# The Dependence of Iron-rich Metal-poor Star Occurrence on Galactic
Environment Supports an Origin in Thermonuclear Supernova Nucleosynthesis

Zachary Reeves William H. Miller III Department of Physics and Astronomy,
Johns Hopkins University, 3400 N Charles St, Baltimore, MD 21218, USA  Kevin
C. Schlaufman William H. Miller III Department of Physics and Astronomy, Johns
Hopkins University, 3400 N Charles St, Baltimore, MD 21218, USA  Henrique
Reggiani Carnegie Fellow  The Observatories of the Carnegie Institution for
Science, 813 Santa Barbara St, Pasadena, CA 91101, USA

(Received 31 January 2023; Revised 27 June 2023; Accepted 10 July 2023)

###### Abstract

It has been suggested that a class of chemically peculiar metal-poor stars
called iron-rich metal-poor (IRMP) stars formed from molecular cores with
metal contents dominated by thermonuclear supernova nucleosynthesis. If this
interpretation is accurate, then IRMP stars should be more common in
environments where thermonuclear supernovae were important contributors to
chemical evolution. Conversely, IRMP stars should be less common in
environments where thermonuclear supernovae were not important contributors to
chemical evolution. At constant $[\text{Fe/H}]\lesssim-1$, the Milky Way’s
satellite classical dwarf spheroidal (dSph) galaxies and the Magellanic Clouds
have lower $[\text{$\alpha$/Fe}]$ than the Milky Way field and globular
cluster populations. This difference is thought to demonstrate the importance
of thermonuclear supernova nucleosynthesis for the chemical evolution of the
Milky Way’s satellite classical dSph galaxies and the Magellanic Clouds. We
use data from the Sloan Digital Sky Survey (SDSS) Apache Point Observatory
Galactic Evolution Experiment (APOGEE) and Gaia to infer the occurrence of
IRMP stars in the Milky Way’s satellite classical dSph galaxies
$\eta_{\text{dSph}}$ and the Magellanic Clouds $\eta_{\text{Mag}}$ as well as
in the Milky Way field $\eta_{\text{MWF}}$ and globular cluster populations
$\eta_{\text{MWGC}}$. In order of decreasing occurrence, we find
$\eta_{\text{dSph}}=0.07_{-0.02}^{+0.02}$,
$\eta_{\text{Mag}}=0.037_{-0.006}^{+0.007}$,
$\eta_{\text{MWF}}=0.0013_{-0.0005}^{+0.0006}$, and a 1-$\sigma$ upper limit
$\eta_{\text{MWGC}}<0.00057$. These occurrences support the inference that
IRMP stars formed in environments dominated by thermonuclear supernova
nucleosynthesis and that the time lag between the formation of the first and
second stellar generations in globular clusters was longer than the
thermonuclear supernova delay time.

Chemical enrichment(225) — Chemically peculiar stars(226) — Dwarf spheroidal
galaxies(420) — Galactic archaeology(2178) — Globular star clusters(656) —
Large Magellanic Cloud(903) — Magellanic Clouds(990) — Milky Way Galaxy(1054)
— Population II stars(1284) — Small Magellanic Cloud(1468) — Stellar
abundances(1577) — Type Ia supernovae(1728)

††facilities: CDS, CTIO:2MASS, Du Pont (APOGEE), FLWO:2MASS, Gaia, Sloan
(APOGEE)††software: astropy (Astropy Collaboration et al., 2013, 2018),
matplotlib (Hunter, 2007) numpy (Harris et al., 2020), pandas (McKinney, 2010;
pandas Development Team, 2020), R (R Core Team, 2023), scipy (Virtanen et al.,
2020)

Astronomical Journal

##  1 Introduction

Thermonuclear supernovae111In this article we use the phrase “thermonuclear
supernovae” to refer to the theoretical concept of electron-degenerate
carbon–oxygen white dwarfs experiencing runway carbon fusion that releases
enough energy to gravitationally unbind the white dwarfs and thereby cause
explosions. are prolific producers of iron-peak elements with a theoretically
predicted average stable yield of more than $0.6~{}M_{\odot}$ of iron-peak
elements but much less $\alpha$ and light odd-$Z$ elements. This is in sharp
contrast to core-collapse supernovae that produce $\alpha$ and light odd-$Z$
elements in roughly the solar ratios but with relatively little iron-peak
production (e.g., Sukhbold et al., 2016).

Based on a compilation of theoretical stable nucleosynthetic yields predicted
by a variety of thermonuclear supernova progenitor channels (i.e., single
degenerate and double degenerate) and explosion mechanisms (e.g., pure
detonations, pure deflagrations, delayed detonations, double detonations,
etc.), Reggiani et al. (2023) proposed the existence of a new class of
chemically peculiar metal-poor stars with $[\text{Fe/H}]\lesssim-1$ and
$[\text{O,F,Ne,Na,Mg,Al,Cl,K,Co,Cu,Zn/Fe}]<0$ formed from molecular cores with
metal contents dominated by thermonuclear supernova nucleosynthesis.222The
yields in that compilation came from Seitenzahl et al. (2013, 2016), Fink et
al. (2014), Ohlmann et al. (2014), Papish & Perets (2016), Leung & Nomoto
(2018, 2020a, 2020b), Nomoto & Leung (2018), Bravo et al. (2019), Boos et al.
(2021), Gronow et al. (2021a, b), and Neopane et al. (2022). They called stars
with these properties iron-rich metal-poor (IRMP) stars, as this part of
elemental abundance space is consistent with thermonuclear supernova
nucleosynthesis but rarely observed in metal-poor stars. They argued that if
their interpretation is correct, then IRMP stars should be more common in
environments where thermonuclear supernovae were relatively more important
contributors to chemical evolution relative to core-collapse supernovae (e.g.,
environments with long star formation durations). On the other hand, they
argued that in environments where thermonuclear supernovae were not important
contributors to chemical evolution relative to core-collapse supernovae (e.g.,
environments with short star formation durations) IRMP stars should be less
common.

One way to test this prediction would be to compare the relative occurrence of
IRMP stars in the Milky Way’s field population, its globular clusters, its
satellite classical dwarf spheroidal (dSph) galaxies, and the Magellanic
Clouds. At constant spectroscopically inferred metallicities
$[\text{Fe/H}]\lesssim-1$333In this article metallicity $[\text{Fe/H}]$ has
its usual meaning
$[\text{Fe/H}]=\log_{10}\left(N_{\text{Fe}}/N_{\text{H}}\right)_{\ast}-\log_{10}\left(N_{\text{Fe}}/N_{\text{H}}\right)_{\odot}$
where $N_{\text{X}}$ are the logarithmic number densities of atoms of an
element X in a stellar photosphere and $N_{\text{H}}\equiv 12$., both the
Milky Way’s classical dSph satellites (Shetrone et al., 2001, 2003; Tolstoy et
al., 2003; Kirby et al., 2009, 2010, 2011a, 2011b) and the Magellanic Clouds
(Pompéia et al., 2008; Van der Swaelmen et al., 2013; Nidever et al., 2020)
have lower spectroscopically inferred ratios of the $\alpha$ elements oxygen,
magnesium, silicon, and calcium to iron $[\text{$\alpha$/Fe}]$444In this
article the $\alpha$ element-to-iron ratio $[\text{$\alpha$/Fe}]$ has its
usual meaning
$[\text{$\alpha$/Fe}]=\log_{10}\left(N_{\alpha}/N_{\text{Fe}}\right)_{\ast}-\log_{10}\left(N_{\alpha}/N_{\text{Fe}}\right)_{\odot}$
where $\alpha$ is the sum of some subset of the elements oxygen, magnesium,
silicon, and calcium. than the Milky Way (e.g., Wallerstein, 1962; Luck &
Bond, 1981, 1985; Peterson, 1981; Gratton, 1983; Magain, 1985, 1989; Gratton &
Ortolani, 1986; Gratton & Sneden, 1988; Ryan et al., 1991; McWilliam et al.,
1995a, b) and its globular clusters (e.g., Cohen, 1978, 1979, 1980, 1981;
Pilachowski et al., 1983). These offsets in $[\text{$\alpha$/Fe}]$ between the
Milky Way field & globular cluster populations and its satellite classical
dSph galaxies & the Magellanic Clouds are usually understood to indicate the
longer durations of low-metallicity star formation and therefore the
relatively more important contributions of thermonuclear supernovae to the
chemical evolution of the latter two environments at low metallicities (e.g.,
Lanfranchi & Matteucci, 2003, 2004, 2007; Lanfranchi et al., 2006, 2008;
Marcolini et al., 2006; Kirby et al., 2011a; Bekki & Tsujimoto, 2012; Nidever
et al., 2020; Reggiani et al., 2021). If the Reggiani et al. (2023)
interpretation of IRMP stars is valid, then IRMP stars should be less common
in the Milky Way field & globular cluster populations than in its satellite
classical dSph galaxies & the Magellanic Clouds.

The nitrogen, sodium, and aluminum abundances of individual stars in globular
clusters have been found to be anticorrelated with the carbon, oxygen, and
magnesium abundances in the same stars. These abundance anticorrelations have
been interpreted as evidence for multiple generations of star formation in
globular clusters (e.g., Sneden et al., 1992; Gratton et al., 2001, 2004;
Carretta et al., 2009; Bastian & Lardo, 2018). The Reggiani et al. (2023)
interpretation of IRMP stars also suggests the possibility that the occurrence
of IRMP stars in globular clusters can be used to constrain the time lag
between the formation of a globular cluster’s first and second stellar
generations. For Type Ia supernovae555In this article we use the phrase “Type
Ia supernovae” to refer to the electromagnetic transients empirically
classified as Type Ia supernovae based on their observed properties. delay
times $\tau_{\text{Ia}}\lesssim 100$ Myr, the Type Ia supernova rate
$\Phi_{\text{Ia}}$ has the value $\Phi_{\text{Ia}}\sim 10^{-12}$ yr-1
$M_{\odot}^{-1}$ (e.g., Totani et al., 2008; Maoz et al., 2011, 2012, 2014;
Graur et al., 2014). Assuming that rate and a typical first generation initial
globular cluster mass $M_{\text{MWGC}}\sim 10^{6}~{}M_{\odot}$ (e.g., Conroy,
2012), order 10 Type Ia supernovae should occur in a newly formed globular
cluster every 10 Myr after the Type Ia delay time has elapsed. While the
occurrence of the short-period binaries necessary to produce most of the
theoretically predicted thermonuclear supernova progenitor systems is a factor
of about three lower in globular clusters’ first generations than in the field
(Carney et al., 2003; Lucatello et al., 2015), after the Type Ia supernovae
delay time has elapsed a few thermonuclear explosions should occur every 10
Myr during the formation of a globular cluster. The Reggiani et al. (2023)
interpretation of IRMP stars therefore implies that if the time lag between
the formation of first and second generation stars in globular clusters was
shorter than the typical thermonuclear supernova delay time, then the
occurrence of IRMP stars in globular clusters should be significantly lower
than in the Milky Way field. If the the time lag between the formation of
first and second generation stars in globular clusters is longer than the
typical thermonuclear supernova delay time, then the occurrence of IRMP stars
in globular clusters and the Milky Way field should be comparable.

We argue that if the Reggiani et al. (2023) interpretation of the origin of
IRMP stars is accurate, then the occurrence of IRMP stars in the Milky Way
field population $\eta_{\text{MWF}}$, the Magellanic Clouds
$\eta_{\text{Mag}}$, and the Milky Way’s satellite classical dSph galaxies
$\eta_{\text{dSph}}$ should be ordered
$\eta_{\text{MWF}}<\eta_{\text{Mag}}\sim\eta_{\text{dSph}}$. If the time lag
between the formation of the first and second generations in globular clusters
was shorter than the thermonuclear supernova delay time, then the occurrence
of IRMP stars in the Milky Way globular cluster population
$\eta_{\text{MWGC}}$ should be
$\eta_{\text{MWGC}}\lesssim\eta_{\text{MWF}}<\eta_{\text{Mag}}\sim\eta_{\text{dSph}}$.
If the time lag between the formation of the first and second generations in
globular clusters was longer than the thermonuclear supernova delay time, then
$\eta_{\text{MWGC}}\sim\eta_{\text{MWF}}<\eta_{\text{Mag}}\sim\eta_{\text{dSph}}$.
In this article, we calculate the occurrence of IRMP stars in the Milky Way’s
satellite classical dSph galaxies, the Magellanic Clouds, the Milky Way field
population, and in Milky Way globular clusters. We describe in Section 2 the
assembly of our analysis samples and quantify in Section 3 the occurrence of
IRMP stars in each environment. We review the implications of those
occurrences in Section 4 and conclude by summarizing our findings in Section
5.

##  2 Data

To calculate the occurrence of IRMP stars in the Milky Way’s satellite
classical dSph galaxies, the Magellanic Clouds, the Milky Way field
population, and in Milky Way globular clusters we use data derived from
spectra that were gathered during the third and fourth phases of the Sloan
Digital Sky Survey (SDSS; Eisenstein et al., 2011; Blanton et al., 2017) as
part of its Apache Point Observatory Galactic Evolution Experiment (APOGEE;
Majewski et al., 2017). These spectra were collected with the APOGEE
spectrographs (Zasowski et al., 2013, 2017; Wilson et al., 2019; Beaton et
al., 2021; Santana et al., 2021) on the New Mexico State University 1-m
Telescope (Holtzman et al., 2010), the Sloan Foundation 2.5-m Telescope (Gunn
et al., 2006), and the 2.5-m Irénée du Pont Telescope (Bowen & Vaughan, 1973).
As part of SDSS Data Release (DR) 17 (Abdurro’uf et al., 2022), these spectra
were reduced and analyzed with the APOGEE Stellar Parameter and Chemical
Abundance Pipeline (ASPCAP; Allende Prieto et al., 2006; Holtzman et al.,
2015; Nidever et al., 2015; García Pérez et al., 2016) using an $H$-band line
list, MARCS model atmospheres, and model-fitting tools optimized for the
APOGEE effort (Alvarez & Plez, 1998; Gustafsson et al., 2008; Hubeny & Lanz,
2011; Plez, 2012; Smith et al., 2013, 2021; Cunha et al., 2015; Shetrone et
al., 2015; Jönsson et al., 2020).

We use the CasJobs portal666http://skyserver.sdss.org/casjobs/ and the query
described in the Appendix to generate our initial sample of photospheric
stellar parameters and elemental abundances for giant stars with
$\log{g}<3.8$. As described in the Appendix, we use a carefully curated set of
data quality flags to ensure the accuracy and precision of those photospheric
stellar parameters and elemental abundances. We set to null any elemental
abundance/elemental abundance uncertainty pair that does not pass the data
quality checks described in the Appendix. Corrections for departures from
local thermodynamic equilibrium are usually small for $H$-band elemental
abundance inferences (e.g., Osorio et al., 2020), and we choose not to apply
them in our analysis.

Following Reggiani et al. (2023), we define an iron-rich metal-poor star as a
star with $[\text{Fe/H}]<-1$ and $[\text{O,Na,Mg,Al,K,Co/Fe}]<0$. Those
elemental abundance ratios form the intersection of the IRMP criteria defined
in Reggiani et al. (2023) and the list of elemental abundances reliably
inferred for giant stars as part of APOGEE
DR17777https://www.sdss.org/dr17/irspec/abundances/. For the purposes of the
occurrence calculation described in the next section, an IRMP star with
$[\text{Fe/H}]<-1$ must have at least one non-null abundance ratio
$[\text{O/Fe}]$, $[\text{Na/Fe}]$, $[\text{Mg/Fe}]$, $[\text{Al/Fe}]$,
$[\text{K/Fe}]$, or $[\text{Co/Fe}]$ and all abundance ratios
$[\text{O,Na,Mg,Al,K,Co/Fe}]$ either sub-solar or null.

To accurately label stars with their correct galactic environments, we first
join the APOGEE data described above with data from Gaia DR2 (Gaia
Collaboration et al., 2016, 2018; Arenou et al., 2018; Evans et al., 2018;
Lindegren et al., 2018; Luri et al., 2018; Riello et al., 2018) and DR3 (Gaia
Collaboration et al., 2016, 2021; Fabricius et al., 2021; Lindegren et al.,
2021a, b; Riello et al., 2021; Rowell et al., 2021; Torra et al., 2021). We
use the apogee_id string to identify the corresponding Gaia DR2 and DR3
source_id long integers by joining with the gaiadr2.tmass_best_neighbour and
gaiadr3.tmass_psc_xsc_best_neighbour tables available in the Gaia archive
(Salgado et al., 2017; Marrese et al., 2019). Occasionally multiple Gaia DR2
and DR3 source_id long integers are matched to the same object in the 2MASS
Point Source Catalog (Skrutskie et al., 2006). In those cases, we associate a
2MASS object with the closest Gaia DR2 and DR3 object that has (1) an absolute
2MASS $K_{\text{s}}$-band magnitude $M_{K}<2.31$ assuming Gaia DR2- or
DR3-prior informed geometric distances (Bailer-Jones et al., 2018, 2021) and
(2) Gaia–2MASS colors $0.5<G-J<2.3$, $0.6<G-H<3.3$, and
$0.6<G-K_{\text{s}}<3.4$ predicted by the MESA Isochrones & Stellar Tracks
(MIST) grid for metal-poor giants in the range $-2.5<[\text{Fe/H}]<-1.0$
(Paxton et al., 2011, 2013, 2015, 2018; Dotter, 2016; Choi et al., 2016).

We then use the Gaia DR2 source_id to identify Milky Way satellite classical
dSph galaxies or Magellanic Clouds members using the Gaia DR2-based membership
lists published in Gaia Collaboration et al. (2018). We identify globular
cluster members using the Gaia DR3 source_id and the Vasiliev & Baumgardt
(2021) lists of stars with globular cluster membership probability greater
than 0.5, and this procedure results in a sample with at least one star from
41 globular clusters over the metallicity range
$-2.3\lesssim[\text{Fe/H}]\lesssim-1.0$.

Most stars observed as part SDSS-III/APOGEE and SDSS-IV/APOGEE-2 were selected
for observation by a procedure that sought to minimize age and metallicity
biases (e.g., Zasowski et al., 2013, 2017), and we use the targeting flag
extratarg = 0 in the table apogeeStar to select those stars for our Milky Way
field sample. To ensure the cleanest Milky Way field sample possible, we then
remove from this sample any stars that are identified as dSph, Magellanic
Cloud, or globular cluster members in Gaia Collaboration et al. (2018) or
Vasiliev & Baumgardt (2021). Because the vast majority of stars with
$[\text{Fe/H}]\lesssim-1$ observed as part of SDSS-III/APOGEE and SDSS-
IV/APOGEE-2 are on halo-like orbits (e.g., Hayes et al., 2018), our Milky Way
field sample can be thought of as a Milky Way halo sample. We list in Table 1
our entire analysis sample including IRMP status and galactic environment. We
report in Table 2 the number of stars classified as IRMP stars in each
environment $N_{\ast,\text{IRMP}}$ along with the number of stars in our
analysis sample in each environment $N_{\ast,\text{tot}}$.

Table 1: Analysis Sample

APOGEE ID | Gaia DR3 source_id | Gaia DR2 source_id | IRMP | Environment
---|---|---|---|---
2M17165079$-$2422565 | 4111066558908989184 | 4111066558908989184 | False | Milky Way
2M17150296$-$2423503 | 4114045307692005632 | 4114045307692005632 | False | Milky Way
2M19154424$-$0604209 | 4211181280154376320 | 4211181280154376320 | False | Milky Way
2M19033822$+$1745138 | 4514220364269464832 | 4514220364269464832 | False | Milky Way
2M16574858$-$2156135 | 4126283868512500864 | 4126283868512500864 | False | Milky Way
2M18501947$+$2948368 | 2041393317228382848 | 2041393317228382848 | False | Milky Way
2M18132084$+$0112054 | 4275831399934633984 | 4275831399934633984 | False | Milky Way
2M17571005$-$3020262 | 4056215664653907456 | 4056215664653907456 | False | Milky Way
2M17415271$-$2715374 | 4060889448072712832 | 4060889448072712832 | False | Milky Way
2M19084424$-$0618527 | 4205916204326948736 | 4205916204326948736 | False | Milky Way

Note. — This table is published in its entirety in the machine-readable
format. A portion is shown here for guidance regarding its form and content.

Table 2: Occurrence of IRMP Stars as a Function of Environment Galactic Environment | $N_{\ast,\text{IRMP}}$ | $N_{\ast,\text{tot}}$ | Occurrence
---|---|---|---
Milky Way | 5 | 4247 | $0.0013_{-0.0005}^{+0.0006}$
Globular Cluster Sum | 0 | 1998 | $<0.00057$
LMC | 4 | 203 | $0.023_{-0.009}^{+0.012}$
SMC | 24 | 572 | $0.043_{-0.008}^{+0.009}$
Magellanic Clouds Sum | 28 | 775 | $0.037_{-0.006}^{+0.007}$
Sagittarius | 0 | 27 | $<0.04$
Ursa Minor | 0 | 8 | $<0.12$
Sextans | 1 | 6 | $0.2_{-0.1}^{+0.2}$
Sculptor | 8 | 70 | $0.12_{-0.03}^{+0.04}$
Draco | 0 | 9 | $<0.11$
Carina | 1 | 31 | $0.05_{-0.03}^{+0.05}$
dSph Galaxies Sum | 10 | 151 | $0.07_{-0.02}^{+0.02}$

The typical elemental abundance inference uncertainties in our analysis sample
are (0.04, 0.23, 0.03, 0.04, 0.08, 0.16) dex for ($[\text{O/Fe}]$,
$[\text{Na/Fe}]$, $[\text{Mg/Fe}]$, $[\text{Al/Fe}]$, $[\text{K/Fe}]$,
$[\text{Co/Fe}]$). In any case, elemental abundance inference uncertainties
are irrelevant for the occurrence analyses presented in Section 3 if (1) the
uncertainty distributions for each elemental abundance inference for each
individual star are symmetric and (2) the uncertainty distributions have
statistically indistinguishable widths across all of the galactic environments
we explored. The individual elemental abundance inference uncertainties
presented in the SDSS DR17 version of the table aspcapStar are reported as
symmetric. Additionally, we confirmed that the individual elemental abundance
uncertainty distributions for oxygen, sodium, magnesium, aluminum, potassium,
and cobalt have statistically indistinguishable widths across all of the
galactic environments we explored. Both of the conditions listed above are
therefore met in our analysis sample. Likewise, we argue that our procedure to
handle data quality issues will not bias the occurrence analyses we present in
Section 3. The reason is that null values impact less than about 0.2% of the
magnesium abundance inferences in our sample. Because we require all non-null
elemental inferences to meet our IRMP criteria, we are able to exclude
essentially all non-IRMP stars from our IRMP sample using magnesium alone
almost regardless of data quality issues.

The recent discovery of a very metal-poor star with elemental abundances best
explained by the nucleosynthesis expected in a pair-instability supernova has
focused attention on that explanation for stars with significantly subsolar
$[\text{Na/Fe}]$ and $[\text{$\alpha$/Fe}]$ abundance ratios (Xing et al.,
2023). While the stars in our analysis sample have subsolar $[\text{Na/Fe}]$
and the $\alpha$-element abundance ratios $[\text{O/Fe}]$ and
$[\text{Mg/Fe}]$, none of the stars in our sample have the strong odd–even
abundance ratios predicted to be produced by pair-instability supernovae
(e.g., Heger & Woosley, 2002). We are therefore confident that the IRMP stars
we identify are related to thermonuclear supernovae.

##  3 Analysis

We model the number of IRMP stars $N_{\ast,\text{IRMP}}$ in a sample of
$N_{\ast,\text{tot}}$ candidates using a binomial distribution. Following
Schlaufman (2014) we exploit the fact that a Beta$(\alpha$,$\beta$)
distribution is a conjugate prior to the binomial distribution and will result
in a Beta distribution posterior for the occurrence of IRMP stars in a sample.
Bayes’s Theorem guarantees

$\displaystyle f(\theta|\mathbf{y})$ $\displaystyle=$
$\displaystyle\frac{f(\mathbf{y}|\theta)f(\theta)}{\int
f(\mathbf{y}|\theta)f(\theta)d\theta},$ (1)

where $f(\theta|\mathbf{y})$ is the posterior distribution of the model
parameter $\theta$, $f(\mathbf{y}|\theta)$ is the likelihood of the data
$\mathbf{y}$ given $\theta$, and $f(\theta)$ is the prior for $\theta$. In
this case, the likelihood is the binomial likelihood that describes the
probability of a number of successes $y$ in $n$ Bernoulli trials each with
probability $\theta$ of success

$\displaystyle f(y|\theta)=\left(\begin{array}[]{cc}n\\\
y\end{array}\right)\theta^{y}\left(1-\theta\right)^{n-y}.$ (4)

As shown by Schlaufman (2014), in this situation using a
Beta($\alpha$,$\beta$) prior on $\theta$ with hyperparameters $\alpha$ and
$\beta$ results in a Beta posterior for $\theta$ of the form
Beta($\alpha+N_{\ast,\text{IRMP}},\beta+N_{\ast,\text{tot}}-N_{\ast,\text{IRMP}}$).

The hyperparameters $\alpha$ and $\beta$ of the prior can be thought of as
encoding a certain amount of prior information in the form of pseudo-
observations. Specifically, $\alpha-1$ is the number of success and $\beta-1$
is the number of failures imagined to have already been observed and therefore
included as prior information on $\theta$. Taking any $\alpha=\beta=i$ where
$i\geq 1$ could be thought of as an uninformative prior in the sense that the
probability of success and failure in the prior distribution are equally
likely. However, if $i$ is large then there is imagined to be a lot of prior
information and the posterior distribution will mostly reflect the prior when
$n\leq i$. On the other hand, if $n\gg i$, then the posterior will be
dominated by the data. For that reason, we take $\alpha=\beta=1$.

We provide the posterior median occurrence of IRMP stars in each galactic
environment in Table 2. We define the lower uncertainty as the difference
between the posterior median and its 16th percentile. Likewise, we define the
upper uncertainty as the difference between the posterior’s 84th percentile
and its median. For an environment with no IRMP stars, we report 1-$\sigma$
upper limits as the 68th percentile of the posterior distribution. We find
that $\eta_{\text{dSph}}=0.07_{-0.02}^{+0.02}$,
$\eta_{\text{Mag}}=0.037_{-0.006}^{+0.007}$,
$\eta_{\text{MWF}}=0.0013_{-0.0005}^{+0.0006}$, and a 1-$\sigma$ upper limit
$\eta_{\text{MWGC}}<0.00057$. In words, IRMP stars are much more common in the
Milky Way’s classical dSph satellites and the Magellanic Clouds than in the
Milky Way field or globular cluster populations. IRMP stars are less common in
globular clusters than in any other galactic environment. We find that the
overlap probability between the IRMP occurrences we observed in the Milky
Way’s classical dSph satellites and the Magellanic Clouds is about one in 91,
equivalent to about 2.3 $\sigma$. We find that the overlap probabilities
between the IRMP occurrences we observe in the Milky Way’s classical dSph
satellites & the Magellanic Clouds and the occurrence of IRMP stars we observe
in the Milky Way field population are about one in $2.8\times 10^{15}$ and one
in $6.2\times 10^{19}$, equivalent to about 8.1 and 9.2 $\sigma$. The overlap
probability between the IRMP occurrences we observe in the Milky Way field and
globular cluster populations is about one in 23, equivalent to about 1.7
$\sigma$. We summarize these occurrence posterior overlap probabilities in
Table 3.

Table 3: Occurrence Posterior Overlap Probabilities Population | Population | $P(\text{Posterior Overlap})$
---|---|---
dSph galaxies | Magellanic Clouds | 1.095 ×10^-2
dSph galaxies | Milky Way field | 3.596 ×10^-16
Magellanic Clouds | Milky Way field | 1.620 ×10^-20
Milky Way field | Milky Way globular clusters | 4.300 ×10^-2

The results presented in Table 2 are averaged over metallicity. To investigate
IRMP occurrence as a function of metallicity, for each class of galactic
environment we divide into ten equal intervals the metallicity range spanned
by our analysis sample for that environment. We then apply the same occurrence
formalism in each individual metallicity interval and plot occurrence as a
function of metallicity for each environment in Figure 1. We find no
significant dependence of the occurrence of IRMP stars on metallicity in our
analysis sample.

Figure 1: Occurrence of iron-rich metal-poor stars as a function of
metallicity in different environments. For the Milky Way field, dSph, and
Magellanic Cloud samples we plot the posterior medians of occurrence as solid
lines and the ranges defined by the 16th and 84th percentiles of the
occurrence posteriors as transparent polygons. For the globular cluster sample
for which we infer an upper limit on IRMP occurrence, we plot the 68th
percentile of the posterior as a solid line and the range defined by the 0th
and 68th percentiles of the occurrence posterior as a transparent polygon.
There is no obvious dependence of IRMP occurrence on metallicity in the Milky
Way’s field population, its globular clusters, its classical dSph galaxies, or
the Magellanic Clouds.

##  4 Discussion

We find that the occurrences of IRMP stars in the Milky Way’s satellite
classical dSph galaxies, the Magellanic Clouds, the Milky Way field
population, and the Milky Way’s globular cluster populations have the values
$\eta_{\text{dSph}}=0.07_{-0.02}^{+0.02}$,
$\eta_{\text{Mag}}=0.037_{-0.006}^{+0.007}$,
$\eta_{\text{MWF}}=0.0013_{-0.0005}^{+0.0006}$, and
$\eta_{\text{MWGC}}<0.00057$. The probability that the IRMP occurrences in the
Milky Way’s satellite classical dSph galaxies and the Magellanic Clouds
overlap is about one in 91, equivalent to about 2.3 $\sigma$. The
probabilities that the IRMP occurrence posterior for the Milky Way field
overlaps with the IRMP occurrence posteriors for Milky Way’s satellite
classical dSph galaxies and the Magellanic Clouds are about one in $2.8\times
10^{15}$ and one in $6.2\times 10^{19}$, equivalent to about 8.1 and 9.2
$\sigma$. The probability that the IRMP occurrences in the Milky Way field and
globular cluster populations overlap is about one in 23, equivalent to about
1.7 $\sigma$. While the absolute values of IRMP star occurrences may be
difficult to interpret, as we argued in the introduction their ordering
$\eta_{\text{MWGC}}\sim\eta_{\text{MWF}}<\eta_{\text{Mag}}\sim\eta_{\text{dSph}}$
has two important implications.

The increased occurrence of IRMP stars in environments like the Milky Way’s
satellite classical dSph galaxies and the Magellanic Clouds where
thermonuclear supernovae were important contributors to chemical evolution
supports the Reggiani et al. (2023) scenario for IRMP star formation in
molecular cores with metal contents dominated by the thermonuclear supernova
nucleosynthesis. The confirmation of this Reggiani et al. (2023) prediction
reinforces the idea that the elemental abundances of individual IRMP stars can
be used to investigate the progenitor systems and explosion mechanisms
responsible for the thermonuclear supernovae that produced much of their metal
contents.

The statistically indistinguishable occurrences of IRMP stars in the Milky
Way’s field and globular cluster populations suggests that the time lags
between the formation of globular clusters’ first and second stellar
generations were longer than the thermonuclear supernova delay time. This is
broadly consistent with the idea from the asymptotic giant branch (AGB)
scenario for globular cluster multiple populations that the explosions of
thermonuclear supernovae associated with a globular cluster’s first stellar
generation quench the star formation event that produced its second stellar
generation (e.g., D’Ercole et al., 2008; Calura et al., 2019; Lacchin et al.,
2021). Given the suspected importance of thermonuclear supernovae for
quenching second generation star formation in globular clusters, it remains to
be explained why globular cluster second generation stars that bear the
imprint of thermonuclear supernova nucleosynthesis are so rare as to not
appear in a sample of nearly 2000 globular cluster members. Our result is also
consistent with scenarios for globular cluster multiple populations invoking a
thermonuclear supernova at the start of a cluster’s evolution (e.g., Marcolini
et al., 2009; Sánchez-Blázquez et al., 2012).

Contributions from both core-collapse and thermonuclear supernovae as well as
$s$\- and $r$-process nucleosynthesis are required to explain the solar
abundance pattern. While the progenitors of core-collapse supernovae are known
to be massive stars and the $s$-process takes place in AGB stars, the
progenitors of thermonuclear supernovae and the astrophysical site of the
$r$-process are more uncertain. Observational constraints on either the
progenitors of thermonuclear supernovae or the astrophysical site of the
$r$-process are therefore valuable. The kilonova GW170817 confirmed that
neutron stars mergers are at least partially responsible for $r$-process
nucleosynthesis (e.g., Abbott et al., 2017; Arcavi et al., 2017). The relative
occurrences of IRMP and $r$-process enhanced stars in the same populations can
be used to compare the relative probabilities of the circumstances that lead
to the formation of IRMP and $r$-process enhanced stars.

We find that the occurrences of IRMP stars are an order of magnitude lower
than the occurrence of $r$-process enhanced stars in both the Milky Way field
and Magellanic Clouds. In the Milky Way field, we find that
$\eta_{\text{IRMP,MWF}}=0.0013_{-0.0005}^{+0.0006}$ while Barklem et al.
(2005) found $\eta_{\text{rII,MWF}}\approx 0.03$ according to the definition
of highly $r$-process enhanced (i.e., r-II stars) from Beers & Christlieb
(2005).888More recent estimates by the $r$-process Alliance have found similar
occurrences (e.g., Hansen et al., 2018; Sakari et al., 2018; Ezzeddine et al.,
2020). In the Magellanic Clouds, we find that
$\eta_{\text{IRMP,Mag}}=0.037_{-0.006}^{+0.007}$ while Reggiani et al. (2021)
found $\eta_{\text{rII,Mag}}=0.38^{+0.14}_{-0.13}$. We conclude that the
circumstances that lead to the formation of IRMP stars occur an order of
magnitude less frequently than the circumstances that lead to the formation of
$r$-process enhanced stars.

##  5 Conclusion

We conclude that iron-rich metal-poor stars with $[\text{Fe/H}]\lesssim-1$ and
$[\text{O,Na,Mg,Al,K,Co/Fe}]<0$ are more common in the Milky Way’s satellite
classical dSph galaxies and the Magellanic Clouds than in the Milky Way field
or globular cluster populations. Because thermonuclear supernovae are thought
to have been more important contributors to the chemical evolution of the
Milky Way’s satellite classical dSph galaxies and the Magellanic Clouds than
to the Milky Way field and globular cluster populations in the range
$[\text{Fe/H}]\lesssim-1$, our inferences confirm the interpretation of iron-
rich metal-poor stars put forward in Reggiani et al. (2023) proposing that
iron-rich metal-poor stars formed from molecular cores with metal contents
dominated by thermonuclear supernova nucleosynthesis. Iron-rich metal-poor
stars can therefore be used to constrain the progenitor systems and explosion
mechanisms of the thermonuclear supernovae responsible for their elemental
abundances. We further find that the occurrences of iron-rich metal-poor stars
in the Milky Way’s field and globular cluster populations are statistically
indistinguishable. This observation implies that the time lag between the
formation of a globular cluster’s first and second stellar generations was
longer than the thermonuclear supernova delay time. It is also consistent with
explanations for globular cluster multiple populations that require early
enrichment by thermonuclear supernovae.

## Acknowledgments

We thank Yossef Zenati for sharing his expertise on Type Ia supernovae.
Support for this work was provided by Johns Hopkins University through a
Summer Provost’s Undergraduate Research Award to Zachary Reeves and by the
Carnegie Institution for Science through a Carnegie Postdoctoral Fellowship
award to Henrique Reggiani. Funding for SDSS-III has been provided by the
Alfred P. Sloan Foundation, the Participating Institutions, the National
Science Foundation, and the U.S. Department of Energy Office of Science. The
SDSS-III web site is http://www.sdss3.org/. SDSS-III is managed by the
Astrophysical Research Consortium for the Participating Institutions of the
SDSS-III Collaboration including the University of Arizona, the Brazilian
Participation Group, Brookhaven National Laboratory, Carnegie Mellon
University, University of Florida, the French Participation Group, the German
Participation Group, Harvard University, the Instituto de Astrofisica de
Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns
Hopkins University, Lawrence Berkeley National Laboratory, Max Planck
Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics,
New Mexico State University, New York University, Ohio State University,
Pennsylvania State University, University of Portsmouth, Princeton University,
the Spanish Participation Group, University of Tokyo, University of Utah,
Vanderbilt University, University of Virginia, University of Washington, and
Yale University. Funding for the Sloan Digital Sky Survey IV has been provided
by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of
Science, and the Participating Institutions. SDSS-IV acknowledges support and
resources from the Center for High Performance Computing at the University of
Utah. The SDSS website is www.sdss.org. SDSS-IV is managed by the
Astrophysical Research Consortium for the Participating Institutions of the
SDSS Collaboration including the Brazilian Participation Group, the Carnegie
Institution for Science, Carnegie Mellon University, Center for Astrophysics —
Harvard & Smithsonian, the Chilean Participation Group, the French
Participation Group, Instituto de Astrofísica de Canarias, The Johns Hopkins
University, Kavli Institute for the Physics and Mathematics of the Universe
(IPMU) / University of Tokyo, the Korean Participation Group, Lawrence
Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP),
Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für
Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik
(MPE), National Astronomical Observatories of China, New Mexico State
University, New York University, University of Notre Dame, Observatário
Nacional / MCTI, The Ohio State University, Pennsylvania State University,
Shanghai Astronomical Observatory, United Kingdom Participation Group,
Universidad Nacional Autónoma de México, University of Arizona, University of
Colorado Boulder, University of Oxford, University of Portsmouth, University
of Utah, University of Virginia, University of Washington, University of
Wisconsin, Vanderbilt University, and Yale 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 publication makes use
of data products from the Two Micron All Sky Survey, which is a joint project
of the University of Massachusetts and the Infrared Processing and Analysis
Center/California Institute of Technology, funded by the National Aeronautics
and Space Administration and the National Science Foundation. This research
has made use of the SIMBAD database, operated at CDS, Strasbourg, France
(Wenger et al., 2000). This research has made use of the VizieR catalog access
tool, CDS, Strasbourg, France. The original description of the VizieR service
was published in Ochsenbein et al. (2000). This research has made use of
NASA’s Astrophysics Data System Bibliographic Services.

SDSS DR17 APOGEE data quality and targeting information are stored as
bitmasks.999https://www.sdss.org/dr17/irspec/apogee-bitmasks Since unreliable
photospheric stellar parameters will lead to unreliable elemental abundances,
we exclude from our analysis stars with the bits TEFF_WARN, LOGG_WARN,
VMICRO_WARN, M_H_WARN, STAR_WARN, CHI2_WARN, COLORTE_WARN, ROTATION_WARN,
SN_WARN, TEFF_BAD, LOGG_BAD, VMICRO_BAD, M_H_BAD, STAR_BAD, CHI2_BAD,
COLORTE_BAD, ROTATION_BAD, or SN_BAD set in the column aspcapflag in the table
aspcapStar. These flags correspond to binary digits 0, 1, 2, 3, 7, 8, 9, 10,
11, 16, 17, 18, 19, 23, 24, 25, 26, and 27. Note that though the bit
corresponding to STAR_WARN should be set if any of the bits TEFF_WARN,
LOGG_WARN, CHI2_WARN, COLORTE_WARN, ROTATION_WARN, or SN_WARN are set we
choose to include all of these bits in our data quality checks. Likewise,
though the bit corresponding to STAR_BAD should be set if any of the bits
TEFF_BAD, LOGG_BAD, CHI2_BAD, COLORTE_BAD, ROTATION_BAD, or SN_BAD are set we
choose to include all of these bits in our data quality checks. We remove
duplicate observations from our analysis sample by rejecting objects with
binary digit 4 set in the column extratarg in the table apogeeStar.

We exclude from our analysis any elemental abundances that are indicated as
suspect. We set to null all elemental abundances with the final value $-9999$
or with any of the bits GRIDEDGE_BAD, CALRANGE_BAD, OTHER_BAD, FERRE_FAIL,
PARAM_MISMATCH_BAD, TEFF_CUT, GRIDEDGE_WARN, CALRANGE_WARN, OTHER_WARN,
PARAM_MISMATCH_WARN, ERR_WARN, or PARAM_FIXED set in a column *_fe_flag in the
table aspcapStar. These flags correspond to binary digits 0, 1, 2, 3, 4, 6, 8,
9, 10, 12, 14, and 16. We ultimately use the following query in the CasJobs
portal to generate our analysis sample.

    SELECT a.apogee_id, b.ra, b.dec, b.glon, b.glat, b.snr, b.extratarg,
    CASE WHEN (((a.teff_flag & 87903) = 0) AND (a.teff > -9999))
       THEN a.teff ELSE null END AS teff,
    CASE WHEN (((a.teff_flag & 87903) = 0) AND (a.teff > -9999))
       THEN a.teff_err ELSE null END AS teff_err,
    CASE WHEN (((a.logg_flag & 87903) = 0) AND (a.logg > -9999))
       THEN a.logg ELSE null END AS logg,
    CASE WHEN (((a.logg_flag & 87903) = 0) AND (a.logg > -9999))
       THEN a.logg_err ELSE null END AS logg_err,
    CASE WHEN (((a.m_h_flag & 87903) = 0) AND (a.m_h > -9999))
       THEN a.m_h ELSE null END AS m_h,
    CASE WHEN (((a.m_h_flag & 87903) = 0) AND (a.m_h > -9999))
       THEN a.m_h_err ELSE null END AS m_h_err,
    CASE WHEN (((a.fe_h_flag & 87903) = 0) AND (fe_h > -9999))
       THEN fe_h ELSE null END AS fe_h,
    CASE WHEN (((a.fe_h_flag & 87903) = 0) AND (fe_h > -9999))
       THEN fe_h_err ELSE null END AS fe_h_err,
    CASE WHEN (((a.o_fe_flag & 87903) = 0) AND ((a.fe_h_flag & 87903) = 0)
       AND (a.o_fe > -9999) AND (a.fe_h > -9999))
       THEN a.o_fe ELSE null END AS o_fe,
    CASE WHEN (((a.o_fe_flag & 87903) = 0) AND ((a.fe_h_flag & 87903) = 0)
       AND (a.o_fe > -9999) AND (a.fe_h > -9999))
       THEN a.o_fe_err ELSE null END AS o_fe_err,
    CASE WHEN (((a.na_fe_flag & 87903) = 0) AND ((a.fe_h_flag & 87903) = 0)
       AND (a.na_fe > -9999) AND (a.fe_h > -9999))
       THEN a.na_fe ELSE null END AS na_fe,
    CASE WHEN (((a.na_fe_flag & 87903) = 0) AND ((a.fe_h_flag & 87903) = 0)
       AND (a.na_fe > -9999) AND (a.fe_h > -9999))
       THEN a.na_fe_err ELSE null END AS na_fe_err,
    CASE WHEN (((a.mg_fe_flag & 87903) = 0) AND ((a.fe_h_flag & 87903) = 0)
       AND (a.mg_fe > -9999) AND (a.fe_h > -9999))
       THEN a.mg_fe ELSE null END AS mg_fe,
    CASE WHEN (((a.mg_fe_flag & 87903) = 0) AND ((a.fe_h_flag & 87903) = 0)
       AND (a.mg_fe > -9999) AND (a.fe_h > -9999))
       THEN a.mg_fe_err ELSE null END AS mg_fe_err,
    CASE WHEN (((a.al_fe_flag & 87903) = 0) AND ((a.fe_h_flag & 87903) = 0)
       AND (a.al_fe > -9999) AND (a.fe_h > -9999))
       THEN a.al_fe ELSE null END AS al_fe,
    CASE WHEN (((a.al_fe_flag & 87903) = 0) AND ((a.fe_h_flag & 87903) = 0)
       AND (a.al_fe > -9999) AND (a.fe_h > -9999))
       THEN a.al_fe_err ELSE null END AS al_fe_err,
    CASE WHEN (((a.k_fe_flag & 87903) = 0) AND ((a.fe_h_flag & 87903) = 0)
       AND (a.k_fe > -9999) AND (a.fe_h > -9999))
       THEN a.k_fe ELSE null END AS k_fe,
    CASE WHEN (((a.k_fe_flag & 87903) = 0) AND ((a.fe_h_flag & 87903) = 0)
       AND (a.k_fe > -9999) AND (a.fe_h > -9999))
       THEN a.k_fe_err ELSE null END AS k_fe_err,
    CASE WHEN (((a.co_fe_flag & 87903) = 0) AND ((a.fe_h_flag & 87903) = 0)
       AND (a.co_fe > -9999) AND (a.fe_h > -9999))
       THEN a.co_fe ELSE null END AS co_fe,
    CASE WHEN (((a.co_fe_flag & 87903) = 0) AND ((a.fe_h_flag & 87903) = 0)
       AND (a.co_fe > -9999) AND (a.fe_h > -9999))
       THEN a.co_fe_err ELSE null END AS co_fe_err
    FROM DR17.aspcapStar a
    INNER JOIN DR17.apogeeStar b ON a.apstar_id = b.apstar_id
    WHERE (a.aspcapflag & 261033871) = 0
    AND (b.extratarg & 16) = 0
    AND a.logg < 3.8

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