# The role of faint population III supernovae in forming CEMP stars in ultra-
faint dwarf galaxies

Myoungwon Jeon1, Volker Bromm2, Gurtina Besla3, Jinmi Yoon4,5, and Yumi Choi6
1School of Space Research, Kyung Hee University, 1732 Deogyeong-daero, Yongin-
si, Gyeonggi-do 17104, Korea
2Department of Astronomy, University of Texas, TX 78712, USA
3Department of Astronomy, University of Arizona, 933 North Cherry Avenue,
Tucson, AZ 85721, USA
4Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA
5Joint Institute for Nuclear Astrophysics—Center for the Evolution of the
Elements (JINA-CEE), USA
6Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218, USA E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

CEMP-no stars, a subset of carbon enhanced metal poor (CEMP) stars
($\rm[C/Fe]\geq 0.7$ and $\rm[Fe/H]\lesssim-1$) have been discovered in ultra-
faint dwarf (UFD) galaxies, with $M_{\rm vir}\approx 10^{8}{\,M_{\odot}}$ and
$M_{\ast}\approx 10^{3}-10^{4}{\,M_{\odot}}$ at $z=0$, as well as in the halo
of the Milky Way (MW). These CEMP-no stars are local fossils that may reflect
the properties of the first (Pop III) and second (Pop II) generation of stars.
However, cosmological simulations have struggled to reproduce the observed
level of carbon enhancement of the known CEMP-no stars. Here we present new
cosmological hydrodynamic zoom-in simulations of isolated UFDs that achieve a
gas mass resolution of $m_{\rm gas}\approx 60{\,M_{\odot}}$. We include
enrichment from Pop III faint supernovae (SNe), with $E_{\rm SN}=0.6\times
10^{51}$ erg, to understand the origin of CEMP-no stars. We confirm that Pop
III and Pop II stars are mainly responsible for the formation of CEMP and
C-normal stars respectively. New to this study, we find that a majority of
CEMP-no stars in the observed UFDs and the MW halo can be explained by Pop III
SNe with normal explosion energy ($E_{\rm SN}=1.2\times 10^{51}$ erg) and Pop
II enrichment, but faint SNe might also be needed to produce CEMP-no stars
with $\rm[C/Fe]\gtrsim 2$, corresponding to the absolute carbon abundance of
$\rm A(C)\gtrsim 6.0$. Furthermore, we find that while we create CEMP-no stars
with high carbon ratio $\rm[C/Fe]\approx 3-4$, by adopting faint SNe, it is
still challenging to reproduce CEMP-no stars with extreme level of carbon
abundance of $\rm A(C)\approx 7.0-7.5$, observed both in the MW halo and UFDs.

###### keywords:

cosmology: theory – galaxies: formation – galaxies: high-redshift – HII
regions – hydrodynamics – intergalactic medium – supernovae: physics.

††pubyear: 2019††pagerange: The role of faint population III supernovae in
forming CEMP stars in ultra-faint dwarf galaxies–A

##  1 Introduction

Over the preceding decade, the discovery of metal-poor stars in dwarf galaxies
has revolutionized our understanding of the formation and evolution of low-
mass dwarf galaxies, with stellar masses $M_{\ast}\lesssim
10^{6}{\,M_{\odot}}$ at $z=0$ (a recent review is given in Simon 2019; see
also Tolstoy et al., 2009; Willman, 2010; McConnachie, 2012; Frebel & Norris,
2015). Stellar archaeology, in particular, allows us to trace back star
formation histories (SFHs) of dwarf galaxies, scrutinizing their detailed
stellar abundances (e.g. Frebel & Bromm, 2012; Webster et al., 2014, 2015; Ji
et al., 2015). For instance, [$\alpha$/Fe], the abundance ratio of alpha
elements (oxygen, magnesium, calcium, and silicon) compared to iron (e.g.
Tolstoy et al., 2009; Norris et al., 2010; Vargas et al., 2013), constitutes a
well-known cosmic clock (Tinsley, 1979), where the break in the [$\alpha$/Fe]
vs. [Fe/H] relation marks the onset of Type Ia supernovae (SNe), thus
providing a measure for the overall duration of star formation.

The carbon to iron ratio, [C/Fe], is often used as another important tracer
for stellar populations and early galactic chemical evolution. Many stars
observed in the Milky Way (MW) and its satellite dwarf galaxies exhibit
enhancement of this ratio, giving rise to a peculiar stellar population called
carbon-enhanced metal-poor (CEMP) stars ($\rm[C/Fe]\geq 0.7$ and
$\rm[Fe/H]\lesssim-1$, see Beers & Christlieb, 2005; Aoki et al., 2007; Norris
et al., 2013 for details). Given the increasing fraction of CEMP stars with
decreasing metallicity in the MW halo and MW satellite galaxies (e.g. Aoki et
al., 2007; Frebel et al., 2010; Lee et al., 2013; Yong et al., 2013; Salvadori
et al., 2015; Placco et al., 2014; Yoon et al., 2018), studying CEMP stars
with very low-metallicity ([Fe/H] $\lesssim-2.0$) provides great insights into
the nature of the early metal-poor star-forming and galactic environments.
Therefore, ultra-faint dwarfs (UFDs), the most metal-poor galaxies with
absolute magnitudes fainter than $M_{V}=-7.7$ $(L\lesssim
10^{5}{\rm\,L_{\odot}}$; Simon, 2019), might provide a compelling laboratory
to search for hints of CEMP stars (e.g. Bland-Hawthorn et al., 2015). In
particular, the chemical signature of CEMP-no stars, a subclass of CEMP stars
without enhancing heavy neutron-capture process elements ($\rm[Ba/Fe]\lesssim
0.0$), might be unique to the first generation of stars, the so-called
Population III (Pop III) (e.g. Bromm & Yoshida, 2011; Bromm, 2013; Hansen et
al., 2016; Yoon et al., 2016). Finding fossil probes of Pop III stars in Local
Group dwarfs is a promising alternative, given the current absence of direct
observations of Pop III stars, which will likely also not be possible with the
upcoming James Webb Space Telescope (JWST) (e.g. Gardner et al., 2006; Schauer
et al., 2020), unless they exploded as particularly superluminous SNe (e.g.
Whalen et al., 2013; Hartwig et al., 2018).

We focus mainly on the formation of CEMP stars, particularly CEMP-no, as they
might preserve the chemical abundance pattern of the first stars. In general,
the stellar carbon abundances both in the observed MW halo and its satellite
dwarf galaxies are broadly divided into two categories111We note that this
dividing line is somewhat in-definitive due to continuous distribution of
[C/Fe] between these populations, though it was defined based on the empirical
data (Aoki et al., 2007).: C-normal ($\rm[C/Fe]<$ 0.7) and C-enhanced
($\rm[C/Fe]\gtrsim 0.7$). The richness of CEMP stars can be found in their
$A$222$A$(C)$=\rm log\epsilon(C)$ is the absolute carbon abundance(C)-[Fe/H]
distribution. Yoon et al. (2016, 2019) recognized that there are three
distinct groups (Group I-III), based on their morphological $A$(C)-[Fe/H]
distribution, each of which has a distinct nucleosynthetic signature,
suggesting different origins. Most relevant groups to this work are Group II
and Group III CEMP-no stars, though Group I CEMP-no with its unusually high
$A$(C) value is also of great interest. The Group II stars in the MW and its
satellite galaxies appear to be an extension of C-normal stars, whose carbon
was co-produced with iron. In contrast, the Group III stars exhibit no
correlation between carbon and iron.

The origin of CEMP-no stars is still actively debated. Possible scenarios
include rapidly-rotating Pop III stars with masses of
$m_{\ast}=40-120{\,M_{\odot}}$ (e.g. Meynet et al., 2006), weakly exploding
Pop III SNe with a progenitor mass of $m_{\ast}=10-40{\,M_{\odot}}$,
accompanied by little mixing and low explosion energy (e.g. Iwamoto et al.,
2005; Heger & Woosley, 2010; Ishigaki et al., 2014), or jet-like explosions
(e.g. Tominaga et al., 2007; Ezzeddine et al., 2019). Further scenarios
propose the mass transfer from an Asymptotic Giant Branch (AGB) star onto a
low-mass, metal-poor companion star in binary systems (e.g. Suda et al., 2004;
Abate et al., 2013; Starkenburg et al., 2014; Arentsen et al., 2019), the
efficiency of dust cooling depending on different dust grains properties (e.g.
Chiaki et al., 2017), or inhomogeneous metal mixing between metal elements
(e.g. Hartwig & Yoshida, 2019). Perhaps, some combination of these scenarios
could explain the origins of the distinct CEMP-no groups. Upcoming extensive
stellar surveys can provide a more in-depth understanding of their origins.

We focus on the contribution of Pop III faint SNe on the formation of CEMP-no
stars in our simulations. Faint Pop III SNe have been extensively discussed in
many other studies to explain the observed CEMP stars in the local UFDs, but
were not considered in our previous study (Jeon et al., 2017). These faint
SNe, where the weak explosion enables carbon to be released into the
interstellar medium (ISM) while iron falls back onto the stellar core, give
rise to high intrinsic [C/Fe] ratios (e.g. Umeda & Nomoto, 2003; Iwamoto et
al., 2005; Tominaga et al., 2014; Ishigaki et al., 2014; Cooke & Madau, 2014;
Komiya et al., 2020). In this study we consider the impact of faint SNe to see
if we can reproduce not only Group II but also Group III CEMP-no stars with
the extreme levels of carbon enhancement ($\rm[C/Fe]\sim 3-4$), which have
never been accomplished.

Further, we investigate the hypothesis by Yoon et al. (2019) that faint Pop
III SNe are likely responsible for the Group III CEMP-no stars with high
$A$(C) $\gtrsim 6.5$, while the Group II CEMP-no stars in more massive dwarf
spheroidal (dSphs) seem to be associated with normal Pop II SNe. Yoon et al.
(2019) argue that higher values of $A$(C) for the CEMP-no stars in local UFDs
can be understood, if their birthplaces were chemically primitive low-mass
system, where the effects of stochastic and early generation star formation
can be maximized as their SFHs are truncated at early stages. This study thus
indicates that the UFD ($M_{\rm vir}\lesssim 10^{8}{\,M_{\odot}}$ at $z=0$)
descendants of low mass dwarfs that host faint Pop III SNe at early times, are
the most likely to host CEMP-no stars

Significant theoretical progress has also been made in studying the formation
and evolution of dwarf galaxies with cosmological simulations (e.g. Sawala et
al., 2010; Wetzel et al., 2015; Garrison-Kimmel et al., 2016). In particular,
hydrodynamic zoom-in simulations have begun to focus on isolated dwarfs
($M_{\rm vir}=10^{8}-10^{9}{\,M_{\odot}}$ at $z=0$), (e.g. Simpson et al.,
2013; Oñorbe et al., 2015; Wheeler et al., 2015; Jeon et al., 2017; Fitts et
al., 2017; Munshi et al., 2019; Wright et al., 2019), and only very recently
start considering UFDs around MW mass hosts (e.g., Applebaum et al., 2020),
representing their baryonic component with high resolution. Recently, this
approach has been further pushed to the limit of resolving individual star-
forming clouds (e.g. Rey et al., 2019, 2020; Wheeler et al., 2019; Agertz et
al., 2020).

In our previous work (Jeon et al., 2017), we focused on galaxies with $M_{\rm
vir}\approx 10^{9}{\,M_{\odot}}$ at $z=0$, considering typical SN feedback and
cosmic reionization, both of which are crucial in suppressing star formation
at this mass scale. In addition, we included the initial metal enrichment from
Pop III stars, and compared the simulated dwarfs with local observations.
However, these systems were on the borderline between UFDs and classical dSph
galaxies, with some systems retaining neutral hydrogen gas to late time (Jeon
et al., 2019), and exhibiting multiple star formation episodes, analogous to
dwarf galaxies such as Leo I and Leo P. Therefore, these are more
appropriately analogs to the lowest mass dSphs and dwarf irregular(dIrr)
galaxies known.

Here, we build on this work, reaching lower masses to explore the stellar
populations and physics that govern the evolution of the lowest mass galaxies
known ($M_{\rm vir}\approx 10^{8}{\,M_{\odot}}$ at $z=0$), with the goal of
explaining the origin of the most extreme CEMP-no stars. Achieving high
resolution is necessary to resolve the ISM, including dense star forming
sites, in such small galaxies. Therefore, we perform simulations with a gas
mass resolution of $m_{\rm gas}\sim 60{\,M_{\odot}}$, an order of magnitude
enhancement over that in Jeon et al. (2017). Lastly, compared to Jeon et al.
(2017), we improve the treatment of metal transport, enabling us to
distinguish the contributions from Pop III and Pop II SNe, by separately
tracking individual enrichment from the two populations.

The paper is organized as follows. We describe the numerical methodology in
Section 2, and present the detailed simulation results in Section 3, with a
focus on the chemical enrichment history of present-day UFD galaxies. We
conclude in Section 4 with a summary and some broader perspectives. For
consistency, all distances are given in physical (proper) units unless noted
otherwise.

##  2 Numerical methodology

###  2.1 Simulation Setup

In this work, simulations have been conducted in a zoomed area, containing six
$M_{\rm vir}\sim 10^{8}{\,M_{\odot}}$ subhaloes (masses evaluated at $z=0$).
To explore how stellar abundance ratios vary depending on which Pop III SNe
explode, we have run two sets of simulations, one using normal SN yields and
one including a fraction of faint SNe. In the latter case, we assume that
70$\%$ of Pop III stars within the $m_{\ast}=10-100{\,M_{\odot}}$ mass range
explode as faint SNe, with the remainder dying as normal SNe. The resulting
key characteristics of the simulated galaxies are summarized in Table 1. Note
that we here ignore the effects of photoionization heating by stars, which
could reduce the fraction of CEMP stars, as star formation in the simulated
UFDs can be reduced. We will discuss the impact of photoionization heating on
the SFHs and chemical abundances of UFD analogs in a follow-up paper.

###  2.2 Gravity, hydrodynamics, and cooling

We have used a modified version of the N$-$body Smoothed Particle
Hydrodynamics (SPH) code GADGET (Springel et al., 2001; Springel, 2005), to
carry out a suite of hydrodynamic zoom-in simulations. We generate the initial
conditions using the cosmological initial conditions code MUSIC (Hahn & Abel,
2011). We have generated zoom-in initial conditions that include at least six
$M_{\rm vir}\sim 10^{8}{\,M_{\odot}}$ haloes at $z=0$. At first, we conduct a
dark matter (DM) only simulation with $128^{3}$ particles in a
$L=3.125h^{-1}~{}\mbox{comoving}~{}\mbox{Mpc}$ box to identify the targeted
region. Then, four consecutive refinements are carried out, giving rise to an
effective resolution of $2048^{3}$. The dark matter and gas masses in the most
refined region are $m_{\rm DM}\approx 500{\,M_{\odot}}$ and $m_{\rm
SPH}\approx 63{\,M_{\odot}}$, respectively, an order of magnitude improvement
over those in Jeon et al. (2017).

We adopt the following cosmological parameters: a matter density of
$\Omega_{\rm m}=1-\Omega_{\Lambda}=0.265$, baryon density of $\Omega_{\rm
b}=0.0448$, present-day Hubble expansion rate of
$H_{0}=71\,\mathrm{km\,s^{-1}Mpc^{-1}}$, a spectral index $n_{\rm s}=0.963$,
and a normalization $\sigma_{8}=0.8$ (Komatsu et al., 2011; Planck
Collaboration, 2016). We use a fixed softening length for DM particles of
$\epsilon_{\rm DM}=$ 10 pc over the entire simulated time, and a variable
softening length for gas particles that is proportional to the SPH kernel
length with a minimum value of $\epsilon_{\rm gas,min}=2.8$ pc. We trace the
abundances of nine atomic and molecular species ($\rm
H,H^{+},H^{-},H_{2},H^{+}_{2},He,He^{+},He^{++},$ and $\rm e^{-}$), as well as
the three deuterium species $\rm D,D^{+}$, and HD, under the influence of a
cosmic UV background (Haardt & Madau, 2011) by solving the coupled, non-
equilibrium rate equations every time-step. We gradually introduce the UV
background, beginning at $z\approx 7$, and linearly increase its strength
until $z=6$, when cosmic reionization is expected to be complete (e.g. Gunn &
Peterson, 1965; Fan et al., 2006).

The UV background is attenuated through $\exp{(-N_{\rm H~{}I}\bar{\sigma}_{\rm
ion}})$, where the column density of neutral hydrogen is $N_{\rm
H~{}I}=hn_{\rm H~{}I}$. Here, $h$ is the SPH kernel size and
$\bar{\sigma}_{\rm ion}$ the frequency-averaged photoionization cross-section
for H I. Additionally, we account for the photodissociation of molecular
hydrogen, $\rm H_{2}$, by soft UV radiation in the Lyman-Werner (LW) band
(11.2 eV$-$13.6 eV) (e.g. Abel et al., 1997), with a rate $k_{\rm
LW}=1.38\times 10^{-12}{\rm s^{-1}}J_{21}$. Here, the normalized LW mean
intensity is $J_{\rm 21}=\bar{J}_{\nu}/(10^{-21}{\rm
erg\,Hz^{-1}s^{-1}cm^{-2}sr^{-1}})$, with $\bar{J}_{\nu}(z)$ being the average
intensity in the LW band, calculated from the spectra in Haardt & Madau
(2011). For simplicity, the treatment for the photodissociation of deuterated
hydrogen, HD, is identical to that of $\rm H_{2}$.

We take into account all relevant primordial cooling processes, including H
and He collisional ionization, excitation and recombination cooling, inverse
Compton cooling, bremsstrahlung, and collisional excitation cooling of $\rm
H_{2}$ and HD. Also, metal cooling from carbon, oxygen, silicon, magnesium,
nitrogen, neon, and iron is considered in their equilibrium states.
Specifically, we adopt the method suggested in Wiersma et al. (2009), where
the cooling rates by each species are interpolated as a function of density,
temperature, and metallicity from the tables that are computed in advance from
the photo-ionization code CLOUDY (Ferland et al., 1998). Given the small dust
content predicted for low-mass galaxies at $z>7$ (Jaacks et al. 2018), we here
ignore $\rm H_{2}$ formation through dust and dust cooling.

Table 1: Characteristics of the simulated UFD analogs at $z=0$ from the simulated region. Two comparison simulations have been performed by adopting two different SN metal yields, corresponding to faint and normal events, respectively. Column (1): Halo name. Column (2): Virial mass (in units of $10^{8}{\,M_{\odot}}$). Column (3): Virial radius (in kpc). Column (4): Stellar mass (in $10^{3}{\,M_{\odot}}$). Column (5): Enclosed mass within half stellar mass radius (in $10^{6}{\,M_{\odot}}$). Column (6): Half stellar mass radius (in pc). Column (7): Average stellar iron-to-hydrogen ratios. Column (8): Average alpha-to-iron ratios of stars. Column (9): 1-dimensional stellar velocity dispersion (in km $\rm s^{-1}$). Column (10): Adopted yield table for Pop III SNe. Note that in some haloes the estimates of $\sigma$ are not available due to the shortage of number of stellar particles within the haloes. Halo | $M_{\rm vir}$ | $r_{\rm vir}$ | $M_{\ast}$ | $M_{\rm 1/2}$ | $r_{1/2}^{\ast}$ | [Fe/H] | [$\rm\alpha/Fe$] | $\sigma_{\ast}$ | yield
---|---|---|---|---|---|---|---|---|---
| $[10^{8}{\,M_{\odot}}]$ | $[\rm kpc]$ | $[10^{3}{\,M_{\odot}}]$ | $[10^{6}{\,M_{\odot}}]$ | $[\rm pc]$ | - | - | $[\rm km\,s^{-1}]$ | -
halo1 N | 1.50 | 10.75 | 10 | 1.59 | 181 | -3.05 | 0.81 | 2.04 | normal SN
halo2 N | 1.36 | 10.45 | 6.67 | 4.35 | 260 | -2.78 | 0.63 | 3.65 | normal SN
halo3 N | 1.22 | 10.0 | 8.57 | 1.47 | 208 | -2.75 | 0.86 | 2.75 | normal SN
halo4 N | 1.15 | 9.77 | 2.38 | 0.34 | 89 | -2.22 | 0.59 | N/A | normal SN
halo5 N | 1.11 | 9.02 | 9.52 | 0.65 | 106 | -2.93 | 0.78 | 3.17 | normal SN
halo6 N | 0.89 | 7.95 | 5.71 | 2.3 | 457 | -2.55 | 0.77 | 2.35 | normal SN
halo7 F | 1.50 | 10.75 | 3.81 | 19.4 | 815 | -3.29 | 1.47 | 4.15 | faint SN
halo8 F | 1.36 | 10.45 | 5.24 | 1.83 | 160 | -2.84 | 0.90 | 2.41 | faint SN
halo9 F | 1.22 | 10.0 | 7.62 | 0.47 | 91 | -3.06 | 0.90 | 3.59 | faint SN
halo10 F | 1.15 | 9.77 | 0.95 | 0.039 | 36 | -1.90 | 1.18 | N/A | faint SN
halo11 F | 1.11 | 9.02 | 5.71 | 0.11 | 51 | -2.31 | 1.15 | 3.30 | faint SN
halo12 F | 0.88 | 7.97 | 9.53 | 4.8 | 373 | -3.44 | 1.85 | 3.98 | faint SN

###  2.3 Star formation physics

Stars are formed from gas clouds at a rate $\dot{\rho}_{\ast}=\rho_{\rm
th}/\tau_{\ast}$, where $\tau_{\ast}=\tau_{\rm ff}/\epsilon_{\rm ff}$ is the
star formation time scale, $\tau_{\rm ff}=[3\pi/(32G\rho_{\rm th})]^{1/2}$ the
free fall time at the threshold density $\rho_{\rm th}$, and $\epsilon_{\rm
ff}$ the star formation efficiency per free fall time (Schmidt, 1959). The
star formation efficiency for Pop III stars has yet to be pinned down
precisely (e.g. Hirano et al., 2015; Stacy et al., 2016). We set
$\epsilon_{\rm ff,Pop~{}III}=\epsilon_{\rm ff,Pop~{}II}\sim 0.01$, which is
similar to a typical star formation efficiency in the local Universe. Then, an
SPH particle is stochastically converted into a collisionless star particle in
a time interval $\Delta t$, if a random number is smaller than min($\Delta
t$/$\tau_{\ast}$,1), to follow a given distribution
$\dot{\rho}_{\ast}=\rho_{\rm th}/\tau_{\ast}$. The star formation timescale is
then given by

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

####  2.3.1 Population III

The characteristic mass of metal-free stars, determined by a complex physical
interplay, is still uncertain (e.g. Bromm, 2013). Compared to the initially
predicted masses of typically a few $\sim 100{\,M_{\odot}}$, the mass scale
has been shifted to a few $\sim 10{\,M_{\odot}}$ by considering protostellar
radiative feedback and disk fragmentation (e.g. Stacy et al., 2010), while
still extending over a broad range of $1-1000{\,M_{\odot}}$ (e.g. Susa et al.,
2014; Hirano et al., 2015; Hosokawa et al., 2016; Stacy et al., 2016). As
explained in Section 2.2, the resolution of our simulations ($m_{\rm
gas}\approx 60{\,M_{\odot}}$) is high enough to represent individual massive
Pop III stars. We have randomly sampled the mass of individual Pop III stars
from an assumed top-heavy initial mass function (IMF) over a range of
$[1-260]{\,M_{\odot}}$ with a functional form of

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

where $m_{\rm char}=30{\,M_{\odot}}$ is the characteristic mass. Above $m_{\rm
char}$, it follows a Salpeter-like IMF, but is exponentially cut off below
that mass (e.g. Chabrier, 2003; Wise et al., 2012). We have adopted a density
threshold of $n_{\rm th}=100~{}\mbox{cm}^{-3}$ above which the gas particle is
converted into a collisionless star particle by following the star formation
prescription described above.

####  2.3.2 Population II

Second-generation stars, formed out of metal-enriched gas, tend to be long-
lived, low-mass stars, unlike the first generation stars. Given their low
mass, the resolution here is insufficient to represent individual Pop II
stars. We therefore model Pop II stars to form as a stellar cluster, comprised
of a single stellar population. Two criteria, a density threshold of $n_{\rm
th}=100~{}\mbox{cm}^{-3}$ and a critical metallicity of $Z_{\rm
crit}=10^{-5.5}{\rm\,Z_{\odot}}$, are imposed for the creation of a Pop II
cluster, requiring that gas particles satisfy both conditions. The choice of
$Z_{\rm crit}=10^{-5.5}{\rm\,Z_{\odot}}$ is motivated by dust-continuum
cooling (e.g. Omukai, 2000; Bromm et al., 2001; Schneider & Omukai, 2010;
Safranek-Shrader et al., 2016), where dust cooling is responsible for further
gas fragmentation at high densities, $n_{\rm H}\gtrsim 10^{16}\rm cm^{-3}$,
enabling the formation of low-mass stars. Once a gas particle crosses the
density threshold, it is converted into a sink particle that immediately
accretes surrounding gas until reaching $M_{\ast,\rm
Pop~{}II}=500{\,M_{\odot}}$, thus representing a Pop II stellar cluster. For
the Pop II IMF, we adopt a standard Salpeter form, $dN/d\log m\approx
m^{-\alpha}$, with a slope $\alpha=1.35$ over the mass range of
$[0.1-100]{\,M_{\odot}}$.

###  2.4 Supernova feedback

In this section, we describe the implementation of the chemical and thermal
feedback from SNe. We consider SN explosions from individual Pop III stars and
from Pop II stellar clusters, separately following the element-by-element
metal species from Pop III and Pop II nucleosynthesis. In doing so, we can
distinguish the level at which a stellar population contributes to the total
metal content of a Pop II cluster. The metals associated with Pop III stars
originate from core-collapse SNe (CCSNe), or powerful pair-instability SNe
(PISNe), depending on the initial mass of the progenitor star, which is
randomly sampled from the assumed Pop III IMF. For the Pop II stellar
clusters, metals are released by winds from AGB stars, and/or by Type II and
Type Ia SNe. The heavy elements from all sources are transported into the
neighboring medium via diffusive mixing, enriching the gas clouds out of which
subsequent metal-enriched stars are formed. The SN explosion energy is
deposited onto the surrounding medium via thermal feedback. We briefly explain
the procedure next.

####  2.4.1 Chemical feedback: Population III stars

Given that the lack of metals renders mass loss by stellar winds almost
negligible (e.g. Kudritzki & Puls, 2000), the final fates of metal-free stars
are solely determined by their initial masses (see, e.g. Karlsson et al., 2013
for a review). For instance, stellar evolution theory predicts that in the
mass range between $10{\,M_{\odot}}$ and $40{\,M_{\odot}}$, Pop III stars are
expected to die as CCSNe. Highly energetic PISNe, which are triggered by
electron-positron pair creation, are expected for massive stars of
$140{\,M_{\odot}}\lesssim m_{\ast}\lesssim 260{\,M_{\odot}}$. Very massive
stars $m_{\ast}>260{\,M_{\odot}}$ might undergo direct collapse into a black
hole, because the thermonuclear energy release is not sufficient to reverse
the infall. We use the values for total ejected masses and metal yields of Pop
III CCSNe from Heger & Woosley (2010), who provide nucleosynthetic yields of
non-rotating primordial stars in the mass range of $10-100{\,M_{\odot}}$ by
exploring a range of explosion energies of $E_{\rm SN}=[0.3-10]\times 10^{52}$
erg and a range of mixing, $\eta=[0.0-0.25]$, between the stellar layers
during the explosion.

In our previous work (Jeon et al., 2017), we adopted a metal yield from Pop
III stars with an explosion energy of $E_{\rm SN}=1.2\times 10^{51}$ and a
mixing efficiency of $\eta=0.015$, which we will refer to as “normal yield".
Provided that faint Pop III SNe might be mainly responsible for the presence
of CEMP stars in the observed local dwarfs (reviewed in Nomoto et al., 2013;
also see Iwamoto et al., 2005; Tominaga et al., 2007; Ishigaki et al., 2014),
we also employ the yield from a faint SN with $E_{\rm SN}=0.6\times 10^{51}$
and $\eta=0.06$ (Heger & Woosley, 2010). We assume that 70$\%$ of Pop III
stars, with masses eligible for a CCSN death, experience a faint explosion,
while the remainder dies as a normal SN, and we refer such mixed occurrence
rate to “faint SN yield". We adopt the yields from Heger & Woosley (2002) for
PISNe. Finally, we only consider faint-SN yields for Pop III SNe, not for Pop
II SNe.

####  2.4.2 Chemical feedback: Population II stars

At the end of the life of Pop II stars, entering the red giant phase, they
experience strong mass loss. For instance, intermediate-mass stars
($0.8{\,M_{\odot}}\lesssim m_{\ast}<8{\,M_{\odot}}$) might lose up to $60\%$
of their mass during the terminal AGB phase. For AGB metal yields, we employ
the values from Marigo (2001), not considering the kinetic energy input from
AGB winds, given that the wind velocity is negligible compared to the velocity
dispersion in the ISM. Another metal input from a Pop II cluster is through
Type II SN explosions of massive stars ($m_{\ast}\gtrsim 8{\,M_{\odot}}$).
Here, we utilize the yields from Portinari et al. (1998), where mass loss on
the main sequence is considered. Metals are ejected over multiple timesteps,
whenever stars distributed according to the assumed IMF undergo SN explosions
within a given hydrodynamic timestep, $\Delta t=0.01-0.1$ Myr. Thus, massive
stars inject metals first, followed by relatively less massive stars. For
simplicity, the total Type II SN energy from a single Pop II cluster is
released at once at the end of the most massive star’s life in the cluster.

White dwarf remnants are the end-products of low-mass stars with masses below
$8{\,M_{\odot}}$. If such a white dwarf exceeds the Chandrasekhar limit,
either by mass transfer from a companion star or the merger of two white
dwarfs, a Type Ia SN is triggered. The large uncertainty originating from the
binary evolution makes it difficult to estimate the Type Ia SN rate, compared
to that of Type II SNe and AGB stars. We adopt empirical delay time functions
(e.g. Barris & Tonry, 2006; Förster et al., 2006), which are characterized by
e-folding times, $\eta(t)=e^{-t/\tau_{\rm Ia}}/\tau_{\rm Ia}$ where $\tau_{\rm
la}=$2 Gyr is the delay time. The SN Ia rate at a given timestep $\Delta t$ is
then $N_{\rm SN~{}Ia}(t;t+\Delta t)=a\int_{t}^{t+\Delta t}{f_{\rm
wd}(t^{\prime})\eta(t^{\prime})dt^{\prime}}$, where $a=0.01$ is a
normalization parameter and $f_{\rm wd}$ is the number of stars that have
evolved into white dwarfs per unit stellar mass (Mannucci et al., 2006). We
apply the Type Ia SN spherically symmetric “W7" model (Thielemann et al.,
2003) for Type Ia SN yields. The corresponding SN energy is also deposited
onto neighboring particles as thermal energy, but this feedback is likely to
be less effective in impacting the surrounding gas because the energy
injection takes place over billions of years.

####  2.4.3 Metal diffusion

Once metals are ejected from a SN explosion, they are evenly deposited onto
neighboring particles, $N_{\rm ngb}=32$, giving rise to the initial
metallicity, $Z_{i}=m_{\rm metal,i}/(m_{\rm SPH}+m_{\rm metal,i})$, where
$m_{\rm metal,i}=M_{\ast}y_{\rm eff}$. Due to the absence of a direct mass
flux among SPH particles, an explicit modelling of metal transport is
necessary. We utilize a diffusion-based method for the transfer of metals
implemented by Greif et al. (2009), where the diffusion strength is determined
by physical quantities at the resolution limit, here the scale of an
individual SPH particle (Klessen & Lin, 2003). The diffusion coefficient,
defined as $D=2$ $\rho$ $\tilde{v}$ $\tilde{l}$, can be expressed through a
characteristic scale, $\tilde{l}$, set by the smoothing length of the SPH
kernel, $\tilde{l}=h$, and the density, $\rho$, of the surrounding gas. The
velocity dispersion within the kernel, $\tilde{v}$, is computed via
$\tilde{v}_{i}^{2}=\frac{1}{N_{\rm ngb}}\sum_{j}|v_{i}-v_{j}|^{2}$, where
$v_{i}$ and $v_{j}$ are the velocities of particles $i$ and $j$ within the
kernel, respectively.

Figure 1: The growth of the virial mass of the UFDs in the zoomed-in region.
The galaxies, initially, start as minihaloes of $M_{\rm vir}\lesssim
10^{6}{\,M_{\odot}}$ at $z>13$ and evolve into systems of a few
$10^{8}{\,M_{\odot}}$ at $z=0$, where we find six $M_{\rm vir}\sim
10^{8}{\,M_{\odot}}$ haloes. We mark the epoch of reionization with the
vertical shaded region, where the UV background is introduced at $z=7$, and
its strength gradually increases up to $z\approx 6$. Figure 2: Star formation
rates for Pop III (black solid lines) and Pop II (blue dotted lines) as a
function of cosmic time in individual galaxies. Note that star formation
activities in all progenitor haloes, at a given epoch, are combined. The
galaxies in the top panels are from the run with normal SN yields, while the
bottom panels exhibit the results for the run assuming faint SN yields.
However, any differences between the two runs are due to the stochastic
implementation of the star formation process in our model, not the result of
using different metal yields. We find that star formation in all simulated UFD
analogs is completely quenched both by SN feedback and reionization at $z\sim
6$. Some cases, for instance, Halo1 N, Halo5 N, and Halo10 F, indicate self-
quenching a few Myr before the onset of reionization, implying that there was
not enough time for the gas evacuated by SN feedback to be replenished prior
to reionization.

####  2.4.4 Thermal feedback

The SN energy of an individual Pop III star is released at the end of its
lifetime in the form of thermal energy onto the neighboring gas particles. We
fix the Pop III SN energy to $E_{\rm CCSN,Pop~{}III}=10^{51}\,\mathrm{erg}$
and $E_{\rm PISN,Pop~{}III}=10^{52}\,\mathrm{erg}$ for an individual Pop III
CCSN and PISN, respectively. For a Pop II cluster, the total SN energy, to be
injected at once at the death of the cluster’s most massive star, is estimated
as $E_{\rm CCSN,Pop~{}II}=\epsilon_{\rm CCSN,Pop~{}II}\times M_{\ast,\rm
Pop~{}II}=1.8\times 10^{52}\,\mathrm{erg}$. Here, $\epsilon_{\rm
CCSN,Pop~{}II}=n_{\rm CCSN,Pop~{}III}\times 10^{51}\,\mathrm{erg}$ is the
total available CCSN energy per unit stellar mass, and $n_{\rm CCSN,Pop~{}II}$
the number of CCSNe in a Pop II cluster for the assumed Salpeter IMF
($[m_{0},m_{1}]=[11,40]{\,M_{\odot}}$). In general, the number of stars per
unit stellar mass resulting in SNe is defined as $n_{\rm
SN}=\int_{m_{0}}^{m_{1}}{\phi(m)}dm$. Here, $m_{0}$ and $m_{1}$ are the
minimum and maximum initial mass of stars encountering a SN explosion, and
$\phi(m)$ is the given IMF. We use the conventional SN energy of
$10^{51}\,\mathrm{erg}$ for Pop II stars. We release the total available SN
energy at once, 3 Myr after the formation of a Pop II cluster, which
corresponds to the lifetime of the most massive Pop II stars.

In order to circumvent the well-known overcooling problem, where the SN energy
is rapidly radiated away if the numerical resolution is not sufficient to
resolve the SN ejecta evolution (e.g. Stinson et al., 2007; Dalla Vecchia &
Schaye 2008; Torrey et al. 2014; Crain et al. 2015; for a comprehensive
discussion, see Read et al. 2016a), we employ the method proposed by Dalla
Vecchia & Schaye (2012), in which SN energy is imparted onto only a reduced
number of neighboring particles. This ensures a temperature jump of $\Delta
T\gtrsim 10^{7.5}$K, which is necessary to render SN feedback on the
surrounding gas effective. Additionally, we use a timestep-limiter (Saitoh &
Makino, 2009, Durier & Dalla Vecchia, 2012) to ensure that the ratio of
timesteps of neighboring particles is smaller than a factor of 4, as well as a
timestep-update procedure (Dalla Vecchia & Schaye, 2012), such that
neighboring gas particles become active in order to immediately react to a
sudden SN energy input.

##  3 Simulation results

In this section, we describe the results obtained from the simulations in
terms of two main categories. First, we discuss the SFH of the simulated UFDs
and show their resulting global properties. Second, we concentrate on the
stellar abundance ratios, and their dependence on the type of Pop III SNe,
normal or faint explosions. In addition, we compare the estimated carbon
abundances and the CEMP population with observational data.

###  3.1 Star formation history

In the zoomed-in region, there are a total of six $M_{\rm vir}\sim
10^{8}{\,M_{\odot}}$ galaxies at $z=0$, constituting our sample of UFD
analogs. Their progenitor haloes began with $M_{\rm vir}\sim
10^{6}{\,M_{\odot}}$ DM minihaloes at $z\gtrsim 13$, and have grown in mass
through mergers and accretion. We have performed two simulations in the
zoomed-in region in order to understand how the resulting stellar metal ratios
might change, depending on which Pop III SNe take place. In the first run, all
Pop III stars in the mass range of $10-100{\,M_{\odot}}$ die as conventional
CCSNe with normal metal yields (Halo1-N$-$Halo6-N). The other run is conducted
by assuming that 70$\%$ of Pop III stars in the CCSN mass range explode as
faint SNe, and the remaining 30$\%$ experience normal SN explosions
(Halo7-F$-$Halo12-F). Halo properties are listed in Table 1, where haloes are
listed in order of decreasing mass. Figure 1 shows the mass growth for
Halo1-N$-$Halo6-N, which is identical for Halo7 F$-$Halo12 F.

Given that stars are stochastically formed, the simulated galaxies experience
different SFHs. Figure 2 shows the star formation rates (SFRs) as a function
of cosmic time for the individual galaxies. We separately track Pop III and
Pop II star formation, by adding the star formation activities from all the
progenitor haloes at a given time. The galaxies in the top panels form in the
run with normal SN yields, while the bottom panels illustrate the SFRs arising
in the run with faint SN yields. We note that different SFHs should be
understood not as a consequence of the SN metal yields used, but reflecting
the randomness of the star formation process. SFRs vary from
$10^{-6}{\,M_{\odot}}\rm\,yr^{-1}$ to $10^{-2}{\,M_{\odot}}\rm\,yr^{-1}$. It
can be seen that star formation in all the simulated galaxies is completely
quenched both by SN feedback and reionization at $z\sim 6$. In some cases,
such as Halo1 N, Halo5 N, and Halo10 F, we encounter self-quenching, such that
star formation was already inhibited a few Myr prior to the onset of
reionization. This is a result of vigorous blow-out of the gas from the host
halo by SN feedback, with insufficient time to allow this material to re-
collapse.

Figure 3: Global properties of the simulated UFD analogs at $z=0$. The panels
(clockwise from upper left) show half-mass stellar radius, 1-d velocity
dispersion, average stellar metallicity, all as a function of stellar mass,
and stellar vs. virial (halo) mass. The resulting quantities for the 12
simulated UFD analogs with normal and faint SN metal yields in this study are
shown as red filled circles and diamonds, respectively (see Table 1), and we
add the results for both dSph and UFD analogs (pink squares) from Jeon et al.
(2017). The predictions for half-mass stellar radius, velocity dispersion and
stellar mass are in good agreement with observed MW UFDs (blue triangles) and
MW dSphs (light blue triangles). The stellar vs. halo mass relation for our
UFD analogs is in line with the empirical fit provided by Behroozi et al.
(2013). Meanwhile, we here predict average stellar metallicities that are
lower by about one dex, compared to the observed UFDs. The reason is that in
this work we resolve individual Pop III stars, enabling Pop II stars to form
immediately after a single Pop III SN explosion, thus leading to a subset of
very low-metallicity Pop II stars. Figure 4: Stellar carbon-to-iron ratios,
[C/Fe], vs. iron abundance, derived from our simulations. Top panels: All Pop
II stellar clusters, regardless of whether they are associated with UFDs at
$z=0$, for the runs with normal (left panel) and faint (right panel) SN metal
yields. We distinguish whether metals come from Pop III (pink circles) or Pop
II (blue circles) SNe, respectively. Evidently, [C/Fe] values from Pop III SNe
tend to be higher than those from Pop II events, implying that Pop III stars
are mainly responsible for high [C/Fe] ratios. We compare the simulated [C/Fe]
values with those observed for CEMP stars in the MW. These stars can be
classified into two groups, Group II (blue squares) and Group III (red
squares), indicated by green and yellow shaded ellipses, respectively (adopted
from Yoon et al. (2016)). As can be seen, CEMP stars with $\rm[C/Fe]\gtrsim
2.5$, consistent with Group III, are only produced via the metal yields from
faint SNe. Bottom panels: Results for stars residing in the simulated UFD
analogs. Here, we compare with [C/Fe] ratios of the observed local UFDs,
denoted by colored cross symbols.

###  3.2 Global properties

We present the global physical properties of the simulated UFD analogs at
$z=0$, as summarized in Figure 3. The panels (clockwise from upper left)
display the half-mass stellar radius ($r_{1/2}$), 1-dimensional velocity
dispersion ($\sigma$), average metallicity (<[Fe/H]>), each as a function of
stellar mass, and stellar vs. virial mass. We include quantities both from the
two cases with normal (red circles) and faint (red diamonds) SN metal yields.
We also exhibit the results from our earlier one in Jeon et al. (2017). In
Jeon et al. (2017) the stellar mass range was $M_{\ast}\approx[4-90]\times
10^{4}{\,M_{\odot}}$, covering both the observed UFDs and dSphs, whereas here,
we only explore the UFD mass range ($M_{\ast}\approx
10^{3}-10^{4}{\,M_{\odot}}$). As shown in the top panels, the half-mass
stellar radius and velocity dispersion, derived for the simulated UFDs and
dSphs, are in line with the values observed for analogous systems in orbit
about the MW (McConnachie, 2012). In the panel for the half-mass stellar
radius, we indicate surface brightness limits of 30 mag arcsec-2 and 32 mag
arcsec-2. Most of the simulated UFDs are observable with current facilities,
whereas some with large half-mass radius are within the fainter limit. We note
that the simulated galaxies with faint SNe tend to have a larger range of
$r_{1/2}$ than that of the normal SN case. It is understood that this is not
because of the difference in the metal yields, but rather due to the
randomness of star formation in the systems.

In interpreting the stellar vs. halo (virial) mass relation, we add results
from additional zoom-in hydrodynamic simulations (Munshi et al., 2013; Simpson
et al., 2013; Shen et al., 2014; Oñorbe et al., 2015; Wheeler et al., 2015;
Jeon et al., 2017; Wheeler et al., 2019), as well as from large-scale
simulations, whose results are encapsulated in the best fits, as shown with
dashed (Behroozi et al., 2013), dotted (Garrison-Kimmel et al., 2016), and
solid (Brook et al., 2014) lines. The simulated UFDs in this work are well
matched to the fit provided by Behroozi et al. (2013). For the stellar
mass$-$metallicity relation, we compare with observational data from Kirby et
al. (2013) and Simon (2019). The average metallicity, derived for our UFD
analogs, varies over a broad range, from <[Fe/H]>$\approx-1.9$ to $-3.6$,
reaching values that are significantly lower than the observations, and what
was found in our earlier work. Our derived range for the total stellar mass in
the UFD analogs ($M_{\ast}\approx 10^{3}-10^{4}{\,M_{\odot}}$), however, is
similar to the observations.

A possible explanation for the presence of such low metallicity stars, as
opposed to our earlier simulations, is the ability to resolve individual Pop
III stars. Here, a single Pop III SN explosion enables the transition in star
formation mode from Pop III to Pop II. For example, Jeon et al. (2014)
explored Pop II star formation in detail after such a single Pop III SN,
suggesting that an individual explosion with a progenitor mass of a few
$10{\,M_{\odot}}$ could enrich the ambient gas to a metallicity of
$Z=[1-4]\times 10^{-4}{\rm\,Z_{\odot}}$, thus causing the transition to Pop II
star formation. A similar metallicity for initial Pop II star formation, $\sim
3\times 10^{-4}{\rm\,Z_{\odot}}$, was reported by Chiaki & Wise (2019). The
reason for the higher average stellar metallicity in our previous work (Jeon
et al., 2017; pink squares in Fig. 3) is the numerical representation of Pop
III stars as a stellar cluster, not as individual stars, resulting in the
absence of low-metallicity outliers.

Such under-prediction of stellar metallicities in UFD analogs is found by
Wheeler et al. (2019) as well. As possible explanations, they suggest the lack
of pre-enrichment by Pop III stars or environmental effects of the more
massive host, from which metals could be transferred onto UFDs. The latter is
neglected in this work. Alternatively, such low metallicity could be a
consequence of unrealistically efficient stellar feedback, which would too
strongly disperse enriched gas, resulting in the absence of high metallicity
stars. Recently, Agertz et al. (2020) demonstrated that stellar metallicities
in UFD-like systems can be reduced by $1-1.5$ dex, when artificially
increasing SN energies by 10-100 times the fiducial value. The other global
properties, such as $r_{1/2}$, $M_{\ast}$, and $\sigma$, of the simulated UFDs
show good agreement with observations. To first order, we can understand this
by pointing out that such global quantities are mainly determined by dark
matter halo mass, whereas stellar metallicity tends to be sensitive to the
adopted subgrid models (Agertz et al., 2020).

###  3.3 Chemical abundances

####  3.3.1 Carbon

##### Pop III vs. Pop II contribution

Figure 4 shows the resulting [C/Fe] from the runs with normal SNe (left
panels) and faint SNe (right panels), comparing with the observational data.
We separately present the [C/Fe] ratios of all Pop II stellar clusters formed
in the high-resolution region at $z=0$ (top panels), and the [C/Fe] estimates
of Pop II clusters residing within the virial volume of the UFD analogs
(bottom panels). The top panels, therefore, contain more stars, including
those in the field, compared to the bottom panels. Furthermore, we consider
whether the metals originate from Pop III (pink circles) or Pop II (blue
circles) SNe, respectively, thus demonstrating that CEMP and C-normal stars
are mainly produced through different channels. For instance, it is evident
that the [C/Fe] values from Pop III stars (pink circles) are likely to be
higher than those from Pop II stars (blue circles) by $\sim 1-2$ dex, implying
that Pop III stars are mainly responsible for CEMP signatures with high [C/Fe]
ratios. On the other hand, C-normal stars appear to be associated with Pop II
enrichment, shown in blue circles. This trend is more pronounced in the case
of faint SNe, where the [C/Fe] ratios from Pop III SNe can reach up to
[C/Fe]$=3-4$, assuming that 70% of Pop III stars die as faint events.

When both cases with faint and normal SNe metal yields are combined, we find
that mono-enriched Pop II clusters by Pop III or Pop II SNe are 15% and 5%,
respectively. Here, mono-enrichment is defined as the case where the metal
contribution from Pop III or Pop II SNe is more than 99%. Therefore, most of
the stars are multi-enriched by metals both from Pop III and Pop II SNe, of
which 66% of the Pop II clusters are predominately polluted by Pop III SNe
meaning that more than 50% of metals arise from Pop III SNe. The remaining 34%
of the stars are found to be born out of gas contaminated mainly by Pop II
SNe.

Figure 5: Carbon abundances as probes of early star formation. $A$(C)-[Fe/H]
diagram (left panels) and [C/Fe]-[Fe/H] relation (right panels) of the
observed MW stars (red and blue squares) and the stars from the simulations,
assuming contributions from normal (green circles) and faint SNe (grey
circles). We show all Pop II clusters found in the zoom-in region, regardless
of whether they are bound to the UFDs. The observed CEMP stars in the MW halo
can be classified into Group II (blue squares) and Group III (red squares),
depending on their distinct locations in the $A$(C)-[Fe/H] space. The dashed
line corresponds to [C/Fe]=0.7, above which stars are defined as CEMP. Only
the stars formed out of gas ejected from faint Pop III SNe reproduce the stars
in the Group III region (yellow shaded ellipse), as can be seen in both the
$A$(C)-[Fe/H] and [C/Fe]-[Fe/H] diagrams. Figure 6: Top panels: Same as Fig.
5, but for the subset of stars that lie within the virial volume of the
simulated UFDs, comparing with the individual observed UFD stars (crosses with
different colors). We note that many Group III stars in the UFDs lack
counterparts in the simulation results, unlike the halo Group III stars.
Bottom panels: Same as the top panels, but comparing with the corresponding
abundances for the observed dSphs from observations (summarized in Yoon et al.
2019, x violet) and simulations (Jeon et al., 2017, pink squares). The
abundances derived in the present work, together with those of Jeon et al.
(2017), are in overall good agreement with the observational data both for
UFDs and dSphs.

##### Group II vs. Group III CEMP stars

We compare the combined group of all simulated Pop II clusters with the CEMP
stars found in the MW halo. As previously explained, Yoon et al. (2016) have
suggested that CEMP stars can be categorized as Group I (mostly, CEMP-$s$ or
CEMP-$r/s\,(i)$ stars, whose carbon is extrinsically enhanced by their AGB
binary companion), Group II ($\rm-5.0<[Fe/H]<-2.5$ and
$5.0<A(\textrm{C})<7.0$), and Group III ($\rm[Fe/H]<-3.5$ and
$A(\textrm{C})<7.5$), based on their distinct location in the $A$(C)-[Fe/H]
space. In particular, the latter two groups, mainly comprised of CEMP-no
stars, show different behaviors: the absolute carbon abundances of Group II
stars tend to be correlated with [Fe/H], whereas $A$(C) of Group III stars
appears to be uncorrelated with [Fe/H] (see Yoon et al., 2016, for more
detailed description). Yoon et al. (2019) have suggested, moreover, that the
CEMP-no stars in the local UFDs reside in both Groups II and III regions,
while those in more massive dSphs appear to be predominantly Group II stars.

Figure 4 shows that our simulations can well reproduce CEMP Group II and Group
III stars, when comparing with those two Group stars from the MW halo CEMP
stars and and the MW satellite dwarf galaxies (squares in the top panels) from
Yoon et al. (2016). We note that these observed carbon abundances are
evolution corrected values (Placco et al., 2014). Interestingly, we find that
the stars with the highest ratios of [C/Fe] $>$ 2.5 (right top panel of Figure
4) can only be produced by faint SNe. Also, the trend that [C/Fe] increases
with decreasing [Fe/H] appears to be found only in the run with faint SNe,
overlapping with the halo Group III stars (red squares encompassed by the
yellow ellipse). Faint SNe are possible for explaining such high [C/Fe]
values, due to their weak explosion, where heavy elements are locked up in the
core, while light elements such as carbon in the outer layers are released
into the ISM. The ambient gas contaminated by this explosion, therefore, is
destined to have a large [C/Fe] value, resulting in CEMP star formation. In
the bottom panels of Figure 4, we display the [C/Fe] ratios of the stars
within the simulated UFD analogs, comparing with those of the observed MW
UFDs333The original references for the abundance data of the UFDs are as
follows: Norris et al., 2010; Lai et al., 2011 (Bootes I); Ji et al., 2016a;
Roederer et al., 2016 (Reticulum II); Norris et al., 2010; Frebel et al., 2014
(Segue I); Ji et al., 2016b; Chiti et al., 2018b; Chiti et al., 2018a (Tucana
II); Frebel et al., 2010 (Ursa Minor II); Spite et al., 2018 (Pisces II);
Simon et al., 2010 (Leo IV); Frebel et al., 2010 (Coma Berenices). (crosses in
the bottom panels) from Yoon et al. (2019).

From further inspection of Figure 4, we draw two conclusions. First, it is
still valid that Group III CEMP-no stars are associated with Pop III SNe,
while C-normal stars appear to arise preferentially from Pop II SNe (Sarmento
et al., 2017; Yoon et al., 2019). Both Pop III and Pop II stars are
responsible for Group II CEMP stars though CEMP stars with [C/Fe]$\sim 2.0$
appear to be mainly contributed from Pop III SNe. Second, we point out that
there are no highly enhanced carbon stars, with [C/Fe]$\approx$3, in the
observed UFDs. The reason why we cannot find such stars in the observed UFDs
can be understood as follows. The MW halo CEMP-no stars with [C/Fe]$\gtrsim 3$
are all Group III and rare ultra metal-poor (UMP, [Fe/H]$<-4.0$) stars. Since
no UMP stars have been found yet in UFD galaxies, the absence of such
extremely carbon enhanced Group III stars is not surprising. The main
observational limitations of finding such stars in the UFDs stem from their
faint magnitude and small number statistics per galaxy. The metal-poor halo
stars in the MW greatly outnumber the member stars in the UFDs, and thus the
probability of finding Group III-like stars in the UFDs will be
correspondingly reduced. Nevertheless, several stars with high [C/Fe] from our
simulations are reasonably matched with the values from the run with faint
SNe, for instance, one star in Bootes I ([Fe/H]$\approx-3.84$, [C/Fe]$\approx
2.69$), and one in Segue I ([Fe/H]$\approx$-3.57, [C/Fe]$\approx 2.39$).

##### Faint vs. normal SN yields

To better understand the nature of CEMP stars in UFDs, we focus on the CEMP
Group morphology, exhibited in the $A$(C)-[Fe/H] diagram of Yoon et al.
(2016). In Figure 5 and Figure 6, we compare the resulting $A$(C) absolute
abundances (left panels) and [C/Fe] ratios (right panels) from the two runs,
adopting faint (grey circles) and normal SN (green circles) metal yields.
Figure 5 encompass all Pop II stars formed in the zoomed region, while Figure
6 presents stars contained only in the simulated UFD analogs. The dashed line
corresponds to the [C/Fe]$=0.7$ boundary, above which stars are considered as
CEMP. As mentioned earlier, the estimated ratios consistent with Group III
stars, shown as red squares with the averaged value of
$A\rm(C)_{avg,obs}\approx 6.8$, only arise via faint SN metal yields (grey
circles), exhibiting $A\rm(C)_{avg}\approx 6.7$. This tendency is also
demonstrated in terms of [C/Fe] ratios such that the averaged [C/Fe] ratio of
Group III stars with faint SNe is $\rm[C/Fe]_{avg}\approx 3.0$, about 0.3 dex
lower than the observed value of $\rm[C/Fe]_{avg,obs}\approx 3.3$, whereas it
is $\rm[C/Fe]_{avg}\approx 2.3$, adopting normal SNe. Both cases with normal
and faint SNe show the trend of the CEMP fraction to increase with decreasing
metallicity. About $15-20$% of the CEMP fraction below $\rm[Fe/H]\approx-2.5$
rises to $\sim 60-70$% at $\rm[Fe/H]<-5.5$. The behaviour of the CEMP fraction
is presented in the Appendix.

Stars in UFDs with high [C/Fe]$\approx 2.5-3.0$ ratios (top right panel of
Figure 6) can be produced, because relative metal ratios are insensitive to
the overall efficiency of the diffusion process. Thus, [C/Fe] ratios are
predominantly determined by initial yields of the faint SNe when metals are
released, as long as the mixing efficiency for each element is the same. Note
that multiple explosions from different progenitor stars, together with the
contribution from other metal sources, such as AGB stars and Type Ia SNe,
might modify the resulting [C/Fe].

On the other hand, our simulations, even for the faint SN run, fail to
reproduce the observed stars in the MW halo and UFDs with high absolute carbon
abundance of A(C)$\approx 7.0-7.5$. As Yoon et al. (2019) pointed out, UFD
systems with smaller gas mass than our current simulations may reproduce such
stars because of less dilution of both carbon and iron abundance, leading to
higher $A$(C) and [Fe/H] values. Such incapacity of producing CEMP-no stars
with high $\rm A(C)>7.0$ might indicate that we should consider UFD analogs
even smaller than $\rm M_{\rm vir}<10^{8}{\,M_{\odot}}$ ($z=0$), in which gas
reservoir eligible for the metal mixing can be minimized. However, we should
mention that the mass of gas able to mix with the metals cannot be arbitrarily
small. Recently, Magg et al. (2020) demonstrated that the gas enclosed in the
final size of the SN remnant could be available for mixing, preventing the
metallicity in subsequent stars from becoming too large. Given that the
minimum dilution mass suggested by Magg et al. (2020) is based on a single SN
explosion, in a case where multiple SN explosions occur in a small halo, we
expect that the resulting metallicity can be boosted further despite the fact
that there should be the minimum dilution gas mass.

##### UFDs vs. dSphs

We also compare the observed $A$(C) and [C/Fe] values from the MW dSphs (data
from Yoon et al. 2019) with those from the simulated low-mass dSphs by Jeon et
al. (2017) in the bottom panels of Figure 6. For the latter, we only plot the
stars in the two dSph analogs with $M_{\rm vir}\approx[2-3]\times
10^{9}{\,M_{\odot}}$ and $M_{\ast}\approx 10^{5}-10^{6}{\,M_{\odot}}$ (at
$z=0$), values that are 10 (3) times larger than the halo (stellar) masses
encountered in this work. Overall, the simulated UFDs in this work and the
dSphs in Jeon et al. (2017) show good agreement with the observational data in
both the $A$(C)-[Fe/H] and [C/Fe]-[Fe/H] relations. In the $A$(C)-[Fe/H]
diagram, the average [Fe/H] of dSphs is shifted toward higher values by $\sim$
1 dex due to their extended SFHs, as was previously established (e.g. Tolstoy
et al., 2009; Salvadori et al., 2015; Yoon et al., 2019). On the other hand,
UFDs have experienced relatively short SFHs, at an epoch before the Universe
was significantly enriched with metals, thus resulting in the prevalence of
metal-poor stars.

Jeon et al. (2017) already suggested that C-normal stars are associated with
Pop II nucleosynthesis, whereas CEMP stars are suggested to arise from normal
Pop III SNe. Note that they only considered normal Pop III SNe in their work,
leading to the absence of CEMP stars with very high ratios of $\rm[C/Fe]>2$.
In this work, however, we demonstrate that stars with $\rm[C/Fe]\gtrsim 2$ are
predominately enriched by metals released by faint SNe. It is still unclear
whether the origin of CEMP stars in UFDs and dSphs is fundamentally different
(e.g. Yoon et al., 2019). However, as UFDs experience truncated SFHs early on,
in contrast to those of dSphs, it is highly plausible that stars in UFDs are
more likely to retain the signature of Pop III stars. Furthermore, some of
them may have hosted faint SNe, resulting in stars with the unusual signature
of very high [C/Fe]. In particular, our simulations confirm the claim in Yoon
et al. (2019) that the CEMP stars in dSphs (with $M_{\rm vir}\approx
10^{9}{\,M_{\odot}}$) predominantly formed from normal CCSN-enriched material,
whereas those in UFDs were born out of the ejecta from both normal and faint
SNe in their low-mass hosts ($M_{\rm vir}\gtrsim 10^{6}{\,M_{\odot}}$). This
latter formation channel is clearly evident in the bottom panels of Figure 6.

Figure 7: Stellar carbon and $\alpha$-element abundances in select haloes. We
consider normal (left two columns) and faint (right two columns) SN metal
yields. Compared to the estimates from observed UFDs (cross colored symbols),
it appears that metals from Pop III stars (pink circles) mainly contribute to
the composition of CEMP stars. On the other hand, the observed stars with
relatively low ratios of [C/Fe] $<0.7$ (C-normal stars) over the metallicity
range of $Z\sim 10^{-2}-10^{-3}{\rm\,Z_{\odot}}$ are in better agreement with
the ratios originating from Pop II stars (blue circles). Meanwhile, assuming
faint SN metal yields (right two columns), the derived ratios from the
simulations tend to be higher than the ones observed in UFDs by $1-2$ dex.

##### Comparison with other work

We note that our results do not imply that our chosen yields uniquely explain
the metal abundances of the local UFDs, because we somewhat arbitrarily assign
those yields. Although we here distinguish Pop III SNe as faint or normal
simply by their explosion energy, metal yields also depend on additional
physics, such as the mixing between stellar layers, even for the same SN
energy (e.g. Joggerst et al., 2009; Heger & Woosley, 2010), or the
dimensionality of the assumed nucleosynthesis model (e.g. Chen et al., 2017).
For our chosen model, the ranges of [C/Fe] ratios that normal and faint SNe
metal yields can produce are $\rm[C/Fe]=[-0.43,2.2]$ and
$\rm[C/Fe]=[-0.38,4.6]$, respectively. As the Pop III progenitor mass
increases, the [C/Fe] ratio generally rises. The values, especially, at the
characteristic mass of Pop III stars are $\rm[C/Fe]\approx 1.3$ (normal SN)
and $\rm[C/Fe]=3.3$ (faint SN). Finding the progenitor masses of the SNe that
give rise to CEMP stars requires to match not only the carbon and iron
abundance, but also a more comprehensive pattern of heavy elements. As an
example, Placco et al. (2016) analyzed metallicity patterns of 20 observed
ultra metal poor (UMP) stars in terms of the Pop III nucleosynthesis model
provided by Heger & Woosley (2010), suggesting that they can be described by
Pop III stars with masses $m_{\ast}=20.5-28{\,M_{\odot}}$, exploding as faint
SNe ($0.3-0.9\times 10^{51}$ erg).

To the contrary, Ishigaki et al. (2018) argued that these stars are well
matched with Pop III stars of $m_{\ast}\lesssim 40{\,M_{\odot}}$, half of
which require hyper-energetic SNe ($\rm E_{SN}\approx 10^{52}erg$) with a
progenitor mass of $m_{\ast}=25{\,M_{\odot}}$, based on the fallback-mixing
model (e.g. Umeda & Nomoto, 2005; Tominaga et al., 2007). The difference
between the two models is that mixing and fallback in the former are achieved
within a spherical shell, whereas the latter assumes jet-like fallback, which
can lead to strong fallback even for hyper-energetic events. Furthermore, the
origin of the two different classes, CEMP and C-normal stars, can be explained
in various ways. Here, we account for this dichotomy only in terms of Pop III
vs. Pop II SN enrichment. Alternatively, the two classes might be the
consequence of inhomogeneous mixing of the ejected elements from a single Pop
III explosion with the pristine gas within local ISM (Ritter et al., 2015;
Sluder et al., 2016; Hartwig & Yoshida, 2019) prior to their formation.

We note that Group III-like stars have not been yet reproduced by any
simulations, even ones considered the inhomogeneous mixing, unlike Group II-
like stars (Hartwig & Yoshida, 2019). Recently, Komiya et al., 2020 have
attempted to reproduce the observed CEMP-no stars using the StarTree, a merger
tree code implementing mixing and fallback models for Pop III faint SNe. They
demonstrated the difficulty of generating the observed CEMP-no stars despite a
variety of choices for the model parameters of faint SNe. One of the suggested
ways of obtaining CEMP-no stars is to reduce the swept-up mass by SNe and the
diffusion coefficient, but it leads to the overproduction of UMP stars
compared to the observational data. Such UMP stars could be the possible
consequence of Pop III faint SNe. For instance, Chiaki et al. (2020), where
they explored the degree of pollution by an individual faint SN in a minihalo,
showed that a faint SN can enrich nearby gas clouds with $\rm A(C)=3.8-4.9$ at
the extremely metal-poor regime, $\rm[Fe/H]\lesssim-8\sim-9$. They explained
the predicted $A$(C) values of the gas clouds, lower than the estimates of the
observed CEMP-no stars ($\rm A(C)>6$), are attributed to the small metal mass
from faint SNe and the fraction of the reincorporated metals into the clouds.
However, as they only considered a single Pop III star formation in a
minihalo, multi-enrichment from several SNe events might boost the level of
enrichment.

We caution that the observational data set provided by Yoon et al. (2016)
should be regarded as an upper limit. According to a recent study by Norris &
Yong (2019), when considering the 3-dimensional (3D), local thermodynamic
equilibrium (LTE) and 3D, non-LTE (NLTE) corrections for iron and carbon, the
estimate of [C/Fe] can be changed significantly. This is because in the
1-dimensional (1D), LTE assumption, carbon is overestimated while iron is
underestimated, resulting in a high [C/Fe] ratio. They show that the number of
CEMP-no stars ([C/Fe]>0.7, [Fe/H]<-2.0) from Yoon et al., 2016, based on 1D
LTE, might decrease by 48% and 73% due to 3D, LTE and 3D, NLTE effects,
respectively. This result, especially, causes a large change in the fraction
of Group II, but the prediction about Group III stars, which intrinsically
have a large amount of carbon, is unlikely to be affected.

####  3.3.2 $\alpha$-elements

In Figure 7, we show two key stellar abundances, [C/Fe] and [$\alpha$/Fe], for
the selected individual UFD analogs in the zoomed-in region, assuming normal
(left two columns) and faint SN yields (right two columns). Here, the observed
UFD $\alpha$ abundances are from Vargas et al. (2013). Even for individual UFD
analogs, the trends found for the combined UFD sample are valid, in that CEMP-
no stars mainly arise from Pop III enrichment, and that [C/Fe] ratios
originating from faint SNe are higher by 1-2 dex than from normal SNe. The
$\rm[\alpha/Fe]$ ratios also show a similar trend: the average value of
<$\rm[\alpha/Fe]$>$=1.24$, when considering faint SNe, is $\sim$0.5 dex higher
than the case with normal SN events (<$\rm[\alpha/Fe]$>$=0.74$).

Compared with our previous work (Jeon et al., 2017), adopting the same normal
yields, the estimate of <$\rm[\alpha/Fe]$>$=0.74$ for the simulated UFDs in
this work is $\sim$0.24 dex higher than the averaged value of
<$\rm[\alpha/Fe]$>$=0.50$ for the more massive dwarfs ($M_{\rm vir}\approx
10^{9}{\,M_{\odot}}$ at $z=0$). This difference implies that the larger the
system, the lower the $\rm[\alpha/Fe]$ ratio, as Type Ia SNe release more iron
during their extended SFHs. Finally, we should note that none of the simulated
UFD analogs reaches the high metallicity of [Fe/H]$\sim-1$, observed in Ursa
Major I (UMa I) and Ursa Major II (UMa II), although they lie in a similar
stellar mass range, $M_{\ast}=1.4\times 10^{4}{\,M_{\odot}}$ (UMa I), and
$M_{\ast}=4.1\times 10^{3}{\,M_{\odot}}$ (UMa II). In the simulations, such
metal rich stars, with [Fe/H]$\approx-1$, can be produced when the stellar
mass of a galaxy reaches $M_{\ast}\approx 8\times 10^{5}{\,M_{\odot}}$ (Jeon
et al., 2017). Such metal-rich stars, however, are unlikely to preserve the
signature of the initial Pop II and Pop III contributions. Instead, their
birth clouds were more likely to be contaminated by the nucleosynthetic yields
from multiple generations of star formation.

##  4 Summary and Conclusions

We have carried out cosmological hydrodynamic zoom-in simulations to
understand the role of faint SNe in the formation of CEMP-no stars in the MW
halo and its satellite galaxies. We investigate the simulated galaxies with
masses of $M_{\rm vir}\approx 10^{8}{\,M_{\odot}}(M_{\ast}\lesssim 10^{5}$) at
$z=0$, which can be considered as direct analogs of UFDs in the local
Universe. In order to resolve such low-mass dwarfs, we achieve high resolution
with $m_{\rm DM}\simeq 500{\,M_{\odot}}$ and $m_{\rm gas}\simeq
60{\,M_{\odot}}$ for dark matter and gas particles, respectively.

Color-magnitude diagrams of local UFDs indicate that they experienced
relatively short SFHs at early times, resulting in only ancient stellar
populations (e.g. Brown et al., 2014; Weisz et al., 2014). As such, UFDs offer
a unique window into the characteristics of the first generation of stars,
formed a few hundred million years after the Big Bang. CEMP-no stars could be
one of the most important empirical features, among metal-poor stars both in
the MW halo and UFDs, which might preserve unique signatures of Pop III stars.
In this work, we explore the origin of CEMP-no stars by considering the
contribution of Pop III faint SNe on their birth clouds. We compare
specifically the role of faint-SNe with that of the normal-SNe on the
formation of CEMP-no stars. By comparing our results with the observed CEMP-no
stars in the MW halo and dwarf galaxies, we have shown in this work that such
weakly exploding Pop III SNe provide one of the favored pathways for
generating CEMP-no stars. We summarize more specific main findings as follows.

  * •

The simulated UFDs stop forming stars due to both reionization and SN
feedback, leading to short SFHs. Some haloes experience self-quenching solely
through SN explosions, halting further star formation already a few Myrs prior
to the onset of reionization. Such event occurs if there is not enough time
for the evacuated gas due to SN feedback to fall back into its host halo
before reionization.

  * •

The global properties of the simulated UFDs, such as stellar mass, velocity
dispersion, and half-mass stellar radius, are in excellent agreement with
observational data. However, we predict a broader metallicity range, including
values similar to observations, but extending to ones that are lower by about
1.0 dex.

  * •

We confirm the results from Jeon et al. (2017) that enrichment from Pop III
stars is mainly responsible for the formation of CEMP-no stars with high
ratios of $\rm[C/Fe]\gtrsim 2$. In contrast, CEMP stars with $\rm[C/Fe]<2$
including C-normal stars ($\rm[C/Fe]<0.7$) are attributed to the metals
ejected from Pop II stars.

  * •

The inclusion of faint SN yields enables the formation of stars with very
large ratios of $\rm[C/Fe]=2-4$ at $\rm[Fe/H]\lesssim-4$, consistent with the
observed stars in the MW halo rather than those in UFDs. Meanwhile, we find
that the [C/Fe] vs. [Fe/H] relation for the stars in the observed UFDs can be
understood in terms of both faint and normal SNe: [C/Fe], [Fe/H], and $A$(C)
values of the stars in the local UFDs are well matched with normal SNe
contribution, whereas some stars with high [C/Fe] or $A$(C) require metal
yields synthesized via faint SNe.

  * •

In the $A$(C)-[Fe/H] diagram, our simulations can reproduce the two CEMP-no
sub-groups, Group II and Group III (Yoon et al., 2016) in the MW halo and
satellite dwarf galaxies. Specifically, we reproduce the trend that Group II
stars are predominantly originated from normal SNe and exhibit a correlation
between $A$(C) and [Fe/H]. In contrast, the high $A$(C) values ($\gtrsim$ 6.5)
of the Group III stars arise mainly from faint SNe yields and do not have a
dependence on [Fe/H].

  * •

Although we find that faint SNe can create Group III-like stars in terms of
$\rm[C/Fe]\approx 3-4$ and $\rm A(C)>6.5$ at $\rm[Fe/H]\lesssim-3.5$, it is
still difficult to generate CEMP-no stars with extreme level of absolute
carbon ($\rm 7.0\lesssim A(C)\lesssim 7.5$), observed both in the MW halo and
UFDs. It might imply that we need even less massive haloes ($\rm M_{\rm
vir}<10^{8}{\,M_{\odot}},z=0$) to reproduce Group III-like CEMP-no stars with
$\rm A(C)>7.0$. Because less dilution of metals with small gas reservoir would
result in CEMP-no stars with high $A$(C) value.

  * •

The simulation-derived [C/Fe] vs. [Fe/H] and $A$(C) vs. [Fe/H] relations for
dSphs from Jeon et al. (2017) are in line with the observed values. The
overall shift towards higher metallicity for dSphs is due to their extended
SFHs, compared to those of UFDs.

Given that detecting the light emitted from the first generation of stars will
be extremely challenging even with the upcoming JWST (e.g. Magg et al., 2018;
Liu & Bromm, 2020), stellar archaeology will play a crucial role to study the
nature of the first stars, in particular, in local dwarf galaxies. This
approach offers an alternative window by providing great details to
characterize the first stars and complementary understanding to far-field
cosmology. Future observations with greatly improved spectroscopic sensitivity
provided by the Giant Magellan Telescope (GMT), the Thirty Meter Telescope
(TMT), and the European Extremely Large Telescope (E-ELT) promise to reveal
the chemical fingerprint left behind by early cosmic history. Furthermore,
metal-poor gas clouds contaminated by the heavy elements released by the
first-generation SNe, can be scrutinized for hints to connect the local
Universe with that at high-$z$ (e.g. Cooke et al., 2017; Jeon et al., 2019).
This is further complemented by probes of the diffuse intergalactic medium at
early cosmic times (Wang et al., 2012). The first stars continue to be elusive
but the combined local and high-redshift searches promise to greatly intensify
the hunt.

## acknowledgements

We thank the anonymous referee for constructive and insightful comments that
improved the clarity of our paper. We are grateful to Volker Springel, Joop
Schaye, and Claudio Dalla Vecchia for permission to use their versions of
gadget. G. B. acknowledges support from HST Grant 15030. J.Y. acknowledges
support by the National Science Foundation under Grant No. PHY-1430152 (JINA
Center for the Evolution of the Elements). The simulations were performed
using the El Gato cluster at the University of Arizona, which is funded by the
National Science Foundation through Grant No. 1228509. We utilized yt for data
visualization and analysis tools. M. J. is supported by the National Research
Foundation (NRF) grant No. 20180564, funded by the Korean government (MSIT).
The authors acknowledge the Texas Advanced Computing Center (TACC) at The
University of Texas at Austin for providing HPC resources under XSEDE
allocation TG-AST120024.

## DATA AVAILABILITY

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

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##  Appendix A fraction of CEMP stars

We display in Figure A1 the fraction of CEMP stars from the two simulations
with faint (grey) and normal (blue) SN metal yields, comparing with the
observational data (Yoon et al., 2016). Note that the observed carbon
abundances are evolution corrected values (Placco et al., 2014).

Figure 8: Cumulative fraction of CEMP stars, defined as $\rm N([C/Fe]\geq
0.7)/N(\leq[Fe/H])$, as a function of [Fe/H]. In both simulations with normal
and faint SN metal yields, the fraction of CEMP stars tends to increase with
decreasing metallicity, showing a good agreement with observational data
provided by Yoon et al. (2016). However, we caution that the observed CEMP
fraction can be reduced up to 73% when 3D, NLTE effects are taken into account
(e.g. Norris & Yong, 2019).