explosion display unique
characteristics that are different from those of a faint SN model, as depicted
by the grey line. We also use STARFIT to identify HN signatures in Pop II
stars generated in our simulated galaxies. An example of this is illustrated
by the cyan line.

Figure 2: The assembly histories of the simulated UFD analog are shown for six
sets of simulations. The evolution of the masses for dark matter (black), gas
(blue), and stars (red) is illustrated as a function of time in the left
panel. The right panel displays the cumulative star formation histories for
Pop III (green) and Pop II (yellow) stars, respectively. The formation of
stars begins at approximately $z\approx 12.9$ within minihaloes with masses of
$M_{\rm vir}\approx 10^{5-6}{\,M_{\odot}}$, which merged over time, eventually
forming a galaxy with a mass of $M_{\rm vir}\approx 3.8\times
10^{8}{\,M_{\odot}}$ by $z=0$. We find that the star formation is halted by
both cosmic reionization and SN feedback at $z=6.4$, resulting in a star
formation period lasting approximately 550 Myr. It is crucial to emphasize
that the emergence of the UFD analog at $z=0$ arises from the mergers of
multiple progenitor haloes, indicating that the stars do not solely originate
from the primary halo but also from other progenitor haloes. In the right
panel, we show the history of stars originating from all progenitor haloes. In
order to enhance comprehension regarding the distinction between stars formed
in situ and those arising from external haloes, we explicitly differentiate
these contributions in Figure 16.

###  2.4 Hypernovae

####  2.4.1 Sets of parameters

To explore the circumstances that allow for the formation of a star similar to
AS0039, we have conducted simulations that altered two variables: the
threshold metallicity required for the formation of Pop II stars and the
fraction of Pop III stars that explode as HNe explosions. Table 1 presents
information about the five different sets of simulations where we vary the two
parameters mentioned previously.

  * •

Critical metallicity: The abundance of Pop III stars and the occurrence of Pop
III HNe are determined by the critical metallicity. If the critical
metallicity is low, mildly enriched gas can form Pop II stars, whereas high
critical metallicity could lead to the formation of Pop III stars, increasing
their abundance. There have been numerous studies aiming at narrowing down the
value of critical metallicity (e.g., Bromm & Loeb, 2003; Santoro & Shull,
2006; Frebel et al., 2007; Dopcke et al., 2013; Chon et al., 2021; Sharda &
Krumholz, 2022). For instance, Bromm & Loeb (2003) suggests that fine-
structure lines of carbon and oxygen dominate the transition from Pop III to
Pop II, with a critical metallicity of $Z_{\rm
crit}=10^{-3.5}{\rm\,Z_{\odot}}$. Alternatively, dust-induced fragmentation
can also be a key driver for the formation of low-mass Pop II stars, even at a
low metallicity of $10^{-5.5}{\rm\,Z_{\odot}}$ (e.g., Tsuribe & Omukai, 2006;
Caffau et al., 2011; Schneider et al., 2012). Since AS0039 has an extremely
low stellar metallicity of $\rm[Fe/H]=-4.11$, we have chosen to use a critical
metallicity of $Z_{\rm crit}=10^{-5.5}$ $Z_{\odot}$ as a reference value,
denoted as Z55 in the simulation names. We compare the results of those
simulations with the run that uses a higher critical metallicity of $Z_{\rm
crit}=10^{-3.5}$ $Z_{\odot}$, as in the run named Z35-F50.

  * •

Frequency of hypernovae: The extent to which Pop III stars undergo HN
explosion at the end of their lives remains uncertain (e.g., Umeda & Nomoto,
2005; Kobayashi et al., 2006; Nomoto et al., 2006; Yoon et al., 2012; Karlsson
et al., 2013; Placco et al., 2015; Ishigaki et al., 2018). To explore the full
range of possibilities, the parameter $f_{\rm HN}$ is varied in this study. To
establish the upper limit, it is assumed that all Pop III stars experience HN
explosion, designated as F100 in the simulation name. Conversely, the lower
limit is set by allowing for a single HN explosion during the assembly history
of the simulated UFD analog. Specifically, two cases are considered: one where
the first Pop III star formed undergoes HN explosion (Z55-early), and another
where the single HN event happens randomly during the assembly process
(Z55-Late).

Based on the findings of Yoon et al. (2012), which propose a possible mass
range of $13{\,M_{\odot}}$ to $84{\,M_{\odot}}$ for HN events, about 50% of
Pop III stars are expected to undergo HN events when using the IMF presented
in equation (2). This fraction is also consistent with the study by Kobayashi
et al. (2006), which utilized simulations of galaxies similar to the Milky Way
(MW) to explain observed chemical abundances, suggesting that to match the
abundance of metal species such as $\rm[Zn/Fe]$, about half of the stars
independent of mass and metallicity should explode as HNe, especially for low
metallicity. In accordance with these findings, we adopt a value of $f_{\rm
HN}$ of 50%, labeled as F50 in the simulation names. We also take into account
the work of Karlsson et al. (2013), who propose that Pop III stars in the mass
range of $m_{\rm PopIII}=25-40{\,M_{\odot}}$ are capable of undergoing HN
explosions, resulting in $f_{\rm HN}\approx 11\%$. To incorporate their
findings, we run a simulation called Z55-Mass, in which HN explosions are
allowed to occur among Pop III stars in this mass range.

####  2.4.2 Finding a hypernova signature

We employ a tool called STARFIT to extract the HN signatures from our
simulations. This tool provides various metal yields that result from
nucleosynthesis models (Heger & Woosley, 2002, 2010; Limongi & Chieffi, 2012;
Just et al., 2015; Grimmett et al., 2018; Limongi & Chieffi, 2018). We utilize
these yields to determine several progenitor characteristics, such as mass,
metallicity, and explosion energy. It is noteworthy that Skúladóttir et al.
(2021) also obtain the progenitor properties of AS0039 using STARFIT, which
are consistent with those of a primordial star having a mass of $m_{\rm
PopIII}=21{\,M_{\odot}}$ and explosion energy of $E_{\rm SN}=10\times 10^{51}$
erg, based on the metal abundances comparison. In Figure 1, we present a
comparison of individual metal abundances between AS0039 (depicted as a red
pentagon) and the best-fit model generated from STARFIT (represented as a blue
line). We also show the abundances of Pop II stars with HN signatures,
obtained from our simulation, as a cyan line, which closely matches the result
from STARFIT. Additionally, we illustrate the metal species produced by a Pop
III star, which has an initial mass of $m_{\rm PopIII}=25{\,M_{\odot}}$ and
exploded as a faint supernova, as a gray line for comparison.

##  3 Simulation results

This section presents the findings of the simulated galaxy. Section 3.1
illustrates the process of mass assembly for the UFD analog. We then examine
the number of progenitor minihaloes that could have Pop II stars with Pop III
HN signatures and the fraction of such stars among all Pop II stars in Section
3.2. Finally, we discuss the estimated chemical abundances of Pop II stars
from the simulations and compare them with observed values.

###  3.1 Mass assembly

Figure 2 shows the mass assembly history of the simulated UFD galaxy analog
(left panel) and the cumulative star formation history (right panel) by
varying the fraction of Pop III stars that explode as HNe and the critical
metallicity for Pop II star formation. In the left panel of Figure 2, each
color represents the dark matter (black), gas (blue), and stellar (red)
masses. The gray-shaped region indicates the epoch of reionization, where the
UV background is introduced and gradually increases in strength. Although the
stochastic nature of star formation may result in slight differences in the
gas and stellar mass during the assembly process, all sets of galaxies with
the same initial conditions have grown into similar galaxies with a dark
matter mass of $\rm M_{\rm DM}\approx 3.8\times 10^{8}~{}\mbox{M}_{\odot}$, a
gas mass of $\rm M_{\rm gas}\approx 6.9\times 10^{5}~{}\mbox{M}_{\odot}$, and
a stellar mass of $\rm M_{\ast}\approx 1.2\times 10^{4}~{}\mbox{M}_{\odot}$ at
$z=0$, which are comparable to those of actual UFD galaxies.

The simulated ratio of baryon mass to DM mass maintains a cosmological value
of $f_{\rm b}=\Omega_{b}/\Omega_{m}\approx 0.17$ up to a redshift of $z=11.5$,
but it drops due to the feedback from Pop III and Pop II stars. Notably, as
shown in the left panel of Figure 2, at around $\rm z\approx 10$, the baryon
fractions in four runs (Z35-F50, Z55-F50, Z55-100, and Z55-Early) decrease to
$f_{\rm b}=0.04$ due to the formation of Pop II stars. These runs produce 2-5
times more stars than the other two runs (Z55-Late and Z55-Mass), leading to a
reduction of the gas fraction. Furthermore, the emergence of the UV background
causes a further decrease in the baryon fraction to below $f_{\rm b}\approx
0.01$ at $z=6$, from $f_{\rm b}\approx 0.08$ at $z=7$. Nonetheless, in all six
sets of simulations, the target halo ultimately reaches a similar baryon
fraction, even in the presence of different HNe frequencies. This outcome can
be attributed to the relatively comparable total energy delivered by all SNe
to the halo. Despite the significant impact of HNe, their events are surpassed
in frequency by the higher occurrence of Pop II SNe. The cumulative energy
contribution from both SNe and HNe into the target halo, with respect to
cosmic time, is illustrated in Figure 15.

Figure 3: The morphology of the simulated galaxy at $z\approx 8.3$ is
illustrated in four panels from left to right, displaying the dark matter
overdensity, hydrogen number density, gas temperature, and gas metallicity
projected along the line of sight within 1.75 kpc (4Rvir) from the galaxy
center. The virial radius of the halo is marked with solid white circles at
the center of the panels. Pop II stars with and without Pop III HN signatures
are represented by cyan and yellow colors, respectively. Moreover, in-situ
stars and ex-situ stars are discerned through the use of star and circle
symbols. These panels clearly demonstrate that stars are formed from multiple
progenitor minihaloes and then merge into the primary halo at a later time.

It is important to note that the formation of the UFD analog at $z=0$ is a
result of small minihaloes merging together, indicating that it has multiple
progenitor minihaloes. For reference, we offer a merger tree of the target
halo in Appendix 17 for the Z55-F50 run. Our simulations reveal that in a
small system such as UFD, the main progenitor does not dominate star formation
at high redshifts, but rather, star formation is initiated in minihaloes of
comparable mass, which merge later. It should be noted that we define a
minihalo as a halo in which at least one Pop III star has formed. The first
star formation episode starts at around $z\approx 12.9$ and ends at $z=6.5$,
resulting in the star formation duration of approximately 550 Myrs. Therefore,
the increase in stellar mass below $z=6$, depicted as the red lines in the
left panel of Figure 2, is due to the merging of progenitor minihaloes. It
should be mentioned that we halt the simulations, except for Z55-F100, when
the redshift reached $z\approx 3$ where the dark matter mass is $\rm M_{\rm
DM}\approx 1.6\times 10^{8}~{}\mbox{M}_{\odot}$, the gas mass is $\rm M_{\rm
gas}\approx 6.2\times 10^{5}~{}\mbox{M}_{\odot}$, and the stellar mass is $\rm
M_{\ast}\approx 1.4\times 10^{4}~{}\mbox{M}_{\odot}$, respectively. At this
point, star formation is completely quenched due to cosmic reionization,
causing the maximum gas density inside the primary halo to drop to $n_{\rm
H}\approx 10^{-4}$ $\rm cm^{-3}$, and no further halo mergers occur. This was
confirmed by running the Z55-F100 simulation down to $z=0$.

In order to explore the process of stellar assembly in more detail, we have
included a plot of the cumulative star formation in the right panel of Figure
2, which shows the star formation for Pop III (green) and Pop II (yellow)
stars separately. Pop III star formation takes place simultaneously in
progenitor minihaloes of the simulated UFD analogs. For most simulations, Pop
III star formation ends around $z=8.5$. However, for the Z35-F50 simulation
(solid line), which has a critical metallicity of $Z_{\rm
crit}=10^{-3.5}~{}Z_{\odot}$ compared to the other simulations with $Z_{\rm
crit}=10^{-5.5}~{}Z_{\odot}$, Pop III stars can be formed even in gas with
higher metallicity. This causes the galaxy in the Z35-F50 simulation to
continue forming Pop III stars until around $z=7.5$, resulting in a higher
stellar mass ratio occupied by Pop III stars by about $10\%$ compared to the
other simulations.

Our simulations show that the majority of minihaloes ($\sim 83\%$) are likely
to produce only a single Pop III star before transitioning to Pop II star
formation. However, a small fraction of minihaloes is capable of producing
multiple Pop III stars, with 11% having two and 3% having three. It is worth
noting that high-resolution simulations typically reveal the formation of Pop
IIIs in small groups (e.g., Stacy et al., 2013; Stacy et al., 2016; Susa,
2019; Liu et al., 2021; Jaura et al., 2022; Chiaki & Yoshida, 2022).
Therefore, given that we allow Pop III stars to form as individual entities
rather than as members of a stellar cluster composed of multiple stars, the
feedback effect we present should be considered a lower limit. This is because
the possibility of several sequential SN explosions might more effectively
suppress subsequent star formation.

To investigate the role of merger events in the assembly of the simulated
UFDs, we classify star formation for Pop III and Pop II stars into in-situ and
ex-situ star formation (see Table 2). In-situ star formation refers to stars
that are formed within the primary halo, which is defined as the halo
contributing the most significant mass to the overall halo mass during the
subsequent time step, especially when we trace back from $z=0$ to higher
redshifts in search of the progenitor halo. Meanwhile, ex-situ star formation
refers to stars that are formed in other progenitor haloes and then merge with
the primary halo at a later time. Across all simulations, the Z35-F50 run has
the highest total in-situ star formation for all stars, accounting for $\rm
26.7\%$, while the Z55-F100 run has the lowest value at $\rm 15.4\%$. The
average in-situ star formation across all simulations is $\rm 19.5\%$, and
approximately $\rm 80\%$ of the stars in the galaxies have grown through
mergers. When comparing the in-situ ratio of Pop III and Pop II stars, the
rate of Pop II is higher by 8%. This is because the duration of Pop III star
formation is shorter due to the transition from Pop III to Pop II, and the
halo mass becomes heavier when Pop II star formation begins, leading to a
higher in-situ rate compared to that of Pop III stars.

The formation and merging of stars in multiple distinct minihaloes in the
simulated galaxy at $z=8.3$ are depicted in Figure 3. Each panel shows the
projected dark matter overdensity, hydrogen number density, gas temperature,
and gas metallicity within 1.75 kpc (4Rvir) from the galaxy center, from left
to right. Solid white circles at the center of each panel mark the virial
radius of the halo. Different symbols represent different types of stars, with
cyan stellar and yellow circle symbols representing Pop II stars with and
without Pop III HN signatures, respectively. The figure illustrates that stars
in the early Universe form in multiple progenitor minihaloes and then merge
onto the primary halo at a later time. We find that the dispersal of gas
observed in the gas density panel, particularly in relatively high-density
clouds, is a consequence of an energetic HN explosion.

Run | Total in-situ | Pop III in-situ | Pop II in-situ
---|---|---|---
Z35-F50 | 26.7% | 20.0% | 30.0%
Z55-F50 | 23.1% | 14.3% | 25.0%
Z55-F100 | 15.4% | 11.1% | 16.7%
Z55-Early | 15.6% | 10.0% | 17.1%
Z55-Late | 18.6% | 12.5% | 20.0%
Z55-Mass | 17.6% | 11.1% | 19.0%
Table 2: The percentage of stars formed through in-situ star formation for each simulation set. Column (1) indicates the run name, column (2) represents the total in-situ fraction, column (3) shows the in-situ fraction for Pop III stars, and column (4) indicates the in-situ fraction for Pop II stars. Run | $N_{\rm mini,Pop~{}III}$ | $N_{\rm mini,HN}$ | $N_{\rm mini,HNsig}$
---|---|---|---
Z35-F50 | 12 | 7 | 4
Z55-F50 | 8 | 3 | 3
Z55-F100 | 8 | 8 | 5
Z55-Early | 8 | 1 | 1
Z55-Late | 8 | 1 | 0
Z55-Mass | 8 | 1 | 1
Table 3: The number of progenitor minihaloes that merge to form a single UFD
analog in each simulation set. Column (1) shows the simulation name, column
(2) indicates the number of progenitor minihaloes that form at least one Pop
III star, column (3) shows the number of minihaloes with Pop III stars that
explode as an HN explosion, and column (4) indicates the number of minihaloes
that contain Pop II stars with inherited HN signatures. Figure 4: The virial
mass of progenitor minihaloes and the number density of star-forming gas in
those haloes for each simulation run. The minihaloes that contain Pop II stars
with the Pop III HNe signatures are marked as filled cyan circles. Meanwhile,
black symbols indicate minihaloes in which Pop III HNe occurred, but no
subsequent Pop II star formation (indicated by triangles) or subsequent Pop II
stars are already contaminated by metals from other supernova events
(represented by stellar symbols). The gas number density is determined
immediately before the formation of Pop II stars, but if the gas is
unavailable due to significant evacuation, the gas density at about 70 Myr
after the Pop III event is used. This time corresponds to the average time
delay for the next star formation observed in the simulations. Figure 5: The
evolution of two different haloes that experienced an HN explosion at similar
virial masses. One of the minihaloes produces Pop II stars with the Pop III HN
signature (solid line), while the other minihalo does not form any Pop II
stars (dashed line). The color of each line represents the DM mass (black),
the gas mass within the viral radius, $R_{\rm vir}$ (blue), and the gas mass
within $2R_{\rm vir}$ (green). The density of star-forming gas in a rapidly
growing dark matter halo (solid line) can be replenished by an influx of gas,
while in a slowly growing dark matter halo (dashed line), it is difficult to
recover gas that has evaporated into the IGM.

###  3.2 Incidence of hypernova pattern

We examine the percentage of progenitor minihaloes containing Pop III stars
that experience HN explosions and the number of minihaloes hosting the
resulting Pop II stars that inherit the Pop III HN signatures within the same
halo for each simulation. The corresponding numbers are summarized in Table 3.
For example, in the Z35-F50 simulation, 12 different progenitor minihaloes
have formed Pop III stars, denoted as $N_{\rm mini,Pop~{}III}$=12. Of these, 7
minihaloes experience Pop III HNe explosions, yielding $N_{\rm mini,HN}=7$.
However, only 4 out of 7 progenitor minihaloes with HNe produce subsequent Pop
II stars with the Pop III HN signature, noted as $N_{\rm mini,HNsig}=4$.
Similarly, in Z55-F50, Pop III HNe events take place in 3 out of 8 progenitor
minihaloes, and all of the subsequent Pop II stars with the Pop III HN
signatures are found within these three minihaloes. On the other hand, if the
frequency of Pop III HNe is reduced, such as a single event, the number of
minihaloes that could contain Pop II stars with HN signatures also decreases.

Figure 4 addresses the main question of the conditions that lead to the
presence or absence of Pop II stars with Pop III HNe signatures. It shows the
number density of star-forming gas within the minihaloes where an HN event is
triggered as a function of their virial masses. Cyan circles on the figure
correspond to minihaloes where Pop II stars with Pop III HNe signatures are
present. On the other hand, the black symbols represent minihaloes where Pop
III HNe occurred, but either no subsequent Pop II star formation (indicated by
triangles) or the subsequent Pop II stars are already polluted by metals from
other supernova events (represented by stellar symbols). Regarding the value
of number density, $n_{\rm H}$, it is chosen immediately before the formation
of a Pop II star. For other cases, the $\rm n_{H}$ value used is about
$\sim$70 Myr after the Pop III event, which corresponds to the average time
delay for the next star formation observed in the simulations.

Figure 6: The fraction of Pop II stars that exhibit HN signatures among all
Pop II stars in the simulated analog, denoted as $f_{\rm PopII,HNsig}$. As the
fraction of Pop III HNe decreases, there is generally a tendency for $f_{\rm
PopII,HNsig}$ to show a declining pattern. Figure 7: The metallicity
distribution of Pop II stars (yellow) found in the simulated UFD analog for
each simulation run, comparing with Pop II stars exhibiting the HN signatures
(cyan). A vertical line is drawn to represent the metallicity of AS0039, which
is $\rm[Fe/H]=-4.11$. With the exception of Z35-F55, which is intended to
prevent the formation of Pop II stars with a metallicity lower than
$10^{-3.5}{\rm\,Z_{\odot}}$, most simulations result in approximately 18% of
UMP stars, defined as $\rm[Fe/H]<-4$.

A total of 7 progenitor minihaloes, 3 from Z35-F50, 3 from Z55-F100, and 1
from Z55-Late runs, are found to lack Pop II stars with Pop III HN signatures.
These 7 cases can be divided into two categories. The first category, which we
call the “unrecoverable case," is characterized by a significant decrease in
the number density of the star-forming region due to the strong feedback of
HNe. As a result, the gas is unable to recover the threshold density of
$n_{\rm H}=100$ $\rm cm^{-3}$, making further star formation impossible. We
refer to the second category as the “contaminated case". To form Pop II stars
with HN signatures, it is necessary that the gas is contaminated only by
metals from HN events. However, in some scenarios, minihalo mergers occur
before the formation of Pop II stars, causing the gas to become polluted by
metals from stars in the merged minihaloes. Consequently, Pop II stars are
formed out of gas with metals composed of those from Pop III HNe and other SN
events. The results of the study show that in the cyan-colored progenitor
minihaloes, the gas is able to recover from Pop III HN feedback and reach a
gas density of $n_{\rm H}>100$ $\rm cm^{-3}$. However, in the “unrecoverable"
cases, the gas density drops below $n_{\rm H}=100$ $\rm cm^{-3}$, with the
Z55-F100 case being the most severely disrupted, where the density falls to
$n_{\rm H}=0.001$ $\rm cm^{-3}$. In the “contaminated" cases, the lack of Pop
II stars with HN signatures is caused not only by HN feedback but also by
metal contamination resulting from mergers. Under these circumstances,
densities of star-forming gas can be achieved up to $n_{\rm H}=10-1000$ $\rm
cm^{-3}$.

Under what conditions can gas within a minihalo form Pop II stars or become
unrecoverable? It is likely that the surrounding environment plays a role in
the observed difference. A comparison of two minihaloes with similar mass but
different environments is presented in Figure 5. One minihalo produces Pop II
stars with the Pop III HN signature (solid line), while the other minihalo
does not form Pop II stars (dashed line). The color of each line represents DM
mass (black), gas mass within the viral radius (blue), and gas mass within two
times the viral radius (green). When an HN explosion occurs with $E_{\rm
SN}=10^{52}$ erg, the halo mass of both minihaloes is comparable, but the
result differs due to the subsequent dark matter growth rate. In a fast-
growing dark matter halo (solid line), the density of the star-forming gas is
restored due to an influx of gas, whereas in a barely growing dark matter halo
(dashed line), the gas that has evaporated into the IGM is difficult to
recover. This is supported by the amount of gas within 2 $R_{\rm vir}$, which
is about four times greater for the fast-growing minihalo than for the slow-
growing halo around 100 Myr after the HN explosion event.

The question being asked is what fraction of Pop II stars produced in the
simulated UFD galaxy analog, which has a total stellar mass of approximately
$10^{4}{\,M_{\odot}}$, contains Pop III HN signatures. To address this, we
identify the number of Pop II stars with Pop III HN signatures among all Pop
II stars within the viral radius of the simulated analog at $z=3$. Figure 6
compares the fraction of Pop II stars with HN signatures, represented as
$f_{\rm PopII,HNsig}=N_{\rm PopII,HNsig}/N_{\rm PopII}$, in various runs.
Except for Z35-F55 and Z55-LATE, in general, $f_{\rm PopII,HNsig}$ tends to
decrease as the fraction of Pop III HNe decreases. Specifically, with the same
critical metallicity of $Z_{\rm crit}=10^{-5.5}$ $Z_{\rm\odot}$, the fraction
is $f_{\rm PopII,HN,sig}=16\%$ for Z55-F100 and decreases to $f_{\rm
PopII,HN,sig}=9.3\%$ for Z55-F50, eventually dropping to $f_{\rm
PopII,HN,sig}=2.3\%$ for Z55-Mass.

Figure 8: The metallicity of Pop II stars, which formed right after the Pop
III star formation, is dependent on the delay time. The delay time is defined
as the time gap between the Pop III SN explosion and the formation of
subsequent Pop II stars. Note that the absolute amount of iron produced by a
normal Pop III SN is lower than that of an HN explosion from a Pop III star
with $m_{\rm PopIII}=21{\,M_{\odot}}$ (Heger & Woosley, 2010), leading to
lower overall [Fe/H] values. Pop II stars that formed after a Pop III HN
explosion (cyan color) typically exhibit a longer delay time of up to about
180 Myr owing to the high-energy explosion, compared to those created after a
normal SN (yellow). The reason for this is that metallicity tends to decrease
with longer delay times, primarily due to increased diffusion unless there is
external enrichment. Figure 9: During the delay time period, the gas evolution
within haloes plays a critical role in determining the metallicity of
subsequently forming stars. In the case of the halo where UMP Pop II stars are
found (black line), there is a rapid gas inflow with a peak value of
$\dot{M}_{\rm gas}\sim$ 0.08 ${\,M_{\odot}}\rm yr^{-1}$, which is
significantly higher than the averaged gas inflow rate of $\sim$0.0025
${\,M_{\odot}}\rm yr^{-1}$ for other haloes (cyan color). The significant
increase in the infall rate observed in this case can be due to a merger event
between the halo where the UMP star is formed and a main progenitor halo,
taking place $\sim$25 Myr before the formation of the UMP star. This rapid
influx of gas plays a crucial role in diluting the metals produced by Pop III
HN, thereby facilitating the formation of UMP stars.

Assuming that half of the Pop III stars explode as HNe, setting a higher
critical metallicity of $Z_{\rm crit}=10^{-3.5}$ $Z_{\rm\odot}$ in the Z35-F50
run results in a higher fraction of Pop II stars with HN signatures,
specifically with a value of $f_{\rm PopII,HN,sig}=13\%$. This is higher than
the $f_{\rm PopII,HN,sig}=9.3\%$ observed in the Z55-F50 run. The reason for
this is that in the Z35-F50 run, there are more Pop III stars, leading to a
higher frequency of HN events. In fact, HN events occur 2.6 times more
frequently in the Z35-F50 run than in the Z55-F50 run. Out of the 6 sets
considered, the runs that have only one HN event (Z55-Early, Z55-Late,
Z55-Mass) all exhibit a $f_{\rm PopII,HNsig}$ that is lower than $3\%$. It
should be noted that the $f_{\rm PopII,HNsig}$ predicted above are likely to
be lower in more massive satellite galaxies than in UFDs. This is because
larger galaxies are expected to have a higher number of Pop II stars. Although
the number of Pop III stars exploding as HNe may also increase with halo mass,
the duration of Pop III star formation in the early universe is very short
$z>7.5$, making Pop II stars the dominant population in more massive galaxies.
As a result, the fraction of Pop II stars with HN signatures compared to the
total Pop II stars is likely to decrease as the halo mass increases.

Figure 10: Comparison of individual metal abundances between our simulation of
Z55-F50 (stellar symbols) and observations. The observations include AS0039
(red pentagon, Skúladóttir et al., 2021), stars in the Sculptor galaxy
(magenta circle, Frebel et al., 2010; Simon et al., 2010; Tafelmeyer et al.,
2010; Starkenburg et al., 2013; Jablonka et al., 2015), and stars in the MW
(grey circle, Cayrel et al., 2004). Pop II stars with HN signatures (cyan)
show [X/Fe] values that are lower than those of normal Pop II stars (yellow)
by $\sim$1 dex for carbon and by 0.5-0.7 dex for silicon and magnesium. The
abundances of Pop II with HN signatures are in good agreement with those of
AS0039. Our simulations demonstrate that the difference in carbon abundance is
due to the type of SN explosion. Specifically, Pop II stars that form out of
gas contaminated by a normal Pop III SN with low iron abundance tend to give
rise to CEMP stars with $\rm[C/Fe]\approx 2$. In contrast, the low carbon
value of $\rm[C/Fe]=-0.5$, which matches the value observed in AS0039, is
attributed to a Pop III HN explosion. Moreover, we find that Pop II stars with
$\rm[C/Fe]\approx 0.6$ are more affected by Pop II SNe than Pop III SNe.

###  3.3 Chemical abundances

Figure 7 shows a comparison between the metallicity distribution of all Pop II
stars (yellow) and Pop II stars with HN signatures (cyan) found in the viral
radius of the UFD analog at $z=3$ for each run. In all runs except Z35-F50,
where the formation of Pop II stars with metallicity below $Z_{\rm
crit}=10^{-3.5}$ $Z_{\odot}$ is not possible, the metallicity of the Pop II
stars ranges from [Fe/H] $\approx-5.5$ to [Fe/H] $\approx-1.5$ (yellow). The
vertical line in Figure 7 represents the stellar metallicity of AS0039, which
is measured to be $\rm[Fe/H]=-4.11$, corresponding to the ultra metal-poor
(UMP) stars ($\rm[Fe/H]<-4$) (e.g., Beers & Christlieb, 2005). When all runs
are combined, the fraction of UMP stars is around 18% out of a total of 204
Pop II stars, with 37 of these stars being UMP stars. As such, the fraction of
UMP stars among only the Pop II stars with HN signatures (cyan) is $\sim$7%,
which is based on a total of 14 Pop II stars with HN signatures, among which
only 1 star is a UMP star. The Pop II star with the HN signature that has the
most similar metallicity to AS0039 is the one with [Fe/H]=-4.17 in the Z55-F50
run. Most of the other Pop II stars with HN signatures have metallicities in
the range of -3.4 to -2.4 for their [Fe/H] values.

The run Z55-early is the simplest and most suitable run to investigate the
conditions for having such a low metallicity like the observed AS0039 in that
only the first Pop III star in the first minihalo explodes as an HN. It still,
however, leads to the formation of a Pop II star with an HN signature, albeit
with a metallicity, $\rm[Fe/H]\approx-2.6$, more than one order of magnitude
higher than that of AS0039. Comparably, when a Pop III HN explodes in a
minihalo that collapses relatively late, like in the runs Z55-late or
Z55-Mass, even if it is a single event, the HN unique signatures can be easily
diluted by metals from other SN events (e.g. Ji et al., 2015). As a result,
none of the Pop II stars with HN signature can be formed in the Z55-late run
owing to external pollution. However, if subsequent star formation occurs
before the gas is contaminated, the unique signature remains, forming Pop II
stars with it, as in the Z55-Mass run.

According to our findings, the metallicity of Pop II stars is related to the
delay time between the SN explosion and subsequent Pop II star formation.
Figure 8 illustrates this correlation by plotting stellar metallicity against
the delay time, which is the interval between the occurrence of a Pop III SN
explosion and the formation of Pop II stars from the gas contaminated by the
SN event. In general, Pop II stars with HN signatures (cyan color) tend to
have higher [Fe/H] values than those formed after a normal Pop III SN
(yellow). This is due to the fact that the absolute yield of iron from a
normal Pop III SN with an energy of $\rm 10^{51}$ erg is lower than that of an
HN explosion from a progenitor mass of $m_{\rm PopIII}=21{\,M_{\odot}}$ (Heger
& Woosley, 2010). Additionally, the high energy associated with HN explosions
leads to longer delay times, up to $\sim$180 Myr, for Pop II stars with HN
signatures. Our simulation results clearly show that the metallicity of Pop II
stars with HN signatures decreases with longer delay times. For instance, Pop
II stars with a metallicity of $\rm[Fe/H]\approx-2.5$ require a delay time of
about $\sim$40 Myr, while the formation of EMP stars needs a delay time of
about $\sim$100 Myr. This is because the metals produced by the HN event would
have been diluted during the long delay time period, leading to a decrease in
the gas metallicity where the Pop II stars are formed. This effect becomes
more pronounced as the delay time increases, and without any external metal
pollution during this period, the subsequent Pop II stars will form with low
metallicities.

Although Pop II stars with HN signatures exhibit [Fe/H] values above
$\rm[Fe/H]\approx-3.3$, we have only generated one UMP star with
$\rm[Fe/H]\approx-4.17$, similar to that of AS0039. To investigate the
conditions that lead to the formation of such UMP stars, we analyze the gas
evolution within the halo in which Pop II stars with HN signatures reside
during the delay time period, as shown in Figure 9. In contrast to other
haloes (cyan color), the halo where the UMP star, presented as the black line,
is formed experiences a rapid gas inflow of about $M_{\rm gas}\approx 5\times
10^{5}{\,M_{\odot}}$ within $\sim$7 Myr, about 22 Myr after the HN explosion,
increasing the gas mass from $M_{\rm gas}\approx 2.8\times
10^{5}{\,M_{\odot}}$ to $M_{\rm gas}\approx 8.8\times 10^{5}{\,M_{\odot}}$.
The resulting gas accretion rate is $\dot{M}_{\rm gas}\sim$ 0.08
${\,M_{\odot}}\rm yr^{-1}$, which is 4 times higher than the average gas
accretion rate onto the halo. This peak value is higher by a factor of 30
compared to the average gas inflow rate of $\dot{M}_{\rm gas}\sim
0.0025{\,M_{\odot}}\rm yr^{-1}$ for other haloes. The observed high infall
rate, in this case, can be attributed to a merger event occurring $\sim$25 Myr
prior to the formation of the UMP star. This merger involves the combination
of a halo hosting a UMP star similar to AS0039 with a main progenitor halo,
resulting in the influx of $M_{\rm gas}\sim 5\times 10^{5}{\,M_{\odot}}$ of
gas. The rapid gas influx into the halo where the UMP star forms plays a
crucial role in diluting the metals produced by the Pop III HN, ultimately
allowing the formation of UMP stars. Consequently, our findings suggest that
low-metallicity stars can form via two possible mechanisms: a prolonged delay
time or a substantial inflow of gas onto a halo, which enables the diffusion
of metals.

Parameter | Description | Best Fit | reference
---|---|---|---
$v_{\rm SV}$ | Baryonic streaming velocity | $0.8\sigma_{\rm SV}$ | (1)
$M_{\rm min}$ | Minimum mass of Pop III stars | $5{\,M_{\odot}}$ | (1)
$M_{\rm max}$ | Maximum mass of Pop III stars | $210{\,M_{\odot}}$ | (1)
${\rm\eta_{III}}$ | Star formation efficiency for Pop III stars | 0.38 | (1)
${\rm\eta_{II}}$ | Star formation efficiency for Pop II stars | 2 | (2)
$\alpha_{\rm out}$ | Slope of outflow efficiency | 0.72 | (2)
$M_{\rm out,norm}$ | Normalization mass of outflow efficiency | $10^{10.5}{\,M_{\odot}}$ | (2)
Table 4: Best-fit parameters for A-SLOTH we adopt for this work. Column 1):
Parameters. Column 2): A short description of the parameters. Column 3):
Values. Column 4): References for the adopted values are as follows: (1)
Hartwig et al. (2023), and (2) Chen et al. (2022).

It should be mentioned that Jeon et al. (2014) suggested a longer recovery
timescale of up to $\sim$300 Myr when using the energy of $E_{\rm SN}=10^{52}$
erg for a Pop III SN. Such difference in timescale compared to our work can be
attributed to two factors. Firstly, Jeon et al. (2014) examined halo masses of
$M_{\rm vir}\approx 5\times 10^{5}{\,M_{\odot}}$, which are $2-10$ times
smaller than the masses used in our study to estimate the recovery time.
Secondly, we do not account for the pre-explosion photoionization by the Pop
III progenitors, which may have caused gas densities to remain high prior to
the SN explosion, resulting in a shorter recovery timescale in our
simulations. Even when considering the photoionization effect, however,
recovery time can vary considerably depending on the halo mass, as illustrated
by Jeon et al. (2014). For example, the recovery time for a $40{\,M_{\odot}}$
Pop III progenitor star that explodes with $E_{\rm SN}=10^{51}$ erg was
$\sim$92 Myr for a halo mass of $M_{\rm vir}=5\times 10^{5}{\,M_{\odot}}$, but
dramatically dropped to $\sim$6 Myr for a halo mass of $M_{\rm vir}=9\times
10^{5}{\,M_{\odot}}$. This is due to the H II region becoming more compact,
which weakens the pre-heating effect and allows gas to rapidly recollapse in
relatively massive haloes.

In Figure 10, we compare the individual abundances of Pop II stars with HN
signatures (cyan star) and normal Pop II stars (yellow star) from our
simulations to observations of stars, such as AS0039 (red pentagon,
Skúladóttir et al., 2021), stars in the Sculptor galaxy (magenta circle,
Frebel et al., 2010; Simon et al., 2010; Tafelmeyer et al., 2010; Starkenburg
et al., 2013; Jablonka et al., 2015), and stars in the MW (grey circle, Cayrel
et al., 2004). The focus of the comparison is on the abundances of Carbon,
Magnesium, and Silicon, which are displayed in three panels in Figure 10. Our
study reveals that the individual abundances of Pop II stars with HN
signatures, depicted as a cyan star, are lower than those of normal Pop II
stars (yellow star), ranging from -1 dex for Carbon to -0.5 dex for Magnesium
and Silicon. The estimated abundances of Pop II stars with HN signatures are
consistent with the best-fit values of AS0039, given the uncertainties in the
observations. Note that the abundances of AS0039 are measured values, and
there could be differences between the observed and the nucleosynthesis
results, even with the best-fit model.

It is worth noting that AS0039 has a peculiar feature in its carbon abundance;
unlike CEMP stars commonly found in dwarf galaxies, which are also considered
signatures of Pop III stars, AS0039 is a carbon-poor star with
$\rm[C/Fe]_{LTE}=-0.75\pm 0.22$. Our simulations clearly exhibit that this
difference in carbon abundance is attributed to the type of Pop III SN.
Specifically, Pop II stars with an exceptionally high [C/Fe] ratio of $\sim$2
tend to form when Pop II stars arise immediately after a normal SN explosion
with low iron abundance, leading to the formation of CEMP stars. In contrast,
the low value of $\rm[C/Fe]\approx-0.46$, which matches the observed value of
AS0039, is the result of the HN explosion (cyan). Furthermore, Pop II stars
with $\rm[C/Fe]\approx 0.6$, which form in gas clouds that are more influenced
by Pop II than Pop III stars, do not exhibit CEMP features. However, these
stars still have distinct features that differ from those with HN signatures,
as shown in AS0039.

We observe the narrow scatter of stellar abundances in normal Pop II stars
showing similar $\rm[X/Fe]$ values compared to those of stars in Sculptor and
the MW. This similarity is likely the result of the short star formation
duration of $\sim$0.5 Gyr in the simulated UFD analog, while Sculptor has had
a star formation duration of $\rm\Delta$t $\approx$ 1-3 Gyr, as reported in
previous studies (Kirby et al., 2011; Weisz et al., 2014; Bettinelli et al.,
2019; de los Reyes et al., 2022), and the MW is undergoing ongoing star
formation (Elia et al., 2022).

##  4 Observability

So far, we have discussed the simulation results for a single dwarf galaxy
with a halo mass of $M_{\rm vir}\approx 10^{8}{\,M_{\odot}}$ at $z=0$, by
varying the fraction of Pop III stars that undergo HN explosions. However, the
important question is to determine the likelihood of observing a Pop III HN
signature in a randomly observed dwarf satellite galaxy within the MW’s volume
and which galaxy masses are most likely to exhibit such signatures. To address
these questions, we employ a semi-analytic approach to estimate the number of
progenitor minihaloes that are expected to contain Pop III HN remnants within
the MW’s volume.

###  4.1 A-SLOTH: semi-analytic model for galaxy formation

We utilize a semi-analytic galaxy formation code called A-SLOTH (Ancient Stars
and Local Observables by Tracing haloes, Hartwig et al., 2023; Magg et al.,
2022) to track the remnants of early generations of stars down to $z=0$ (e.g.,
Magg et al., 2018; Hartwig & Yoshida, 2019; Chen et al., 2022). This approach
involves using the Extended Press-Schechter (EPS) formalism (e.g., Press &
Schechter, 1974; Lacey & Cole, 1993) to generate halo merger trees for an MW-
like galaxy or obtaining them from N-body simulations. Particularly, A-SLOTH
adopts the halo merger tree extracted from the Caterpillar project (Griffen et
al., 2016), which provides 30 sets of merger trees for MW-sized galaxies using
dark matter-only simulations. By traversing through these merger trees,
A-SLOTH is able to ascertain the baryonic components of each halo in the tree
based on the implemented physics within the code, starting from the first star
formation in minihaloes.

One of the key benefits of using a semi-analytic approach is its computational
efficiency, which allows for rapid exploration of the optimal parameters that
describe baryonic physics. Further information on the specific baryonic
physics incorporated in A-SLOTH can be found in Hartwig et al. (2023).
Compared to other semi-analytic models, A-SLOTH stands out by including the
relevant physics of early star formation, allowing for the formation of
individual Pop III and massive Pop II stars, and taking into account the
impact of their mechanical and chemical feedback.

The models are calibrated based on six distinct observables to determine the
best-fit values of the free parameters that govern baryonic physics. These
include the optical depth to Thomson scattering, the stellar mass of the MW,
the cosmic star formation rates at high redshift, the distribution of stellar
masses among the MW’s satellite galaxies, the fraction of extremely metal-poor
stars (EMP) (i.e., [Fe/H]$<$-3) in the halo, and the ratios of UMP (i.e.,
[Fe/H]$<$-4) to EMP stars. For this study, we adopt not only the proposed
values of the free parameters by Hartwig et al. (2023) but also the values by
Chen et al. (2022), where they acquire the best-fit values by focusing on the
relationship between the stellar mass and halo mass and adjusting the Pop II
star formation models to match observed values. Table 4 summarizes the
parameters for A-SLOTH that we use in this work.

Figure 11: The cumulative number of satellite galaxies obtained from 30 sets
of merger trees for the MW-like galaxies using A-SLOTH (black lines), with a
red line indicating observational data for comparison (McConnachie, 2012;
Muñoz et al., 2018). It is worth noting that the blue-shaded region refers to
galaxies with stellar masses below $2.9\times 10^{5}M_{\odot}$, which are
incomplete in observations. Although A-SLOTH is calibrated based on various
physical quantities, such as the mass of the MW galaxy at $z=0$ and global
star formation histories, it is likely to predict a higher number of low-mass
galaxies ($M_{\ast}\lesssim 2\times 10^{4}M_{\odot}$) by a factor of 2-10
compared to what is observed.

In Figure 11, we show the cumulative number of satellite galaxies resulting
from 30 sets of merger trees of the MW-like galaxy using A-SLOTH, indicated by
the black lines, compared to the observational data represented by the red
line (McConnachie, 2012; Muñoz et al., 2018). It is important to note that the
observations of galaxies with stellar masses below $M_{\ast}\approx 2\times
10^{5}{\,M_{\odot}}$, which are represented by the blue-shaded region, are
still incomplete (e.g., Carlsten et al., 2021). The mean stellar mass of the
MW-like galaxy, calculated by averaging over 30 sets of A-SLOTH simulations,
is approximately $M_{\ast}\approx 5.3\times 10^{10}{\,M_{\odot}}$, which is
consistent with the observed stellar mass of the MW galaxy of $4.86-6\times
10^{10}{\,M_{\odot}}$ (e.g., McMillan, 2017). The A-SLOTH simulation, however,
is likely to predict a large amount of low-mass satellite galaxies
($M_{\ast}\lesssim 2\times 10^{4}{\,M_{\odot}}$) that exceed what is actually
observed by a factor of 2-10. This discrepancy, commonly known as the “missing
satellite problem", (e.g., Moore et al., 1999; Klypin et al., 1999; Bullock &
Boylan-Kolchin, 2017) may indicate that there are numerous low-mass galaxies
that remain undiscovered due to observational limitations or that the stellar
feedback implemented in the simulation for small galaxies is not strong enough
to suppress star formation. The following sections discuss the likelihood of
detecting Pop III remnants with HN signatures in two cases. One case will
account for the difference between observations and A-SLOTH simulations, while
the other will not consider this discrepancy.

###  4.2 The effect of Pop III hypernovae

We have employed A-SLOTH to examine the prevalence of Pop III HN explosion
signatures in the MW dwarf satellites. We have experimented with the fraction
of Pop III stars that die as HN explosions, defined as $f_{\rm HN}$, in five
different scenarios: 1) all Pop III stars end up as HNe, $f_{\rm HN}$=100%, as
in our Z55-F100; 2) 50% of Pop III stars die as HNe, comparable to our Z35-F50
and Z55-F50; 3) a small proportion of Pop III stars (either 5% or 1%) expire
as HNe, which we compare to Z55-early and Z55-late; 4) Pop III stars having
stellar mass from $25{\,M_{\odot}}$ to $40{\,M_{\odot}}$ end as HNe, in line
with Z55-Mass. Note that a Pop III HN event is triggered with an explosion
energy of $10^{52}$ ergs. During each simulation, we identify progenitor
minihaloes that are considered to preserve Pop III HNe signatures within the
satellite galaxies of the MW-like galaxy.

minihaloes that exhibit HN signatures are defined as those containing Pop II
stars, which are formed from gas contaminated by Pop III HNe via internal or
external enrichment. If a Pop III star undergoes an HN explosion within a
minihalo, it is assumed that subsequent Pop II stars born immediately after
the explosion may display an HN signature on their surface. In the case of
external enrichment, Pop II stars are formed without prior Pop III star
formation but are contaminated with HN metals originating from an HN event in
an adjacent minihalo. It is crucial to note that we only consider minihaloes
with Pop II stars formed immediately after contamination with a Pop III HN
explosion, as our simulations have shown that only these stars can maintain HN
signatures. Otherwise, the unique signatures are likely to be mixed and washed
out by metals from other SN events.

Figure 12: The number of progenitor minihaloes that have undergone at least
one Pop III HNe explosion in an MW-like galaxy, with respect to halo peak mass
(left panels) and stellar mass (right panels). It is evident that more massive
haloes tend to harbor a greater number of minihaloes undergoing Pop III HNe
events, as clearly depicted by the linear fit represented as a dotted line.
Additionally, we mark the halo that has undergone a single Pop III HN event
using a horizontal dotted line. The color of the circle symbol corresponds to
one of the 30 different MW-like galaxy realizations using A-SLOTH. The average
total number of minihaloes per MW-like galaxy, <$N_{\rm mini,HNsig}$>, is
approximately <$N_{\rm mini,HNsig}$>=583 and <$N_{\rm mini,HNsig}$>=75 for two
scenarios considered: one where all Pop III stars explode as HNe (upper
panels), and another where the range for Pop III HNe is between
$M_{\rm\ast,PopIII}=25{\,M_{\odot}}$ and $M_{\rm\ast,PopIII}=40{\,M_{\odot}}$
(bottom panels).

Figure 12 displays the number of progenitor minihaloes containing Pop III HN
signatures in an MW-like galaxy, represented with respect to the halo peak
mass (left panels) and stellar mass (right panels) of the MW’s satellite
analogs. The peak mass refers to the highest halo mass attained by each
satellite analog as it moves through the merger tree. The circle symbol in
Figure 12 represents all 30 realizations of the MW-like galaxy, with a
different color for each realization. Especially, Figure 12 compares two
scenarios: the first one assumes that Pop III star formation with 100% HN
occurrence rate, $f_{\rm HN}=100\%$ (top panels), while the second scenario
assumes that Pop III HNe is triggered within a mass range of $25{\,M_{\odot}}$
to $40{\,M_{\odot}}$, giving rise to $f_{\rm HN}=15\%$ (bottom panels). When
the results of all 30 runs are considered, the average number of minihaloes
with HN signature, denoted as <$N_{\rm mini,HNsig}$>, is found to be <$N_{\rm
mini,HNsig}$>$=583$ and <$N_{\rm mini,HNsig}$>$=75$ for the cases with $f_{\rm
HN}=100\%$ and $f_{\rm HN}=15\%$, respectively. In the runs where $f_{\rm
HN}=1\%$, the average value is notably lower, <$N_{\rm mini,HNsig}$> = 5,
while the highest and lowest values are $N_{\rm mini,HNsig}=11$ and $N_{\rm
mini,HNsig}=1$, respectively.

The number of progenitor minihaloes with Pop III HN signature within a
satellite galaxy increases as the galaxy mass increases, as illustrated by the
linear fit represented by the dotted line in Figure 12. For example, in the
scenario with $f_{\rm HN}=100\%$, dwarf galaxies with a stellar mass of
$M_{\ast}\gtrsim 10^{9}{\,M_{\odot}}$ \- similar to the Large Magellanic Cloud
(LMC), which has a stellar mass of $M_{\ast}\approx 10^{9.1}{\,M_{\odot}}$ \-
would contain $N_{\rm mini,HNsig}\approx 110$ progenitor minihaloes. However,
this number decreases to $N_{\rm mini,HNsig}\approx 8$ for galaxies with a
mass similar to that of the Sculptor dwarf galaxy, $M_{\ast}\approx
10^{6.2}{\,M_{\odot}}$ (e.g., Muñoz et al., 2018). In UFD galaxies with
stellar masses of $M_{\ast}\lesssim 10^{5}{\,M_{\odot}}$, the number of
progenitor minihaloes becomes very low, with $N_{\rm mini,HNsig}\lesssim 3$.
The tendency of more massive galaxies containing a greater number of HN
signatures remains consistent even when the frequency of HNe, $f_{\rm HN}$, is
decreased. However, the total number of minihaloes is reduced in scenarios
where $f_{\rm HN}=15\%$. For instance, for dwarf galaxies with stellar masses
of $M_{\ast}\gtrsim 10^{9}{\,M_{\odot}}$, $M_{\ast}\approx
10^{6}{\,M_{\odot}}$, and $M_{\ast}\lesssim 10^{5}{\,M_{\odot}}$, the
corresponding number of minihaloes, $N_{\rm mini,HNsig}$, becomes 11, 2, and
less than one, respectively.

###  4.3 The likelihood of finding HN signatures

The question then is identifying the satellite galaxy mass at which we are
most likely to discover stars with Pop III HN signatures while searching for a
galaxy similar to the MW. To address this question, Figure 13 displays the
fraction of progenitor minihaloes featuring Pop III HN signatures within the
satellite galaxies of the MW-like halo with respect to the halo peak and
stellar mass of satellite analogs at $z=0$. The resulting distribution is
based on a series of 30 A-SLOTH runs for each scenario, with each run assuming
a different value of $f_{\rm HN}$. As a reference, we show the result of the
run with $f_{\rm HN}=100\%$ at the upper panels and compare it with other runs
where $f_{\rm HN}$ decreases from 50% to 1% (bottom panels). Given the
prevalence of progenitor minihaloes bearing HN signatures, it becomes apparent
that the likelihood of detecting these minihaloes increases as the value of
$f_{\rm HN}$ rises.

However, while keeping $f_{\rm HN}$ constant, the likelihood of discovering
minihaloes with Pop III HN signatures is highest in galaxies with low mass,
specifically those with halo peak and stellar mass within the range of $M_{\rm
peak}=10^{8}-10^{9}{\,M_{\odot}}$ and
$M_{\ast}=10^{3.5}-10^{4.5}{\,M_{\odot}}$, respectively. For the simulation
with $f_{\rm HN}=100\%$, these low-mass galaxies show a fraction of 40% for
containing such minihaloes. As shown in the bottom panels of Figure 13, this
trend is also valid for other runs with different $f_{\rm HN}$. For instance,
if about 1% of Pop III stars undergo HNe, then an MW-like galaxy is predicted
to contain a total of 5 minihaloes with the HN characteristics, which are
still more likely to be found in small, low-mass satellite dwarfs. It should
be, however, emphasized that this trend described above, i.e., the highest
probability of finding minihaloes with Pop III HN signatures in low-mass
galaxies, could be simply due to the fact that the A-SLOTH model predicts a
higher number of low-mass satellites than is observed, as depicted in Figure
11. In other words, as demonstrated in Figure 12, a single large galaxy could
possess a greater number of minihaloes with Pop III HN signatures than low-
mass galaxies, but the total count of low-mass galaxies within the MW volume
is higher than that of massive galaxies.

Figure 13: The fraction of progenitor minihaloes experiencing a Pop III HN
explosion within the satellite galaxies of the MW-like halo, while altering
the value of $f_{\rm HN}$, with respect to the halo peak and stellar masses
for the satellites at $z=0$. The top panels consider a scenario where all Pop
III stars undergo HNe, while the bottom panels examine cases where the
fraction of Pop III HNe, $f_{\rm HN}$, varies from $1\%$ to $50\%$.
Considering the abundances of progenitor minihaloes featuring HN signatures,
it is evident that the probability of identifying these minihaloes increases
as $f_{\rm HN}$ rises. Meanwhile, when $f_{\rm HN}$ is held constant, the
probability of observing progenitor minihaloes with HN signature is higher in
smaller haloes compared to larger ones. It means that if an observation is
conducted randomly, the chance of discovering a progenitor minihalo is greater
in low-mass satellites than in massive ones. This trend is consistent across
all scenarios with varying $f_{\rm HN}$. This is due to the fact that A-SLOTH
is likely to have a higher number of low-mass satellites than massive
galaxies. Figure 14: The same as Figure 13, but it takes into account the
actual number of observed galaxies in the MW. As seen in Figure 11, A-SLOTH
predicts more low-mass galaxies than are actually observed. To address this,
the fraction of progenitor minihaloes that have undergone HNe is recalculated
by adjusting for the difference between the actual observations and the
predictions of A-SLOTH. This involves decreasing or increasing the number of
low and high-mass galaxies by the difference. The result is that the
probability of discovering a progenitor minihalo that has experienced HNe with
a fixed $f_{\rm HN}$ is highest at halo peak mass and stellar mass of $M_{\rm
peak}\approx 10^{10.5}{\,M_{\odot}}$ and $M_{\ast}\approx
10^{7.5}{\,M_{\odot}}$, respectively.

In order to take into account the discrepancy between the observation and
those A-SLOTH runs, in Figure 14, we adjust the fraction of minihaloes with HN
signatures by incorporating this difference. This is achieved by reducing the
number of satellite galaxies in the low-mass galaxy regime to approximate the
observed number while increasing the number in the high-mass range.
Consequently, the distribution of minihaloes with HN signatures exhibits a
peak among larger satellite galaxies. The highest fraction values,
approximately around 40%, are found in the region of halo peak masses $M_{\rm
peak}\approx 10^{10}-10^{11}{\,M_{\odot}}$ and stellar masses $M_{\ast}\approx
10^{7}-10^{8}{\,M_{\odot}}$, respectively. The following significant fraction
is approximately 18%, corresponding to galaxies with halo peak masses $M_{\rm
peak}\approx 10^{9}-10^{9.5}{\,M_{\odot}}$ and stellar masses $M_{\ast}\approx
10^{5}-10^{5.5}{\,M_{\odot}}$, respectively. Also, we should mention that the
total number of minihaloes decreases by a factor of $\sim 2$ due to the
incorporation of the inconsistency between observations and the A-SLOTH
simulations. This is because A-SLOTH is inclined to predict a higher abundance
of low-mass satellite galaxies, which are incomplete in observational data.

In summary, according to the results of the A-SLOTH simulation, the most
probable dwarf galaxies to contain signatures of HNe associated with Pop III
stars have a stellar mass of $M_{\ast}=10^{3.5}-10^{4.5}{\,M_{\odot}}$, which
is similar to the UFD galaxies like Bootes I, Hercules, CVn II, UMa I, Leo IV,
Hydra II, Columba I, Leo V, ComBer, Indus II, UMa II, and Pisces II. On the
other hand, when accounting for the discrepancy between observations and the
A-SLOTH runs, galaxies with $M_{\ast}\approx 10^{7}-10^{8}{\,M_{\odot}}$,
similar to Sagittarius and Fornax, or with $M_{\ast}\approx
10^{5}-10^{5.5}{\,M_{\odot}}$, corresponding to CVn I, Sextans, Draco, Crater
II, are the most probable galaxies to search for to find fossil records of HN
signatures of Pop III stars.

We should emphasize that the only evidence of an HN signature associated with
Pop III stars in the MW satellite galaxies is AS0039 in the Sculptor galaxy.
Although A-SLOTH simulations suggest that there may be many low-mass dwarfs
with HN signatures, the lack of observation in the UFD regime may be due to
incomplete observations owing to their dimness. Alternatively, if assuming
that the missing satellite problem is solved (e.g., Wetzel et al., 2015; Read
& Erkal, 2019; Engler et al., 2021) and we use the results that account for
the discrepancy between observations and A-SLOTH data, HN signatures are
expected to be found in massive satellite galaxies. The discovery of only one
HN signature related to Pop III stars in Sculptor implies that the likelihood
of Pop III stars ending as HN is probably lower than 1%, according to the
A-SLOTH simulation, which predicts only two minihaloes with HN signatures
assuming $f_{\rm HN}=1\%$. Furthermore, this number of two minihaloes can be
considered an upper limit, as our hydrodynamic simulations indicate that only
80% of Pop II stars inherit HN signatures when a Pop III HN event occurs. In
some cases, the gas may be evaporated or polluted following a Pop III HN,
preventing further star formation or the preservation of HN signatures in
subsequent Pop II stars.

It is important to mention that A-SLOTH lacks information regarding the
metallicity of stars. As stated in Section 4.2, if a Pop III star experiences
an HN explosion within a minihalo, it is assumed that subsequent Pop II stars
born immediately after the explosion might exhibit an HN signature on their
surfaces. We plan to delve deeper into this aspect in our forthcoming
research. While quantifying the frequency of AS0039-like stars, displaying HN
signatures while maintaining low metallicity, among Pop II stars with HN
signatures proves challenging, our hydrodynamic simulations have revealed that
generating stars akin to AS0039 requires specific conditions like the rapid
infall of pristine gas. Such conditions present difficulties in producing
these stars. When considering the amalgamated results of both A-SLOTH and our
hydrodynamic simulations, our findings suggest that the appropriate fraction
of HN in line with observations is likely $f_{\rm HN}\lesssim 1\%$.

##  5 Summary and Conclusion

This study aims to explore the origin of metal-poor stars observed in nearby
dwarf galaxies, which could harbor remnants of the earliest generation of
stars. Our focus is particularly on AS0039, a star in the Sculptor galaxy,
exhibiting distinct features that suggest its association with hypernova (HN)
explosions from Pop III stars. To investigate the conditions under which such
stars can form, we have performed six sets of cosmological zoom-in simulations
on ultra-faint dwarf (UFD) analogs with a mass of $M_{\rm vir}\approx
10^{8}{\,M_{\odot}}$ at $z=0$. To explore whether Pop II stars in our
simulations exhibit Pop III HN signatures, we vary two parameters: the
critical metallicity for Pop II star formation and the fraction of Pop III
stars that undergo HN explosions, defined as $f_{\rm HN}$. The fraction is
varied from 100% to the lower limit where a single HN event occurs during the
assembly of the simulated galaxy to cover the full range of possibilities.

By analyzing the resulting fraction of Pop II stars exhibiting HN signatures
and their metallicity, we have identified the potential environmental
conditions for forming metal-poor stars such as AS0039. Furthermore, we also
investigate the likelihood of discovering Pop II remnants that contain HN
signatures in nearby dwarf satellite galaxies. To do this, we use a semi-
analytic approach with the A-SLOTH code that allows us to efficiently explore
the parameter space and overcome the limitation of this work, which is
confined to a single UFD analog.

Our main findings are summarized as follows.

  * •

According to our simulations, the process of star formation in UFD galaxies is
complex, involving the merging of multiple minihaloes. Our results suggest
that the main progenitor does not dominate star formation at high redshifts.
Instead, we observe that star formation is initiated in minihaloes of
comparable mass, which then merge later. Across all simulations, the average
in-situ star formation is found to be 19.5%, and about $\sim$80% of the stars
in the simulated galaxies have grown through mergers.

  * •

For each simulation run, the number of progenitor minihaloes that contain Pop
II stars exhibiting Pop III SN signatures, $N_{\rm mini,HNsig}$, varies from
zero to 5 depending on the fraction of Pop III stars that die as HNe. However,
the presence of a Pop III HN event does not guarantee the formation of Pop II
stars with relics of such SN explosions. This can be attributed to the strong
feedback from Pop III HNe, preventing further star formation or the
contamination of gas by metals from merged minihaloes prior to the formation
of Pop II stars, leading to the unique HN signatures being diluted and washed
out. Moreover, as the fraction of Pop III HNe decreases, the proportion of Pop
II stars with HN signatures denoted as $f_{\rm PopII,HNsig}$, tends to
decrease as well. Specifically, $f_{\rm PopII,HNsig}$ declines from 16% for
Z55-F100 to 2.3% for Z55-Mass.

  * •

The metallicity of Pop II stars within the simulated galaxies ranges of
$\rm-5.5<[Fe/H]<-1.5$, while Pop II stars with HN signatures are typically
found in the range from $\rm[Fe/H]\approx-3.3$ to $\rm[Fe/H]\approx-2.4$, with
one outlier at $\rm[Fe/H]=-4.17$, similar to the observed AS0039 star. We find
that the halo, where such ultra metal-poor (UMP) stars are found, undergoes a
rapid gas inflow with a peak gas accretion rate of $\dot{M}_{\rm gas}\sim$0.08
${\,M_{\odot}}\rm yr^{-1}$, which is significantly higher than the averaged
gas inflow rate of $\sim$0.0025 ${\,M_{\odot}}\rm yr^{-1}$ for other haloes.
This suggests that the formation of the UMP star AS0039 in the Sculptor dwarf
galaxy could have been facilitated by a halo that experienced a rapid gas
inflow.

  * •

The metallicity of Pop II stars formed after Pop III star formation is highly
dependent on the delay time, which refers to the time interval between the Pop
III supernova explosion and the formation of subsequent Pop II stars. This is
due to the fact that, unless there is external enrichment, metallicity usually
declines with increased diffusion associated with longer delay times. This
could offer another explanation for the formation of Pop II stars with low
metallicities, such as AS0039.

  * •

The estimated individual metal abundances of Pop II stars exhibiting HN
signatures are in agreement with the best-fit values for AS0039. We confirm
that, aside from Pop III HN events, other progenitors, such as Pop III stars
exploding with a typical SN energy of $E_{\rm SN}=10^{51}$ ergs or Pop II
stars, are unable to produce metal abundances consistent with those found in
AS0039. Furthermore, we demonstrate that carbon-enhanced metal-poor stars can
be formed via Pop III stars and that the carbon abundances of Pop II stars
show characteristics that differ from those displaying HN signatures.

  * •

Utilizing the semi-analytic A-SLOTH code, we find that the average number of
minihaloes containing HN signatures in an MW-like galaxy is <$N_{\rm
mini}$>$=583$ and <$N_{\rm mini}$>$=75$ for cases where $f_{\rm HN}=100\%$ and
$f_{\rm HN}=15\%$, respectively, based on the results of all 30 sets. The
number of progenitor minihaloes with HN signatures within a satellite galaxy
increases with the galaxy mass. For example, dwarf galaxies with a stellar
mass of $M_{\ast}\gtrsim 10^{9}{\,M_{\odot}}$, similar to the Large Magellanic
Cloud, would contain $N_{\rm mini}\approx 110$ progenitor minihaloes if
$f_{\rm HN}=100\%$. However, this number decreases to $N_{\rm mini}\lesssim
10$ for galaxies with a mass of $M_{\ast}\lesssim 10^{6}{\,M_{\odot}}$.

  * •

Our analysis suggests that the likelihood of discovering a progenitor minihalo
with HN signatures while maintaining a constant value of $f_{\rm HN}$ is
higher in low-mass satellites ($M_{\rm peak}=10^{8}-10^{9}{\,M_{\odot}}$ and
$M_{\ast}=10^{3.5}-10^{4.5}{\,M_{\odot}}$) compared to more massive ones.
However, we also find that the semi-analytic A-SLOTH code tends to over-
predict the number of low-mass satellites compared to what is observed in the
local Universe. This discrepancy could be due to observational incompleteness
caused by the faintness of low-mass galaxies. Taking this into account, we
find that the most likely dwarf galaxies to contain HN signatures are shifted
towards more massive satellite galaxies, with a probability of 40% in the
range of $M_{\rm peak}\approx 10^{10}-10^{11}{\,M_{\odot}}$ and
$M_{\ast}\approx 10^{7}-10^{8}{\,M_{\odot}}$. The subsequent highest
probability of discovering minihaloes with HN signatures is associated with
galaxies in the range of $M_{\rm peak}\approx 10^{9}-10^{9.5}{\,M_{\odot}}$
and $M_{\ast}\approx 10^{5}-10^{5.5}{\,M_{\odot}}$.

It is worth noting that the simulated galaxy in this study has less mass,
approximately two orders of magnitude lower than the Sculptor galaxy, where
AS0039 was discovered. The Sculptor galaxy is classified as a dwarf spheroidal
(dSph) galaxy and has a mass of $M_{\ast}\approx 1.8\times
10^{6}{\,M_{\odot}}$. Nevertheless, the results of this study indicate that
stars like AS0039 could have formed during the early stages of the evolution
of the Sculptor galaxy. This is supported by the fact that the formation of
Pop III stars occurs early in the Universe with a cosmic time of $t_{\rm
H}\lesssim 0.75$ $\rm Gyr$, and the remnants of Pop III stars are only found
in Pop II stars that formed shortly after. This suggests that early star
formation is a key factor in producing stars with characteristics similar to
AS0039, regardless of whether the galaxy is a dSph or not. However, the
analysis using A-SLOTH indicates that the probability of discovering HN
signatures in dwarf galaxies is dependent on the number of satellite galaxies
with a specific mass. Given the current limitations in observations, it is
more probable to find stars with relics from the first generation of stars in
more massive satellite galaxies.

Considering the current limitations in observations, the discovery of only one
star, AS0039, among the observed satellite galaxies suggests that the fraction
of Pop III stars that undergo HN explosions is extremely low. According to the
A-SLOTH analysis, assuming that only 1% of Pop III stars die as HNe, only two
minihaloes are predicted to contain Pop II stars with Pop III HN signatures,
implying the fraction of Pop III stars exploding as HNe likely to be less than
1%. According to Yoon et al. (2012), Pop III stars with masses between
$13{\,M_{\odot}}$ and $83{\,M_{\odot}}$ could experience HN explosions
depending on their degree of rotation. Certainly, the fraction of Pop III
stars that end in HNe is determined by the assumed initial mass function
(IMF). Our adopted IMF predicts an $f_{\rm HN}\approx 54\%$ over the possible
progenitor masses for HN under chemically homogeneous evolution. Conversely,
our results, when combined with such nucleosynthesis findings, could provide
insights into the rotational degree of the first generation of stars.

Despite the JWST being a powerful tool for studying early objects formed in
the early Universe, it is anticipated that directly observing individual
first-generation stars will be extremely challenging (e.g., Schauer et al.,
2020; Woods et al., 2021; Katz et al., 2023; Larkin et al., 2023).
Consequently, the role of stellar and galactic archaeology in inferring the
nature of the first stars will be crucial, providing a complementary
understanding of far-field cosmology. Detailed chemical abundances in metal-
poor stars within local dwarf galaxies can provide insight into questions such
as the end of life of the first stars, their mass and spin, and their birth
environment. Moreover, the near-field cosmology approach will be bolstered by
future observations using advanced telescopes like the Giant Magellan
Telescope (GMT), the Thirty Meter Telescope (TMT), and the European Extremely
Large Telescope (E-ELT), which promise to offer improved spectroscopic
sensitivity to uncover the chemical signature left behind by early cosmic
history.

## acknowledgements

We express our gratitude to the anonymous referee for their constructive and
insightful feedback, which has significantly enhanced the clarity of our
paper. We thank Hartwig Tilman for the valuable discussions and for graciously
sharing the A-SLOTH code with us. We are grateful to Volker Springel, Joop
Schaye, and Claudio Dalla Vecchia for permission to use their versions of
gadget. T. L. and M. J. are supported by the National Research Foundation
(NRF) grants No. 2021R1A2C109491713 and No. 2022M3K3A1093827, funded by the
Korean government (MSIT).

## DATA AVAILABILITY

The simulation data and results of this paper may be available upon request.

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##  Appendix A EVOLUTION OF THE TARGET HALO

In Figure 15, we have analyzed the amount of feedback energy from both SNe and
HNe on the target halo across cosmic time. Note that the energy associated
with a single Pop III SN is $E_{\rm SN}=10^{51}$ erg, while for a Pop III HN,
it is $E_{\rm SN}=10^{52}$ erg. For a single Pop II star particle, represented
by a stellar mass of $500M_{\odot}$, the SN energy is equivalent to $E_{\rm
SN}=5\times 10^{51}$ erg. Figure 16 illustrates the formation history of Pop
II stars within the target halo by tracing their origins. In-situ stars
originating from the primary progenitor halo are indicated by green symbols,
while those emerging from other progenitor haloes are denoted by pink symbols.

Figure 15: The accumulation of feedback energy from both SNe and HNe exerted
on the target halo is depicted for the six simulation sets. The feedback
energy arising from Pop III SNe is represented by the green line, Pop III HNe
by the cyan line, Pop II SNe by the yellow line, and the cumulative total
feedback energy by the black line. Each individual simulation set is
differentiated by a different line style. Interestingly, despite the higher
energy release of a Pop III HN ($E_{\rm SN}=10^{52}$ erg) compared to a Pop
III SN ($E_{\rm SN}=10^{51}$ erg) and Pop II SNe ($E_{\rm SN}=5\times 10^{51}$
erg), the overall energy contribution is more likely to be dominated by Pop II
SNe due to the infrequent occurrence of Pop III HNe. Across all six simulation
sets, the target halo ultimately converges to a comparable baryon fraction, as
demonstrated in the left panel of Figure 2. Figure 16: The formation history
of Pop II stars within the target halo. The number of stars originating in-
situ within the main progenitor halo are denoted by green star symbols, while
ex-situ stars from other progenitor haloes are represented by pink star
symbols. The right y-axis is dedicated to showing the stellar mass,
represented by the continuous red line, identical to the red lines found in
the left panel of Figure 2.

##  Appendix B MERGER HISTORY OF THE TARGET HALO

Figure 17: The merger tree of the target halo within the Z55-F50 simulation at
$z\approx 3$. Each line on the diagram represents a progenitor halo with a
dark matter mass exceeding $M_{\rm vir}\approx 10^{5}M_{\odot}$ and is color-
coded in accordance with its mass. Specifically, haloes with $M_{\rm
vir}>10^{6}{\,M_{\odot}}$ are represented in green, transitioning to yellow as
the mass increases to around $M_{\rm vir}\approx 10^{8}{\,M_{\odot}}$. Despite
the target halo being formed from a composite of multiple progenitor haloes,
the number of progenitor haloes containing Pop II stars with Pop III
signatures is estimated to be approximately $N_{\rm mini,PopIII}\approx 10$.
These stars are predominantly formed within the mass range of haloes
$10^{6}{\,M_{\odot}}\lesssim M_{\rm vir}\lesssim 4\times 10^{6}{\,M_{\odot}}$,
consistent with the findings depicted in Figure 4.