# Spectacular nucleosynthesis from early massive stars

Alexander P. Ji Department of Astronomy & Astrophysics, University of Chicago,
5640 S Ellis Avenue, Chicago, IL 60637, USA  Kavli Institute for Cosmological
Physics, University of Chicago, Chicago, IL 60637, USA  Joint Institute for
Nuclear Astrophysics – Center for Evolution of the Elements (JINA), East
Lansing, MI 48824, USA  Sanjana Curtis NSF Astronomy and Astrophysics
Postdoctoral Fellow  Department of Astronomy & Astrophysics, University of
Chicago, 5640 S Ellis Avenue, Chicago, IL 60637, USA  Department of Astronomy,
University of California, Berkeley, Berkeley, CA 94720, USA  Nicholas Storm
Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany
Vedant Chandra Center for Astrophysics $\mid$ Harvard & Smithsonian, 60 Garden
St, Cambridge, MA 02138, USA  Kevin C. Schlaufman Johns Hopkins University
William H. Miller III Department of Physics & Astronomy, 3400 N Charles St,
Baltimore, MD 21218, USA  Tuve Fellow, Carnegie Institution for Science Earth
& Planets Laboratory, 5241 Broad Branch Road NW, Washington, DC 20015, USA
Keivan G. Stassun Department of Physics and Astronomy, Vanderbilt University,
Nashville, TN 37235, USA  Alexander Heger School of Physics and Astronomy,
Monash University, Melbourne, Vic 3800, Australia  Joint Institute for Nuclear
Astrophysics – Center for Evolution of the Elements (JINA), East Lansing, MI
48824, USA  Center of Excellence for Astrophysics in Three Dimensions
(ASTRO-3D), Stromlo, ACT 2611, Australia  Marco Pignatari Konkoly Observatory,
Research Centre for Astronomy and Earth Sciences, HUN-REN, Konkoly Thege
Miklós út 15-17, H-1121 Budapest, Hungary  CSFK, MTA Centre of Excellence,
Budapest, Konkoly Thege Miklós út 15-17, H-1121, Hungary  E. A. Milne Centre
for Astrophysics, University of Hull, Hull HU6 7RX, UK  Adrian M. Price-Whelan
Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Ave, New
York, NY 10010, USA  Maria Bergemann Max Planck Institute for Astronomy,
Königstuhl 17, D-69117 Heidelberg, Germany  Guy S. Stringfellow Center for
Astrophysics and Space Astronomy, University of Colorado, 389 UCB, Boulder, CO
80309-0389, USA  Carla Fröhlich Department of Physics, North Carolina State
University, Raleigh NC 27695, USA  Joint Institute for Nuclear Astrophysics –
Center for Evolution of the Elements (JINA), East Lansing, MI 48824, USA
Henrique Reggiani Carnegie Fellow  The Observatories of the Carnegie
Institution for Science, 813 Santa Barbara Street, Pasadena, CA 91101, USA
Erika M. Holmbeck NHFP Hubble Fellow  The Observatories of the Carnegie
Institution for Science, 813 Santa Barbara Street, Pasadena, CA 91101, USA
Jamie Tayar Department of Astronomy, University of Florida, Bryant Space
Science Center, Stadium Road, Gainesville, FL 32611, USA  Shivani P. Shah
Department of Astronomy, University of Florida, Bryant Space Science Center,
Stadium Road, Gainesville, FL 32611, USA  Emily J. Griffith NSF Astronomy and
Astrophysics Postdoctoral Fellow  Center for Astrophysics and Space Astronomy,
University of Colorado, 389 UCB, Boulder, CO 80309-0389, USA  Chervin F. P.
Laporte Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona,
Martí i Franquès 1, E-08028 Barcelona, Spain  Institut d’Estudis Espacials de
Catalunya (IEEC), E-08034 Barcelona, Spain  Andrew R. Casey School of Physics
& Astronomy, Monash University, Wellington Road, Clayton 3800, Victoria,
Australia  ARC Centre of Excellence for All Sky Astrophysics in 3
Dimensions(ASTRO 3D), Canberra, ACT 2611, Australia  Keith Hawkins Department
of Astronomy, The University of Texas at Austin, 2515 Speedway Boulevard,
Austin, TX 78712, USA  Danny Horta Center for Computational Astrophysics,
Flatiron Institute, 162 Fifth Ave, New York, NY 10010, USA  William Cerny
Department of Astronomy, Yale University, New Haven, CT 06520, USA  Pierre
Thibodeaux Department of Astronomy & Astrophysics, University of Chicago, 5640
S Ellis Avenue, Chicago, IL 60637, USA  Sam A. Usman Department of Astronomy &
Astrophysics, University of Chicago, 5640 S Ellis Avenue, Chicago, IL 60637,
USA  João A. S. Amarante Institut de Ciencies del Cosmos (ICCUB), Universitat
de Barcelona (IEEC-UB), Martí i Franquès 1, E08028 Barcelona, Spain  Jeremiah
Horrocks Institute, University of Central Lancashire, Preston, PR1 2HE, UK
Rachael L. Beaton Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA  Phillip A. Cargile Center for Astrophysics $\mid$
Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Cristina
Chiappini Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte
16, D-14482 Potsdam, Germany  Charlie Conroy Center for Astrophysics $\mid$
Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Jennifer A.
Johnson Department of Astronomy, The Ohio State University, 140 W. 18th
Avenue, Columbus, OH 43210, USA  Center for Cosmology and AstroParticle
Physics, Ohio State University, 191 West Woodruff Avenue, Columbus, OH 43210,
USA  Juna A. Kollmeier The Observatories of the Carnegie Institution for
Science, 813 Santa Barbara Street, Pasadena, CA 91101, USA  Canadian Institute
for Theoretical Astrophysics, University of Toronto, Toronto, ON, M5S-98H,
Canada  Haining Li Key Lab of Optical Astronomy, National Astronomical
Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang, Beijing
100012, People’s Republic of China  Sarah Loebman Department of Physics,
University of California, Merced, 5200 N Lake Road, Merced, CA 95343, USA
Georges Meynet Department of Astronomy of Geneva University, Switzerland
Dmitry Bizyaev Apache Point Observatory and New Mexico State University, P.O.
Box 59, Sunspot, NM, 88349-0059, USA  Sternberg Astronomical Institute, Moscow
State University, Moscow  Joel R. Brownstein Department of Physics and
Astronomy, University of Utah, 115 S. 1400 E., Salt Lake City, UT 84112, USA
Pramod Gupta Department of Astronomy, University of Washington, Box 351580,
Seattle, WA 98195, USA  Sean Morrison Department of Astronomy, University of
Illinois at Urbana-Champaign, Urbana, IL 61801, USA  Kaike Pan Apache Point
Observatory and New Mexico State University, P.O. Box 59, Sunspot, NM,
88349-0059, USA  Solange V. Ramirez  The Observatories of the Carnegie
Institution for Science, 813 Santa Barbara Street, Pasadena, CA 91101, USA
Hans-Walter Rix Max Planck Institute for Astronomy, Königstuhl 17, D-69117
Heidelberg, Germany  José Sánchez-Gallego Department of Astronomy, University
of Washington, Box 351580, Seattle, WA 98195, USA Alexander P. Ji
<EMAIL_ADDRESS>
###### Abstract

Stars formed with initial mass over 50 $M_{\odot}$ are very rare today, but
they are thought to be more common in the early universe. The fates of those
early, metal-poor, massive stars are highly uncertain. Most are expected to
directly collapse to black holes, while some may explode as a result of
rotationally powered engines or the pair-creation instability. We present the
chemical abundances of J0931+0038, a nearby low-mass star identified in early
followup of SDSS-V Milky Way Mapper, which preserves the signature of unusual
nucleosynthesis from a massive star in the early universe. J0931+0038 has
relatively high metallicity ([Fe/H] $=-1.76\pm 0.13$) but an extreme odd–even
abundance pattern, with some of the lowest known abundance ratios of [N/Fe],
[Na/Fe], [K/Fe], [Sc/Fe], and [Ba/Fe]. The implication is that a majority of
its metals originated in a single extremely metal-poor nucleosynthetic source.
An extensive search through nucleosynthesis predictions finds a clear
preference for progenitors with initial mass $>50M_{\odot}$, making J0931+0038
one of the first observational constraints on nucleosynthesis in this mass
range. However the full abundance pattern is not matched by any models in the
literature. J0931+0038 thus presents a challenge for the next generation of
nucleosynthesis models and motivates study of high-mass progenitor stars
impacted by convection, rotation, jets, and/or binary companions. Though rare,
more examples of unusual early nucleosynthesis in metal-poor stars should be
found in upcoming large spectroscopic surveys.

††facilities: Sloan, Magellan (MIKE), Gaia††software:  MOOG (Sneden, 1973;
Sobeck et al., 2011), Turbospectrum (Plez, 2012), TSFitPy (Gerber et al.,
2023), smhr (Casey, 2014; Ji et al., 2020a), emcee (Foreman-Mackey et al.,
2013), gala (Price-Whelan, 2017; Price-Whelan et al., 2022), minesweeper
(Cargile et al., 2020), dynesty (Speagle, 2020), isochrones (Morton, 2015),
MultiNest (Feroz & Hobson, 2008; Feroz et al., 2009, 2019), R (R Core Team,
2023), StarFit (Heger & Woosley, 2010), numpy (van der Walt et al., 2011),
scipy (Jones et al., 2001), matplotlib (Hunter, 2007), pandas (Mckinney,
2010), seaborn (Waskom et al., 2016), and astropy (Astropy Collaboration et
al., 2013; Price-Whelan et al., 2018)

##  1 Introduction

The chemical abundances of metal-poor stars provide an archaeological snapshot
of the first massive stars (e.g., Frebel & Norris, 2015). When those stars
died, they ejected elements that polluted the interstellar and intergalactic
medium. Stars forming out of this minimally polluted gas would be metal-poor,
and the low-mass metal-poor stars could survive until today, where they can be
found in our Milky Way. The atmospheres of these low-mass stars thus provide a
window to nucleosynthesis in the first massive stars. Since even JWST is
unable to directly observe the first massive stars (e.g., Schauer et al.,
2020), these chemical abundances are one of the few ways to understand how the
first stars formed and died. Theoretically, one of the most robust predictions
is that the first metal-free stars should have a top-heavy initial mass
function with characteristic mass $\gtrsim 10\mathrm{\,M_{\odot}}$ (e.g.,
Bromm, 2013; Klessen & Glover, 2023). This prediction, however, is still not
confirmed observationally, nor is there a clear understanding of when or how
the initial mass function transitions to its present-day shape (e.g., Offner
et al., 2014; Sharda & Krumholz, 2022).

Decades of searches have led to the discovery and chemical characterization of
hundreds of extremely metal-poor stars with $\mbox{[Fe/H]}\lesssim-3$ (e.g.,
Beers et al., 1992; Cayrel et al., 2004; Frebel et al., 2006; Schlaufman &
Casey, 2014; Aguado et al., 2016; Starkenburg et al., 2017; Li et al., 2018;
Da Costa et al., 2019). Their chemical compositions reveal a variety of
processes occurring in the early universe. The majority of these metal-poor
stars broadly look like they have been enriched by core-collapse supernovae,
possibly following a standard Salpeter initial mass function (e.g., Cayrel et
al., 2004; Heger & Woosley, 2010). A prominent signature is the carbon-
enhanced metal-poor stars, which make up the majority of stars at
$\mbox{[Fe/H]}\lesssim-4$ (e.g., Norris et al., 2013; Placco et al., 2014) and
may suggest the first stars preferentially explode as faint supernovae (e.g.,
Umeda & Nomoto, 2002) or have extremely rapid rotation and winds (e.g., Meynet
et al., 2006; Chiappini, 2013). A few iron-poor stars have been found without
carbon enhancement, making them stars with the lowest overall metallicities
(e.g., Caffau et al., 2013; Starkenburg et al., 2017). There also have been
many signatures of high energy hypernovae, accompanied by a variety of
neutron-capture nucleosynthesis signatures (e.g., Ezzeddine et al., 2019; Yong
et al., 2021; Skúladóttir et al., 2021). Recently, the first signature of pair
instability supernovae has finally been found (Xing et al. 2023, though a
core-collapse supernova interpretation has also been suggested by Jeena et al.
2023).

Interestingly, when comparing the abundances of metal-poor stars to
nucleosynthesis models, almost all the supernova progenitors have initial
masses less than 50 $\mathrm{\,M_{\odot}}$ (e.g., Placco et al., 2015; Fraser
et al., 2017; Ishigaki et al., 2018). This could be because more massive stars
typically collapse directly to black holes, either directly or after pair-
instability pulsation-driven mass loss, and thus do not release any metals
into the universe (e.g., Heger et al., 2003; Yoon et al., 2012).

The community’s attention has primarily been focused on extremely metal-poor
stars with $\mbox{[Fe/H]}\lesssim-3$. Such metal-poor stars are likely
enriched by only a few, or even just one supernova (Audouze & Silk, 1995; Ryan
et al., 1996), so it is reasonable to compare their chemical abundances to
nucleosynthesis models of individual supernova explosions. However in
principle, it is possible to find stars dominated by nucleosynthesis in a
small number of supernovae at higher metallicities. For example, it is well-
known that pair instability supernovae (PISNe) produce so much calcium and
iron that they immediately enrich stars to $\mbox{[Fe/H]}\sim-2$, which would
make them difficult to discover in surveys looking for the most Fe-poor stars
(Karlsson et al., 2008; Salvadori et al., 2019). Identifying such relatively
metal-rich stars with unique elemental compositions is difficult, because the
vast majority of stars at $\mbox{[Fe/H]}>-3$ have experienced ordinary
chemical evolution, so it is hard to distinguish interesting stars from a vast
background of ordinary stars. Stars at higher metallicities could be hiding
signatures of a different population of supernovae that produce large amounts
of iron.

Here, we present the discovery and chemical composition of the spectacular
star 2MASS J09311004+0038042 (Gaia DR3 3841101888330639872, abbreviated as
J0931$+$0038), which was identified in early SDSS-V data. J0931$+$0038 has a
relatively high metallicity $\mbox{[Fe/H]}=-1.76$, but its extreme low
abundances of other elements like Na, K, Sc, and Ba show it is dominated by
nucleosynthesis from a single source. The star’s composition is unlike any
star that has been seen before, and its high metallicity and abundance pattern
imply a progenitor star with initial mass over 50 $\mathrm{\,M_{\odot}}$, one
of the first and most complete observational constraints on nucleosynthesis in
this mass range. However, we have been unable to find satisfactory
nucleosynthesis models to explain the full abundance pattern. Section 2
describes our target selection, observations, and chemical abundance analysis.
Section 3 compares the results of the abundance analysis to existing stellar
abundances. We discuss the origin of this star in Section 4 and conclude in
Section 5. An extended Appendix provides details on the abundance analysis
(Appendix A) and nucleosynthesis fits (Appendix B).

##  2 Observations and Analysis

Figure 1: Spectrum of J0931$+$0038 (black line and grey shaded uncertainty
band). For comparison, two stars with similar stellar parameters are plotted:
a MIKE spectrum of a normal star from our SDSS sample in purple, and a
Keck/HIRES spectrum of the r-process enhanced star BD$+17^{\circ}3248$ in
blue. Visible by eye are the low abundances of Na, Ti, Sc, and Ba; the
enhancement in Sr, Y, Mn, Ni, and Zn; and the detected Mo, Ru, and Pd lines.
BD$+17^{\circ}3248$ is highly r-process enhanced, but J0931$+$0038 has
stronger lines of Sr, Mo, Ru, and Pd while the Ba line is barely detected (it
is blended with a weak Zr line).

###  2.1 Target Selection and Observations

J0931$+$0038 was observed by SDSS-V (Kollmeier et al., 2017; Almeida et al.,
2023, De Lee et al., in prep) in the metal poor halo program, which uses spare
fibers to target stars with photometric metallicities $\mbox{[Fe/H]}<-2$. This
particular star was identified as a metal-poor candidate with SkyMapper DR2
photometry (Onken et al., 2019) and observed with the low-resolution optical
BOSS spectrograph. The BOSS spectra were analyzed using MINESweeper (Cargile
et al., 2020), which performs a spectrophotometric fit including the Gaia DR3
parallax, broadband photometry, and the MIST isochrones (Choi et al., 2016).
The MINESweeper parameters were $T_{\mathrm{eff}}=5220$K, $\log\,g=2.57$,
$\mathrm{\,[Fe/H]}=-1.9$, and $\mathrm{\,[\alpha/Fe]}=0.03$, showing it to be
a metal-poor and alpha-poor red giant. The star has an eccentric halo orbit
and is likely unassociated with any known structures (see Appendix A).

We observed J0931$+$0038 with Magellan/MIKE (Bernstein et al., 2003) for three
hours on 2023 April 13, obtaining a high signal-to-noise $R\sim 30,000$
spectrum (100/pixel or 70/resolution element at 4000Å). The data were reduced
with CarPy (Kelson, 2003). Portions of this spectrum are shown in Fig 1,
compared to two stars of similar stellar parameters and metallicities: a
Keck/HIRES spectrum of the r-process enhanced star BD$+17^{\circ}3248$
(Johnson & Bolte, 2002; Cowan et al., 2002); and a Magellan/MIKE spectrum of
Gaia DR3 3963318275114883584, a star with ordinary composition. Just visually,
the spectrum of J0931$+$0038 displays extraordinarily weak Na, Ti, Sc, and Ba
lines; unusually strong lines of Sr, Y, Mn, Ni, and Zn; and clear detections
of Mo, Ru, and Pd.

###  2.2 Abundance Analysis

We performed a standard analysis using 1D ATLAS model atmospheres (Castelli &
Kurucz, 2004) and the MOOG radiative transfer code including scattering
(Sneden, 1973; Sobeck et al., 2011) and assuming local thermodynamic
equilibrium (LTE)111https://github.com/alexji/moog17scat. The line list was
selected from a combination of lines from Roederer et al. (2018) and Ji et al.
(2020a), with atomic data adopted from linemake
222https://github.com/vmplacco/linemake (Placco et al., 2021). Stellar
parameters were derived by fixing spectrophotometric temperatures and then
determining other stellar parameters spectroscopically, resulting in
$T_{\mathrm{eff}}=5200\pm 100$K, $\log\,g=2.75\pm 0.20$, $\nu_{t}=1.65\pm
0.3\mathrm{\,km\,s^{-1}}$, $\mbox{[M/H]}=-1.9\pm 0.1$, and
$\mathrm{\,[\alpha/Fe]}=0.0$. Chemical abundances were determined using smhr
(Casey, 2014)333https://github.com/andycasey/smhr with a mix of equivalent
widths and syntheses. Upper limits were calculated using synthetic spectra.
The adopted abundance uncertainty includes line-to-line scatter, signal-to-
noise, and stellar parameter uncertainties. [Fe/H] uncertainties are on the
total metallicity, while [X/Fe] uncertainties are relative to [Fe/H]. Non-LTE
(NLTE) corrections were mostly calculated using TSFitPy
444https://github.com/TSFitPy-developers/TSFitPy (Gerber et al., 2023). The
actual [Fe/H] abundance after NLTE corrections is $\mbox{[Fe/H]}=-1.76\pm
0.13$. We also estimated evolutionary corrections for C and N based on metal-
poor giants in APOGEE DR17 (Abdurro’uf et al., 2022). Full details of the
analysis are given in Appendix A.

Figure 2: [X/Fe] (in NLTE when possible) vs atomic number. The grey boxplots
for each element $X$ are [X/Fe] from 4866 stars in the SAGA literature
compilation (Suda et al., 2008) with $-3.5<\mbox{[Fe/H]}<-1.5$, to maximize
the intrinsic [X/Fe] range. The SAGA abundances have been moved to the Magg et
al. (2022a) abundance scale, and they have been shifted by the NLTE correction
of J0931$+$0038 in Table 1. The box-and-whisker plots indicate the median and
25th-75th percentile with the box and the 1st-99th percentile with the
whiskers. The abundance of Na, K, Sc, and Ba are among the lowest abundances
of these elements ever measured. The uncertainty for Fe is the overall
metallicity uncertainty, while for other elements it is the precision relative
to Fe. Note the plotted Li value is [Li/Fe], and A(Li)=1.15.

##  3 Abundance Results

Table 1 presents the chemical abundances of J0931$+$0038, in NLTE where
available. Figure 2 shows [X/Fe] compared to the SAGA database after removing
upper limits (Suda et al., 2008). We adopt the Solar abundance scale from Magg
et al. (2022a), using Asplund et al. (2009) to fill in missing elements. The
SAGA database abundances are shifted to this abundance scale. The SAGA
database predominantly consists of LTE abundances, so for comparison we also
shift the SAGA abundances by the NLTE corrections for J0931$+$0038 in Table 1.

There are four remarkable features in the abundance pattern of J0931$+$0038\.
First, the light elements from C to Sc display an extremely strong odd-even
effect, comparable only to the recently discovered “pair instability” star
J1010$+$2358 (Xing et al., 2023). Second, the abundances of the light iron-
peak elements Sc, Ti, and V are extremely low, similar to some metal-poor
stars in the bulge, halo, and dwarf galaxies (Casey & Schlaufman, 2015; Ji et
al., 2020b). Third, the heavier iron-peak elements Mn, Ni, and Zn are quite
enhanced, which matches some extremely metal-poor stars associated with
hypernovae (Ezzeddine et al., 2019; Yong et al., 2021; Skúladóttir et al.,
2021). Fourth, the neutron-capture elements around the first peak (magic
neutron number $N=50$) from Sr to Pd are highly enhanced similar to stars like
HD122563 and HD88609 (Honda et al., 2007), but the [Ba/Fe] is one of the
lowest values ever measured, comparable to the most extreme stars in ultra-
faint dwarf galaxies (Ji et al., 2019). While each of these four features has
been seen before in individual stars, J0931$+$0038 displays one of the most
extreme versions of each feature and combines all of them in one star.
Additionally, all previously known stars with such extreme abundance features
have been found in the very metal-poor regime at $\mbox{[Fe/H]}\lesssim-2.5$,
but J0931$+$0038 has a metallicity over 5${\times}$ higher
$\mbox{[Fe/H]}=-1.76$.

Table 1: Chemical Abundances

Species | $N$ | $\log\epsilon$ | [X/H] | [X/Fe] | $\sigma$ | $\Delta_{\rm NLTE}$
---|---|---|---|---|---|---
Li I | 1 | $1.15$ | $+0.10$ | $+1.86$ | 0.12 |  $\cdots$
C-H | 2 | $6.07$ | $-2.49$ | $-0.73$ | 0.22 | $+0.10$
N-H | 1 | $5.36$ | $-2.62$ | $-0.86$ | limit | $-0.10$
O I | 3 | $7.23$ | $-1.54$ | $+0.22$ | 0.17 | $-0.06$
Na I | 2 | $2.80$ | $-3.49$ | $-1.73$ | 0.09 | $-0.10$
Mg I | 8 | $5.52$ | $-2.03$ | $-0.27$ | 0.11 | $-0.02$
Al I | 1 | $4.15$ | $-2.28$ | $-0.52$ | 0.50 | $+0.65$
Si I | 8 | $5.80$ | $-1.79$ | $-0.03$ | 0.13 | $-0.17$
K I | 2 | $2.05$ | $-3.09$ | $-1.33$ | 0.14 | $-0.20$
Ca I | 30 | $4.73$ | $-1.64$ | $+0.12$ | 0.13 | $+0.02$
Sc II | 3 | $-0.06$ | $-3.13$ | $-1.37$ | 0.09 |  $\cdots$
Ti II | 30 | $2.56$ | $-2.38$ | $-0.62$ | 0.10 | $+0.12$
V II | 7 | $1.48$ | $-2.41$ | $-0.65$ | 0.10 |  $\cdots$
Cr II | 5 | $3.75$ | $-1.99$ | $-0.23$ | 0.12 |  $\cdots$
Mn I | 10 | $4.06$ | $-1.46$ | $+0.30$ | 0.06 | $+0.34$
Fe I | 181 | $5.74$ | $-1.76$ | $+0.00$ | 0.13 | $+0.11$
Co I | 4 | $3.37$ | $-1.58$ | $+0.18$ | 0.10 | $+0.11$
Ni I | 26 | $5.04$ | $-1.20$ | $+0.56$ | 0.15 | $+0.31$
Cu I | 1 | $2.64$ | $-1.55$ | $+0.21$ | 0.19 | $+0.35$
Zn I | 2 | $3.17$ | $-1.38$ | $+0.38$ | 0.08 |  $\cdots$
Rb I | 1 | $2.61$ | $+0.09$ | $+1.85$ | limit |  $\cdots$
Sr II | 3 | $1.85$ | $-1.02$ | $+0.74$ | 0.07 | $+0.03$
Y II | 24 | $1.27$ | $-0.94$ | $+0.82$ | 0.11 | $-0.00$
Zr II | 15 | $1.87$ | $-0.71$ | $+1.05$ | 0.08 |  $\cdots$
Nb II | 1 | $1.34$ | $-0.12$ | $+1.64$ | limit |  $\cdots$
Mo I | 1 | $0.55$ | $-1.33$ | $+0.43$ | 0.16 |  $\cdots$
Ru I | 1 | $0.68$ | $-1.07$ | $+0.69$ | 0.14 |  $\cdots$
Rh I | 1 | $0.34$ | $-0.57$ | $+1.19$ | limit |  $\cdots$
Pd I | 1 | $0.46$ | $-1.11$ | $+0.65$ | 0.14 |  $\cdots$
Ag I | 1 | $-0.15$ | $-1.09$ | $+0.67$ | limit |  $\cdots$
Ba II | 1 | $-2.33$ | $-4.51$ | $-2.75$ | 0.13 | $+0.18$
Eu II | 1 | $-1.79$ | $-2.31$ | $-0.55$ | limit |  $\cdots$

Note. — The Magg et al. (2022a) solar normalization is used. NLTE corrections
have already been applied and are shown for reference. For C and N,
$\Delta_{\rm NLTE}$ is an estimate for the evolutionary correction. The
correction listed is for each element’s $\log\epsilon$, so [X/Fe] has an
additional correction for [Fe/H] already applied. The abundance uncertainty
for all elements is for the relative value [X/Fe], except for [Fe/H] which is
the absolute metallicity uncertainty. Upper limits are denoted “limit” in the
$\sigma$ column.

##  4 Discussion

###  4.1 A Single Enrichment Source

Figure 3:  Composition of J0931$+$0038 (red square) for Na, Ba, Mg, and Sr
compared to the SAGA database (grey points), higher mass classical dwarf
galaxies (blue squares), and lower mass ultra-faint dwarf galaxies (yellow
diamonds). The dashed black line is an outlier-clipped 3rd order polynomial
fit to the SAGA data. The horizontal red line is the [X/H] of J0931$+$0038\.
From the top two panels, the red shaded region indicates $\mbox{[Fe/H]}<-3$,
the ISM metallicity range that alone would contribute all of the Na, Ba, and
other under-abundant elements like N, K, and Sc observed in J0931$+$0038\. The
bottom two panels, Mg and Sr, show that explaining the low N, Na, K, Sc, and
Ba by simply adding Fe (e.g. with a Type Ia supernova) would require extremely
high abundances of other elements.

J0931$+$0038 has a relatively high metallicity and would normally be
considered heavily contaminated by chemical evolution, but the very low
abundances of N, Na, K, Sc, and Ba imply that it has negligible contamination
from general chemical evolution in the interstellar medium (ISM). Figure 3
illustrates this, by plotting [X/H] vs [Fe/H] of J0931$+$0038 and the SAGA
database, including dwarf galaxy stars from JINAbase (Abohalima & Frebel 2018;
other elements shown in Appendix A). It is clear that J0931$+$0038 is not part
of any overall chemical evolution trend, either in Milky Way halo stars or in
all known dwarf galaxies.

A newly formed star’s metallicity is the sum of the metallicities of the
background ISM and the diluted ejecta from any recent nucleosynthetic sources.
Thus, one way to interpret Figure 3 is that 100% of the Na and Ba in
J0931$+$0038 comes from swept up ISM material. This would imply that it formed
from ISM composition of $\mbox{[Fe/H]}\sim-3.5$ (red dashed lines in Figure
3). A recent nucleosynthetic event would have to raise the ISM metallicity by
a factor of $\gtrsim$50 from $\mbox{[Fe/H]}\sim-3.5$ to
$\mbox{[Fe/H]}=-1.76\pm 0.13$, without adding _any_ N, Na, K, Sc, or Ba. Thus,
the extreme low abundance of these elements implies that the majority of
metals in J0931$+$0038 have to be made in “one shot”, i.e. from a single
nucleosynthetic event, rather than the continuous sum of multiple sources as
expected in ordinary chemical evolution. This is a conservative
interpretation, because if the nucleosynthetic event produced any N, Na, K,
Sc, or Ba, the ISM would have been even lower metallicity, possibly even
primordial composition.

The presence of multiple extreme abundance ratios in J0931$+$0038 also favors
a single source of elements, rather than combining multiple stellar sources.
Each extreme ratio is erased by mixing with ordinary ISM, so invoking multiple
element sources requires spatial and temporal coincidence, as the
homogenization time in dwarf galaxies is only ${\sim}100-300$ Myr (see
references in Ji et al., 2023). For example, it is tempting to invoke a Type
Ia supernova in combination with a massive star supernova to explain the high
metallicity, low odd-even, and unusual Fe peak abundances (in an analogy to
the “iron-rich metal-poor stars,” Reggiani et al. 2023). The C-Ca and neutron-
capture elements in J0931$+$0038 can not come from the Type Ia, so must
instead originate from ISM material mixed with the Type Ia ejecta. However,
this ISM would need to have one of the highest [Mg, Si, Ca/Fe] abundances ever
observed, as well as simultaneously the highest [Sr, Y, Zr/Fe] abundances
known. This is illustrated in Fig 3: of the elements shown, only Fe is
produced in Type Ia SNe, so the horizontal red lines indicate the track of
Type Ia SN enrichment. If J0931$+$0038 originated from the shaded red [Fe/H]
region and was enriched to high [Fe/H] by a Type Ia SN, it must have had the
highest [Mg/Fe] and [Sr/Fe] ever observed. Thus, a Type Ia supernova can only
be invoked if it occurs simultaneously in the same region of a galaxy as an
extreme core-collapse supernovae that produced the high abundance of Mg, Sr,
and other elements, which would be an implausible coincidence. A similar
argument precludes most other combinations of multiple sources, though it may
be plausible to combine two core-collapse supernovae that originate from the
same binary system.

###  4.2 Maximum metallicity of supernova models

An extraordinary nucleosynthetic event is needed to produce the high
metallicity of J0931$+$0038 in one shot. We can constrain this by modeling the
maximum metallicity achievable from stars forming directly out of a supernova
explosion mixed with pristine gas. A supernova with a given explosion kinetic
energy will sweep up a minimum mass of gas before the material can turn into
stars (e.g., Cioffi et al., 1988; Ryan et al., 1996; Macias & Ramirez-Ruiz,
2018; Ji et al., 2020b; Magg et al., 2020; Kolborg et al., 2022). This imposes
an _upper limit_ on [Fe/H]: it is possible to dilute the supernova metal yield
into more gas, but not less.

To compare this to J0931$+$0038, we take the explosion energy and iron yield
for a wide range of supernova nucleosynthesis models covering different
progenitor masses, fallback, energies, and metallicities up to
$\mbox{[Z/H]}<-1.5$ (Heger & Woosley, 2002, 2010; Nomoto et al., 2013;
Grimmett et al., 2018; Ebinger et al., 2020). We translate the explosion
energy into a minimum gas mass using:

$M_{\rm dil,min}\approx 1.9\times
10^{4}\mathrm{\,M_{\odot}}\,E_{51}^{0.96}n_{0}^{-0.11}$ (1)

from Magg et al. (2020). Though this limit was derived assuming spherical
symmetry and a homogeneous ISM, it was validated by cosmological radiation
hydrodynamic simulations (Magg et al., 2022b). $E_{\rm 51}$ is the kinetic
energy in units of $10^{51}$ erg (or 1 B) and $n_{0}$ is the ISM density in
units of cm-3. Assuming a hydrogen mass fraction $X=0.75$ and
A(Fe)${}_{\odot}=7.50$, the _maximum_ metallicity achievable by a given
supernova model and ISM density is given by:

$\mbox{[Fe/H]}<-2.40+\log\frac{M_{\rm Fe}}{0.1\mathrm{\,M_{\odot}}}-0.96\log
E_{51}+0.11\log n_{0}$ (2)

This calculation assumes a homogeneous ISM, but inhomogeneous mixing tends to
exacerbate the problem, as the denser gas that turns into stars is more
resistant to metal pollution (Magg et al., 2020, 2022b).

We plot this maximum [Fe/H] with $n_{0}=1$ for several nucleosynthesis models
in the top panel of Figure 4. The [Fe/H] of J0931$+$0038 is shown by a red
shaded band, and it can only be achieved in extreme explosions of massive
stars: either progenitor stars with $M>50\mathrm{\,M_{\odot}}$, or pair
instability supernovae with initial mass $M\gtrsim 200\mathrm{\,M_{\odot}}$.
Less massive progenitors simply do not produce enough iron or dilute into a
small enough hydrogen mass to explain the metallicity of J0931$+$0038\. The
one exception is an engine-driven supernova by Ebinger et al. (2020), which
has $M_{\rm Fe}\sim 0.1\mathrm{\,M_{\odot}}$ and energy $E\approx 0.3$B. These
models are the most self-consistent CCSN explosions shown, but they do not
include any fallback from a reverse shock, which is estimated to be about 0.1
$\mathrm{\,M_{\odot}}$ (Perego et al., 2015) and would substantially lower the
maximum [Fe/H]. The other core-collapse supernova and hypernova models are
exploded with parameterized models, where the explosion energy and
mixing/fallback are varied freely or fixed to reproduce certain observations.
At a fixed progenitor, higher explosion energies eject more Fe but dilute into
more gas.555This figure shows only a selection of zero-metallicity supernovae
for clarity, but all models in these and other grids are shown in Appendix B.

Figure 4:  Initial mass vs maximum [Fe/H], [C/O], [Na/Mg], [Mg/Fe], and
[Zn/Fe] for zero-metallicity supernovae from five yield grids: CCSN from Heger
& Woosley 2010 (HW10, fiducial mixing, $E=0.3-2.4$B in steps of 2x); HN from
Grimmett et al. 2018 (G18, no mixing, $E=5,10,50,100$B); PISN from Heger &
Woosley 2002 (HW02); all types of SN from Nomoto et al. 2013 (NKT13), and CCSN
from Ebinger et al. 2020 (E20). Point sizes are proportional to log explosion
energy (0.3-100B). The horizontal red lines and shaded regions show the
abundance of J0931$+$0038\. Top row: maximum [Fe/H] strongly prefers higher
mass progenitor stars with $M>50\mathrm{\,M_{\odot}}$. Larger explosion
energies tend to synthesize more Fe but dilute into more H, with the balance
indicated by vertical trends in point sizes. Second row: [C/O] rules out low-
mass CCSN ($M\lesssim 20\mathrm{\,M_{\odot}}$). Third and fourth row: [Na/Mg]
and [Mg/Fe] disfavor intermediate-mass CCSN ($20-80\mathrm{\,M_{\odot}}$).
Higher energy HN match the abundances better and allow progenitors down to
$40\mathrm{\,M_{\odot}}$, but these all strongly violate the [Fe/H]
constraint. E20 is removed from the [Na/Mg] plot as the Na yields are not
predicted. Fifth row: PISNe ($M>140\mathrm{\,M_{\odot}}$) are unable to
produce significant Zn. Bottom row: estimated stellar fate given initial mass
for a single, metal-poor, non-rotating star (Heger et al., 2003).

###  4.3 Nucleosynthetic Origin

Figure 5:  Representative best matching nucleosynthesis models. Abundances of
J0931$+$0038 are given as red squares with error bars. In the top panel, the
large open blue circles connected by a solid line indicate the best-fit HN
model (Grimmett et al., 2018) The dotted blue line with small points and
dashed blue line with small open circles indicate adding the HN to a high-
entropy proton-rich wind pattern (Bliss et al., 2018) and weak r-process
pattern (Holmbeck et al., 2023), respectively. In the bottom panel, the solid
purple circles with solid line indicate the best-fit PISN model (Heger &
Woosley, 2002). The dotted purple line with small open circles indicates the
same model with a modified i-process (calculated using the framework in
Roederer et al. 2022, see Appendix B for details). The HN is the best fit to
the lighter elements and has leeway to fit the heavier elements, but the high
energy underpredicts [Fe/H]. The PISN easily matches the high [Fe/H], and we
speculate that a full calculation of a metal-enriched PISN progenitor and
explosion with i-process could remedy the disadvantages seen here.

We searched through several grids of nucleosynthesis models to determine what
type of supernova could explain the abundance pattern of J0931$+$0038\. Here,
we discuss the key element ratios that distinguish between progenitors, as
illustrated in Figure 4. We primarily examine zero-metallicity supernova
progenitors, as they have the largest range of model predictions, as well as
lower neutron fractions that naturally result in a strong odd-even effect.
However, we find no reason to exclude progenitors up to the ISM constraint
$\mbox{[Fe/H]}\lesssim-3$ (Fig 3). Overall, the best models all invoke
$M\gtrsim 50\mathrm{\,M_{\odot}}$ progenitors, and the best match out of
current models is achieved by metal-free $80\mathrm{\,M_{\odot}}$ hypernovae
(Fig 5). However, we were unable to find any model that could explain all
abundance features. A detailed discussion is given in Appendix B for
nucleosynthesis experts.

We first reject electron-capture supernovae ($M\sim 8-10\mathrm{\,M_{\odot}}$,
Doherty et al. 2017; Wanajo et al. 2018), pulsational pair-instability
supernovae (PPISNe, $100\lesssim M/\mathrm{\,M_{\odot}}\lesssim 140$, Woosley
2017), and general relativistic instability supernovae
($M>10^{4}\mathrm{\,M_{\odot}}$, Chen et al. 2014) as possibilities. These all
produce extremely high ratios of [C, N, O/Fe] inconsistent with J0931$+$0038.

We next examine deaths of $10-100\mathrm{\,M_{\odot}}$ stars. We split these
models into lower energy core-collapse supernovae (CCSNe) powered by the
ordinary neutrino-driven mechanism ($E\lesssim 2$B); and higher energy
hypernovae (HNe), which likely require extra energy from rotation and jets,
perhaps driven by black hole accretion disks or millisecond magnetars (see
references in Grimmett et al., 2021). It is broadly expected that
$10-40\mathrm{\,M_{\odot}}$ stars can explode as both CCSNe and HNe, while
$40-100\mathrm{\,M_{\odot}}$ stars probably need extra energy from a HNe to
explode if they do at all (Heger et al., 2003, bottom row of Fig 4)666It is
well-known that the explosion landscape from $10-100\mathrm{\,M_{\odot}}$ is
not monotonic in initial mass, instead showing islands of explodability (e.g.,
Pejcha & Thompson, 2015; Sukhbold et al., 2016; Burrows et al., 2018; Boccioli
et al., 2023). However, due to reduced mass loss in metal-poor stars, current
self-consistent models of neutrino-driven explosions have all stars above
40$\mathrm{\,M_{\odot}}$ collapsing to black holes (Ebinger et al., 2020)..
The most common SNe with $M\lesssim 20\mathrm{\,M_{\odot}}$ can be rejected
due to their higher C/O yield ratios, a robust prediction of stellar evolution
(Ishigaki et al., 2018, second row of Fig 4). Above $20\mathrm{\,M_{\odot}}$,
CCSNe eject large amounts of hydrostatically synthesized elements like O and
Mg, resulting in high [Na/Mg] and [Mg/Fe] ratios that conflict with
J0931$+$0038 (third and fourth rows of Fig 4). However, higher energy
explosions can reduce the [Na/Mg] and [$\alpha$/Fe] yields to be consistent
with J0931$+$0038 (see HN models from Grimmett et al. 2018 in Fig 4). Both
CCSNe and HNe can likely synthesize the light neutron-capture elements seen in
J0931$+$0038, either through neutrino-driven winds (Fröhlich et al., 2006;
Bliss et al., 2018; Wanajo et al., 2018) or accretion disk winds (Pruet et
al., 2004; Surman et al., 2006; Siegel et al., 2019), though it is hard to
reproduce the exact pattern observed.

Overall, $40-100\mathrm{\,M_{\odot}}$ HNe can broadly match most major
abundance features of J0931$+$0038\. The best match we found is a
80$\mathrm{\,M_{\odot}}$ 22B model (Grimmett et al., 2018) shown in Fig 5.
However, we emphasize that the full nucleosynthetic pattern is not fit by
_any_ existing model. In particular, the Fe peak abundances are extremely
difficult to explain: models must simultaneously produce low [Sc,Ti,V/Fe]
(associated with lower energy) and high [Ni,Zn/Fe] (associated with higher
energy); and high [Mn/Fe] (associated with high neutron fractions) but low
odd-even ratios (associated with low neutron fractions). The higher energy HNe
with $E\gtrsim 10$B that give the best matches to the nucleosynthesis pattern
predict maximum metallicities $\mbox{[Fe/H]}\ll-2$, strongly violating the
metallicity constraint. Additionally, the low N and Ba restrict the
progenitor’s rotation, as rotational mixing increases N and would over-produce
Ba through the s-process if there are seed nuclei (Ekström et al., 2008;
Pignatari et al., 2008; Frischknecht et al., 2016; Choplin et al., 2018). This
motivates considering other sources.

One intriguing possibility is that J0931$+$0038 was enriched by a pair
instability supernova (PISN). Metal-free high mass PISNe with $M\gtrsim
200\mathrm{\,M_{\odot}}$ produce a very large amount of Fe, a strong odd-even
effect, and low [$\alpha$/Fe] ratios (Heger & Woosley, 2002; Takahashi et al.,
2018). These “smoking gun” signatures of PISNe qualitatively match
J0931$+$0038\. However, all existing PISNe models produce negligible
$\mbox{[Zn/Fe]}<-1$ and no neutron-capture elements (Heger & Woosley, 2002;
Salvadori et al., 2019, 5th row of Fig 4). Thus, standard PISNe are unable to
explain J0931$+$0038’s abundance pattern. Still, the strong association with
PISN motivated some additional exploration, and we found that the intermediate
neutron-capture (i-process) nucleosynthesis in PISN progenitors could be a
promising mechanism. The i-process can occur if convection causes protons to
be ingested into a He shell (Herwig et al., 2014; Woodward et al., 2015;
Roederer et al., 2016; Clarkson et al., 2018; Banerjee et al., 2018), which
generates neutrons that capture onto seed nuclei. With the right neutron
exposure and initial composition (see Appendix B), the i-process converts Fe
into enhanced Zn and Sr-Pd without significant Ba, which qualitatively matches
J0931$+$0038\. This explanation would require a metal-enriched PISN
progenitor, implying that luminous PISNe could be found at later times than
usually assumed (Hartwig et al., 2018). We show this speculative model in
Figure 5, which simply adds the i-process pattern to a PISN yield.

##  5 Conclusion

We have presented the extreme chemical abundance pattern of the star
J0931$+$0038 (Figure 2). The low abundances of Na, K, Sc, and Ba and the high
abundances of Fe peak elements and Sr-Pd show that most of the metals in this
star came from a single nucleosynthetic source (Figure 3). The high overall
metallicity, low [C/O] ratio, and strong odd-even effect together combine to
prefer progenitors with mass $>50\mathrm{\,M_{\odot}}$ (Figure 4). However,
the detailed abundance pattern, especially in the iron peak, is not fully
explained by any existing models of nucleosynthesis in massive stars (Figure
5). One possibility is the source might be a hypernova with progenitor mass
$\sim 80\mathrm{\,M_{\odot}}$, which would be the first example of an early
supernova from a star with initial mass between $50-100\mathrm{\,M_{\odot}}$.
Alternatively, the star might indicate i-process nucleosynthesis in the
progenitor of a metal-enriched pair instability supernova, which would be the
first example of a metal-enriched PISN. There may be other pathways that we
did not consider.

J0931$+$0038 shows that current models of massive, metal-poor star
nucleosynthesis are still quite limited, challenging the next generation of
models. We suggest that J0931$+$0038 points to the inherent multi-dimensional
nature of nucleosynthesis in massive stars, such as convective nuclear burning
that likely impacts the iron peak yields (e.g., Herwig et al., 2014; Woodward
et al., 2015; Curtis et al., 2019; Fields & Couch, 2020; Burrows & Vartanyan,
2021; Sieverding et al., 2023). We highlight rotation and jets for massive
stars $\sim 80\mathrm{\,M_{\odot}}$ and i-process from proton ingestion in
massive PISN progenitors as fruitful paths for exploration. Another important
consideration is binarity, as essentially all massive stars are in binaries,
and most in interacting binaries (Sana et al., 2012). There are still no
studies of nucleosynthesis in metal-poor or metal-free supernovae of
interacting binaries. This may be important especially because metal-poor
stars don’t lose much mass through winds, but they can lose significant mass
through binary interactions (de Mink et al., 2008). To our knowledge there
also have been no studies of nucleosynthesis from interacting stars
sufficiently massive for a PISN, and it would be interesting to see if
interactions could produce black hole or neutron star remnants that would
remedy the deficiencies of single PISN models. Finally, we note that whatever
produces the abundance signature of J0931$+$0038 is probably very rare,
otherwise this pattern would probably have already been previously discovered
in the thousands of existing metal-poor stellar abundance data (Suda et al.,
2008; Abohalima & Frebel, 2018; Li et al., 2022). Converting this frequency to
a volumetric rate estimate would require a model of dwarf galaxy and stellar
halo formation, which is outside of the scope of this Letter.

Though we focused here on the nucleosynthetic implications, we speculate that
J0931$+$0038’s unique composition implies that the rare supernova events that
could explain this signature should also be found in upcoming large transient
surveys, such as Rubin/LSST (LSST Science Collaboration et al., 2009). If the
chemical signature is due to an unusual PISN, the heavy Fe peak and neutron-
capture elements point to the presence of a neutron star or black hole remnant
involved in the explosion, which may result in unusual observational features
of slowly evolving superluminous supernovae (Gal-Yam, 2019; Nicholl, 2021). If
the chemical signature is instead due to a massive CCSN or HN, there should be
supernovae of massive stars with low kinetic energy but relatively high 56Ni
luminosity (e.g., SN2008ha Foley et al., 2010; Moriya et al., 2010). Finally,
if binarity is needed, it is possible that J0931$+$0038 has implications for
features or outliers in the compact binary merger mass spectrum (Abbott et
al., 2023; Farah et al., 2023).

J0931$+$0038 was identified in the first year of SDSS-V observing and after
only one semester of followup of the metal-poor and low-$\alpha$ stars. The
rapid discovery suggests that many more rare nucleosynthesis events like this
should be found in the current and upcoming era of large spectroscopic
surveys, and J0931$+$0038 emphasizes the importance of searching in multiple
abundance dimensions rather than just at low metallicities. The unique
chemical signature of J0931$+$0038 would also make it very easy to chemically
identify companions from any accreted kinematic group. We searched for stars
in APOGEE DR17 with similar kinematics and low Mg abundances from Horta et al.
(2023) and examined all stars with low [Al/Mg] ratios that could potentially
be analogues of this star. We were unable to find any candidates, but the
current generation of large spectroscopic surveys may turn up future
counterparts.

## Acknowledgements

We acknowledge extremely helpful comments from the referee, Stan Woosley, that
significantly improved the readability and clarity of this paper. This paper
includes data gathered with the 6.5 meter Magellan Telescopes located at Las
Campanas Observatory, Chile. A.P.J. acknowledges the University of Chicago’s
Research Computing Center for their support. This work benefited from a
workshop supported by the National Science Foundation under Grant No.
OISE-1927130 (IReNA), the Kavli Institute for Cosmological Physics, and the
University of Chicago Data Science Institute. A.P.J. acknowledges Ani Chiti
and Guilherme Limberg for helpful conversations. We acknowledge support
awarded by the U.S. National Science Foundation (NSF) grants: AST-2206264
(A.P.J., P.T., S.A.U.), OISE-1927130 (IReNA; A.P.J., M.P.), PHY-1430152 (JINA-
CEE; A.P.J., M.P.), AST-2303869 (AAPF; S.C.), and AST-2202135 (AAPF; E.J.G.).
We acknowledge funding from the European Research Council (ERC) under several
of the European Union’s Horizon 2020 research and innovation programmes: Grant
agreement Nos. 101008324 (ChETEC-INFRA; M.P.), 949173 (M.B.), 852839 (J.A.,
C.L.), and 833925 (STAREX; G.M.). A.H. was supported, in part, by the
Australian Research Council (ARC) Centre of Excellence (CoE) for All Sky
Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013
and acknowledges software development support from Astronomy Australia
Limited’s ADACS scheme (Project IDs AHeger_2022B, AHeger_2023A) for the
development of the StarFit code used here. M.P. thanks the support from the
NKFI via K-project 138031 and the ERC Consolidator Grant (Hungary) programme
(RADIOSTAR, G.A. n. 724560). M.P. acknowledges the support to NuGrid from STFC
(through the University of Hull’s Consolidated Grant ST/R000840/1), and
ongoing access to viper, the University of Hull High Performance Computing
Facility. M.P. acknowledges the support from the ”Lendület-2023” LP2023-10
Programme of the Hungarian Academy of Sciences (Hungary).M.B. is supported
through the Lise Meitner grant from the Max Planck Society. We acknowledge
support by the Collaborative Research centre SFB 881 (projects A5, A10),
Heidelberg University, of the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation). H. R. acknowledges support from a Carnegie Fellowship.
C.F. was supported by United States Department of Energy, Office of Science,
Office of Nuclear Physics (award number DE-FG02-02ER41216).

Funding for the Sloan Digital Sky Survey V has been provided by the Alfred P.
Sloan Foundation, the Heising-Simons Foundation, the National Science
Foundation, and the Participating Institutions. SDSS acknowledges support and
resources from the Center for High-Performance Computing at the University of
Utah. The SDSS web site is www.sdss.org.

SDSS is managed by the Astrophysical Research Consortium for the Participating
Institutions of the SDSS Collaboration, including the Carnegie Institution for
Science, Chilean National Time Allocation Committee (CNTAC) ratified
researchers, the Gotham Participation Group, Harvard University, Heidelberg
University, The Johns Hopkins University, L’Ecole polytechnique fédérale de
Lausanne (EPFL), Leibniz-Institut für Astrophysik Potsdam (AIP), Max-Planck-
Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für
Extraterrestrische Physik (MPE), Nanjing University, National Astronomical
Observatories of China (NAOC), New Mexico State University, The Ohio State
University, Pennsylvania State University, Smithsonian Astrophysical
Observatory, Space Telescope Science Institute (STScI), the Stellar
Astrophysics Participation Group, Universidad Nacional Autónoma de México,
University of Arizona, University of Colorado Boulder, University of Illinois
at Urbana-Champaign, University of Toronto, University of Utah, University of
Virginia, Yale University, and Yunnan University.

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.

This research has made use of NASA’s Astrophysics Data System Bibliographic
Services; the arXiv preprint server operated by Cornell University; and the
SIMBAD databases hosted by the Strasbourg Astronomical Data Center. This
research has made use of the Keck Observatory Archive (KOA), which is operated
by the W. M. Keck Observatory and the NASA Exoplanet Science Institute
(NExScI), under contract with the National Aeronautics and Space
Administration.

##  Appendix A Observational Analysis Details

###  A.1 BOSS/MINESweeper Analysis

The SDSS-V BOSS (Gunn et al., 2006; Smee et al., 2013) spectra of J0931$+$0038
(Gaia DR3 3841101888330639872, $\ell,b=233.178248,+35.189507$) were observed
on 2022 April 25, reduced using the BOSS data reduction pipeline (Bolton et
al. 2012; Dawson et al. 2013, Morrison et al. in prep), and analyzed using
MINESweeper (Cargile et al., 2020), which performs a spectrophotometric fit
simultaneously to the BOSS spectrum, the Gaia DR3 parallax (Brown et al.,
2021), and all available broadband photometry (Gunn et al., 1998; Skrutskie et
al., 2006; Mainzer et al., 2014; Chambers et al., 2016). Stars are constrained
to lie on MIST isochrones (Choi et al., 2016), and stellar parameters are
sampled using the dynesty nested sampling code (Speagle, 2020). The
spectroscopic fit was restricted to the region around Mg b (4750-5550 Å), as
this is the region where the spectral models have been well-calibrated for the
H3 Survey (Conroy et al., 2019). MINESweeper provides the effective
temperature, surface gravity, bulk metallicity, and [$\alpha$/Fe] abundance
based on this fit, where the $\alpha$ is primarily determined by the Mg b
lines. The MINESweeper parameters and formal uncertainties for J0931$+$0038
were $T_{\mathrm{eff}}=5220\pm 30$K, $\log\,g=2.57\pm 0.06$,
$\mathrm{\,[Fe/H]}=-1.9\pm 0.1$, and $\mathrm{\,[\alpha/Fe]}=0.03\pm 0.17$.

The uniform MINESweeper analysis of all SDSS-V halo targets provides their 3D
positions and velocities and enables investigation of their kinematics. The
total specific energy was calculated using the latest MilkyWayPotential2022 in
gala (Price-Whelan, 2017; Price-Whelan et al., 2022), which matches the
rotation curve data from Eilers et al. (2019). The energy and three components
of angular momentum of J0931$+$0038 are shown in Figure 6 as a large red star,
compared to all other stars observed by the SDSS-V halo cartons from Internal
Product Launch 2 as small black points. The energy and $L_{Z}$ clearly show
J0931$+$0038 is a halo star, with an eccentric radial orbit ($e=0.84$,
pericenter=1.1kpc) consistent with the Gaia-Sausage-Enceladus (GSE) dwarf
galaxy merger (Belokurov et al., 2018; Helmi et al., 2018). However,
cosmological simulations suggest that this region of kinematic space is
crowded, so the majority of metal-poor stars on GSE-like orbits actually do
not come from GSE (Brauer et al., 2022; Orkney et al., 2023). Tailored GSE-
like merger models also show that its debris is confined to a region
$|L_{x}|,|L_{y}|\lesssim 800\mathrm{\,kpc}\mathrm{\,km}\mathrm{\,s}^{-1}$
(Naidu et al., 2021; Amarante et al., 2022). Indeed J0931$+$0038 lies outside
the bulk of GSE stars in $L_{X}-L_{Y}$ space, which emphasizes the importance
of checking multiple kinematic quantities when correlating halo structures.
J0931$+$0038 is thus likely accreted as part of a now-disrupted dwarf galaxy,
but probably not the large GSE merger itself.

Figure 6: Kinematics of J0931$+$0038 (red star) compared to red giants
observed by the SDSS-V halo program. Stars plausibly belonging to the Gaia
Sausage Enceladus (GSE) merger are highlighted in blue.

###  A.2 Stellar Parameters

Our analysis primarily used the 1D ATLAS model atmospheres (Castelli & Kurucz,
2004) and the MOOG radiative transfer code (Sneden, 1973) including scattering
(Sobeck et al., 2011) and assuming local thermodynamic equilibrium (LTE). The
abundance analysis was conducted in the smhr environment (Casey, 2014). The
line lists and atomic data were selected from a combination of lines from
Roederer et al. (2018) and Ji et al. (2020a), with atomic data adopted from
linemake (Placco et al., 2021). Stellar parameters were determined using a
combination of spectroscopy, photometry, isochrones, and Gaia parallax. We
adopted an effective temperature of 5200K based on the MINESweeper
spectrophotometric results, then determined other parameters
spectroscopically. The surface gravity required to balance the neutral and
ionized iron abundances was $\log\,g=2.75$, the microturbulence required to
balance the Fe II line abundances was 1.65 km/s, with a model metallicity of
-1.9 and using solar-scaled abundances for the ATLAS atmosphere composition
($\mathrm{\,[\alpha/Fe]}=0$).

Stellar parameters and uncertainties were checked using two independent fits
to the spectral energy distribution and parallax. First, we performed an
analysis of the broadband spectral energy distribution (SED) of the star
together with the Gaia DR3 parallax (with a systematic offset applied; see,
e.g., Stassun & Torres, 2021) following the procedures described in Stassun &
Torres (2016); Stassun et al. (2017, 2018). We pulled the $JHK_{S}$ magnitudes
from 2MASS, the W1–W3 magnitudes from WISE, the $G_{\rm BP}$ and $G_{\rm RP}$
magnitudes from Gaia, the $grizy$ magnitudes from Pan-STARRS, and the NUV
magnitude from GALEX. We also used the Gaia spectrophotometry spanning 0.4—1.0
$\mu$m. Altogether, the available photometry spans the full stellar SED over
the wavelength range 0.2–10 $\mu$m. The GALEX flux in particular helps to
constrain the metallicity and the Gaia spectrophotometry provides an
especially strong constraint on the overall absolute flux calibration. We then
performed a fit using PHOENIX stellar atmosphere models (Husser et al., 2013),
with the free parameters being the effective temperature ($T_{\rm eff}$) and
metallicity ([Fe/H]), as well as the extinction, which we set to the maximum
line-of-sight value $A_{V}=0.15\pm 0.02$ from the Galactic dust maps of
Schlegel et al. (1998) due to the system’s large distance. We initially
assumed a surface gravity $\log g\approx 2.5$ given the likely evolutionary
state of the star. The resulting fit has a best-fit $T_{\rm eff}=5250\pm 50$ K
and [Fe/H] = $-2.3\pm 0.3$. Integrating the (unreddened) model SED gives the
bolometric flux at Earth, $F_{\rm bol}=7.988\pm 0.092\times 10^{-11}$ erg s-1
cm-2. Taking the $F_{\rm bol}$ and $T_{\rm eff}$ together with the Gaia
parallax, gives the stellar radius, $R_{\star}=8.65\pm 0.9R_{\odot}$. In
addition, we estimate the stellar mass to be $M_{\star}=0.8\pm
0.1\mathrm{\,M_{\odot}}$, as J0931$+$0038 is a metal-poor old red giant. The
mass and radius together confirm $\log\,g\approx 2.5$.

Second, we also derived the stellar parameters of J0931$+$0038 using the
isochrones (Morton, 2015) package to execute with MultiNest (Feroz & Hobson,
2008; Feroz et al., 2009, 2019) a simultaneous Bayesian fit of the MIST
isochrone grid (Paxton et al., 2011, 2013, 2018, 2019; Jermyn et al., 2023;
Dotter, 2016; Choi et al., 2016) to a curated collection of data for the star.
We fit (1) Galaxy Evolution Explorer (GALEX) GUVcat_AIS NUV (Bianchi et al.,
2017), Sloan Digital Sky Survey (SDSS) Data Release (DR) 18 $ugiz$ (Fukugita
et al., 1996; Gunn et al., 1998; York et al., 2000; Doi et al., 2010;
Abdurro’uf et al., 2022), Gaia DR2 $G$ (Gaia Collaboration et al., 2016, 2018;
Arenou et al., 2018; Evans et al., 2018; Riello et al., 2018), Two-micron All-
sky Survey (2MASS) $JHK_{\text{s}}$ (Skrutskie et al., 2006), and Wide-field
Infrared Survey Explorer CatWISE2020 $W1W2$ photometry (Wright et al., 2010;
Marocco et al., 2021), (2) a zero point-corrected Gaia DR3 parallax (Gaia
Collaboration et al., 2021; Fabricius et al., 2021; Lindegren et al., 2021a,
b; Rowell et al., 2021; Torra et al., 2021), and (3) an estimated reddening
value based on a three-dimensional reddening map (Green et al., 2014, 2019).
We use a log uniform age prior between 8.0 Gyr and 13.7 Gyr, a uniform
reddening prior between the estimated reddening value minus/plus five times
its uncertainty, and a distance prior proportional to volume between the
Bailer-Jones et al. (2021) geometric distance minus/plus five times its
uncertainty. We find the photospheric stellar parameters
$T_{\text{eff}}=5140_{-10}^{+20}$ K, $\log{g}=2.51_{-0.07}^{+0.07}$, and
$[\text{Fe/H}]=-1.63_{-0.01}^{+0.07}$.

As discussed in the main text, we adopted stellar parameters of
$T_{\mathrm{eff}}=5200\pm 100$K, $\log\,g=2.75\pm 0.20$, $\nu_{t}=1.65\pm
0.3\mathrm{\,km\,s^{-1}}$, $[M/H]=-1.9\pm 0.1$, and
$\mathrm{\,[\alpha/Fe]}=0.0$. The temperature uncertainty of 100K resulted in
correlated $\log\,g$ and metallicity offsets of 0.20 dex and 0.1 dex. The
microturbulence uncertainty of 0.3 km/s is very conservative and represents
the most extreme values found during line strength balance both in LTE and
non-LTE in all permutations. These were later propagated into all abundance
uncertainties.

###  A.3 LTE Abundance Analysis

Chemical abundances were determined in 1D LTE using MOOG and ATLAS in smhr,
with a mix of equivalent widths for isolated, unblended lines and syntheses
for molecular bands, lines with hyperfine structure, or moderately blended
lines. The local continuum and smoothing were allowed to vary for each
feature. Syntheses were fit by minimizing a chi-square statistic (for more
details, see Ji et al. 2020a). The final chemical abundance for each species
was found as the unweighted average of individual line abundances. The Fe in
[X/Fe] refers to Fe I. For non-detections, we synthesize a best-fit spectrum
with no line, then calculate a formal $5\sigma$ upper limit by increasing the
abundance until the $\chi^{2}$ changes by $5^{2}$. This assumes no
uncertainties in the continuum, which is a good assumption given the high S/N
of our spectrum, except for the N-H molecule where we visually estimated a
very conservative upper limit for N-H (formally $>10\sigma$) with a synthetic
spectrum.

Systematic abundance uncertainties due to stellar parameters were found by
redetermining the chemical abundances at two alternate stellar parameter
values based on the stellar parameter uncertainty: ($T_{\mathrm{eff}}$,
$\log\,g$, $\nu_{t}$, [M/H]) = (5100 K, 2.55, 1.65, $-2.0$) and (5200 K, 2.75,
1.95, $-1.9$). For Fe I, we sum the total difference in [Fe I/H] in quadrature
for these two sets of stellar parameters and adopt that as the stellar
parameter uncertainty on the absolute metallicity of the star. For species
other than Fe I, we adopt the difference in [X/Fe I] for each of these
variations as the stellar parameter uncertainty and sum them in quadrature.
The latter accounts for the fact that [X/H] and [Fe/H] are highly correlated
with respect to stellar parameters, so the relative abundance uncertainty is
smaller (which is the relevant uncertainty when considering the total
abundance pattern).

To investigate the systematic effect of our model atmosphere, line list, and
radiative transfer code, we also analyzed a subset of the lines using 1D
spherical MARCS model atmospheres (Gustafsson et al., 2008), the most recent
version of Turbospectrum in TSFitPy (Plez, 2012; Gerber et al., 2023), and a
linelist from Gaia-ESO (Heiter et al., 2021) with gaps filled and the range
further extended with VALD (Kupka et al., 1999). We adopt the MARCS model
atmospheres, and the analysis used slightly different stellar parameters:
$T_{\mathrm{eff}}=5200\,$K, $\log\,g=2.60$,
$\nu_{t}=1.6\mathrm{\,km\,s^{-1}}$, $\mathrm{\,[Fe/H]}=-1.85$, and
$\mathrm{\,[\alpha/Fe]}=+0.4$ (due to standard MARCS grid). The final LTE
abundance differences are all within 0.1 dex, with the exception of aluminum
which will be discussed later. We thus decided to adopt a minimum 0.1 dex
systematic uncertainty per line, such that the total systematic uncertainty
goes down as the square root of the number of lines.

In summary, the adopted abundance uncertainty is the quadrature sum of four
components: the line-to-line standard deviation for a given species, a minimum
systematic of 0.1 dex divided by the square root of the number of lines per
element, the stellar parameter error after changing $T_{\mathrm{eff}}$ and
$\log\,g$ with their correlated uncertainties, and the stellar parameter error
after changing $\nu_{t}$ by 0.3 $\mathrm{\,km\,s^{-1}}$.

###  A.4 Non-LTE Corrections

Non-LTE (NLTE) corrections for most elements were determined using TSFitPy
(Gerber et al., 2023). We fit the same lines used for the MOOG/ATLAS analysis,
but restricted to the wavelength range 3700-9200Å using the Gaia-ESO linelist
with gaps filled and the range extended using the VALD line list. The NLTE
corrections were determined using the standard concept of the NLTE abundance
correction (Bergemann & Nordlander, 2014), which represents the difference in
abundance that is required to match the equivalent width (EW) of a NLTE model
line to that of the LTE line computed using the identical values of stellar
parameters. The elements and model atom references were: Oxygen (Bergemann et
al., 2021), Sodium (Larsen et al., 2022), Magnesium (Bergemann et al., 2017),
Silicon (Bergemann et al., 2013; Magg et al., 2022a), Calcium (Mashonkina et
al., 2017; Semenova et al., 2020), Titanium (Bergemann, 2011), Manganese
(Bergemann et al., 2019), Iron (Bergemann et al., 2012b; Semenova et al.,
2020), Cobalt (Bergemann et al., 2010; Yakovleva et al., 2020), Nickel
(Bergemann et al., 2021; Voronov et al., 2022), Strontium (Bergemann et al.,
2012a, Gallagher et al. in prep.), Yttrium (Storm & Bergemann, 2023), and
Barium (Gallagher et al., 2020). The average NLTE correction from all lines
was taken as the total NLTE correction for that element.

A few elements are not currently included in TSFitPy, and we describe their
NLTE corrections below.

Aluminum. Only the 3961Å line is usable, and it is heavily blended with a
strong Ca and H feature. The abundance of Al is extremely uncertain as a
result. We measure [Al/Fe] in LTE through spectrum synthesis, and the LTE
abundances from MOOG and TSFitPy differed by 0.2 dex, likely dominated by
treatment of the blending Ca and H feature. We then adopt the NLTE correction
from the grid of Nordlander & Lind (2017) to get a $+0.65$ dex correction to
[Al/Fe]. Preliminary calculations with other unpublished Al model atoms in
TSFitPy suggested a smaller correction of $+0.33$ dex. We thus adopt a very
large uncertainty of 0.5 dex for the Al abundance to represent both the
blending and NLTE correction uncertainty.

Potassium. The K abundance is derived from equivalent widths of both 7699Å and
7665Å line, which are both unaffected by telluric lines in this star.
Examining stars with similar stellar parameters in Reggiani et al. (2019),
NLTE corrections for K from the 7699 line range from $-0.17$ to $-0.24$ dex.
We adopt a $-0.2$ dex correction, and increase the K uncertainty by adding 0.1
dex in quadrature.

Copper. We use the equivalent width of the 5105Å line and adopt an empirical
correction of $+0.35$ dex from Roederer & Barklem (2018). This matches
theoretical calculations (Andrievsky et al., 2018; Korotin et al., 2018) and
we increase the uncertainty by adding 0.15 dex in quadrature to reflect the
scatter from the theoretical calculations.

Elements without corrections. Roederer et al. (2022) provide a detailed
accounting of what corrections might be expected based on comparisons of
neutral and ionized lines in a star HD222925 with $\mbox{[Fe/H]}=-1.5$ and
$T_{\mathrm{eff}}=5640$K. Based on this we do not expect significant NLTE
corrections for zinc, zirconium, molybdenum or ruthenium; while possible NLTE
corrections for rhodium and palladium are unconstrained.

###  A.5 Evolutionary State Corrections

J0931$+$0038 has $\log\,g=2.75$, so it has passed the first dredge up but not
the red giant branch bump, and a small amount of C is converted to N. To
account for this difference, we examined metal-poor red giants in APOGEE DR17
with $\mathrm{\,[Fe/H]}<-1.5$. Stars after the first dredge up have [C/N]
higher by 0.2 dex, where [C/Fe] is lower by 0.1 dex and [N/Fe] is higher by
0.1 dex. For J0931$+$0038, we thus increase [C/H] by $+0.1$ dex, decrease the
[N/H] upper limit by $-0.1$ dex, and increase each element’s uncertainty by
adding 0.2 dex in quadrature.

We also measured a Li abundance of A(Li)$=1.15\pm 0.12$. Given the $\log\,g$
of this star, this Li abundance is consistent with Li depletion in the first
dredge up (e.g., Tayar & Joyce, 2022), a good independent check on the stellar
parameters.

###  A.6 Binarity and Photometric Variability

J0931$+$0038 displays no evidence for a present-day binary companion. The
heliocentric radial velocity for MIKE was found to be $105.5\pm
0.4\mathrm{\,km\,s^{-1}}$ (measured with the method in Ji et al., 2020b),
while Gaia DR3 RVS reports $104.3\pm 4.0\mathrm{\,km\,s^{-1}}$. These
velocities are consistent within uncertainties. The velocity scatter from
multiple Gaia RVS transits is large but typical for stars of similar spectral
type, distance, and signal-to-noise (Chance et al., 2022), and there is no
evidence for excess astrometric scatter (Penoyre et al., 2020).

Photometric variability could also be used to identify binary companions or
measure solar-like oscillations. J0931$+$0038 does not show up in Hon et al.
(2021) as a solar-like oscillator. We obtained the TESS light curve of
J0931$+$0038 (TIC 383218318) using TESScut (Brasseur et al., 2019) with a
custom aperture and subtracting background flux. Following Avallone et al.
(2022), we normalized and smoothed each of the sectors and took a Fourier
transform of the resulting light curve. We do not see any evidence of periodic
variability in the TESS light curve that would suggest detectable rotational
modulation or oscillations, though J0931$+$0038 is relatively faint for TESS
and has a limited time baseline.

###  A.7 Comparison to Notable Stars

Figure 7 shows the [X/Fe] of J0931$+$0038 compared to four notable stars:
three hypernova candidate stars with varying neutron-capture element
abundances HE1327$-$2326 (Frebel et al., 2005; Ezzeddine et al., 2019), SMSS
J2003$-$1142(Yong et al., 2021), and AS0039 (Skúladóttir et al., 2021); and
the pair instability supernova star J1010$+$2358 (Xing et al. 2023, though
note it has recently been argued that this star is also consistent with an
extreme CCSN, Jeena et al. 2023).

It is clear that J0931$+$0038 has an extreme abundance pattern even compared
to these other notable stars. Because of its relatively high metallicity, it
is also easier to measure many more elements. The clear signature is that the
odd elements Na, Al, K, and Sc ($Z=11,13,19,21$) in J0931$+$0038 are lower
than almost all the other stars, with the exception of the PISN star
J1010$+$2358\. The carbon and oxygen abundances ($Z=6,8$) are relatively low,
in contrast with more metal-poor stars that tend to be carbon-enhanced like
HE1327$-$2326 and SMSS J1605$-$1443\. Mn ($Z=25$) is unusually high, as nearly
all metal-poor stars have [Mn/Fe] $<0$. Co through Zn ($Z=27-30$) are also
elevated, which is usually associated with hypernovae (Ezzeddine et al., 2019;
Yong et al., 2021).

The three literature hypernova stars have very different neutron-capture
patterns. HE1327$-$2326 has high Sr ($Z=38$) but no Ba ($Z=56$), attributed to
an aspherical hypernova (Ezzeddine et al., 2019). SMSS J2003$-$1142 has a full
r-process pattern from Sr to Eu (and beyond), attributed to a
magnetorotationally driven hypernova (Yong et al., 2021). AS0039 is a star in
the Sculptor dwarf galaxy also suggested to be consistent with a high energy
but spherical hypernova, and it has very low Sr and Ba (Skúladóttir et al.,
2021). It appears that hypernovae are able to generate a whole range of
neutron-capture nucleosynthesis, as might be expected based on potentially
variable strengths of the central engine. Our star J0931$+$0038 has a full
complement of first neutron-capture peak elements from Sr to Pd and nothing
beyond, which makes it most similar to HE1327$-$2326’s much sparser abundance
pattern. Note that the pattern is flat in [X/Fe], which differs substantially
from the “pure” r-process pattern in SMSS J2003$-$1142 as well as theoretical
r-process predictions (Holmbeck et al., 2023).

Figure 7: Chemical abundances of J0931$+$0038 compared to four other notable
stars. LAMOST J1010$+$2358 has a pure signature of a pair instability
supernova, while the other three are metal-poor stars whose compositions are
currently best explained with hypernovae models.

###  A.8 Comparison to Typical Metal-Poor Stars

Figure 8: [X/H] vs [Fe/H] for SAGA (grey points) and dwarf galaxy stars (blue
is classical dSph, yellow is ultra-faint dwarf). J0931$+$0038 is shown as a
large red square. The dotted line indicates [X/Fe]=0, and the dashed line is
the best-fit to the SAGA stars that we use as an empirical ISM composition.
Note that the comparison abundances have been shifted by the NLTE and
evolutionary corrections for J0931$+$0038.

As a complement to Figures 2 and 3, Figure 8 shows [Fe/H] vs [X/H] for 21
elements. The grey points are halo stars from the SAGA database (Suda et al.,
2008), and blue and yellow points are an extended dwarf galaxy compilation
from JINAbase (Abohalima & Frebel, 2018). The literature abundances have been
shifted by the NLTE and evolutionary corrections from Table 1. We show the
one-to-one line ([X/Fe]=0) as a dotted black line, and an outlier-clipped
polynomial fit to the SAGA abundances as a dashed black line (best-fit
indicated on each panel), which represents the typical ISM composition at any
given metallicity. At its [Fe/H], J0931$+$0038 is a visible low outlier in the
Na, Al, K, Sc, Ti, V, Ba, and Eu panels, while simultaneously being a high
outlier in Mn, Co, Ni, Cu, Zn, and Sr.

##  Appendix B Nucleosynthesis Origin

We performed an extensive literature search for nucleosynthesis predictions
that could match J0931$+$0038\. In this section, we will mostly ignore the
metallicity constraint from J0931$+$0038 (Section 4.1) and instead focus on
what sites or conditions could produce the observed abundance pattern.

###  B.1 Brief nucleosynthesis summary

We start by briefly summarizing some key element ratios and the main physics
of the supernova progenitor and explosion that drives their values, discussing
them in the context of J0931$+$0038.

  * •

The [C/O] value is a good indicator of the zero-age main-sequence mass of the
progenitor, where a lower value indicates a more massive star (e.g., Ishigaki
et al., 2018). The low [C/O] value of J0931$+$0038 is typically found for
yields of massive progenitors with ZAMS mass $\gtrsim$20$M_{\odot}$ (Heger &
Woosley, 2010; Nomoto et al., 2013). We note that this ratio and the overall
products of carbon burning are subject to uncertainties in the
12C($\alpha$,$\gamma$)16O rate and the treatment of convection (e.g., Imbriani
et al., 2001; El Eid et al., 2004; deBoer et al., 2017; Farmer et al., 2019).
Additionally, binary interactions may affect [C/O] predictions, though current
models in solar-metallicity stars suggest interactions increase C yields
(Farmer et al., 2021, 2023).

  * •

[N/O] can potentially help constrain rotation in the progenitor, as nitrogen
is typically enhanced in rotating stars (e.g., Choplin et al., 2018). However,
while J0931$+$0038 has a very low upper limit on the abundance of nitrogen, we
found it is insufficient to rule out rotating metal-poor progenitors, as the
large N enhancement would still be below our detection threshold (Ekström et
al., 2008; Limongi & Chieffi, 2018).

  * •

The extreme odd-even effect seen for elements from C to Sc, characterized by
low values of [Na/Mg] and [K/Ca], occurs in stars with low neutron-fractions.
Such values are typically associated with PISNe (Heger & Woosley, 2002;
Kozyreva et al., 2014; Takahashi et al., 2018) but also occur to a lesser
extent in any massive zero or low-metallicity progenitor (Heger & Woosley,
2010; Nomoto et al., 2013; Limongi & Chieffi, 2018). The low [Na/Mg]
especially prefers higher initial mass progenitors with
$M>70\mathrm{\,M_{\odot}}$. Rotation can “fill in” the odd elements as well
(e.g., Choplin et al., 2018).

  * •

The low alpha abundances e.g. [Mg/Fe] indicate a low ratio of hydrostatic to
explosively synthesized elements, which tends to occur either in lower mass
CCSN progenitors ($\lesssim 15\mathrm{\,M_{\odot}}$, McWilliam et al. 2013;
Carlin et al. 2018) or also in the most massive PISNe (Heger & Woosley, 2002;
Salvadori et al., 2019).

  * •

The composition of the iron group from Sc to Zn depends sensitively on the
details of the supernova explosion, such as explosion energy, remnant mass,
convection, jets, and more. All of these elements are produced during
explosive silicon burning, with different degrees of contribution from
complete and incomplete burning and likely important 3D effects (e.g., Curtis
et al., 2019; Sieverding et al., 2023). J0931$+$0038 has an unusual iron group
composition, showing very low [Sc, Ti, V/Fe] along with high [Mn, Ni, Zn/Fe].
We were unable to find any existing supernova yield model matching the whole
Fe peak pattern.

  * •

The elements from Sr and heavier are formed primarily through the slow (s-)
and rapid (r-) neutron-capture processes, though proton-capture and
i-processes are possible as well. In J0931$+$0038, the very low [Ba/Fe] rules
out a strong, neutron-rich r-process (e.g., from neutron star mergers,
Holmbeck et al., 2023) and the main s-process (e.g., Lugaro et al., 2012).
Most remaining scenarios to explain the high [Sr–Pd/Fe] invoke nucleosynthesis
associated with the formation of neutron stars or black holes, with the
i-process activated in external He-rich layers as an alternative.

Figure 9: Light element ratios vs initial mass for CCSN (left column; HW10,
G18, NKT13, LC12, LC18, E20, R18), HN and PISN (center column; HW10, G18,
NKT13, HW02), and rotation velocity (right column, LC18 only). N and Na are
not plotted for E20. In the right column, the same mass and metallicity at
different rotation velocities are connected by solid lines
($<50\mathrm{\,M_{\odot}}$) or dashed lines ($\geq 50\mathrm{\,M_{\odot}}$).
These figures explain the first rows of Table 2. Figure 10: Iron peak element
ratios vs initial mass for CCSN (left column; HW10, G18, NKT13, LC12, LC18,
E20, R18), HN and PISN (center column; HW10, G18, NKT13, HW02), and rotation
velocity (right column, LC18 only). In the right column, the same mass and
metallicity at different rotation velocities are connected by solid lines
($<50\mathrm{\,M_{\odot}}$) or dashed lines ($\geq 50\mathrm{\,M_{\odot}}$).
These figures explain the middle rows of Table 2.

In Figures 9 (light elements) and 10 (Fe peak elements), we show plots of all
the key element ratios with respect to progenitor initial mass and explosion
energy for eight models that span the range of predictions: primordial
supernovae from Heger & Woosley (2002) (HW02), Heger & Woosley (2010) (HW10),
Limongi & Chieffi (2012) (LC12), Nomoto et al. (2013) (N13), Grimmett et al.
(2018) (G18), and Ebinger et al. (2020) (E20); and low metallicity supernovae
from Limongi & Chieffi (2018) (LC18, including rotation and keeping the most
massive stars that may not explode), Ritter et al. (2018) (R18), as well as
NKT13, E20. We somewhat arbitrarily put a line at 2.5B to split models between
CCSN and HN. We cut models to only those with metallicity $<-1.5$ solar. Note
that the models by LC12, LC18, and R18 do not have explosion energies
provided, so we do not include those on the explosion energy figures; and the
progenitor models in E20 did not include odd elements, so we removed it from
the N and Na panels for Fig 9. The horizontal red lines and shaded region
indicate the observed value and uncertainty in J0931$+$0038, including an
upper limit for [N/O].

The comparison between these figures and J0931$+$0038 are qualitatively
summarized by Table 2. Green check marks are given when nearly all models in a
particular category can match J0931$+$0038\. We add use a check mark with a
question mark if existing models would work, but we felt there were large
theoretical uncertainties or important exceptions. Red X marks indicate that
current theoretical models suggest a particular criterion is impossible for
some category of models. The orange X with question mark indicates that most
models do not satisfy the criterion, but we felt there were large theoretical
uncertainties and/or large variations in existing predictions. The “rapid
rotation” column uses the LC18 conclusions, though the behavior could
potentially change in other models. Overall, we can see that the
$50-100\mathrm{\,M_{\odot}}$ HN column has no observation fully ruling it out,
although there are substantial uncertainties. The massive PISN column has the
most solid check marks, but it is solidly ruled out by the Fe peak and
neutron-capture elements. (The neutron-capture elements will be discussed more
in Appendix B.4.)

A few rows in Table 2 merit more discussion. We originally expected the low
[N/O] limit to substantially constrain rotation velocities or initial masses
(Meynet et al., 2006; Ekström et al., 2008; Placco et al., 2016), but it turns
out that since [N/O] is so low in most metal-free SNe, even a 100x increase is
not that constraining. However increased rotation does substantially impact
[Na/Fe], as well as all the odd Fe peak elements. It is also strongly
constrained by the low Ba, since the s-process in fast-rotating massive stars
would increase Ba substantially (Chiappini, 2013; Choplin et al., 2018).

We see that Fe peak synthesis is very uncertain in both CCSNe and HNe,
reflecting uncertainties in the explosion mechanism. The lighter Fe peak
elements (Sc, V) tend to prefer higher mass CCSNe or HNe, and almost no CCSN
or HN models can explain the low [Ti/Fe]. The high Mn is problematic: for CCSN
and HN, it can only be matched by lower mass, higher metallicity progenitors
with rapid rotation or fine-tuned mixing/fallback (which would not produce
high [Fe/H] ratios). However those same LC18 models also greatly overpredict
the Sc, Ti, and V abundances. The low-mass PISNe also produce the appropriate
[Mn/Fe], but only because they produce so little Fe. Higher explosion energies
($E>10$B) can produce high [Zn/Fe] ratios, but Ni is difficult overall except
in lower mass CCSNe.

Table 2: Death Matrix Criterion | CCSN | HN | PISN | Add Rapid
---|---|---|---|---
Mass ($\mathrm{\,M_{\odot}}$) |  $<$20 | 20–50 | 50–100 |  $<$20 | 20–50 | 50–100 | 140–200 | 200–260 | Rotation
High [Fe/H] $\sim-1.8$ | ✗ | ✗? | ✗? | ✗ | ✗ | ✗? | ✗ | ✓ |  $\cdots$
Low [C/O] $\sim-1.0$ | ✗ | ✓? | ✓? | ✗ | ✓ | ✓ | ✓ | ✓ | No change
Low [N/O] $<-1.0$ | ✓? | ✓? | ✗? | ✓ | ✓ | ✓? | ✓ | ✓ | Increase up to 100x
Low [Na/Mg] $\sim-1.5$ | ✓? | ✗ | ✓? | ✓? | ✓? | ✓ | ✓ | ✓? | Varying predictions
Low [Mg/Fe] $\sim-0.3$ | ✓ | ✗ | ✗ | ✓ | ✓? | ✓? | ✗ | ✓ | Little change
Low [Sc,Ti,V/Fe] $<-0.5$ | ✗? | ✓? | ✓? | ✗ | ✓? | ✓? | ✗ | ✓ | Increase by 2-10x
High [Mn/Fe] $\sim 0.3$ | ✗? | ✗? | ✗? | ✗? | ✗? | ✗? | ✓? | ✗ | Increase by 2-3x
High [Ni,Zn/Fe] $\sim 0.5$ | ✓? | ✗? | ✗? | ✓? | ✓? | ✓? | ✗ | ✗ | Little change
High [Sr–Pd/Fe] $>0.5$ | ✓? | ✓? | ✓? | ✓? | ✓? | ✓? | ✗ | ✗ | Increases all
Low [Ba/Fe] $\sim-2.8$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | Increases Ba
Explosion Expected | ✓ | ✓? | ✗ | ✓ | ✓? | ✓? | ✓ | ✓ | Helps explodability.

###  B.2 Search Through Single Star Nucleosynthesis Yields

Table 3: Nucleosynthesis Yield Grids

Key | Explosion | Mass Range ($\mathrm{\,M_{\odot}}$) | Energy (B) | Metallicity (Solar) | Comments/Other Parameters
---|---|---|---|---|---
HW10 CC | Piston (S4) | 10-100 | 0.3-2.4 | 0 | Mixing: none to 0.251
HW10 HN | Piston (S4) | 10-100 | 3, 5, 10 | 0 | Mixing: none to 0.251
G18 CC | Piston (S4) | 10-80 | 0.1-2.0 | 0 | Mixing: none to 0.251
G18 HN | Piston (S4) | 10-80 | 2.5-200 | 0 | Mixing: none for $E>5$B
HW02 | PISN | 140-260 | 9-87 | 0 | Initial mass from He core mass
|  |  |  |  | Energy calculated self-consistently
NKT13 CC | Thermal Bomb | 11-140 | 1 | $0$ | Mixing and fallback
NKT13 HN | Thermal Bomb | 20-140 | 10-71 | $0$ | Mixing and fallback
NKT13 PI | PISN | 140-300 | 16-50 | 0 | Energy calculated self-consistently
LC12 | Kinetic Bomb | 13-80 | N/A | 0 | –
LC18 | Kinetic Bomb | 13-120 | N/A | $10^{-3,-2}$ | Rotation: 0, 150, 300 km/s
|  |  |  |  | Includes all forced explosion models
E20 | Engine-driven | 11-31 | 0.3-1.7 | $0,10^{-4}$ | Energy calculated self-consistently
R18 | Shock and Cool | 12-25 | N/A | $10^{-2.3}$ | Delayed explosions

Note. — The ✓ and ✗ signify whether nearly all models in a particular category
are found to match or fail to match a given criterion. The ✓? denotes that
most models in a category satisfy the criterion, but there are large
uncertainties and/or important exceptions. Similarly, the ✗? denotes that most
models do not satisfy the criterion, but there are large uncertainties and/or
large variations in predictions. All Fe peak predictions for CCSNe and HNe
have significant uncertainties. The last row indicates whether an explosion is
theoretically expected in this mass range for metal-poor progenitors.

Note. — Restricted to metallicities $\mbox{[Z/H]}<-1.5$. Other models not
searched are NKT13 $Z/Z_{\odot}=10^{-1.3,-0.7,-0.4,0,+0.4}$, LC18
$Z/Z_{\odot}=0.1,1$, R18 $Z/Z_{\odot}=10^{,-1.3,-0.5,-0.2,0}$.

We performed an extensive search of supernova yield grids covering a wide
range of possible nucleosynthesis sites, covering elements from C to Zn:
primordial core-collapse supernovae exploded with a piston (Heger & Woosley,
2010, assuming the S4 location), thermal bomb (Nomoto et al., 2013), and
kinetic bomb (Limongi & Chieffi, 2012) with various assumptions for mixing and
fallback; core-collapse supernovae of higher metallicities (Nomoto et al.,
2013; Ritter et al., 2018), with rotation (Limongi & Chieffi, 2018) and
engine-driven explosions (Ebinger et al., 2020); hypernovae of varying
energies (Nomoto et al., 2013; Grimmett et al., 2018); and primordial pair
instability supernovae (Heger & Woosley, 2002; Nomoto et al., 2013). We also
examined core-collapse supernovae of solar metallicity binary stripped stars
(Farmer et al., 2023) and thermonuclear Type Ia supernovae (references in
Reggiani et al., 2023), though none of these were good fits so we do not
discuss them further. We only included models with [Z/H] $<-1.5$, except the
binary stripped star supernovae where only solar metallicity models exist. We
also qualitatively considered how abundance patterns would be affected by
nucleosynthesis of jets interacting with stellar envelopes (Grimmett et al.,
2021) and rotation (Ekström et al., 2008; Frischknecht et al., 2016), as these
references did not provide full yield tables of all elements. A summary of the
searched models is given in Table 3.

Figure 11:  Results of grid search through CCSN, PISN, and HN models for
different permutations of elements. The best fit model is shown in the legend,
dashed blue = CCSN, dotted orange = PISN, solid green = HN. Reduced $\chi^{2}$
is shown in the legend. See text for details.

To investigate the yield grids, we used two search algorithms: Starfit which
does $\chi^{2}$ minimization, Heger & Woosley 2010; and a code based on Ji et
al. (2020b) that minimizes the mean absolute deviation (normalized by
abundance uncertainty), which is more robust to outliers. In both searches,
the gas dilution is a free parameter, i.e. we allow the abundance pattern of
each model to shift arbitrarily up and down in log space, ignoring the total
metallicity constraint that would rule out essentially all models. The two
different search strategies resulted in the same overall conclusions.

No model or site was found to adequately reproduce the entire observed
abundance pattern, so the best fit models depended heavily on the choice of
elements to fit. After examining many permutations, it became clear that the
lighter elements with $Z\leq 20$ could generally be fit by many types of SNe,
but the iron peak was never well-fit. We thus present the best-fit CCSN, HN,
and PISN models for four permutations of elements in Figure 11: (1) including
all elements from $Z=6-30$, (2) fitting elements from $Z=6-24$ and $Z=26$ to
exclude the enhancements in heavier Fe peak elements as well as the difficult
element Mn, (3) fitting elements from $Z=6-20$ and $26-30$ to remove the
deficiency of lighter Fe peak elements, and (4) fitting $Z=6-20$ and $Z=26$ to
remove all Fe peak elements other than iron.

When fitting all elements from C to Zn (top left panel), the best fits were
achieved by low mass SN, 12.4$\mathrm{\,M_{\odot}}$ primordial SN from Heger &
Woosley (2010), but with a reduced $\chi^{2}$ of 15.5 that indicates a
terrible fit. This model is able to explain elements from Na-Si and Ca, but it
fails C and O and the entire Fe peak. Other CCSN models have similar issues.
If we remove all Fe peak elements other than Fe (top-right panel), we see that
there is no CCSN or PISN able to reproduce all the light elements. Low-mass
CCSN fail due to C/O as shown, while high-mass ordinary energy CCSN produce
too little Fe. The moderate-sized odd-even effect in J0931$+$0038 suggests
lower mass PISNe, but these produce insufficient Fe. However, a massive (80
$\mathrm{\,M_{\odot}}$) high-energy (23B) hypernova from Grimmett et al.
(2018) is able get a near-perfect fit to the light elements while producing
enough iron ($\chi^{2}_{r}=0.9$). This scenario does not change much if we add
back in Sc, Ti, V, and Cr (bottom left panel), where the CCSN and PISN
continue to have issues but the 80 $\mathrm{\,M_{\odot}}$ HN still works well
($\chi^{2}_{r}=1.1$). However if instead we exclude the light Fe peak and add
back the heavy Fe peak (bottom right), again no model gives a satisfactory
fit.

This exploration suggests that if a single star is to produce the abundance
pattern, the best candidate is an 80 $\mathrm{\,M_{\odot}}$ hypernova. This
can explain all the light elements from C to Cr, and the exact Fe peak can be
adjusted based on the energy. Plausibly, fixes to the heavy Fe peak pattern
and enhanced Mn could come from nucleosynthesis in jets and/or induced by
rotation or other 3D effects, which are not extensively explored in existing
model grids. However, current nucleosynthesis models suggest this does _not_
work, as jets tend to co-produce Sc/Ti/V and Co-Zn (Tominaga, 2009; Grimmett
et al., 2021). Additionally, all these higher energy HN models violate the
metallicity constraint (Section 4.1). One other option is adding i-process to
PISNe, which could resolve some of the problems with those models (see
Appendix B.4).

###  B.3 Combining Two Sites

Figure 12: Best-fit results of fitting abundances of J0931$+$0038 (red points)
combining CCSN, HN, and PISN with each other. The large panels shows the fits
in [X/H], while the smaller panels indicates the residual (data - model). The
blue and orange lines indicate two different models described in the upper
left legend of each panel, and the black line indicates their sum. The top-
right of the large panels shows reduced chi squared and the error-normalized
mean absolute deviation. Reference Key: E20 (Ebinger et al., 2020), G18
(Grimmett et al., 2018), HW02 (Heger & Woosley, 2002), HW10 (Heger & Woosley,
2010), N13 (Nomoto et al., 2013), R18 (Ritter et al., 2018). See Section B.3
for discussion.  Figure 13: Best-fit results of fitting abundances of
J0931$+$0038 (red points) combining CCSN, HN, and PISN with SN Ia and ISM.
Same lines as Fig 12. Reference Key: B19 (Bravo et al., 2019), E20 (Ebinger et
al., 2020), F14 (Fink et al., 2014), G18 (Grimmett et al., 2018), HW02 (Heger
& Woosley, 2002), R18 (Ritter et al., 2018). See Section B.3 for discussion.

As no individual site provided a satisfactory fit to the entire abundance
pattern from C to Zn ($Z=6-30$), we next ran joint fits between all possible
pairs of sites. Note that combining two sites is not a plausible explanation
for J0931$+$0038 (see Section 4.1), but this exploration can identify physical
conditions in existing calculations that could explain parts of the abundance
pattern if combined into one site. It is expensive to consider all pairs and
there is no analytic solution allowing arbitrary dilution, so we approximated
the solution by first fitting each yield to the star individually following Ji
et al. (2020b), then performing a brute force optimization of the minimum
absolute deviation (normalized by abundance error) by allowing the dilution of
each yield to drift by $-3.0$ to $+1.0$ dex in units of 0.1 dex from the
initial fit. For simplicity we ignored the N upper limit.

For this exercise, we split our yield tables into CCSN (CC), HN, PISN (PI),
and SN Ia (IA). The Heger & Woosley (2010) and Grimmett et al. (2018) yield
tables spanned a large range of energies, so we somewhat arbitrarily split
them into CC and HN at $E=2.5$B. We also created an empirical ISM model using
abundances from SAGA (Suda et al., 2008), fitting third order polynomials to
[Fe/H] vs [X/H] as shown in Figure 8 and assuming [X/Fe]$=0$ for elements not
in that figure. We created ISM compositions at $\mathrm{\,[Fe/H]}=-3.5$ to
$-1.5$ in steps of 0.5 dex and included them as a separate yield table in our
fits.

The results are shown in Figures 12 and 13. Fig 12 shows a search for the
optimal combination of CC$+$CC, HN$+$HN, and PI$+$PI (top row) and crossing SN
types CC$+$HN, CC$+$PI, and HN$+$PI (bottom row). Fig 13 crosses each SN type
with SN Ia (top row) and ISM (bottom row). These specific fits were chosen to
have the smallest possible minimum absolute deviation of all combinations.
Close ties were broken by choosing models that illustrate specific physics.

The immediate overall conclusion is that no pairs of models can fit the entire
abundance pattern, despite the vastly expanded model space compared to single
site fits. The reduced $\chi^{2}$ and mean absolute deviation (MAD) should be
near 1 for reasonable fits, and the lowest MAD is 1.9. There is enough freedom
that the light elements with $Z\leq 20$ are generally fit well. However, the
Fe peak from $Z=21-30$ has many issues, especially for Sc ($Z=21$), Mn
($Z=25$), and the overall enhanced Co-Zn ($Z=27-30$). Fitting all three of
these simultaneously is not possible even after searching through over 20,000
yield sets.

Two models show up repeatedly in these fits as being able to solve some of the
Fe peak problems. First, in the top row of Fig 13, off-center deflagration
explosions of Chandrasekhar mass white dwarfs (here showing yields from Fink
et al. 2014) are able to achieve a high [Mn/Fe] and [Ni/Fe] ratio that broadly
matches J0931$+$0038, though no SN Ia is able to produce similarly high levels
of Zn. Though white dwarfs are likely not relevant progenitors for
nucleosynthesis in J0931$+$0038 (see Section 4.1), the high neutron fractions
achieved in those white dwarfs could potentially be achieved in massive stars,
although there is tension with the low neutron fractions needed to have a
large odd-even effect. Second, the 15 $\mathrm{\,M_{\odot}}$ CC model from
Ritter et al. (2018) shows up several times in both figures because it is able
to produce large amounts of Co-Zn. This model ejects a large amount of
material near the mass cut that was in nuclear statistical equilibrium (NSE),
resulting in a very strong alpha-rich freezeout that produces this pattern, as
well as some heavier elements all the way up to Mo ($Z=42$; see fig. 28 of
Ritter et al. 2018, Woosley & Hoffman 1992). Ejecting substantial amounts of
this NSE material is a promising future path to reproducing the abundance
pattern of J0931$+$0038\. One example of this could be late-time mass loss
induced by close binary interactions. The lighter elements (C-Ca) could be
hydrostatically synthesized by a $80\mathrm{\,M_{\odot}}$ progenitor to match
J0931$+$0038, but late mass loss from binary stripping after the CO core mass
is set could push the mass cut closer to the center of the star. Note that
Case C mass transfer (after igniting central He burning) is a typical outcome
of massive metal-poor star binary evolution (de Mink et al., 2008).

Finally, the models including ISM did not work well. As expected, the ISM in
the PISN+ISM was able to fix the overly strong odd-even effect in the light
elements for the 260$\mathrm{\,M_{\odot}}$ PISN, but it could not contribute
to the problems with the Fe peak. Though we allowed the ISM to be
metallicities from $\mathrm{\,[Fe/H]}=-3.5$ to $-1.5$, the $-3.5$ ISM always
came to the forefront primarily because it helped most models fit the [C/O]
ratio better while also filling in any missing amount of Na, K, or Sc. It is
worth noting that the [C/O] ratio in our ISM model is likely too low, since it
is only possible to detect O in the data when it is highly enhanced (and
similar for N).

###  B.4 Full fits from $Z=6-56$ including neutron capture elements

There are few models that self-consistently predict nucleosynthesis yields of
both lighter and heavier elements. We thus constructed plausible combinations
of our best-fit explosion models (HN and PISN) and heavy-element
nucleosynthesis patterns (computed through simulation-based or parameterized
trajectories), combining them using the two-component search from Starfit
(Heger & Woosley, 2010). Our goal was to create realistic abundance patterns
for scenarios that could simultaneously explain both the light and heavy
elements in J0931$+$0038\. These results were used to create the models
including neutron-capture elements in Fig 5. A PISN combined with an
$i$-process emerges as one possible explanation for simultaneously producing
the observed abundance pattern and high metallicity of J0931$+$0038, although
no such theoretical models currently exist in the literature. A hypernova
combined with an $r/i$-process or a neutrino-driven wind (if such an explosion
occurs) may also provide a good match to the observed abundances. In this
section we elaborate on general considerations for heavy element
nucleosynthesis, followed by discussion of which combinations are realistic.

Considering the heavy elements in J0931$+$0038 ($Z>35$), the enhancement in Sr
all the way out to Pd, combined with low Ba and Eu, provides a strong
constraint on the conditions needed for their synthesis. There will be
insignificant contributions from the main r-process that synthesizes a
relatively large amount of Ba and Eu (e.g. Holmbeck et al., 2023) and the main
s-process that synthesizes a large amount of Ba relative to Sr in metal-poor
stars (e.g., Lugaro et al., 2012). The i-process generally has a similar
challenge as the s-process of overproducing Ba (e.g., Hampel et al., 2016;
Côté et al., 2018). This is mostly driven by the assumption of solar scaled
initial abundances for stellar simulations at low metallicity, where an early
increase of the Ba production is mostly fed from seed abundances in the Sr-Zr
region. The i-process production at the first neutron-magic peak of Rb-Zr is
instead due to neutron captures on the Fe seeds (e.g., Herwig et al., 2011),
and it does not depend on their initial abundances. Finally, most $\nu$-driven
wind models only produce significant amounts of elements up to Mo but are
unable to extend out to Pd (Fröhlich et al., 2006; Wanajo, 2006; Wanajo et
al., 2018).

From published model grids, we find that a weak r-process with $Y_{e}\sim$0.25
and entropy of 12$k_{B}$/baryon (or something slightly more neutron-poor)
allows the synthesis of the first-peak elements without producing a
substantial amount of Ba (e.g., Nishimura et al., 2017; Holmbeck et al.,
2023). The detailed pattern of any individual $Y_{e}$ trajectory does not
match our observations, but a mixture of ejecta conditions is expected and can
likely be combined to reproduce the detailed pattern (e.g., Farouqi et al.,
2010; Holmbeck et al., 2019). We also find that a high entropy (120
$k_{B}$/nucleon) and proton-rich ($Y_{e}=0.54$) neutrino-driven wind
trajectory is able to match the light elements out to Pd, although it is not
clear if such conditions can be achieved in actual supernovae (Bliss et al.,
2018).

In Section 4 we discussed a computational experiment for i-process
nucleosynthesis where we reduced abundances of elements heavier than Fe. This
is justified as metal-poor gas is deficient in the neutron-capture elements
compared to iron (see Figure 8 and Cescutti et al. 2013). Our i-process models
thus use the nucleosynthesis framework from Bertolli et al. (2013) and
Roederer et al. (2016, 2022), but reduce the initial heavy element abundances
with respect to Fe by ten times (e.g., $\mbox{[Sr/Fe]}=-1$ and
$\mbox{[Ba/Fe]}=-1$). With this change, it is possible to satisfy the low Ba
constraint and at the same time obtain an efficient production in the Rb-Ru
mass region as observed in J0931$+$0038\. However, while the i-process
produces heavy elements, the abundances of intermediate mass elements (in
particular the less abundant odd elements) can also be affected. An example is
the observed enhancement of Sc with respect to Ca in the post-AGB star
Sakurai’s object, where Sc is co-produced with heavy elements in the Rb-Zr
region (Herwig et al., 2011). Another example is extra production of Na and Al
(e.g., Clarkson et al., 2018).

We now discuss whether the production of heavy elements through the channels
described above is a realistic possibility in CCSN, HN, and PISN explosions.
CCSNe/HNe are thought to be accompanied by heavy element production in
neutrino-driven winds from a NS remnant, either through a weak r-process or
under proton-rich conditions, although the detailed properties of these winds
are being investigated (Pruet et al., 2006; Fröhlich et al., 2006; Arcones &
Montes, 2011; Arcones & Thielemann, 2013; Wanajo, 2013; Fujibayashi et al.,
2015). A weak r-process with $Y_{e}\lesssim$0.25 could potentially occur in
accretion disk winds around a black hole (e.g., Pruet et al., 2004; Surman et
al., 2006). Altogether, the production of enhanced light neutron-capture
elements out to Pd in such winds suggests scenarios involving material ejected
from a neutron star or black hole accretion disk. These remnants are a natural
and expected outcome of CCSN/HN explosions, lending support to the scenarios
where a HN is combined with a weak r-process or proton-rich neutrino-driven
wind. On the other hand, PISNe leave no remnant behind, and hence cannot
produce neutron-capture elements through these channels.

The other possibility for producing heavy elements, the intermediate (i-)
neutron-capture process, is a recently revived process of interest (e.g.,
Hampel et al., 2016; Roederer et al., 2016; Côté et al., 2018). The source of
i-process in massive metal-poor stars is proton ingestion due to mixing with
convective He shells (Cowan & Rose, 1977; Banerjee et al., 2018; Clarkson et
al., 2018). However, it is not yet clear if 3D simulations including
convection are able to trigger the proton ingestion that would induce the
i-process (Herwig et al., 2014; Woodward et al., 2015). Nonetheless, this
possibility lends support to the scenario where a HN combined with an
i-process could explain the abundances in J0931$+$0038.

If massive metal-poor progenitors of CCSNe or HNe can be affected by proton
ingestion events that activate the i-process, we can expect that the same may
happen for PISN progenitors. If this occurs, the i-process in a PISN
progenitor could not only produce the neutron-capture elements, but it might
also help fill in the overly low light odd element abundances, while also
increasing the abundance of Zn that otherwise rules out PISN models. However,
there are no PISN models available yet taking into account the impact of such
events within their integrated yields. Future generations of PISN models
including proton ingestion and the supernova explosion will be paramount to
explore this scenario in greater detail.

## References

  * Abbott et al. (2023) Abbott, R., Abbott, T. D., Acernese, F., et al. 2023, Physical Review X, 13, 011048, doi: 10.1103/PhysRevX.13.011048
  * Abdurro’uf et al. (2022) Abdurro’uf, Accetta, K., Aerts, C., et al. 2022, ApJS, 259, 35, doi: 10.3847/1538-4365/ac4414
  * Abohalima & Frebel (2018) Abohalima, A., & Frebel, A. 2018, ApJS, 238, 36, doi: 10.3847/1538-4365/aadfe9
  * Aguado et al. (2016) Aguado, D. S., Allende Prieto, C., González Hernández, J. I., et al. 2016, A&A, 593, A10, doi: 10.1051/0004-6361/201628371
  * Almeida et al. (2023) Almeida, A., Anderson, S. F., Argudo-Fernández, M., et al. 2023, ApJS, 267, 44, doi: 10.3847/1538-4365/acda98
  * Amarante et al. (2022) Amarante, J. A. S., Debattista, V. P., Beraldo e Silva, L., Laporte, C. F. P., & Deg, N. 2022, ApJ, 937, 12, doi: 10.3847/1538-4357/ac8b0d
  * Andrievsky et al. (2018) Andrievsky, S., Bonifacio, P., Caffau, E., et al. 2018, MNRAS, 473, 3377, doi: 10.1093/mnras/stx2526
  * Arcones & Montes (2011) Arcones, A., & Montes, F. 2011, ApJ, 731, 5, doi: 10.1088/0004-637X/731/1/5
  * Arcones & Thielemann (2013) Arcones, A., & Thielemann, F. K. 2013, Journal of Physics G Nuclear Physics, 40, 013201, doi: 10.1088/0954-3899/40/1/013201
  * Arenou et al. (2018) Arenou, F., Luri, X., Babusiaux, C., et al. 2018, A&A, 616, A17, doi: 10.1051/0004-6361/201833234
  * Asplund et al. (2009) Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481, doi: 10.1146/annurev.astro.46.060407.145222
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * Audouze & Silk (1995) Audouze, J., & Silk, J. 1995, ApJ, 451, L49, doi: 10.1086/309687
  * Avallone et al. (2022) Avallone, E. A., Tayar, J. N., van Saders, J. L., et al. 2022, ApJ, 930, 7, doi: 10.3847/1538-4357/ac60a1
  * Bailer-Jones et al. (2021) Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Demleitner, M., & Andrae, R. . 2021, AJ, 161, 147, doi: 10.3847/1538-3881/abd806
  * Banerjee et al. (2018) Banerjee, P., Qian, Y.-Z., & Heger, A. 2018, ApJ, 865, 120, doi: 10.3847/1538-4357/aadb8c
  * Beers et al. (1992) Beers, T. C., Preston, G. W., & Shectman, S. A. 1992, AJ, 103, 1987, doi: 10.1086/116207
  * Belokurov et al. (2018) Belokurov, V., Erkal, D., Evans, N. W., Koposov, S. E., & Deason, A. J. 2018, Monthly Notices of the Royal Astronomical Society, 478, 611, doi: 10.1093/mnras/sty982
  * Bergemann (2011) Bergemann, M. 2011, MNRAS, 413, 2184, doi: 10.1111/j.1365-2966.2011.18295.x
  * Bergemann et al. (2017) Bergemann, M., Collet, R., Amarsi, A. M., et al. 2017, ApJ, 847, 15, doi: 10.3847/1538-4357/aa88cb
  * Bergemann et al. (2012a) Bergemann, M., Hansen, C. J., Bautista, M., & Ruchti, G. 2012a, A&A, 546, A90, doi: 10.1051/0004-6361/201219406
  * Bergemann et al. (2013) Bergemann, M., Kudritzki, R.-P., Würl, M., et al. 2013, ApJ, 764, 115, doi: 10.1088/0004-637X/764/2/115
  * Bergemann et al. (2012b) Bergemann, M., Lind, K., Collet, R., Magic, Z., & Asplund, M. 2012b, MNRAS, 427, 27, doi: 10.1111/j.1365-2966.2012.21687.x
  * Bergemann & Nordlander (2014) Bergemann, M., & Nordlander, T. 2014, arXiv e-prints, arXiv:1403.3088, doi: 10.48550/arXiv.1403.3088
  * Bergemann et al. (2010) Bergemann, M., Pickering, J. C., & Gehren, T. 2010, MNRAS, 401, 1334, doi: 10.1111/j.1365-2966.2009.15736.x
  * Bergemann et al. (2019) Bergemann, M., Gallagher, A. J., Eitner, P., et al. 2019, A&A, 631, A80, doi: 10.1051/0004-6361/201935811
  * Bergemann et al. (2021) Bergemann, M., Hoppe, R., Semenova, E., et al. 2021, MNRAS, 508, 2236, doi: 10.1093/mnras/stab2160
  * Bernstein et al. (2003) Bernstein, R., Shectman, S. A., Gunnels, S. M., Mochnacki, S., & Athey, A. E. 2003, Proc. SPIE, 4841, 1694, doi: 10.1117/12.461502
  * Bertolli et al. (2013) Bertolli, M. G., Herwig, F., Pignatari, M., & Kawano, T. 2013, arXiv e-prints, arXiv:1310.4578, doi: 10.48550/arXiv.1310.4578
  * Bianchi et al. (2017) Bianchi, L., Shiao, B., & Thilker, D. 2017, ApJS, 230, 24, doi: 10.3847/1538-4365/aa7053
  * Bliss et al. (2018) Bliss, J., Arcones, A., & Qian, Y. Z. 2018, ApJ, 866, 105, doi: 10.3847/1538-4357/aade8d
  * Boccioli et al. (2023) Boccioli, L., Roberti, L., Limongi, M., Mathews, G. J., & Chieffi, A. 2023, ApJ, 949, 17, doi: 10.3847/1538-4357/acc06a
  * Bolton et al. (2012) Bolton, A. S., Schlegel, D. J., Aubourg, É., et al. 2012, AJ, 144, 144, doi: 10.1088/0004-6256/144/5/144
  * Brasseur et al. (2019) Brasseur, C. E., Phillip, C., Fleming, S. W., Mullally, S. E., & White, R. L. 2019, Astrocut: Tools for creating cutouts of TESS images, Astrophysics Source Code Library, record ascl:1905.007.  http://ascl.net/1905.007
  * Brauer et al. (2022) Brauer, K., Andales, H. D., Ji, A. P., et al. 2022, ApJ, 937, 14, doi: 10.3847/1538-4357/ac85b9
  * Bravo et al. (2019) Bravo, E., Badenes, C., & Martínez-Rodríguez, H. 2019, MNRAS, 482, 4346, doi: 10.1093/mnras/sty2951
  * Bromm (2013) Bromm, V. 2013, Reports on Progress in Physics, 76, 112901, doi: 10.1088/0034-4885/76/11/112901
  * Brown et al. (2021) Brown, A. G., Vallenari, A., Prusti, T., et al. 2021, Astronomy and Astrophysics, 649, 1, doi: 10.1051/0004-6361/202039657
  * Burrows & Vartanyan (2021) Burrows, A., & Vartanyan, D. 2021, Nature, 589, 29, doi: 10.1038/s41586-020-03059-w
  * Burrows et al. (2018) Burrows, A., Vartanyan, D., Dolence, J. C., Skinner, M. A., & Radice, D. 2018, Space Sci. Rev., 214, 33, doi: 10.1007/s11214-017-0450-9
  * Caffau et al. (2013) Caffau, E., Bonifacio, P., Sbordone, L., et al. 2013, A&A, 560, A71, doi: 10.1051/0004-6361/201322488
  * Cargile et al. (2020) Cargile, P. A., Conroy, C., Johnson, B. D., et al. 2020, ApJ, 900, 28, doi: 10.3847/1538-4357/aba43b
  * Carlin et al. (2018) Carlin, J. L., Sheffield, A. A., Cunha, K., & Smith, V. V. 2018, ApJ, 859, L10, doi: 10.3847/2041-8213/aac3d8
  * Casey (2014) Casey, A. R. 2014, ArXiv e-prints.  https://arxiv.org/abs/1405.5968
  * Casey & Schlaufman (2015) Casey, A. R., & Schlaufman, K. C. 2015, ApJ, 809, 110, doi: 10.1088/0004-637X/809/2/110
  * Castelli & Kurucz (2004) Castelli, F., & Kurucz, R. L. 2004, ArXiv Astrophysics e-prints
  * Cayrel et al. (2004) Cayrel, R., Depagne, E., Spite, M., et al. 2004, A&A, 416, 1117, doi: 10.1051/0004-6361:20034074
  * Cescutti et al. (2013) Cescutti, G., Chiappini, C., Hirschi, R., Meynet, G., & Frischknecht, U. 2013, A&A, 553, A51, doi: 10.1051/0004-6361/201220809
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv, arXiv:1612.05560.  https://arxiv.org/abs/1612.05560
  * Chance et al. (2022) Chance, Q., Foreman-Mackey, D., Ballard, S., et al. 2022, arXiv e-prints, arXiv:2206.11275, doi: 10.48550/arXiv.2206.11275
  * Chen et al. (2014) Chen, K.-J., Heger, A., Woosley, S., et al. 2014, ApJ, 790, 162, doi: 10.1088/0004-637X/790/2/162
  * Chiappini (2013) Chiappini, C. 2013, Astronomische Nachrichten, 334, 595, doi: 10.1002/asna.201311902
  * Choi et al. (2016) Choi, J., Dotter, A., Conroy, C., et al. 2016, The Astrophysical Journal, 823, 102, doi: 10.3847/0004-637x/823/2/102
  * Choplin et al. (2018) Choplin, A., Hirschi, R., Meynet, G., et al. 2018, A&A, 618, A133, doi: 10.1051/0004-6361/201833283
  * Cioffi et al. (1988) Cioffi, D. F., McKee, C. F., & Bertschinger, E. 1988, ApJ, 334, 252, doi: 10.1086/166834
  * Clarkson et al. (2018) Clarkson, O., Herwig, F., & Pignatari, M. 2018, MNRAS, 474, L37, doi: 10.1093/mnrasl/slx190
  * Conroy et al. (2019) Conroy, C., Bonaca, A., Cargile, P., et al. 2019, ApJ, 883, 107, doi: 10.3847/1538-4357/ab38b8
  * Côté et al. (2018) Côté, B., Denissenkov, P., Herwig, F., et al. 2018, ApJ, 854, 105, doi: 10.3847/1538-4357/aaaae8
  * Cowan & Rose (1977) Cowan, J. J., & Rose, W. K. 1977, ApJ, 212, 149, doi: 10.1086/155030
  * Cowan et al. (2002) Cowan, J. J., Sneden, C., Burles, S., et al. 2002, ApJ, 572, 861, doi: 10.1086/340347
  * Curtis et al. (2019) Curtis, S., Ebinger, K., Fröhlich, C., et al. 2019, ApJ, 870, 2, doi: 10.3847/1538-4357/aae7d2
  * Da Costa et al. (2019) Da Costa, G. S., Bessell, M. S., Mackey, A. D., et al. 2019, MNRAS, 489, 5900, doi: 10.1093/mnras/stz2550
  * Dawson et al. (2013) Dawson, K. S., Schlegel, D. J., Ahn, C. P., et al. 2013, AJ, 145, 10, doi: 10.1088/0004-6256/145/1/10
  * de Mink et al. (2008) de Mink, S. E., Pols, O. R., & Yoon, S. C. 2008, in American Institute of Physics Conference Series, Vol. 990, First Stars III, ed. B. W. O’Shea & A. Heger, 230–232, doi: 10.1063/1.2905549
  * deBoer et al. (2017) deBoer, R. J., Görres, J., Wiescher, M., et al. 2017, Reviews of Modern Physics, 89, 035007, doi: 10.1103/RevModPhys.89.035007
  * Doherty et al. (2017) Doherty, C. L., Gil-Pons, P., Siess, L., & Lattanzio, J. C. 2017, PASA, 34, e056, doi: 10.1017/pasa.2017.52
  * Doi et al. (2010) Doi, M., Tanaka, M., Fukugita, M., et al. 2010, AJ, 139, 1628, doi: 10.1088/0004-6256/139/4/1628
  * Dotter (2016) Dotter, A. 2016, ApJS, 222, 8, doi: 10.3847/0067-0049/222/1/8
  * Ebinger et al. (2020) Ebinger, K., Curtis, S., Ghosh, S., et al. 2020, ApJ, 888, 91, doi: 10.3847/1538-4357/ab5dcb
  * Eilers et al. (2019) Eilers, A.-C., Hogg, D. W., Rix, H.-W., & Ness, M. K. 2019, ApJ, 871, 120, doi: 10.3847/1538-4357/aaf648
  * Ekström et al. (2008) Ekström, S., Meynet, G., Chiappini, C., Hirschi, R., & Maeder, A. 2008, A&A, 489, 685, doi: 10.1051/0004-6361:200809633
  * El Eid et al. (2004) El Eid, M. F., Meyer, B. S., & The, L. S. 2004, ApJ, 611, 452, doi: 10.1086/422162
  * Evans et al. (2018) Evans, D. W., Riello, M., De Angeli, F., et al. 2018, A&A, 616, A4, doi: 10.1051/0004-6361/201832756
  * Ezzeddine et al. (2019) Ezzeddine, R., Frebel, A., Roederer, I. U., et al. 2019, ApJ, 876, 97, doi: 10.3847/1538-4357/ab14e7
  * Fabricius et al. (2021) Fabricius, C., Luri, X., Arenou, F., et al. 2021, A&A, 649, A5, doi: 10.1051/0004-6361/202039834
  * Farah et al. (2023) Farah, A. M., Edelman, B., Zevin, M., et al. 2023, arXiv e-prints, arXiv:2301.00834, doi: 10.48550/arXiv.2301.00834
  * Farmer et al. (2021) Farmer, R., Laplace, E., de Mink, S. E., & Justham, S. 2021, ApJ, 923, 214, doi: 10.3847/1538-4357/ac2f44
  * Farmer et al. (2023) Farmer, R., Laplace, E., Ma, J.-z., de Mink, S. E., & Justham, S. 2023, ApJ, 948, 111, doi: 10.3847/1538-4357/acc315
  * Farmer et al. (2019) Farmer, R., Renzo, M., de Mink, S. E., Marchant, P., & Justham, S. 2019, ApJ, 887, 53, doi: 10.3847/1538-4357/ab518b
  * Farouqi et al. (2010) Farouqi, K., Kratz, K.-L., Pfeiffer, B., et al. 2010, ApJ, 712, 1359, doi: 10.1088/0004-637X/712/2/1359
  * Feroz & Hobson (2008) Feroz, F., & Hobson, M. P. 2008, MNRAS, 384, 449, doi: 10.1111/j.1365-2966.2007.12353.x
  * Feroz et al. (2009) Feroz, F., Hobson, M. P., & Bridges, M. 2009, MNRAS, 398, 1601, doi: 10.1111/j.1365-2966.2009.14548.x
  * Feroz et al. (2019) Feroz, F., Hobson, M. P., Cameron, E., & Pettitt, A. N. 2019, The Open Journal of Astrophysics, 2, 10, doi: 10.21105/astro.1306.2144
  * Fields & Couch (2020) Fields, C. E., & Couch, S. M. 2020, ApJ, 901, 33, doi: 10.3847/1538-4357/abada7
  * Fink et al. (2014) Fink, M., Kromer, M., Seitenzahl, I. R., et al. 2014, MNRAS, 438, 1762, doi: 10.1093/mnras/stt2315
  * Foley et al. (2010) Foley, R. J., Brown, P. J., Rest, A., et al. 2010, ApJ, 708, L61, doi: 10.1088/2041-8205/708/1/L61
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306, doi: 10.1086/670067
  * Fraser et al. (2017) Fraser, M., Casey, A. R., Gilmore, G., Heger, A., & Chan, C. 2017, MNRAS, 468, 418, doi: 10.1093/mnras/stx480
  * Frebel et al. (2006) Frebel, A., Christlieb, N., Norris, J. E., Aoki, W., & Asplund, M. 2006, ApJ, 638, L17, doi: 10.1086/500592
  * Frebel & Norris (2015) Frebel, A., & Norris, J. E. 2015, ARA&A, 53, 631.  https://arxiv.org/abs/1501.06921
  * Frebel et al. (2005) Frebel, A., Aoki, W., Christlieb, N., et al. 2005, Nature, 434, 871, doi: 10.1038/nature03455
  * Frischknecht et al. (2016) Frischknecht, U., Hirschi, R., Pignatari, M., et al. 2016, MNRAS, 456, 1803, doi: 10.1093/mnras/stv2723
  * Fröhlich et al. (2006) Fröhlich, C., Martínez-Pinedo, G., Liebendörfer, M., et al. 2006, Phys. Rev. Lett., 96, 142502, doi: 10.1103/PhysRevLett.96.142502
  * Fujibayashi et al. (2015) Fujibayashi, S., Yoshida, T., & Sekiguchi, Y. 2015, ApJ, 810, 115, doi: 10.1088/0004-637X/810/2/115
  * Fukugita et al. (1996) Fukugita, M., Ichikawa, T., Gunn, J. E., et al. 1996, AJ, 111, 1748, doi: 10.1086/117915
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1, doi: 10.1051/0004-6361/201629272
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1, doi: 10.1051/0004-6361/201833051
  * Gaia Collaboration et al. (2021) —. 2021, A&A, 649, A1, doi: 10.1051/0004-6361/202039657
  * Gal-Yam (2019) Gal-Yam, A. 2019, ARA&A, 57, 305, doi: 10.1146/annurev-astro-081817-051819
  * Gallagher et al. (2020) Gallagher, A. J., Bergemann, M., Collet, R., et al. 2020, A&A, 634, A55, doi: 10.1051/0004-6361/201936104
  * Gerber et al. (2023) Gerber, J. M., Magg, E., Plez, B., et al. 2023, A&A, 669, A43, doi: 10.1051/0004-6361/202243673
  * Green et al. (2019) Green, G. M., Schlafly, E., Zucker, C., Speagle, J. S., & Finkbeiner, D. 2019, ApJ, 887, 93, doi: 10.3847/1538-4357/ab5362
  * Green et al. (2014) Green, G. M., Schlafly, E. F., Finkbeiner, D. P., et al. 2014, ApJ, 783, 114, doi: 10.1088/0004-637X/783/2/114
  * Grimmett et al. (2018) Grimmett, J. J., Heger, A., Karakas, A. I., & Müller, B. 2018, MNRAS, 479, 495, doi: 10.1093/mnras/sty1417
  * Grimmett et al. (2021) Grimmett, J. J., Müller, B., Heger, A., Banerjee, P., & Obergaulinger, M. 2021, MNRAS, 501, 2764, doi: 10.1093/mnras/staa3819
  * Gunn et al. (1998) Gunn, J. E., Carr, M., Rockosi, C., et al. 1998, The Astronomical Journal, 116, 3040, doi: 10.1086/300645
  * Gunn et al. (1998) Gunn, J. E., Carr, M., Rockosi, C., et al. 1998, AJ, 116, 3040, doi: 10.1086/300645
  * Gunn et al. (2006) Gunn, J. E., Siegmund, W. A., Mannery, E. J., et al. 2006, AJ, 131, 2332, doi: 10.1086/500975
  * Gustafsson et al. (2008) Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A&A, 486, 951, doi: 10.1051/0004-6361:200809724
  * Hampel et al. (2016) Hampel, M., Stancliffe, R. J., Lugaro, M., & Meyer, B. S. 2016, ApJ, 831, 171, doi: 10.3847/0004-637X/831/2/171
  * Hartwig et al. (2018) Hartwig, T., Bromm, V., & Loeb, A. 2018, MNRAS, 479, 2202, doi: 10.1093/mnras/sty1576
  * Heger et al. (2003) Heger, A., Fryer, C. L., Woosley, S. E., Langer, N., & Hartmann, D. H. 2003, ApJ, 591, 288, doi: 10.1086/375341
  * Heger & Woosley (2002) Heger, A., & Woosley, S. E. 2002, ApJ, 567, 532, doi: 10.1086/338487
  * Heger & Woosley (2010) —. 2010, ApJ, 724, 341, doi: 10.1088/0004-637X/724/1/341
  * Heiter et al. (2021) Heiter, U., Lind, K., Bergemann, M., et al. 2021, A&A, 645, A106, doi: 10.1051/0004-6361/201936291
  * Helmi et al. (2018) Helmi, A., Babusiaux, C., Koppelman, H. H., et al. 2018, Nature, 563, 85, doi: 10.1038/s41586-018-0625-x
  * Herwig et al. (2011) Herwig, F., Pignatari, M., Woodward, P. R., et al. 2011, ApJ, 727, 89, doi: 10.1088/0004-637X/727/2/89
  * Herwig et al. (2014) Herwig, F., Woodward, P. R., Lin, P.-H., Knox, M., & Fryer, C. 2014, ApJ, 792, L3, doi: 10.1088/2041-8205/792/1/L3
  * Holmbeck et al. (2019) Holmbeck, E. M., Frebel, A., McLaughlin, G. C., et al. 2019, ApJ, 881, 5, doi: 10.3847/1538-4357/ab2a01
  * Holmbeck et al. (2023) Holmbeck, E. M., Sprouse, T. M., & Mumpower, M. R. 2023, European Physical Journal A, 59, 28, doi: 10.1140/epja/s10050-023-00927-7
  * Hon et al. (2021) Hon, M., Huber, D., Kuszlewicz, J. S., et al. 2021, ApJ, 919, 131, doi: 10.3847/1538-4357/ac14b1
  * Honda et al. (2007) Honda, S., Aoki, W., Ishimaru, Y., & Wanajo, S. 2007, ApJ, 666, 1189, doi: 10.1086/520034
  * Horta et al. (2023) Horta, D., Schiavon, R. P., Mackereth, J. T., et al. 2023, MNRAS, 520, 5671, doi: 10.1093/mnras/stac3179
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: http://dx.doi.org/10.1109/MCSE.2007.55
  * Husser et al. (2013) Husser, T. O., Wende-von Berg, S., Dreizler, S., et al. 2013, A&A, 553, A6, doi: 10.1051/0004-6361/201219058
  * Imbriani et al. (2001) Imbriani, G., Limongi, M., Gialanella, L., et al. 2001, ApJ, 558, 903, doi: 10.1086/322288
  * Ishigaki et al. (2018) Ishigaki, M. N., Tominaga, N., Kobayashi, C., & Nomoto, K. 2018, ApJ, 857, 46, doi: 10.3847/1538-4357/aab3de
  * Jeena et al. (2023) Jeena, S. K., Banerjee, P., Chiaki, G., & Heger, A. 2023, MNRAS, 526, 4467, doi: 10.1093/mnras/stad3028
  * Jermyn et al. (2023) Jermyn, A. S., Bauer, E. B., Schwab, J., et al. 2023, ApJS, 265, 15, doi: 10.3847/1538-4365/acae8d
  * Ji et al. (2019) Ji, A. P., Simon, J. D., Frebel, A., Venn, K. A., & Hansen, T. T. 2019, ApJ, 870, 83, doi: 10.3847/1538-4357/aaf3bb
  * Ji et al. (2020a) Ji, A. P., Li, T. S., Hansen, T. T., et al. 2020a, AJ, 160, 181, doi: 10.3847/1538-3881/abacb6
  * Ji et al. (2020b) Ji, A. P., Li, T. S., Simon, J. D., et al. 2020b, ApJ, 889, 27, doi: 10.3847/1538-4357/ab6213
  * Ji et al. (2023) Ji, A. P., Simon, J. D., Roederer, I. U., et al. 2023, AJ, 165, 100, doi: 10.3847/1538-3881/acad84
  * Johnson & Bolte (2002) Johnson, J. A., & Bolte, M. 2002, ApJ, 579, 616, doi: 10.1086/342829
  * Jones et al. (2001) Jones, E., Oliphant, T., Peterson, P., et al. 2001, SciPy: Open source scientific tools for Python.  http://www.scipy.org/
  * Karlsson et al. (2008) Karlsson, T., Johnson, J. L., & Bromm, V. 2008, ApJ, 679, 6, doi: 10.1086/533520
  * Kelson (2003) Kelson, D. D. 2003, PASP, 115, 688, doi: 10.1086/375502
  * Klessen & Glover (2023) Klessen, R. S., & Glover, S. C. O. 2023, ARA&A, 61, 65, doi: 10.1146/annurev-astro-071221-053453
  * Kolborg et al. (2022) Kolborg, A. N., Martizzi, D., Ramirez-Ruiz, E., et al. 2022, ApJ, 936, L26, doi: 10.3847/2041-8213/ac8c98
  * Kollmeier et al. (2017) Kollmeier, J. A., Zasowski, G., Rix, H.-W., et al. 2017, arXiv e-prints, arXiv:1711.03234, doi: 10.48550/arXiv.1711.03234
  * Korotin et al. (2018) Korotin, S. A., Andrievsky, S. M., & Zhukova, A. V. 2018, MNRAS, 480, 965, doi: 10.1093/mnras/sty1886
  * Kozyreva et al. (2014) Kozyreva, A., Blinnikov, S., Langer, N., & Yoon, S. C. 2014, A&A, 565, A70, doi: 10.1051/0004-6361/201423447
  * Kupka et al. (1999) Kupka, F., Piskunov, N., Ryabchikova, T. A., Stempels, H. C., & Weiss, W. W. 1999, A&AS, 138, 119, doi: 10.1051/aas:1999267
  * Larsen et al. (2022) Larsen, S. S., Eitner, P., Magg, E., et al. 2022, A&A, 660, A88, doi: 10.1051/0004-6361/202142243
  * Li et al. (2018) Li, H., Tan, K., & Zhao, G. 2018, ApJS, 238, 16, doi: 10.3847/1538-4365/aada4a
  * Li et al. (2022) Li, H., Aoki, W., Matsuno, T., et al. 2022, ApJ, 931, 147, doi: 10.3847/1538-4357/ac6514
  * Limongi & Chieffi (2012) Limongi, M., & Chieffi, A. 2012, ApJS, 199, 38, doi: 10.1088/0067-0049/199/2/38
  * Limongi & Chieffi (2018) —. 2018, ApJS, 237, 13, doi: 10.3847/1538-4365/aacb24
  * Lindegren et al. (2021a) Lindegren, L., Bastian, U., Biermann, M., et al. 2021a, A&A, 649, A4, doi: 10.1051/0004-6361/202039653
  * Lindegren et al. (2021b) Lindegren, L., Klioner, S. A., Hernández, J., et al. 2021b, A&A, 649, A2, doi: 10.1051/0004-6361/202039709
  * LSST Science Collaboration et al. (2009) LSST Science Collaboration, Abell, P. A., Allison, J., et al. 2009, arXiv e-prints, arXiv:0912.0201, doi: 10.48550/arXiv.0912.0201
  * Lugaro et al. (2012) Lugaro, M., Karakas, A. I., Stancliffe, R. J., & Rijs, C. 2012, ApJ, 747, 2, doi: 10.1088/0004-637X/747/1/2
  * Macias & Ramirez-Ruiz (2018) Macias, P., & Ramirez-Ruiz, E. 2018, ApJ, 860, 89, doi: 10.3847/1538-4357/aac3e0
  * Magg et al. (2022a) Magg, E., Bergemann, M., Serenelli, A., et al. 2022a, A&A, 661, A140, doi: 10.1051/0004-6361/202142971
  * Magg et al. (2022b) Magg, M., Schauer, A. T. P., Klessen, R. S., et al. 2022b, ApJ, 929, 119, doi: 10.3847/1538-4357/ac5aac
  * Magg et al. (2020) Magg, M., Nordlander, T., Glover, S. C. O., et al. 2020, MNRAS, 498, 3703, doi: 10.1093/mnras/staa2624
  * Mainzer et al. (2014) Mainzer, A., Bauer, J., Cutri, R. M., et al. 2014, Astrophysical Journal, 792, 30, doi: 10.1088/0004-637X/792/1/30
  * Marocco et al. (2021) Marocco, F., Eisenhardt, P. R. M., Fowler, J. W., et al. 2021, ApJS, 253, 8, doi: 10.3847/1538-4365/abd805
  * Mashonkina et al. (2017) Mashonkina, L., Sitnova, T., & Belyaev, A. K. 2017, A&A, 605, A53, doi: 10.1051/0004-6361/201731236
  * Mckinney (2010) Mckinney, W. 2010
  * McWilliam et al. (2013) McWilliam, A., Wallerstein, G., & Mottini, M. 2013, ApJ, 778, 149, doi: 10.1088/0004-637X/778/2/149
  * Meynet et al. (2006) Meynet, G., Ekström, S., & Maeder, A. 2006, A&A, 447, 623, doi: 10.1051/0004-6361:20053070
  * Moriya et al. (2010) Moriya, T., Tominaga, N., Tanaka, M., Maeda, K., & Nomoto, K. 2010, ApJ, 717, L83, doi: 10.1088/2041-8205/717/2/L83
  * Morton (2015) Morton, T. D. 2015, isochrones: Stellar model grid package, Astrophysics Source Code Library.  http://ascl.net/1503.010
  * Naidu et al. (2021) Naidu, R. P., Conroy, C., Bonaca, A., et al. 2021, ApJ, 923, 92, doi: 10.3847/1538-4357/ac2d2d
  * Nicholl (2021) Nicholl, M. 2021, Astronomy and Geophysics, 62, 5.34, doi: 10.1093/astrogeo/atab092
  * Nishimura et al. (2017) Nishimura, N., Sawai, H., Takiwaki, T., Yamada, S., & Thielemann, F. K. 2017, ApJ, 836, L21, doi: 10.3847/2041-8213/aa5dee
  * Nomoto et al. (2013) Nomoto, K., Kobayashi, C., & Tominaga, N. 2013, ARA&A, 51, 457, doi: 10.1146/annurev-astro-082812-140956
  * Nordlander & Lind (2017) Nordlander, T., & Lind, K. 2017, A&A, 607, A75, doi: 10.1051/0004-6361/201730427
  * Norris et al. (2013) Norris, J. E., Yong, D., Bessell, M. S., et al. 2013, ApJ, 762, 28, doi: 10.1088/0004-637X/762/1/28
  * Offner et al. (2014) Offner, S. S. R., Clark, P. C., Hennebelle, P., et al. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S. Klessen, C. P. Dullemond, & T. Henning, 53–75, doi: 10.2458/azu_uapress_9780816531240-ch003
  * Onken et al. (2019) Onken, C. A., Wolf, C., Bessell, M. S., et al. 2019, PASA, 36, e033, doi: 10.1017/pasa.2019.27
  * Orkney et al. (2023) Orkney, M. D. A., Laporte, C. F. P., Grand, R. J. J., et al. 2023, arXiv e-prints, arXiv:2303.02147, doi: 10.48550/arXiv.2303.02147
  * Paxton et al. (2011) Paxton, B., Bildsten, L., Dotter, A., et al. 2011, ApJS, 192, 3, doi: 10.1088/0067-0049/192/1/3
  * Paxton et al. (2013) Paxton, B., Cantiello, M., Arras, P., et al. 2013, ApJS, 208, 4, doi: 10.1088/0067-0049/208/1/4
  * Paxton et al. (2018) Paxton, B., Schwab, J., Bauer, E. B., et al. 2018, ApJS, 234, 34, doi: 10.3847/1538-4365/aaa5a8
  * Paxton et al. (2019) Paxton, B., Smolec, R., Schwab, J., et al. 2019, ApJS, 243, 10, doi: 10.3847/1538-4365/ab2241
  * Pejcha & Thompson (2015) Pejcha, O., & Thompson, T. A. 2015, ApJ, 801, 90, doi: 10.1088/0004-637X/801/2/90
  * Penoyre et al. (2020) Penoyre, Z., Belokurov, V., Wyn Evans, N., Everall, A., & Koposov, S. E. 2020, MNRAS, 495, 321, doi: 10.1093/mnras/staa1148
  * Perego et al. (2015) Perego, A., Hempel, M., Fröhlich, C., et al. 2015, ApJ, 806, 275, doi: 10.1088/0004-637X/806/2/275
  * Pignatari et al. (2008) Pignatari, M., Gallino, R., Meynet, G., et al. 2008, ApJ, 687, L95, doi: 10.1086/593350
  * Placco et al. (2014) Placco, V. M., Frebel, A., Beers, T. C., & Stancliffe, R. J. 2014, ApJ, 797, 21, doi: 10.1088/0004-637X/797/1/21
  * Placco et al. (2015) Placco, V. M., Frebel, A., Lee, Y. S., et al. 2015, ApJ, 809, 136, doi: 10.1088/0004-637X/809/2/136
  * Placco et al. (2021) Placco, V. M., Sneden, C., Roederer, I. U., et al. 2021, linemake: Line list generator, Astrophysics Source Code Library, record ascl:2104.027.  http://ascl.net/2104.027
  * Placco et al. (2016) Placco, V. M., Frebel, A., Beers, T. C., et al. 2016, ApJ, 833, 21, doi: 10.3847/0004-637X/833/1/21
  * Plez (2012) Plez, B. 2012, Turbospectrum: Code for spectral synthesis, Astrophysics Source Code Library, record ascl:1205.004.  http://ascl.net/1205.004
  * Price-Whelan et al. (2022) Price-Whelan, A., Sipőcz, B., Wagg, T., et al. 2022, adrn/gala: v1.6.1, v1.6.1, Zenodo, doi: 10.5281/zenodo.7299506
  * Price-Whelan (2017) Price-Whelan, A. M. 2017, The Journal of Open Source Software, 2, doi: 10.21105/joss.00388
  * Price-Whelan et al. (2018) Price-Whelan, A. M., Sipőcz, B. M., Günther, H. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f
  * Pruet et al. (2006) Pruet, J., Hoffman, R. D., Woosley, S. E., Janka, H. T., & Buras, R. 2006, ApJ, 644, 1028, doi: 10.1086/503891
  * Pruet et al. (2004) Pruet, J., Thompson, T. A., & Hoffman, R. D. 2004, ApJ, 606, 1006, doi: 10.1086/382036
  * R Core Team (2023) R Core Team. 2023, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria.  https://www.R-project.org/
  * Reggiani et al. (2023) Reggiani, H., Schlaufman, K. C., & Casey, A. R. 2023, AJ, 166, 128, doi: 10.3847/1538-3881/ace68c
  * Reggiani et al. (2019) Reggiani, H., Amarsi, A. M., Lind, K., et al. 2019, A&A, 627, A177, doi: 10.1051/0004-6361/201935156
  * Riello et al. (2018) Riello, M., De Angeli, F., Evans, D. W., et al. 2018, A&A, 616, A3, doi: 10.1051/0004-6361/201832712
  * Ritter et al. (2018) Ritter, C., Herwig, F., Jones, S., et al. 2018, MNRAS, 480, 538, doi: 10.1093/mnras/sty1729
  * Roederer & Barklem (2018) Roederer, I. U., & Barklem, P. S. 2018, ApJ, 857, 2, doi: 10.3847/1538-4357/aab71f
  * Roederer et al. (2016) Roederer, I. U., Karakas, A. I., Pignatari, M., & Herwig, F. 2016, ApJ, 821, 37, doi: 10.3847/0004-637X/821/1/37
  * Roederer et al. (2018) Roederer, I. U., Sakari, C. M., Placco, V. M., et al. 2018, ApJ, 865, 129, doi: 10.3847/1538-4357/aadd92
  * Roederer et al. (2022) Roederer, I. U., Lawler, J. E., Den Hartog, E. A., et al. 2022, ApJS, 260, 27, doi: 10.3847/1538-4365/ac5cbc