Spectacular Nucleosynthesis from Early Massive Stars

Stars that formed with an initial mass of over 50 M ⊙ 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 follow-up of the SDSS-V Milky Way Mapper, which preserves the signature of unusual nucleosynthesis from a massive star in the early Universe. J0931+0038 has a relatively high metallicity ([Fe/H] = −1.76 ± 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 >50 M ⊙, 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 the 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.


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 lowmass 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 ≳ 10 M ⊙ (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 [Fe/H] ≲ −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 [Fe/H] ≲ −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 M ⊙ (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 [Fe/H] ≲ −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 [Fe/H] ∼ −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 [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 [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 M ⊙ , 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).

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 [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 eff = 5220K, log g = 2.57, [Fe/H] = −1.9, and [α/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 ∼ 30, 000 spectrum (100/pixel or 70/resolution element at 4000 Å).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 • 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.

Abundance Analysis
We performed a standard analysis using 1D AT-LAS 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)1 .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 linemake2 (Placco et al. 2021).Stellar parameters were derived by fixing spectrophotometric temperatures and then determining other stellar parameters spectroscopically, resulting in T eff = 5200 ± 100K, log g = 2.75 ± 0.20, ν t = 1.65 ± 0.3 km s −1 , [M/H] = −1.9± 0.1, and [α/Fe] = 0.0.Chemical abundances were determined using smhr (Casey 2014)3 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 TSFitPy4 (Gerber et al. 2023).The actual [Fe/H] abundance after NLTE corrections is [Fe/H] = −1.76± 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.

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 neutroncapture 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 [Fe/H] ≲ −2.5, but J0931+0038 has a metallicity over 5× higher [Fe/H] = −1.76.

A Single Enrichment Source
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 [Fe/H] ∼ −3.5 (red dashed lines in Figure 3).A recent nucleosynthetic event would have to raise the ISM metallicity by a factor of ≳50 from [Fe/H] ∼ −3.5 to [Fe/H] = −1.76± 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 nu-  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 [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.cleosynthetic 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 ∼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  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.

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 [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: 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 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) ⊙ = 7.50, the maximum metallicity achievable by a given supernova model and ISM density is given by: (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(Magg et al. , 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 M ⊙ , or pair instability supernovae with initial mass M ≳ 200 M ⊙ .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 Fe ∼ 0.1 M ⊙ and energy E ≈ 0.3B.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 M ⊙ (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.5

Nucleosynthetic Origin
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 ex-    (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.
clude progenitors up to the ISM constraint [Fe/H] ≲ −3 (Fig 3).Overall, the best models all invoke M ≳ 50 M ⊙ progenitors, and the best match out of current models is achieved by metal-free 80 M ⊙ 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 next examine deaths of 10 − 100 M ⊙ stars.We split these models into lower energy core-collapse supernovae (CCSNe) powered by the ordinary neutrino-driven mechanism (E ≲ 2B); 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 M ⊙ stars can explode as both CCSNe and HNe, while 40 − 100 M ⊙ stars probably need extra energy from a HNe to explode if they do at all (Heger et al. 2003, bottom row of Fig 4) 6 .The most common SNe with M ≲ 20 M ⊙ 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 M ⊙ , 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 [α/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 M ⊙ HNe can broadly match most major abundance features of J0931+0038.The best match we found is a 80 M ⊙ 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 ≳ 10B that give the best matches to the nucleosynthesis pattern predict maximum metallicities [Fe/H] ≪ −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).Metalfree high mass PISNe with M ≳ 200 M ⊙ produce a very large amount of Fe, a strong odd-even effect, and low [α/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 [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.

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 M ⊙ (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 ∼ 80 M ⊙ , which would be the first example of an early supernova from a star with initial mass between 50 − 100 M ⊙ .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 multidimensional 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 ∼ 80 M ⊙ 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 56 Ni 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-α 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.The SDSS-V BOSS (Gunn et al. 2006;Smee et al. 2013) spectra of J0931+0038 (Gaia DR3 3841101888330639872, ℓ, 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 [α/Fe] abundance based on this fit, where the α is primarily determined by the Mg b lines.The MINESweeper parameters and formal uncertainties for J0931+0038 were T eff = 5220 ± 30K, log g = 2.57 ± 0.06, [Fe/H] = −1.9± 0.1, and [α/Fe] = 0.03 ± 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 | ≲ 800 kpc km 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.

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 ( [α/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. (2017Stassun et al. ( , 2018)).We pulled the JHK S magnitudes from 2MASS, the W1-W3 magnitudes from WISE, the G BP and G RP magnitudes from Gaia, the grizy magnitudes from Pan-STARRS, and the NUV magnitude from GALEX.We also used the Gaia spectrophotometry spanning 0.4-1.0µm.Altogether, the available photometry spans the full stellar SED over the wavelength range 0.2-10 µm.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 eff ) and metallicity ([Fe/H]), as well as the extinction, which we set to the maximum line-of-sight value A V = 0.15 ± 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 ≈ 2.5 given the likely evolutionary state of the star.The resulting fit has a best-fit T eff = 5250 ± 50 K and [Fe/H] = −2.3± 0.3.Integrating the (unreddened) model SED gives the bolometric flux at Earth, F bol = 7.988 ± 0.092 × 10 −11 erg s −1 cm −2 .Taking the F bol and T eff together with the Gaia parallax, gives the stellar radius, R ⋆ = 8.65 ± 0.9R ⊙ .In addition, we estimate the stellar mass to be M ⋆ = 0.8 ± 0.1 M ⊙ , as J0931+0038 is a metal-poor old red giant.The mass and radius together confirm log g ≈ 2.5.

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 5σ upper limit by increasing the abundance until the χ 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 > 10σ) 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 eff , log g, ν 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 eff = 5200 K, log g = 2.60, ν t = 1.6 km s −1 , [Fe/H] = −1.85,and [α/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 eff and log g with their correlated uncertainties, and the stellar parameter error after changing ν t by 0.3 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 3700-9200 Å 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 3961 Å 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 7699 Å and 7665 Å 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 5105 Å 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 [Fe/H] = −1.5 and T eff = 5640K.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 [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 ± 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 ± 0.4 km s −1 (measured with the method in Ji et al. 2020b), while Gaia DR3 RVS reports 104.3 ± 4.0 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).

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

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 ≳20M ⊙ (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 12 C(α,γ) 16 O 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(Farmer et al. , 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 lowmetallicity progenitor (Heger & Woosley 2010;Nomoto et al. 2013;Limongi & Chieffi 2018).The low [Na/Mg] especially prefers higher initial mass progenitors with M > 70 M ⊙ .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 (≲ 15 M ⊙ , 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 sprocess (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.
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) 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  These figures explain the middle rows of Table 2.  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.
progenitor models in E20 did not include odd elements, so we removed it from the N and Na panels for 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 M ⊙ 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 > 10B) can produce high [Zn/Fe] ratios, but Ni is difficult overall except in lower mass CCSNe.

B.2. Search Through Single Star Nucleosynthesis Yields
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.
To investigate the yield grids, we used two search algorithms: Starfit which does χ 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 ≤ 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 M ⊙ primordial SN from Heger & Woosley (2010), but with a reduced χ 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 M ⊙ ) high-energy (23B) hypernova from Grimmett et al. (2018) is able get a near-perfect fit to the light elements while producing enough iron (χ 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 M ⊙ HN still works well (χ 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 M ⊙ 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
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 = 2.5B.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 [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.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 χ 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 ≤ 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 M ⊙ 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 M ⊙ 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 M ⊙ PISN, but it could not contribute to the problems with the Fe peak.Though we allowed the ISM to be metallicities from [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 ν-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 ∼0.25 and entropy of 12k 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. (2016Roederer et al. ( , 2022)), but reduce the initial heavy element abundances with respect to Fe by ten times (e.g., [Sr/Fe] = −1 and [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 ≲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.

Figure 1 .
Figure1.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 • 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 • 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).
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 [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.

Figure 5 .
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 inRoederer 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.

Figure 6 .
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.

Figure 7 .
Figure7.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.

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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.
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].

Figure 11 .
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 χ 2 is shown in the legend.See text for details.

Figure 12 .
Figure12.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.
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.

Li C O Na Mg Al Si K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Sr Y Zr Mo Ru Pd
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 < [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 Table1.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.

Table 1 .
Chemical Abundances 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.

Table 2 .
Death Matrix