11institutetext:  Dipartimento di Fisica e Astronomia, Universitá degli Studi
di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italy.
11email<EMAIL_ADDRESS>22institutetext: INAF/Osservatorio
Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy.

# Tracing Pop III supernovae with extreme energies
through the Sculptor dwarf spheroidal galaxy††thanks: ESO ID 107.22SJ; Based
on observations made with ESO VLT at the La Silla Paranal observatory under
programs ID 107.22SJ, and 0101.B-0189, 0101.D-0210, as well as on data
obtained from the ESO Science Archive Facility

Á. Skúladóttir 1122 I. Vanni 1122 S. Salvadori 1122 R. Lucchesi 11

The Sculptor dwarf spheroidal galaxy is old and metal-poor, making it ideal to
study the earliest chemical enrichment in the Local Group. We followed up the
most metal-poor star known in this (or any external) galaxy, AS0039, with
high-resolution ESO VLT/UVES spectra. Our new analysis confirmed its low
metallicity, $\rm[Fe/H]_{LTE}=-3.90\pm 0.15$, and that it is extremely C-poor,
with $\rm A(C)=+3.60$, which corresponds to $\rm[C/Fe]_{LTE}=-0.33\pm 0.17$
(accounting for internal mixing). This adds to the evidence of Sculptor being
intrinsically C-poor at low $\rm[Fe/H]\lesssim-3$. However, here we also
report a new discovery of a carbon-enhanced metal-poor star in Sculptor,
DR20080, with no enhancement of Ba (CEMP-no), indicative of enrichment by
zero-metallicity low-energy supernovae, $E_{\textsl{SN}}<1\times 10^{51}$.
This is the first evidence of a dual population of CEMP-no and C-normal stars
in Sculptor at $\rm[Fe/H]\leq{-3}$. The fraction of CEMP-no stars is still
low, $f^{\textsl{Scl}}_{\textsl{CEMP}}=9^{+11}_{-8}\%$ at
$\rm-4\leq[Fe/H]\leq-3$, compared to the significantly higher fraction in the
Milky Way halo, $f^{\textsl{MW}}_{\textsl{CEMP}}\approx 40\%$. To further
investigate the early chemical enrichment of Sculptor, we re-derive chemical
abundances of light, $\alpha$-, iron peak, and neutron-capture elements in all
Sculptor stars at $\rm[Fe/H]\leq-2.8$, with available high-resolution spectra.
Our results show that at these low [Fe/H], Sculptor is deficient in light
elements (e.g. C, Na, Al, Mg) relative to both the Milky Way halo, and ultra-
faint dwarf galaxies, pointing towards significant contribution of high-energy
supernovae. Furthermore, the abundance pattern of the star AS0039 is best
fitted with a zero-metallicity hypernova progenitor, $E_{\textsl{SN}}=10\times
10^{51}$, with a mass of $M=20$ M⊙. Our results in Sculptor, at
$\rm[Fe/H]\leq-3$, therefore suggest significant enrichment by both very low-
energy supernovae and hypernovae, solidifying this galaxy as one of the
benchmarks for understanding the energy distribution of the first supernova in
the Universe.

###### Key Words.:

Galaxies: dwarf galaxies – Galaxies: individual (Sculptor dwarf spheroidal) –
Galaxies: abundances – Galaxies: evolution

##  1 Introduction

The properties of the first stars in the Universe remain elusive. Although the
impact of the first stellar generation was significant, as they provided the
first ionizing radiation, metals and dust in the Universe, their study is
challenging. No metal-free (Pop III) star has been observed to date, and it is
unclear whether the newly launched JWST telescope will be able to directly
observe Pop III galaxies (Wang et al., 2022) or Pop III supernovae (SN; e.g.
Regős et al. 2020; Yan et al. 2023).

At the present moment, the most convincing observational constraints for the
properties of Pop III stars come from observing ancient stars in the Milky Way
and its satellite galaxies. In particular, the carbon-enhanced metal-poor
stars (CEMP-no; $\rm[C/Fe]>+0.7$, no Ba or Eu enhancements; e.g. Beers &
Christlieb 2005; Norris et al. 2013; Bonifacio et al. 2015; Norris & Yong
2019) are commonly accepted as the direct descendants of Pop III stars,
$10\lesssim M_{\star}/M_{\odot}\lesssim 100$, which ended their lives as faint
supernovae, polluting their environments mainly with C and the lighter
elements ($Z<20$) resulting in very high [C/Fe] ratios (e.g. Iwamoto et al.,
2005a; Marassi et al., 2014; de Bennassuti et al., 2017; Hartwig et al., 2018;
Welsh et al., 2022; Rossi et al., 2023). The fraction of these CEMP-no stars
in the Milky Way becomes higher towards lower metallicity, with
$f^{\textsl{MW}}_{\textsl{CEMP}}=40\%$ at $\rm[Fe/H]\leq-3$, and as high as
$f^{\textsl{MW}}_{\textsl{CEMP}}=80\%$ at $\rm[Fe/H]\leq-4$ (e.g. Placco et
al., 2014). The small ultra-faint dwarf galaxies (UFD) seem to follow the same
pattern, with very high ratios of CEMP-no stars, compatible with the Milky Way
halo (e.g. Salvadori et al. 2015; Ji et al. 2020). However, the situation is
less clear in the more massive dwarf galaxies.

Figure 1: Position on the sky (left) and location on the RGB (right) for our
Sculptor stellar sample, based on Gaia DR3 (Table 2). Star symbols with labels
are stars with new spectra, for the first time analysed here; while large blue
circles are stars with available literature spectra, reanalysed here. Small,
light blue points are stars from Gaia eDR3 within 1.5 deg radius of the center
of Sculptor.

The Sculptor dwarf spheroidal (dSph) galaxy is one of the the best studied
systems at low metallicity (Tafelmeyer et al., 2010; Frebel et al., 2010a;
Kirby & Cohen, 2012; Starkenburg et al., 2013; Skúladóttir et al., 2015b;
Skúladóttir et al., 2021; Jablonka et al., 2015; Simon et al., 2015; Chiti et
al., 2018). Its stellar population is predominantly old, $>10\,$ Gyr (de Boer
et al., 2012; Bettinelli et al., 2019), metal-poor,
$\rm\langle[Fe/H]=-1.8\rangle$, and its chemical abundances are relatively
homogeneous (Kirby et al., 2009, 2010; Skúladóttir et al., 2015a; Skúladóttir
et al., 2017, 2018, 2019; Hill et al., 2019; de los Reyes et al., 2020). Until
now, however, only one very metal-poor ($\rm[Fe/H]\leq-2$) star has been
discovered to be C-rich relative to the normal population (and with
$\rm[Ba/Fe]<0$), i.e. the CEMP-no star ET0097 at $\rm[Fe/H]=-2$ (Skúladóttir
et al., 2015b), while none has been confirmed with intermediate- to high-
resolution spectroscopy at $\rm[Fe/H]\leq-3$. The fraction of CEMP-no stars
therefore seems significantly smaller than in the Milky Way,
$f^{\textsl{Scl}}_{\textsl{CEMP}}<25\%$ at $\rm[Fe/H]\leq-3$ (Starkenburg et
al., 2013; Skúladóttir et al., 2015b).

As valuable as the CEMP-no stars are, they are only expected to probe a
limited fraction of the parameter space of the first stars, characterised by
low energy of their supernovae. The Pop III stars are predicted to end their
lives as SN of a range of explosion energies (Heger & Woosley, 2002), but this
remains poorly explored. However, recently, stars have been identified in
Sculptor (Skúladóttir et al., 2021) and the Milky Way halo (Placco et al.,
2021; Mardini et al., 2022) which show evidence of being imprinted by high-
energy SNe. It still remains unclear whether the smaller UFDs would be able to
retain the products of such high energy Pop III SNe (e.g. Rossi et al. in
prep.). The initial mass function (IMF) at birth of Pop III stars has been
predicted to be top-heavy (e.g. Hirano et al., 2015; Sharda & Krumholz, 2022;
Sharda et al., 2023), i.e. that the first stars were typically more massive
than present day stars. This conclusion is supported by models using the non-
detection of Pop III to constrain the IMF of the first stars (Magg et al.,
2018, 2019; Rossi et al., 2021). In particular, Pop III stars in the mass
range $140\leq M_{\star}/M_{\odot}\leq 260$ are predicted to explode as pair-
instability supernovae (PISN), enriching their environment with unique yields,
showing very strong odd-even effect (e.g. Heger & Woosley, 2002; Salvadori et
al., 2019; Aguado et al., 2023). Small UFD galaxies are unlikely to be able to
retain the products of the very energetic PISN. Their descendants are
therefore more likely to be found in more massive systems such as dSph
galaxies, or the Galactic bulge (Pagnini et al., 2023).

The ancient and metal-poor Sculptor dSph offers a unique opportunity to expand
our current knowledge of the first population of stars in the Universe. Being
significantly larger, $M_{tot}\gtrsim 4\times 10^{8}$ (Battaglia et al., 2008)
than the UFD galaxies, Sculptor is likely to retain more of the products of
high-energy SN, which might be lost in galaxies with a smaller potential well.
Currently, Sculptor is the external galaxy with most known stars at
$\rm[Fe/H]\leq-3$, many of which have been observed with high-resolution
spectra, necessary for detailed and high-precision abundance analysis. Here we
add pieces to the Pop III puzzle with: (i) an analysis of a new high-quality
spectra of one of the most metal-poor star in any external galaxy, AS0039;
(ii) the discovery of the first CEMP-no star in Sculptor at $\rm[Fe/H]\leq-3$;
and (iii) a homogeneous (re)analysis of the 11 most metal-poor stars in
Sculptor which have high-resolution ($R\gtrsim 20\,000$) spectra, including
one unpublished star at $\rm[Fe/H]=-2.8$. Thereby we provide the most complete
picture of the earliest chemical evolution of any external galaxy to date.

Table 1: Observational log for the new spectra, analysed here for the first time. Star | ESO facility | Exp time | $\lambda$ | Resolution | S/N
---|---|---|---|---|---
|  | [h] | [nm] |  |  [pxl-1]
AS00039 | UVES (blue) | 12 | 326-454 | 20 000 | 31@444nm
| UVES (red) | 12 | 458-668 | 40 000 | 43@666nm
DR20080 | X-Shooter (UVB) | 1 | 300-550 | 5 400 | 12@444nm
| X-Shooter (VIS) | 1 | 550-1020 | 8 900 | 18@600nm
UHAL004 | FLAMES/GIRAFFE | 4 | 397-427 | 6 000 | 26@444nm
| FLAMES/UVES | 20 | 480-680 | 47 000 | 32@600nm
Table 2: Positions, magnitudes and atmospheric parameters of the stellar sample, including references to literature work (in parenthesis when the spectrum is different from that analysed here). Typical random errors on the stellar parameters are: $\Delta\mathrm{T_{eff}}=86\,$K; $\Delta\mathrm{\log g}=0.14$; and $\Delta\mathrm{v_{turb}}=0.1\,\mathrm{km\,s^{-1}}$.  Star | RA | Dec. | G | $\mathrm{T_{eff}}$ | $\mathrm{\log g}$ | $\mathrm{v_{turb}}$ | Ref.
---|---|---|---|---|---|---|---
| hh:mm:ss | hh:mm:ss | mag | [K] |  | $\mathrm{km\,s^{-1}}$ |
HR sample |  |  |  |  |  |  |
AS00039 | 00:58:45.60 |  $-$ 33:42:21.8 | 16.932 | 4372 | 0.76 | 2.0 | (1)
AF20549 | 01:00:47.84 |  $-$ 33:41:03.2 | 17.940 | 4758 | 1.37 | 1.8 | 2,3
JS14296 | 00:59:38.76 |  $-$ 33:46:14.6 | 18.783 | 4929 | 1.79 | 1.7 | 3
JS66402 | 01:00:00.41 |  $-$ 33:29:15.5 | 18.774 | 4985 | 1.81 | 1.7 | 3
MT00749 | 01:00:05.02 |  $-$ 33:61:16.6 | 17.973 | 4797 | 1.41 | 1.8 | 3,4
MT00750a | 01:00:01.15 |  $-$ 33:59:21.4 | 18.271 | 4876 | 1.56 | 1.8 | 3,4
PJ00206 | 01:01:26.76 |  $-$ 33:02:59.8 | 16.687 | 4359 | 0.65 | 2.0 | 5,(6)
PJ03059 | 01:01:22.25 |  $-$ 33:46:21.9 | 17.538 | 4618 | 1.14 | 1.9 | 5
PJ03111 | 00:57:10.22 |  $-$ 33:28:35.8 | 17.460 | 4650 | 1.13 | 1.9 | 5,(6)
PJ07402 | 00:57:34.85 |  $-$ 33:39:45.7 | 17.758 | 4608 | 1.22 | 1.8 | 5,(6)
UHAL004 | 01:01:49.43 |  $-$ 33:54:10.4 | 16.521 | 4202 | 0.49 | 2.0 | -
LR sample |  |  |  |  |  |  |
DR20080 | 00:57:44.16 |  $-$ 33:61:14.3 | 17.839 | 4682 | 1.29 | 1.8 | -
ES03170 | 01:01:47.48 |  $-$ 33:47:27.6 | 18.385 | 4962 | 1.65 | 1.8 | 6
a) No available spectra of the CH G-band.
1) Skúladóttir et al. 2021; 2) Frebel et al. 2010a; 3) Simon et al. 2015; 4)
Tafelmeyer et al. 2010;
5) Jablonka et al. 2015; 6) Starkenburg et al. 2013

##  2 Observational data

###  2.1 New data

Here we present previously unpublished data of three Sculptor stars: AS0039,
DR20080 and UHAL004. Their spectra is described in Table 1, while their basic
properties, such as positions and photometric values are in Table 2 and Fig.
1, according to Gaia Early Data Release 3 (eDR3; Gaia Collaboration et al.
2021).

The stars AS00039 and DR20080 in the Sculptor dSph were discovered to be
metal-poor through a large ESO VLT/FLAMES survey of the Ca II near-infrared
triplet (ESO ID 0102.B-0786; Tolstoy et al. 2023). They were followed up by
the same programme with VLT/X-Shooter, for confirmation of their low-
metallicity, and here we report basic results (Fe and C) for DR20080 using
this spectrum. The discovery X-Shooter spectrum of AS0039 was analysed and the
results published in Skúladóttir et al. (2021). Here we present an analysis
based on a new, higher quality UVES spectrum. The star AS00039 shows evidence
of being a binary, with $v_{\textit{rad}}=130.5\pm 1.0\,\mathrm{km\,s^{-1}}$
(Aug-Sep 2021), significantly different from $v_{\textit{rad}}=135\pm
1\,\mathrm{km\,s^{-1}}$ reported from the X-Shooter spectrum (Dec 2018;
Skúladóttir et al. 2021). Gaia identifies one other star within 5” from
AS0039, however its colours are not compatible with the RGB of the Sculptor
dSph ($G=19.02$, $G_{BP}-G_{RP}=1.96$; see Fig. 1), so the companion star is
not identified. Finally, the star UHAL004 was observed via the VLT/FLAMES
program with ID 0101.D-0210(A), and discovered to be very metal-poor. The
available spectra consists of FLAMES/UVES and FLAMES/GIRAFFE spectra, as
listed in Table 1.

###  2.2 Archival data

To have a clear and homogeneous picture of the earliest chemical enrichment in
Sculptor, spectra of all previously published stars with $\rm[Fe/H]\leq-3$
(Tafelmeyer et al., 2010; Starkenburg et al., 2013; Jablonka et al., 2015)
were retrieved from the ESO archive. In addition, fully reduced spectra for
three stars, observed with Magellan/MIKE, were obtained through private
communication w/ A. Frebel and J. Simon (Frebel et al., 2010a; Simon et al.,
2015). For convenience, all archival stars are given new names here, referring
to the initials of the first author where the spectra we use was first
presented (see Table 2).

Several of the archival stars have been analysed in more than one publication,
either with the same spectra (Tafelmeyer et al., 2010; Frebel et al., 2010a;
Simon et al., 2015), or different spectra (Starkenburg et al., 2013; Jablonka
et al., 2015). Details of the spectral properties are listed in the respective
papers. We note that the star ES03170 does not, to our knowledge, have
available high resolution ($R\gtrsim 20\,000$) spectra, and the star MT00750
is lacking spectral coverage to measure the C abundance. The positions and
magnitudes of the entire stellar sample is listed in Table 2. Finally, we note
that the stars JS14296 and JS66402 are the faintest of the HR sample, and
accordingly also those with the lowest S/N (Simon et al., 2015).

Table 3: The chemical abundance measurements (LTE) for the Sculptor stellar
sample. HR sample
---
|  | AS0039 | UHAL004 | AF20549 | JS14296 | JS66402 | MT00749 | MT00750 | PJ00206 | PJ03059 | PJ03111 | PJ07402
El. | $\log\epsilon_{\odot}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$
Fe | 7.46 | $-3.90$ | 0.11 | $-2.80$ | 0.12 | $-3.46$ | 0.12 | $-3.57$ | 0.12 | $-3.38$ | 0.14 | $-2.96$ | 0.12 | $-3.85$ | 0.11 | $-3.40$ | 0.11 | $-2.96$ | 0.11 | $-3.79$ | 0.12 | $-3.19$ | 0.11
C${}_{\textsl{obs}}$ | 8.46 | $-0.96$ | 0.20 | $-1.18$ | 0.20 | $<-0.15$ | $-$ | $<0.36$ | $-$ | $<0.27$ | $-$ | $-$ | $-$ | $-0.21$ | 0.24 | $-1.46$ | 0.24 | $-0.75$ | 0.17 | $-0.48$ | 0.24 | $-0.57$ | 0.20
C${}_{\textsl{corr}}$ | 8.46 | $-0.33$ | 0.20 | $-0.41$ | 0.20 | $<0.31$ | $-$ | $<0.43$ | $-$ | $<0.35$ | $-$ | $-$ | $-$ | $-0.02$ | 0.24 | $-0.74$ | 0.24 | $-0.01$ | 0.17 | $0.19$ | 0.24 | $0.11$ | 0.20
Na | 6.22 | $-0.30$ | 0.07 | $0.20$ | 0.09 | $-0.26$ | 0.08 | $-0.23$ | 0.13 | $-0.15$ | 0.13 | $-0.24$ | 0.08 | $-0.07$ | 0.09 | $-$ | $-$ | $-$ | $-$ | $-0.28$ | 0.08 | $-0.31$ | 0.11
Mg | 7.55 | $0.22$ | 0.05 | $0.54$ | 0.08 | $0.04$ | 0.24 | $-0.42$ | 0.17 | $0.37$ | 0.26 | $0.55$ | 0.07 | $0.22$ | 0.09 | $0.31$ | 0.11 | $0.54$ | 0.06 | $0.29$ | 0.15 | $0.33$ | 0.09
Al | 6.43 | $-0.69$ | 0.10 | $-$ | $-$ | $<-1.07$ | $-$ | $<-0.76$ | $-$ | $<-0.85$ | $-$ | $-$ | $-$ | $-0.48$ | 0.20 | $-0.87$ | 0.17 | $-0.72$ | 0.15 | $-0.86$ | 0.15 | $-1.02$ | 0.22
Si | 7.51 | $0.07$ | 0.15 | $-$ | $-$ | $0.62$ | 0.27 | $0.02$ | 0.31 | $-0.03$ | 0.31 | $-$ | $-$ | $0.00$ | 0.17 | $-0.08$ | 0.20 | $0.05$ | 0.18 | $0.10$ | 0.16 | $0.09$ | 0.24
Ca | 6.30 | $0.06$ | 0.11 | $0.30$ | 0.09 | $0.10$ | 0.09 | $0.25$ | 0.17 | $0.03$ | 0.18 | $0.22$ | 0.07 | $0.09$ | 0.10 | $0.28$ | 0.08 | $0.34$ | 0.07 | $0.02$ | 0.17 | $0.39$ | 0.06
Sc | 3.14 | $-0.10$ | 0.08 | $-$ | $-$ | $0.01$ | 0.12 | $-0.02$ | 0.18 | $-0.12$ | 0.14 | $-$ | $-$ | $0.08$ | 0.07 | $-0.07$ | 0.28 | $-0.04$ | 0.13 | $-0.11$ | 0.06 | $-0.35$ | 0.12
Ti | 4.97 | $0.63$ | 0.06 | $0.41$ | 0.16 | $0.08$ | 0.08 | $0.30$ | 0.09 | $0.11$ | 0.10 | $0.02$ | 0.07 | $0.24$ | 0.07 | $0.03$ | 0.06 | $0.39$ | 0.07 | $0.37$ | 0.07 | $-0.09$ | 0.08
Cr | 5.62 | $-0.21$ | 0.13 | $-0.35$ | 0.13 | $-0.53$ | 0.08 | $-0.45$ | 0.29 | $-0.79$ | 0.07 | $-0.37$ | 0.15 | $-0.48$ | 0.08 | $-0.51$ | 0.11 | $-0.50$ | 0.12 | $-0.34$ | 0.11 | $-0.43$ | 0.13
Mn | 5.42 | $-0.25$ | 0.23 | $-$ | $-$ | $-1.16$ | 0.30 | $-0.59$ | 0.31 | $-0.73$ | 0.31 | $-$ | $-$ | $-0.97$ | 0.12 | $-0.45$ | 0.30 | $-0.70$ | 0.26 | $-0.57$ | 0.12 | $-0.03$ | 0.18
Co | 4.94 | $0.07$ | 0.08 | $-$ | $-$ | $0.30$ | 0.31 | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $0.15$ | 0.15 | $0.06$ | 0.07 | $0.10$ | 0.10 | $0.09$ | 0.10 | $0.10$ | 0.11
Ni | 6.20 | $0.19$ | 0.09 | $0.05$ | 0.13 | $-$ | $-$ | $-0.09$ | 0.21 | $0.13$ | 0.21 | $0.24$ | 0.12 | $-0.03$ | 0.11 | $-0.16$ | 0.13 | $0.03$ | 0.12 | $0.11$ | 0.12 | $-0.07$ | 0.28
Zn | 4.56 | $0.83$ | 0.30 | $0.44$ | 0.27 | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $0.40$ | 0.15 | $-$ | $-$ | $0.29$ | 0.23 | $0.12$ | 0.25 | $0.71$ | 0.30 | $0.43$ | 0.25
Sr | 2.83 | $-0.73$ | 0.17 | $-$ | $-$ | $<-2.07$ | $-$ | $<-1.76$ | $-$ | $-1.25$ | 0.30 | $-$ | $-$ | $-1.12$ | 0.19 | $-0.58$ | 0.22 | $-0.06$ | 0.21 | $-1.22$ | 0.19 | $-0.28$ | 0.26
Ba | 2.27 | $-1.12$ | 0.15 | $-0.46$ | 0.13 | $<-1.21$ | $-$ | $<-1.12$ | $-$ | $-0.62$ | 0.14 | $<-1.41$ | $-$ | $-1.12$ | 0.09 | $<-1.67$ | $-$ | $-0.60$ | 0.10 | $-0.96$ | 0.15 | $<-1.38$ | $-$
LR sample
|  | DR0080 | ES03170 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
El. | $\log\epsilon_{\odot}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$ | [X/Fe] | $\delta_{\text{[X/Fe]}}$ |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Fea | 7.46 | $-3.00$ | 0.14 | $-3.00$ | 0.14 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Cobs | 8.46 | $0.49$ | 0.17 | $-0.46$ | 0.17 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Ccorr | 8.46 | $1.02$ | 0.17 | $-0.12$ | 0.17 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Ba | 2.27 | $<-0.5$ | - | - | - |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
a) [Fe/H] is listed instead of [X/Fe].

##  3 Atmospheric Parameters

###  3.1 Effective temperature $\mathrm{T_{eff}}$

The effective temperatures, $\mathrm{T_{eff}}$, were determined using
photometry from Gaia eDR3 (Gaia Collaboration et al., 2021) and the
$G_{BP}-G_{RP}$ calibration from Mucciarelli & Bellazzini (2020). We evaluate
the extinction by converting the known extinction of $E(V-I)=0.027$ in the
direction of Sculptor111https://ned.ipac.caltech.edu/forms/calculator.html
(Schlafly & Finkbeiner, 2011) to $E(G_{BP}-G_{RP})=0.024$ (Busso et al.,
2018). A typical random error of $\Delta\mathrm{T_{eff}}=86$ K is adopted, as
the quadratic sum arising from: uncertainties in the the photometry, 0.01 mag
for $G_{BP}$ and $G_{RP}$ (Gaia Collaboration et al., 2021); an error on
[Fe/H], 0.20 dex; and the $\sigma_{\mathrm{T_{eff}}}$ of the $G_{BP}-G_{RP}$
calibration for giants, 83 K (Mucciarelli & Bellazzini, 2020).

Spectroscopic temperatures have been shown to be typically lower than the
photometric scales. Furthermore, Mucciarelli & Bonifacio (2020) showed that
this difference increases towards lower metallicity, and concluded that this
is likely a direct consequence of 3D NLTE effects of individual Fe I lines.
This effect can be limited by rejecting lines with excitation potential $<1.4$
eV, as done e.g. in Tafelmeyer et al. (2010) and Jablonka et al. (2015). As
expected, our photometric $\mathrm{T_{eff}}$ scale is thus higher compared to
those that used the spectroscopic method,
$\langle\Delta\mathrm{T_{eff}}\rangle\,\approx+200$ K compared to the works of
Frebel et al. (2010a), Tafelmeyer et al. (2010), and Simon et al. (2015); and
$\langle\Delta\mathrm{T_{eff}}\rangle\,\approx+100$ K with Jablonka et al.
(2015); while our $\mathrm{T_{eff}}$ scale agreed on average within 50 K with
the photometric $\mathrm{T_{eff}}$ of Starkenburg et al. (2013).

###  3.2 Surface gravity $\mathrm{\log g}$

The surface gravities, $\mathrm{\log g}$, were evaluated using Gaia eDR3
photometry and the standard relation:

$\log g_{\star}=\log
g_{\odot}+\log{\frac{\text{M}_{\star}}{\text{M}_{\odot}}}+4\log{\frac{T_{\textsl{eff,}\star}}{T_{\textsl{eff,}\odot}}}+0.4\,(M_{\textsl{bol,}\star}-M_{\textsl{bol,}\odot})$
(1)

Here the distance modulus is $(m-M)_{0}\leavevmode\nobreak\
=\leavevmode\nobreak\ 19.67\pm 0.16$ (Gaia Collaboration et al., 2018), and
the mass of the star is assumed to be $\text{M}_{\star}\leavevmode\nobreak\
=\leavevmode\nobreak\ 0.8\pm 0.2$ M⊙. The solar values used are the following:
$\log\leavevmode\nobreak\ g_{\odot}=4.44$, $T_{\textsl{eff,}\odot}=5772$ K and
$M_{\textsl{bol,}\odot}=4.74$. The typical random error is $\Delta\mathrm{\log
g}=0.14$, arising from error in the $G$ photometry (negligible),
$\mathrm{T_{eff}}$, and M⋆.

Analogous to $\mathrm{T_{eff}}$, our $\mathrm{\log g}$ scale is higher than
the spectroscopically determined scale. This is a direct consequence of the
different 3D NLTE effects of Fe I and Fe II lines (e.g. Amarsi et al., 2016)
whose equilibrium is typically enforced by the spectroscopic method. Therefore
$\mathrm{\log g}-\mathrm{\log g}_{\textsl{AF}}=+0.5$ when compared to Frebel
et al. (2010a), and $\langle\mathrm{\log g}-\mathrm{\log
g}_{\textsl{JS}}\rangle=+0.3$ with Simon et al. (2015), while other studies
agree on average within $\leq 0.06$ dex (Tafelmeyer et al., 2010; Starkenburg
et al., 2013; Jablonka et al., 2015).

###  3.3 The microturbulence velocity

For the microturbulence velocity, $\mathrm{v_{turb}}$, we use the empirical
relation presented in Kirby et al. (2009):

$\mathrm{v_{turb}}=((2.13\pm 0.05)-(0.23\pm 0.03)\cdot\mathrm{\log
g})\,\mathrm{km\,s^{-1}}$ (2)

The typical error is $\Delta\mathrm{v_{turb}}=0.1\,\mathrm{km\,s^{-1}}$, as
derived from the errors included in the equation, along with the error on
$\log g$ (Sec. 3.2). This relationship is well tested along a wide range of
[Fe/H], and has shown not to produce any significant trends with equivalent
width (e.g. Reichert et al., 2020; Lucchesi et al., 2020), and none were found
in a specific test we did for AS0039, the star with the lowest metallicity.

##  4 Chemical abundance analysis

Our stellar sample includes 13 stars in the Sculptor dSph galaxy at
$\rm[Fe/H]\leq-2.8$. However, two out of these, DR20080 and ES03170, do not
have HR spectra available, and for those stars we only measure Fe and C (along
with Ba) to increase the statistics for the fraction of CEMP-no stars in
Sculptor at low [Fe/H]. For the remaining 11 stars with HR spectra, we perform
a full abundance analysis. All measured abundances are listed in Table 3. The
solar abundances were adopted from Asplund et al. (2021), and all literature
data discussed and shown in this paper have been put on the same scale.

###  4.1 Stellar atmosphere models and linelists

The stellar atmosphere models are adopted from MARCS222marcs.astro.uu.se
(Gustafsson et al., 2008) for stars with standard composition, 1D, and
assuming local thermodynamic equilibrium (LTE), interpolated to match the
stellar parameters for the target stars. The abundance analysis was made with
the spectral synthesis code TURBOSPEC333ascl.net/1205.004 (Alvarez & Plez,
1998; Plez, 2012), and all individual measurements take blends of other
elements into account. Atomic parameters were adopted from the
VALD444http://vald.astro.uu.se database (Kupka et al. 1999), retrieved in
October 2019. Finally, the molecular list for CH is obtained from Masseron et
al. (2014).

###  4.2 Chemical abundance measurements

Chemical abundances and/or upper limits were measured for 2 elements from the
LR spectra (2 stars): Fe, C, along with an upper limit of Ba for DR20080; and
up to 16 elements from the HR spectra (11 stars): Fe, C, Mg, Na, Al, Si, Ca,
Sc, Ti, Cr, Mn, Co, Ni, Zn, Sr, and Ba. Typical errors arising from the
uncertainties in stellar parameters were estimated based on a representative
star for the sample: $\rm[Fe/H]=-3.4$; $T_{\textsl{eff}}=4650\,K$;
$\mathrm{\log g}=1.2$; and $v_{t}=1.9$ km/s. Individual components of the
error were estimated from synthetic spectra, as arising from $\Delta
T_{\textsl{eff}}=86$ K, $\Delta\mathrm{\log g}=0.14$ and $v_{t}=0.1$ km/s, and
then combined quadratically. Thus we estimated $\rm\Delta[Fe/H]=0.11$, and
$\rm\Delta[X/Fe]\approx 0.1-0.10$ for individual elements measured from atomic
lines, $\rm\Delta[X/Fe]$, while $\rm\Delta[C/Fe]=0.15$. The error resulting
from stellar parameters was added quadratically to the random observational
errors. All measured abundances, upper limits, and uncertainties are listed in
Table 3.

Figure 2: X-Shooter spectra for the CEMP-no star in our sample, DR20080 (red),
at $\rm[Fe/H]=-3$. For a fair comparison the X-Shooter spectra of PJ07402 at
the same $\rm[Fe/H]=-3$, is also shown in blue (Starkenburg et al., 2013).
However, for the full chemical abundance analysis of PJ07402, here we use a HR
UVES spectra from Jablonka et al. (2015).

The C abundance was measured from the CH G-band at $\sim$430 nm in 12 out of
our 13 stars (MT00749 lacked the spectral coverage). The strength of these
molecular lines are affected by the assumed O abundance, which influences how
much of C is locked into CO. The available spectra did not allow us to
reliably measure the O abundance, hence we adopt $\rm[O/Fe]=+0.6$,
corresponding to the average value at $\rm-2.5\leq[Fe/H]\leq-2$ in Sculptor
(Hill et al., 2019), and this is also in agreement with the Milky Way halo
(Amarsi et al., 2019). A combination of low C, high $\mathrm{T_{eff}}>4750$ K,
and low S/N lead to only upper limits for the stars AF20549, JS14296, and
JS66402. Fig. 2 shows the spectra of the only CEMP star in the sample,
DR20080, around the G-band, comparing it to a C-normal star.

The light, odd element Na was measured with the Na I D resonance lines at
589.0, and 589.6 nm, while the Al abundance came from one blue neutral line at
396.2 nm. Both elements were measured in 9 stars, but spectral coverage was
missing for two stars in each case.

Elemental abundances for three $\alpha$-elements were measured, Mg, Si and Ca,
as well as the often grouped-together element Ti. We used two Mg I lines in
the blue at 382.8 and 383.8 nm, and the Mg I triplet at 516.7, 517.2, and
518.3 nm. The Si abundance was determined from one neutral line at 390.6 nm,
while five Ca I lines were used: 422.7, 430.3, 445.5, 612.2, and 616.2 nm.
Finally, Ti was measured by 28 Ti II lines, ranging from 370-530 nm. In Fig. 3
the spectral fits are shown for two lines (Mg I and Ca I) for the new UVES
spectrum of AS0039.

Figure 3: Spectrum of AS0039 (black), showing lines of Mg I (left), and Ca I
(right). Red shows the best fit, blue is $\pm 0.4$ from that, and gray shows
synthetic spectra without the elements in question. Figure 4: Spectra of the
strong resonance Mn I triplet for the three most metal-poor stars in our
sample, $\rm[Fe/H]\approx-3.85$.

For the odd iron peak elements, we measured Sc using four Sc II lines at
424.7, 431.4, 432.1, and 432.5 nm. The Mn was measured from the Mn I triplet
at 403 nm, shown in Fig. 4 for the three most metal-poor stars in our sample.
Using eight weak Co I lines from 384 to 413 nm we were able to measure Co in 7
of our stars. Due to lack of blue spectral coverage, we were unable to measure
Sc, Mn or Co in MT00749 and UHAL004. In addition, the low S/N in JS14296 and
JS66402 prevented us from making reliable Co measurements, and the Co in
AF20549 is only based on one line (413 nm).

We measured four even iron-peak elements: Cr, Fe, Ni, and Zn. In total six Cr
I lines were used for the measurement of Cr, at 425.4, 427.5, 429.0, and the
triplet at 520 nm. The Fe abundance was measured from up to 61 Fe I lines in
the wavelength range $400-570\,$nm, as this was the range covered by most
spectra. For the intermediate-resolution X-Shooter spectra (DR20080, and
ES03170) the same linelist was used. However due to the lower resolution, some
of the weaker lines were not reliably measureable in these stars, though this
was somewhat compensated by the above average $\rm[Fe/H]=-3$, compared to the
rest of the sample. Thus for DR20080, [Fe/H] was measured using 29 Fe I lines,
while ES03170 was based on 35 lines (this star had spectra with higher S/N).
Up to six Ni I lines were used, at 380.7, 383.2, 385.8, 391.3, 397.4 and 547.7
nm. For the stars JS14296, JS66402, MT00749, and UHAL004 the Ni abundance is
only based on the reddest line at 547.7 nm. For AF20549 even this line was too
weak to measure. Finally, Zn was measured in the 8 stars with the highest S/N,
using the line at 481.1 nm

The neutron-capture elements Sr and Ba were measured, using two Sr II lines at
407.8 and 421.6 nm, and up to three Ba II lines at 455.4, 614.2, and 649.7 nm.
The wavelength range of the bluest line was unfortunately only covered in five
stars, AF20549, JS14296, JS66402, MT00749, and MT00750, but all HR spectra
included the wavelength covering of the two redder lines. An upper limit of
$\rm[Ba/Fe]<-0.5$ was measured for the star DR20080, from the 614.2 nm line in
the X-Shooter spectrum, confirming it to be a CEMP-no star.

###  4.3 AS0039 - NLTE abundances

For detailed comparison with theoretical models (Sec. 6), accurate chemical
abundances are fundamental. Thus, we provide non-LTE (NLTE) corrections to the
abundance measurements of AS0039, the most metal-poor star in our sample. The
NLTE chemical abundances for AS0039, along with the size of the NLTE
corrections, are listed in Table 4.

The chemical abundance measurements of Fe I, Ca I, and Ti II were corrected
for NLTE effects, on a line-to-line bases, according to Mashonkina et al.
(2016), using the publicly available online
tool.555http://spectrum.inasan.ru/nLTE/ The abundances of Mg, Si, Cr, and Co
were corrected with the MPIA-NLTE database666https://nlte.mpia.de/gui-
siuAC_secE.php (Bergemann & Cescutti, 2010; Bergemann et al., 2010, 2013,
2017). The Na correction was derived with the INSPECT
database777http://inspect-stars.com/, based on the work of Lind et al. (2011),
and the Al correction is based on Nordlander & Lind (2017). The NLTE
correction of Mn was based on the most metal-poor giant models provided by
Bergemann et al. (2019). Finally, the Zn NLTE corrections were adopted from
Takeda et al. (2005). Corrections of Sc, Sr, and Ba are expected to be small
(e.g. Bergemann et al., 2012; Zhang et al., 2014) and were neglected here. For
the molecular CH lines, 3D corrections are not available but are expected to
result in lower abundances (Caffau et al., 2011b; Norris & Yong, 2019)
compared to the $\rm[C/H]_{\text{LTE}}$ used in this work.

When there were several lines of the species available, the NLTE corrections
reduced the scatter between lines in all cases except for Ti II. However, the
NLTE corrections for Ti II are on the order of $\sim$+0.03 dex, and thus
negligible compared to the random errors of singular lines.

Table 4: The NLTE chemical abundances of the star AS0039.  El. | $\log\epsilon_{\odot}$ |  $\Delta$[X/H]${}_{\text{NLTE}}$ | [X/Fe]${}_{\text{NLTE}}$ | $\delta_{\text{[X/Fe]}}$
---|---|---|---|---
Fea | 7.46 | $+0.26$ | $-3.64$ | 0.11
C${}_{\textsl{corr}}$ | 8.46 | $-$ | $-0.59$ | 0.20
Na | 6.22 | $+0.02$ | $-0.53$ | 0.07
Mg | 7.55 | $+0.19$ | $+0.15$ | 0.05
Al | 6.43 | $+1.00$ | $+0.05$ | 0.10
Si | 7.51 | $-0.16$ | $-0.35$ | 0.15
Ca | 6.30 | $+0.28$ | $+0.08$ | 0.11
Sc | 3.14 | $-$ | $-0.36$ | 0.08
Ti | 4.97 | $+0.03$ | $+0.40$ | 0.06
Cr | 5.62 | $+0.76$ | $+0.29$ | 0.13
Mn | 5.42 | $+0.47$ | $-0.04$ | 0.23
Co | 4.94 | $+0.78$ | $+0.59$ | 0.08
Ni | 6.20 | $+0.26$ | $+0.19$ | 0.09
Zn | 4.56 | $+0.06$ | $+0.63$ | 0.30
a) [Fe/H] is listed instead of [X/Fe].

###  4.4 Comparison to the literature

By comparing our results to the previous literature studies of the 9
reanalysed star in our sample (Table 2), it becomes clear that our metallicity
scale is higher, $\rm\langle[Fe/H]-[Fe/H]_{\textsl{lit}}\rangle=+0.17$. This
is a direct consequence of adopting the photometric $\mathrm{T_{eff}}$ scale,
which is higher than the spectroscopic scale (see Sect. 3, and general
discussion in Mucciarelli & Bonifacio 2020). The difference in abundance
ratios is smaller, with e.g.
$\rm\langle[Mg/Fe]-[Mg/Fe]_{\textsl{lit}}\rangle=+0.08$. When compared to
Chiti et al. (2018), there are five stars in common (AF20549, JS14296,
MT00750, PJ03059 and ES03170, respectively 10_8_1072, 11_1_4296, 10_7_923,
10_8_320 and 10_8_61 in Chiti et al. 2018), with an average
$\rm\langle[Fe/H]-[Fe/H]_{\textsl{Chiti}}\rangle=+0.01$, and $\sigma=0.17$.
Out of these five stars, four only have upper limit measurements by us and/or
Chiti et al. (2018). For PJ03059, the one star with C measurements by both
works, $\rm\langle[C/Fe]-[C/Fe]_{\textsl{Chiti}}\rangle=-0.36$, which is in
agreement within the errors.

The LTE chemical abundances for AS0039 based on the HR UVES spectra are in
general agreement with those from the discovery X-Shooter spectrum
(Skúladóttir et al., 2021). In the present work the metallicity is higher,
$\rm[Fe/H]_{UVES}-[Fe/H]_{X-Shooter}=+0.21$, with average differences in
abundance ratios
$\rm\langle[X/Fe]_{\textsl{UVES}}-[X/Fe]_{\textsl{X-Shooter}}\rangle=-0.03$,
and the differences have an average size of
$\rm\langle\,|\,[X/Fe]_{\textsl{UVES}}-[X/Fe]_{\textsl{X-Shooter}}\,|\,\rangle=+0.23$.
A notable outlier is Ca, with $\rm[Ca/Fe]_{X-Shooter}=+0.65\pm 0.11$ and
$\rm[Ca/Fe]_{\textsl{UVES}}=+0.06\pm 0.12$. For the weak lines used in both
works (422.7 and 616.2 nm) it is quite likely that unfortunately placed noise
affected the X-Shooter measurements. However, these lines were in good
agreement with the strong infrared Ca II triplet (849.9, 854.2 and 866.2 nm)
in the X-Shooter spectra. Unfortunately the UVES spectra does not have the
wavelength coverage of the Ca II triplet, preventing further comparison. With
the exception of Ca, the chemical abundances of AS0039 as measured with
X-Shooter are consistent with the higher quality UVES analysis.

Figure 5: Abundance ratios of [C/Fe] with $\log g$ in Sculptor (blue), the
Milky Way (gray) and UFDs (yellow), both as measured (top panel), and after
applying corrections for internal mixing (bottom panel) according to Placco et
al. (2014). Green lines in top panel note the predicted evolutionary track of
[C/Fe] in stars born with $\rm[C/Fe]=+0.7$, and 0, repeated with dotted lines
in the bottom panel for visual aid. Milky Way ref.: Roederer et al. (2014).
UFD ref.: listed in Sec. 5.

##  5 The metal-poor chemical abundances in Sculptor

The chemical abundance measurements (LTE) of our Sculptor stars are listed in
Table 3, and shown in Figs 5-11. In the following subsections we will discuss
the results and put them in context with the metal-poor Milky Way halo and the
UFDs. In particular, in Sec. 5.6, we quantitatively compare the overall
abundance patterns in different galaxies.

For the Milky Way we use literature data from: Cayrel et al. (2004);
Christlieb et al. (2004); Norris et al. (2007); Caffau et al. (2011a); Yong et
al. (2013); Hansen et al. (2014); Keller et al. (2014); Roederer et al.
(2014); Frebel et al. (2015); Bonifacio et al. (2015); Li et al. (2015);
Bonifacio et al. (2018); François et al. (2018); Starkenburg et al. (2018);
Aguado et al. (2019); Ezzeddine et al. (2019); Lombardo et al. (2022). For the
UFDs we use data from the JINA
database888https://jinabase.pythonanywhere.com/(Abohalima & Frebel, 2018),
which includes: Norris et al. (2010); Simon et al. (2010); Frebel et al.
(2010b, 2016a); Ishigaki et al. (2014); Roederer et al. (2016); François et
al. (2016); Ji et al. (2016c); Frebel et al. (2016b). For C abundances we also
include the following UFD references: Lai et al. (2011); Ji et al. (2020). For
duplicate entries of the same stars, the original publication is used. All
literature abundances are put on the solar scale of Asplund et al. (2021), see
Tables 3 and 4.

Figure 6: Abundance ratios of [C/Fe] with [Fe/H] in Sculptor (blue
stars/circles), the Milky Way (gray squares) and UFDs (yellow stars),
corrected for internal mixing (Placco et al., 2014), excluding CEMP-$s$ stars.
Ref. listed in Sec. 5.

Figure 7: The light odd elements, [Na/Fe] and [Al/Fe] with [Fe/H] for Sculptor
(blue), the Milky Way (gray), and UFDs (yellow). Star symbols represent
Sculptor stars analysed here using new spectra, while blue circles are stars
reanalysed on archival spectra.

Figure 8: The $\alpha$-elements, [Mg/Fe], [Si/Fe], and [Ca/Fe], along with
[Ti/Fe], with [Fe/H] for Sculptor (blue), the Milky Way (gray), and UFDs
(yellow). Star symbols represent Sculptor stars analysed here using new
spectra, while blue circles are stars reanalysed on archival spectra.

Figure 9: The iron-peak elements Sc, Cr, Mn, Co, Ni and Zn relative to Fe, as
a function of [Fe/H] for Sculptor (blue), the Milky Way (gray), and UFDs
(yellow). Star symbols represent Sculptor stars analysed here using new
spectra, while blue circles are stars reanalysed on archival spectra.

###  5.1 Carbon

The C abundance on the surface of RGB stars is modified by internal dredge-up
and mixing (e.g. Gratton et al., 2000; Spite et al., 2006). To correct for
this effect, we used the online tool999http://vplacco.pythonanywhere.com/
provided by Placco et al. (2014). Fig. 5 shows both the measured abundances,
$\rm[C/Fe]_{\textsl{obs}}$, and those corrected for mixing,
$\rm[C/Fe]_{\textsl{corr}}$ as a function of $\log g$. The average size of the
correction for the Sculptor sample is
$\rm\langle\,\Delta[C/Fe]\,\rangle=+0.5$. We note that adopting lower $\log g$
would lead to higher corrections. In general our $\log g$ scale is in good
agreement with the literature (Sec. 3.2), with the exception of Frebel et al.
(2010a) and Simon et al. (2015), where $\Delta\log g\gtrsim 0.3$. However for
those three stars we were only able to provide upper limits, see Fig. 5, and
our results are in general agreement with Frebel et al. (2010a) and Simon et
al. (2015), which categorised these stars as C-normal.

In the case of $\rm[C/Fe]_{\textsl{obs}}$ (Fig. 5, top) there is a steep
negative gradient with evolutionary stage, i.e. decreasing $\mathrm{\log g}$,
as is expected from theory. After applying the corrections, the trend is
flattened at $\log g<1$. However, we note that the three most evolved stars
are still significantly lower in $\rm[C/Fe]_{\textsl{corr}}$ compared to the
other C-normal stars, with $\rm[C/Fe]_{\textsl{corr}}=-0.5$, while other
C-normal stars are consistent with $\rm[C/Fe]_{\textsl{corr}}\approx 0.0$.
Given that these three most evolved stars (AS0039, PJ00306, and UHAL004) cover
the entire metallicity range of the sample, it is likely that this is an
artificial effect, produced either by underestimation of the C-corrections at
low $\mathrm{\log g}<1$ and/or differences in 3D effects of the CH band. If
the corrections are underestimated at low $\log g$, our presented abundances
are too low, however, adding 3D corrections to the abundances derived from the
G-band, will lower these abundances (e.g. Norris & Yong, 2019). For the lack
of a better alternative we accept the abundances as presented, with the
aforementioned caveats. In any case, it is unambiguous that these three
evolved stars are all C-normal, $\rm[C/Fe]<+0.7$.

Fig. 6 shows $\rm[C/Fe]_{\textsl{corr}}$ (from here on labelled [C/Fe]) as a
function of [Fe/H]. In the Sculptor sample of 12 stars at
$\rm-4<[Fe/H]\leq-2.8$, only one star, DR20080, is carbon-enhanced,
$\rm[C/Fe]>+0.7$ (see also Fig. 2). This star has $\rm[Ba/Fe]<-0.5$ (Table 3),
and is therefore a bonafide CEMP-no star. This gives a fraction
$f_{\textsl{CEMP}}^{\textsl{Scl}}=9^{+11}_{-8}\%$ at $\rm[Fe/H]\leq-3.0$,
while the fractions measured in the literature in the Milky Way and UFDs are
$f_{\textsl{CEMP}}\approx 40\%$ (Placco et al., 2014; Ji et al., 2020).
Furthermore we emphasise that at $\rm[Fe/H]<-3.5$ there is no known CEMP-no
star in Sculptor, while the fraction in the Milky Way halo and UFDs is
$f_{\textsl{CEMP}}>60\%$. Therefore it is evident that although CEMP-no stars
do exist in Sculptor (Skúladóttir et al. 2015b; and here) their fraction is
significantly lower in Sculptor compared to the Milky Way halo and the UFDs.
This dearth of CEMP-no stars in Sculptor has been noted previously in the
literature (e.g. Starkenburg et al., 2013; Skúladóttir et al., 2015b;
Skúladóttir et al., 2021), and is further solidified with this work. This
clearly points to a different chemical enrichment in Sculptor at the earliest
epochs, compared to both the Milky Way halo and the UFDs. This is further
discussed in Sec.6.

###  5.2 Light odd elements, Na and Al

The abundances of the light odd elements Na and Al are shown in Fig. 7.
Sculptor follows the lower envelope of [Na/Fe] values observed in the Milky
Way and UFDs, with all but the most metal-rich star, UHAL004, having subsolar
$\rm[Na/Fe]<0$. A similar picture arises with [Al/Fe], where the Sculptor
abundances are typically lower than the median of the Milky Way. The UFDs show
a bimodal behavior in [Al/Fe], either being similar to Sculptor, or very high
with $\rm[Al/Fe]>0$. We note that all the supersolar abundances in UFDs in
Fig. 7 are from the same reference (François et al., 2016), but the authors
find similar results for several UFDs (Boötes II, Hercules, Leo IV).

From Fig. 7 it is clear that Sculptor is significantly lower in the abundances
of light odd elements, Na and Al, relative to Fe, compared to other depicted
galaxies. The low Na is likely closely related to the dearth of CEMP-no stars
in Sculptor, since such stars are known to often also have high Na and Al
(e.g. Norris et al., 2013). But even when only considering C-normal RGB stars,
the Sculptor values are typically lower than the median of Milky Way data,
suggesting an intrinsic lack of these elements in the earliest chemical
enrichment of Sculptor.

Figure 10: Abundance ratios of the neutron-capture elements in Sculptor
(blue), the Milky Way (gray) and UFDs (yellow): [Sr/Fe] (left) and [Ba/Fe]
(middle) as a function of [Fe/H], and [Sr/Ba] (right) as a function of [Ba/H].
For reference, the [Sr/Ba] value of the r-process enhanced star CS 22892-052
(Sneden et al., 2003) is noted with a green dashed line. Star symbols
represent Sculptor stars analysed here using new spectra, while blue circles
are stars reanalysed on archival spectra. Milky Way ref.: Roederer et al.
(2014). UFD ref. are listed in the beginning of Sec. 5.

###  5.3 The $\alpha$-elements

The $\alpha$-elements Mg, Si, and Ca, along with the often grouped-together
Ti, are shown relative to Fe in Fig. 8. In the elements Mg, and Ca there is a
decreasing trend of [Mg,Ca/Fe] towards lower [Fe/H]. This was already
identified in the literature compilation of these Sculptor stars (Skúladóttir
et al., 2021), where low Mg and/or low Ca at $\rm[Fe/H]<-3.5$ were previously
noted in Sculptor stars by Tafelmeyer et al. (2010); Frebel et al. (2010a);
Jablonka et al. (2015); and Simon et al. (2015). Here we confirm that this is
not a result of inhomogenities between different works. This trend is not seen
in the Milky Way halo, nor in the UFDs. However, data in other dSph galaxies
is lacking at these low $\rm[Fe/H]<-3.5$, hence it is unclear whether this
trend is typical for dSph galaxies or if it is unique to Sculptor.

Our analysis also suggests a lower Si in Sculptor compared to the Milky Way
halo and UFDs. This was also found in individual stars by Tafelmeyer et al.
(2010) and Simon et al. (2015), while the results of Jablonka et al. (2015)
were more in line with the Milky Way. The star AF20549 was found to have very
high $\rm[Si/Fe]=0.96\pm 0.39$ by Frebel et al. (2010a), which is in agreement
with the value obtained here, $\rm[Si/Fe]=0.62\pm 0.26$, given the large
errors in this moderate S/N spectra. We emphasise that Si is measured using
only one line, making it more uncertain than the other $\alpha$-elements
reported here.

Contrary to the $\alpha$-elements, Ti does not show any clear evidence of
behaving differently in Sculptor and the other galaxies depicted in Fig. 8.
Furthermore there is no signature of a decreasing nor an increasing trend of
[Ti/Fe] with [Fe/H]. Therefore, only the traditional $\alpha$-elements, Mg,
Si, and Ca, are different in Sculptor at the lowest $\rm[Fe/H]<-3.5$, compared
to the Milky Way halo and the UFDs.

###  5.4 Iron-peak elements

Fig. 9 shows the [X/Fe] for the iron-peak elements Sc, Cr, Mn, Co, Ni, and Zn
as a function of [Fe/H]. The abundances of [Sc/Fe] in Sculptor are in general
agreement with the Milky Way halo and UFDs, especially at the lowest
$\rm[Fe/H]<-3.5$, while the higher values of $\rm[Sc/Fe]>+0.2$ are missing in
Sculptor while observed in the other galaxies at $\rm[Fe/H]>-3.3$. Similarly
to Na, Al, and Sc, [Cr/Fe] in Sculptor also follows the lower envelope of the
Milky Way, being consistent with the UFDs. Furthermore, [Co/Fe] is lower in
Sculptor compared to the other galaxies.

On the other hand, the Mn in Sculptor is in very good agreement with both the
Milky Way halo and UFDs, showing a very large scatter in [Mn/Fe] and typically
subsolar values (in LTE). We note that the three most metal-poor stars in
Sculptor generally agree remarkably well in their abundance patterns (Figs
7-9), however, in [Mn/Fe] there is significant differences in their values.
Furthermore, for these three stars, the [Mn/Fe] is anti-correlated with their
$\mathrm{T_{eff}}$ (see Fig. 4). We note that the abundances presented here,
and shown in Fig. 9, have not been corrected for NLTE effects which are
predicted to be around $\rm\Delta[Mn/H]_{\text{NLTE}}\approx+0.5$ in Bergemann
et al. (2019), or even as high as $\rm\Delta[Mn/H]_{\text{NLTE}}\approx+1$ in
some works (Bergemann & Gehren, 2008). The complete NLTE abundances therefore
might reduce the differences. However, the available work on NLTE does not
predict such sharp differences in the $\mathrm{T_{eff}}$ range presented here,
therefore the $\mathrm{T_{eff}}$-[Mn/Fe] anti-correlation is plausibly only a
coincidence based on low number statistics.

Finally, both Ni and Zn Sculptor is in very good agreement with the Milky Way
halo evolution as well as the UFDs. In particular, Ni, which is easier to
measure and thus has less random errors, shows roughly $\rm[Ni/Fe]\approx 0$
in Sculptor, as well as the Milky Way and the smaller UFDs. Similar to the
Milky Way halo (e.g. Cayrel et al., 2004; Lombardo et al., 2022), Sculptor has
increasing [Zn/Fe] ratios toward lower [Fe/H]. Very few Zn measurements are
available in UFDs, but in general they are consistent with the larger
galaxies.

Overall we find less differences between Sculptor and the other galaxies in
the iron-peak elements, compared to the lighter elements presented in Figs
6-8. Given the uncertainties and possible systematic errors we conclude that
the iron-peak elements in Sculptor have a similar behaviour as the other
galaxies, albeit not always identical.

###  5.5 Neutron-capture elements

The neutron-capture elements Sr and Ba, relative to Fe, are shown in Fig. 10.
We note that the four UFD stars with $\rm[Ba/Fe]>0$ and $\rm[Sr/Fe]>0$ belong
to $r$-process enhanced Reticulum II (Ji et al., 2016a, b; Roederer et al.,
2016). Excluding these outliers, the [Sr/Fe] and [Ba/Fe] ratios in Sculptor
are in good agreement with UFDs, as well as the Milky Way halo. At the
earliest stages in these galaxies, AGB stars had not yet become a dominant
source of these elements, leading to extremely low, sub-solar ratios, relative
to Fe. We note that the scatter in our [Sr/Fe] and [Ba/Fe] measurements is
significant, providing clear evidence of inhomogeneous mixing in these
elements at the earliest times in Sculptor. A compatible result (albeit with
fewer data points) was found by Reichert et al. (2020), as well as Mashonkina
et al. (2016).

The right panel of Fig. 10 shows the [Sr/Ba] ratio. Again, Sculptor is in very
good agreement with the Milky Way halo and the UFDs at low $\rm[Ba/H]<-3$. As
a reference, we denote the [Sr/Ba] of the $r$-process enhanced star CS
22892-052 (Sneden et al., 2003). However, very r-process enriched stars, with
$\rm[Eu/Fe]>+1$, cover a more than a dex spread in
$\rm-0.7\lesssim[Sr/Ba]\lesssim+0.7$ (Holmbeck et al., 2020). Similarly, very
s-process enriched CEMP-s stars, cover a similar range in [Sr/Ba] (e.g. Hansen
et al., 2019; Goswami et al., 2021). Traditionally a specific weak $r$\-
and/or $s$-processes (e.g. Travaglio et al., 2004; Arcones & Montes, 2011) are
provoked to explain the high [Sr/Ba] ratios observed in some halo stars (e.g.
Honda et al., 2004), in dwarf galaxies (e.g. Skúladóttir et al., 2015b;
Susmitha et al., 2017; Spite et al., 2018), and in one $\omega$ Centauri star
(Yong et al., 2017). The abundance pattern of such stars have been
successfully explained, e.g. with fast rotating, low-metallicity massive stars
(Cescutti et al., 2013; Choplin et al., 2017, 2018; Yong et al., 2017;
Skúladóttir et al., 2020), but the origin of these stars is still being
debated. Based on the observational scatter in [Sr/Ba] in both s-process
enriched stars as well as r-process rich, it seems likely that the [Sr/Ba]
ratio is sensitive to the physical conditions on each site, as well as
possibly Sr having contribution from several processes.

Figure 11: The average abundance pattern at $\rm-4\leq[Fe/H]\leq-2.7$ in
Sculptor (blue), the Milky Way (gray), and UFDs (yellow), with the error of
the mean, $\sigma$/$\sqrt{N-1}$. Informative upper limits (lower than the mean
value) are included. Furthermore, all C measurements and upper limits in
Sculptor are included. References are the same as in Figs 6-9. Figure 12:
Comparison between the measured chemical abundance pattern, [X/Fe], of the
star AS0039 (red) in LTE (squares) and NLTE (stars) with model predictions
(lines) for the pure descendants of a Pop III $20\,\mathrm{M_{\odot}}$ star
with fixed mixing $f_{mix}=0.063$. Different colors denote different SN
explosion energies for Pop III stars: $0.3\times 10^{51}$ erg (blue),
$1.2\times 10^{51}$ erg (green), $5\times 10^{51}$ erg (yellow), and $10\times
10^{51}$ erg (orange).

###  5.6 The general abundance pattern

Fig. 11 shows the average abundance pattern from the data shown in Figs 6-9,
at the metallicity range of the Sculptor data, $\rm-4<[Fe/H]<-2.7$, with the
error of the mean, $\sigma$/$\sqrt{N-1}$. Upper limits in Sculptor and the
UFDs that are informative, i.e. lower than the mean [X/Fe], are included as
measurements. All upper limits in [C/Fe] are included for the Sculptor
average. Despite this very conservative estimate of
$\rm\langle[C/Fe]\rangle_{\textsl{Scl}}$, it is clear that Sculptor is
remarkably devoid of C compared to the Milky Way halo and the UFDs (see also
Fig. 6).

Furthermore, the lighter elements show a similar trend, where in particular
Na, Al, and Si have significantly lower values in Sculptor compared to other
galaxies. Less significantly, [Mg/Fe] and [Ca/Fe] in Sculptor are lower than
in the Milky Way and UFDs. We note that Mg and Ca are consistent with the
other systems at higher $\rm[Fe/H]\gtrsim-3.5$, and only deviate at the lowest
[Fe/H]. However, when looking at elements from Ti and heavier in Fig. 11 it is
clear that the abundance pattern in Sculptor converges with the Milky Way halo
and the UFDs, and the different galaxies are generally in very good agreement.

The peculiarities of the Sculptor average abundance pattern are likely closely
associated with the galaxy’s dearth of CEMP-no stars (Sec. 5.1; e.g.
Skúladóttir et al. 2015b). Indeed, CEMP-no stars - especially at low [Fe/H] -
have shown an enhancement of the lighter elements ($Z\lesssim 20$), while the
heavier elements are more in line with C-normal stars in the Milky Way halo
(e.g. Norris et al. 2013). This is clear evidence that low-energy SN, the
progenitors of CEMP-no stars (e.g. Iwamoto et al. 2005b; Rossi et al. 2023;
Vanni et al. 2023), have not had as great an impact on Sculptor as the Milky
Way halo and the UFDs. Ultimately, this raises the question from where the
earliest chemical enrichment in Sculptor arises.

##  6 Primordial Hypernovae in Sculptor

To interpret the chemical abundances of the Sculptor stars we use the
parametric model for early chemical enrichment presented in Salvadori et al.
(2019) to study the signature of very massive Pop III stars and then extended
in Vanni et al. (2023 in press; and 2023 in prep.) to uncover the imprint of
Pop III stars with different mass and explosion energy. This broad and general
model studies the chemical abundances in the primordial galaxies after the
pollution of a single Pop III star with mass,
$M_{*}\in[10;1000]\,\mathrm{M_{\odot}}$, SN explosion energy,
$E_{\textsl{SN}}\in[0.3;100]\times 10^{51}$ erg and mixing,
$f_{mix}\in[0;0.25]$. We exclude, for this work, stars with
$M_{*}>100\>\mathrm{M_{\odot}}$ (and $E_{\textsl{SN}}>10\times 10^{51}$ erg)
and use for the remaining ones the yields from Heger & Woosley (2010).
Moreover, the model explores how these abundances change with the
contamination of normal Pop II stars at different levels. The unknowns on the
early phases of the stellar formation and evolution are wrapped in three free
parameters: the star formation efficiency of Pop III stars, the dilution
factor of the metals and the fraction of metals coming from Pop III stars with
respect to the total. See Vanni et al. (2023, in press) and Salvadori et al.
(2019) for further details and a comprehensive explanation of the model
properties.

###  6.1 The progenitor of AS0039

The star AS0039 is the most metal-poor star known in any external galaxy. The
abundance pattern of this star is in general agreement with other two Sculptor
stars at similar $\rm[Fe/H]_{LTE}<-3.7$ (see Fig. 6-10), and due to its
brightness (see Fig. 1, and Table 2) its S/N is higher (see e.g. Fig. 4). Thus
in the following, we use AS0039 as representative of the earliest chemical
enrichment in Sculptor and use the NLTE abundances provided in Table 4.

In Fig. 12 we compare the abundances of AS0039 computed in both LTE (square
points) and NLTE (star points), with the abundances predicted by our model for
the pure (100%) descendants of Pop III stars with fixed mass,
$20\,\mathrm{M_{\odot}}$, and mixing, $f_{mix}=0.063$, for four different SN
explosion energies (Heger & Woosley, 2010).

First, we notice that the abundances of AS0039 better agree with the
descendants of high-energy, $E_{\textsl{SN}}\geq 5\times 10^{51}$ erg, Pop III
SNe (yellow and orange points), that are the only ones for which the model
predicts [C/Fe] $<0$. Moreover, our models predict very similar abundances for
the descendants of low- and high-energy SNe for the elements heavier than Sc,
while they are very different for the lighter metals, most of all C. It
suggests that the abundances of the elements lighter than Sc might be the key
to understand the pollution history of AS0039 and the other environments
presented in Fig. 11: the Milky Way stellar halo, UFDs and Sculptor. Indeed,
the abundance ratios presented in the Figs. 11 and 12, if compared, suggest
that, on average, Sculptor has been polluted by more energetic primordial SNe
with respect to the Milky Way halo and the UFDs, which, on the other side,
might have been more dominated by the ejecta of low-energy Pop III SNe (Rossi
et al. (2023); and in prep).

Figure 13: Comparison of the observed abundances of AS0039 (NLTE) to
theoretical predictions for pure descendants of Pop III stars, varying their
SN explosion energy, mixed fraction and initial mass. In the upper panel we
fixed the initial mass to $\mathrm{20\,M_{\odot}}$, in the lower panel the
mixed fraction to $\mathrm{f_{mix}=0.063}$. Best fits are magenta, while the
worst fits, with $\chi^{2}\geq 5$ (i.e. $\geq 5$ times the minimum), are shown
with red color.  Figure 14: Density maps of the [C/Fe] with respect to [Fe/H]
as predicted by our model for the descendants of Pop III stars (shaded areas)
and measured abundances (LTE) of stars in Sculptor (blue circles), Sextans
(medium-blue hexagons), Carina (light-blue hexagons) and Fornax (purple
pentagons), the UFDs (yellow triangles), and the Milky Way (grey squares). All
measured [C/Fe] abundances have been corrected for internal mixing (Placco et
al., 2014). Black arrow shows the expected size and direction of how measured
stellar abundances will change because of NLTE effects in [Fe/H]. The shaded
areas are colored depending on the type of stars that polluted the
descendants: 100% Pop III low-energy SNe (grey, $E_{\textsl{SN}}<1.5\times
10^{51}$ erg), 100% Pop III hypernovae (red, $E_{\textsl{SN}}>5.0\times
10^{51}$ erg), 50% low-energy Pop III and 50% core-collapse Pop II SNe
(green). The densest areas (and most probable abundances) are coloured with
darker shades. In all cases $f_{mix}=0.063$. Ref. for the Milky Way and UFDs
are listed in Sec. 5. Ref for dSph galaxies: Tafelmeyer et al. (2010);
Lucchesi et al. (2020); Lucchesi et al. in prep.

Given the good agreement between AS0039 and the descendants of high-energy Pop
III SNe for a given mass and mixing, we directly compare its abundances with
theoretical models varying the mass, the SN explosion energy and the mixing of
the Pop III progenitor star. We compute the $\chi^{2}$ between the chemical
abundances of AS0039 and the ones predicted by 100% Pop III descendants as
follows:

$\rm\chi^{2}_{\circ}=\sum^{N}_{i=1}\dfrac{\left([X_{i}/Fe]_{obs}-[X_{i}/Fe]_{th}\right)^{2}}{\rm\left(\sigma^{2}_{[X_{i}/Fe]_{obs}}+\sigma^{2}_{[X_{i}/Fe]_{th}}\right)},$
(3)

where $\rm[X_{i}/Fe]_{obs,th}$ and $\rm\sigma^{2}_{[X_{i}/Fe]_{obs,th}}$ are
the measured and theoretical abundance ratios and standard deviations. In
order to account for the uncertainties on Pop III stellar yields, quantified
by Nomoto et al. (2013) and Hartwig et al. (2018) in
$\rm\sigma_{[X_{i}/Fe]_{th}}\sim 0.3-1.0\leavevmode\nobreak\ dex$, we assume
$\rm\sigma^{2}_{[X_{i}/Fe]_{th}}=0.25$. Finally, we define scaled
$\rm\chi^{2}=\chi^{2}_{\circ}/$min($\chi^{2}_{\circ}$).

The best fit suggests that AS0039 was primarily enriched by a Pop III
hypernovae, $E_{\textsl{SN}}=10\times 10^{51}$ erg, with $M_{*}\approx
20\,\mathrm{M_{\odot}}$, regardless of the mixing. This results is in
agreement with the best fit computed with the online abundance-fitting tool
Starfit101010https://starfit.org/ (see Heger & Woosley, 2010). However, there
are degeneracies in the models and, taking into account uncertainties of the
chemical abundances, there can be several models that produce satisfactory
fits. Therefore it is important to explore the parameter space, to ensure that
the best fit does not represent a single solution, but is representative of
the best solution space.

The results of the $\chi^{2}$ analysis are presented in Fig. 13, where we show
the goodness of fit with different colors when varying the mass, the mixing
and the SN explosion energy of the Pop III progenitor. To simplify, we provide
examples with fixed $M_{*}=20\,\mathrm{M_{\odot}}$, in the top panel, and
fixed $f_{mix}=0.063$, in the bottom panel. Regardless of the mixing, for a 20
$\mathrm{M_{\odot}}$ Pop III progenitor, the descendants of Pop III hypernovae
($E_{SN}\geq 5\times 10^{51}$ erg) have the minimum $\chi^{2}$, while the
worst agreement is with the descendants of Pop III SNe with $E_{SN}\leq
1.2\times 10^{51}$ erg. For fixed $f_{mix}$, it is evident that the number of
descendants with a good agreement with AS0039 drastically decreases for the
lowest-energy Pop III SN progenitors. Indeed, we find the minimum $\chi^{2}$
for the descendants of high-energy SNe ($E_{SN}\geq 2.4\times 10^{51}$ erg)
with masses between 12 $\mathrm{M_{\odot}}$ and 40 $\mathrm{M_{\odot}}$.

The best fit to the abundance pattern of AS0039, as well as exploration of the
parameter space (Figs.12-13), strongly suggest this star was primarily
enriched by a primordial Pop III hypernova, with $M\approx 20$ M⊙. Since
AS0039 has a similar abundance pattern to other low $\rm[Fe/H]_{LTE}<-3.7$
stars in the galaxy, this points to an earliest chemical enrichment in
Sculptor that was dominated by high-energy SNe. Assuming the same NLTE
corrections derived for AS0039, we find that also the two stars MT00750 and
PJ03111 are best fitted by the descendants of high-energy Pop III SNe. In
particular, MT00750 agrees with the descendant of a $15\>\mathrm{M_{\odot}}$
hypernova ($E_{SN}=10\times 10^{51}$ erg) without dependence on $f_{mix}$,
while PJ03111 with the descendant of a $14.4\>\mathrm{M_{\odot}}$ high-energy
SN ($E_{SN}=2.4\times 10^{51}$ erg) with $f_{mix}=0.0251$.

###  6.2 The imprints of high-energy SN in Sculptor

In Fig. 14 we compare the results of our model (Vanni et al. 2023, in press)
for [C/Fe] as a function of [Fe/H] for observational data in the dSph
galaxies: Sculptor, Fornax, Carina and Sextans; along with those observed in
the Milky Way and UFDs. We note that literature data are typically only
provided in LTE, however, NLTE affects in iron in metal-poor giants are
expected to be on the order of $\rm\Delta[Fe/H]\approx+0.25$ (see Table 4),
and will effect [Fe/H] as well as [C/Fe] (shown with arrow in Fig. 14). The
[C/Fe] will be even lower when taking 3D effects into account, affecting C
measurements from molecular lines (Norris & Yong, 2019).

We show the [C/Fe] abundances predicted by our model for the descendants of
pure low energy Pop III SN (gray), and pure hypernovae descendants (red), i.e.
$100\%$ metals from these different types of Pop III SNe. Furthermore, we show
an intermediate case, where the descendants have been polluted only at a 50%
level by low-energy Pop III SNe and the remaining 50% metals are provided by
normal Pop II SNe (green area). The density diagrams are created exploring all
the possible initial masses of Pop III stars (i.e. $10-100\,M_{\odot}$), with
a mixing of $f_{mix}=0.063$. The contribution of Pop II stars is, on the other
hand, integrated over a normal Larson IMF (see Salvadori et al., 2019).

The majority of the stars pertaining to the dSph galaxies are carbon normal
(the maximum is $\rm[C/Fe]\approx+1$), while the MW and UFDs have stars with
$\rm[C/Fe]\geq+2.0$. The high values of [C/Fe] in these two latter
environments can be explained only with the pure descendants of low-energy Pop
III SNe, with $E_{\textsl{SN}}<1.5\times 10^{51}$ erg, which expel low amounts
of iron (see Vanni et al. 2023; and submitted to MNRAS). The stars with lower
[C/Fe] values, agree better with the pollution of both low-energy Pop III SNe
and Pop II stars. However, when taking into account the predicted NLTE
effects, the [C/Fe] values of most stars in Sculptor and Carina are too low to
be explained with these two cases. Indeed, their very low [C/Fe] value can
only be explained by a strong imprint by Pop III hypernovae.

##  7 Conclusions

We present an analysis of a newly obtained HR UVES spectrum for AS0039 in the
Sculpor dSph galaxy, providing both LTE and NLTE abundances. This star is
confirmed to be the most-metal-poor star in any external galaxy, with
$\rm[Fe/H]_{LTE}=-3.90$ and $\rm[C/Fe]_{LTE}=-0.33$ (corrected for internal
mixing). To avoid systematic errors, we re-analyse all the archival spectra
available to us at $\rm[Fe/H]\leq-3$ in Sculptor, and provide an analysis for
two stars published for the first time in this work: UHAL004 at
$\rm[Fe/H]=-2.8$ and a CEMP-no star, DR20080, discovered here at
$\rm[Fe/H]=-3$.

Out of the 11 Sculptor stars with carbon measurements at $\rm[Fe/H]\leq-3$,
only one is a CEMP-no star, giving a fraction of
$f_{\textsl{CEMP}}^{\textsl{Scl}}=9^{+11}_{-8}\%$, at odds with fractions
measured in the Milky Way and UFDs, $f_{\textsl{CEMP}}\approx 40\%$ (Placco et
al., 2014; Ji et al., 2020). This is a further confirmation that Sculptor is
remarkably devoid of CEMP-no stars, as noted by previous works (Starkenburg et
al., 2013; Skúladóttir et al., 2015b; Skúladóttir et al., 2021).

Here, we show clearly that these peculiarities in Sculptor reach beyond
carbon. Compared to the Milky Way and UFDs, the metal-poor Sculptor stars have
lower [X/Fe] ratios in light elements (e.g. Na, Al, Mg, Si). On the other
hand, heavier elements, from Ti and beyond, are generally in good agreement
with chemical abundances both in the Milky Way halo and UFDs. This unique
abundance pattern in Sculptor is consistent with enrichment from Pop III stars
with high explosion energy, $E_{\textsl{SN}}>2\times 10^{51}$ erg, which are
predicted to produce low ratios of [X/Fe] for lighter elements, while heavier
elemental ratios ([X/Fe], $Z\gtrsim 20$) are less sensitive to explosion
energy (Heger & Woosley, 2002). The average abundance pattern of the Milky Way
and UFDs is remarkably similar, while being clearly different from that of
Sculptor. This result is somewhat at odds with the prediction that the Milky
Way halo is mostly made up by massive dSph galaxies (e.g. Deason et al.,
2016). However, it is unclear how the earliest chemical enrichment of those
Milky Way progenitors differentiated to that of the present day satellite dSph
galaxies.

When comparing our Sculptor results with theoretical models, the (NLTE)
abundance pattern of the most metal-poor star in our sample, AS0039, is best
explained by it being mainly enriched by a zero-metallicity hypernovae,
$E_{\textsl{SN}}=10\times 10^{51}$ erg, with a mass $M=20$ M⊙ in good
agreement with previous analyses of the discovery X-Shooter spectrum
(Skúladóttir et al., 2021). This result is robust, and obtained regardless of
the adopted mixing.

The [C/Fe] abundances measured in Sculptor were compared to our general
parametric model, further confirming this conclusion. The very low [C/Fe]
abundances suggest that the Sculptor dSph galaxy hosted at least one Pop III
hypernova, which dominated its earliest enrichment, overshadowing the impact
of lower energy SNe. We emphasise that Pop III faint SN are still likely to
have occurred in the galaxy (and/or in its progenitors) since they are needed
to explain the existence of CEMP-no stars (see also Salvadori et al., 2015),
which have been detected at $\rm[Fe/H]=-3$ (DR20080), and $\rm[Fe/H]=-2$
(Skúladóttir et al., 2015b).

Our results show that Sculptor is massive enough to be able to retain the
products of such energetic events. This suggests that dSph galaxies are key
objects to study the full parameter space of the Pop III stars, i.e. their
mass distribution and the energy distribution of their SNe. This is further
supported by available data in other dSph galaxies, which have low [C/Fe] and
relatively few CEMP-no stars, compared to the Milky Way and UFDs.

The upcoming large spectroscopic surveys will provide more data on dSph
galaxies, in particular 4DWARFS: the 4MOST survey of dwarf galaxies and their
stellar streams (Skúladóttir et al. 2023, ESO Messenger, in press) is expected
to make a great leap forward. However, to be able to fully exploit the data to
reveal the properties of the first stars, sophisticated physically-driven
models (e.g. Rossi et al. 2021; Rossi et al. 2023), targeted at the earliest
chemical enrichment in dSph galaxies are crucially needed. By combining data
with models, the Sculptor dwarf spheroidal galaxy - and other similar galaxies
- might be our best chance at understanding the energy distribution of the
first supernovae in the Universe.

###### Acknowledgements.

The authors thank J. Simon and A. Frebel for readily sharing their data. This
project has received funding from the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation programme (grant
agreement No. 804240). This work has made use of data from the European Space
Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the
Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

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