#  HD 222925: a New Opportunity to Explore the Astrophysical and Nuclear
Conditions of _r_ -process Sites

Erika M. Holmbeck  Observatories of the Carnegie Institution for Science, 813
Santa Barbara St., Pasadena, CA 91101, USA  Joint Institute for Nuclear
Astrophysics – Center for the Evolution of the Elements (JINA-CEE), USA
Hubble Fellow  Rebecca Surman  Department of Physics, University of Notre
Dame, Notre Dame, IN 45565, USA  Joint Institute for Nuclear Astrophysics –
Center for the Evolution of the Elements (JINA-CEE), USA  Ian U. Roederer
Department of Astronomy, University of Michigan, 1085 S. University Ave., Ann
Arbor, MI 48109, USA  Joint Institute for Nuclear Astrophysics – Center for
the Evolution of the Elements (JINA-CEE), USA  G. C. McLaughlin  Department of
Physics, North Carolina State University, Raleigh, NC 27695, USA  Joint
Institute for Nuclear Astrophysics – Center for the Evolution of the Elements
(JINA-CEE), USA  Anna Frebel  Department of Physics and Kavli Institute for
Astrophysics and Space Research, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Joint Institute for Nuclear Astrophysics – Center
for the Evolution of the Elements (JINA-CEE), USA

(Received 14 October 2022)

###### Abstract

With the most trans-iron elements detected of any star outside the Solar
System, HD 222925 represents the most complete chemical inventory among _r_
-process-enhanced, metal-poor stars. While the abundance pattern of the
heaviest elements identified in HD 222925 agrees with the scaled Solar _r_
-process residuals, as is characteristic of its _r_ -process-enhanced
classification, the newly measured lighter _r_ -process elements display
marked differences from their Solar counterparts. In this work, we explore
which single astrophysical site (if any) produced the entire range of elements
($34\leq Z\leq 90$) present in HD 222925. We find that the abundance pattern
of lighter _r_ -process elements newly identified in HD 222925 presents a
challenge for our existing nucleosynthesis models to reproduce. The most
likely astrophysical explanation for the elemental pattern of HD 222925 is
that its light _r_ -process elements were created in rapidly expanding ejecta
(e.g., from shocked, dynamical ejecta of compact object merger binaries).
However, we find that the light _r_ -process-element pattern can also be
successfully reproduced by employing different nuclear mass models, indicating
a need for a fresh investigation of nuclear input data for elements with
$46\lesssim Z\lesssim 52$ by experimental methods. Either way, the new
elemental abundance pattern of HD 222925—particularly the abundances obtained
from space-based, ultraviolet (UV) data—call for a deeper understanding of
both astrophysical _r_ -process sites and nuclear data. Similar UV
observations of additional _r_ -process-enhanced stars will be required to
determine whether the elemental abundance pattern of HD 222925 is indeed a
canonical template for the _r_ -process at low metallicity.

Nucleosynthesis (1131), Nuclear astrophysics (1129), R-process (1324),
Population II stars (1284), Nuclear physics (2077)

††journal: ApJ

##  1 Introduction

Recently, Roederer et al. (2022a) derived chemical abundances of the bright,
metal-poor (${\rm[Fe/H]}=-1.46$) star HD 222925 in and around the second _r_
-process peak from UV observations. These new measurements place HD 222925 as
the star with the most elements measured in its spectrum, second only to the
Sun. Totaling 42 trans-iron elements ($Z>30$), HD 222925 is only missing a
confident abundance determination for eight of the neutron-capture elements
that have stable or long-lived isotopes. Like many _r_ -process-rich stars,
the main _r_ -process pattern ($Z\geq 56$) of HD 222925 shows stunning
agreement with the Solar _r_ -process residuals. However, its pattern diverges
from the Solar pattern among the light _r_ -process elements ($34\leq Z\leq
52$, see Figure 1). Hints of this discrepancy were seen with ground-based,
optical observations (Roederer et al., 2018) and are now more apparent with
spaced-based, UV observations. Comparisons to other _r_ -process-enhanced,
metal-poor stars indicate that the abundance pattern of HD 222925 is not
atypical for its type; it appears to differ from other _r_ -process-enhanced
stars only in the number of elements measured. Having the most complete
abundance pattern of any star outside of the Solar system, along with a low
metallicity, HD 222925 could be a new, better, standard by which to compare
_r_ -process nucleosynthesis simulations. However, the divergence from the
Solar pattern among the lighter _r_ -process elements raises new questions
about the _r_ -process site. Is the elemental abundance pattern of HD 222925
fully representative of other _r_ -process-enhanced stars at low metallicity,
and if so, what does this mean for the _r_ -process site that enriched the gas
from which they formed?

Nucleosynthesis calculations within the past few decades have expanded from
comparing their simulation yields to only the Solar abundance pattern to
including in their comparisons the abundance patterns of _r_ -process-rich,
metal-poor stars (e.g., Wanajo, 2013; Hansen et al., 2014; Vassh et al.,
2020). The Solar system abundances are still the most complete observational
information we have for the _r_ -process, since they can be split into
contributions on the _isotopic_ level. In contrast, abundances derived from
other stellar spectra are necessarily elemental (except for a handful of cases
in which approximate isotopic ratios can be determined). Unlike the Sun,
however, the low metallicity of _r_ -process-enhanced stars suggests fewer
progenitor sources of heavy elements and a higher likelihood that a single
simulation output accurately represents the _r_ -process source that
originally enriched the star’s prenatal gas cloud. In this work, we expand on
these recent efforts in nucleosynthesis studies by using HD 222925 to
reconstruct astrophysical conditions of (potentially canonical) _r_ -process
sites at low metallicity.

There is a long tradition in _r_ -process studies of approximating the
combination of astrophysical conditions that best reproduces the Solar _r_
-process abundances (Kratz et al., 1993; Freiburghaus et al., 1999). In the
same spirit, Holmbeck et al. (2019) introduced the “Actinide-Dilution with
Matching” (ADM) model to characterize the physical differences between _r_
-process sites as a function of elemental abundance differences in _r_
-process-enhanced, metal-poor stars. This model builds a distribution of
astrophysical conditions (e.g., ejecta entropy or initial electron fraction)
by simultaneously matching key elemental abundance ratios derived from
observed stellar spectra through randomly sampling nucleosynthesis network
abundance outputs corresponding to different astrophysical conditions.
Specifically, this model can explain the star-to-star differences in actinide
abundances, finding that a moderate increase of material ejected at very low
initial electron fractions ($Y_{e}$) could sufficiently explain all observed
levels of actinide enhancements.

In this work, we use the ADM approach to explore possible combinations of
astrophysical ejecta that could potentially be responsible for the HD 222925
abundance pattern, including the distinctly non-Solar light _r_ -process
element abundances. In doing do, we attempt to reconstruct the progenitor
astrophysical conditions which gave rise to the heavy-element pattern of HD
222925. If HD 222925 is to be the new standard _r_ -process abundance pattern
template, we will have effectively reconstructed the canonical _r_ -process
site responsible for the observational signatures in metal-poor stars. First,
in Section 2 we examine notable features of HD 222925 that the ideal site
reconstruction will reproduce. Next, in Section 3 and 4 we apply the ADM
method to HD 222925 and examine the suitability of its pattern as
representative of the canonical _r_ -process site under different
astrophysical and nuclear conditions. Finally, we comment on what the results
in Section 3 and 4 reveal about the uniquely complete abundance pattern of HD
222925 and the _r_ -process that enriched the gas from which it formed.

##  2 Key Elemental Trends of HD 222925

In our previous application of the ADM model (Holmbeck et al., 2019), only
three elements were used: Zr, Dy, and Th, chosen in order to gauge the
relative amounts of light (Zr) and actinide (Th) material compared to the main
(Dy) _r_ -process. In that work, we were not as concerned with specific
matches to the entire detailed abundance pattern, and rather argued that too
many elemental constraints may lead to an artificially constrained result,
especially considering the state of nuclear physics uncertainties and their
effect on _r_ -process calculations. However, HD 222925 displays specific
abundance features, unique in their UV observations, with which we seek to
supplement and challenge our Zr-Dy-Th-based model. Here we comment on those
elements which distinguish this star from the Solar _r_ -process residuals and
how those particular elements will guide our ADM model choices. For reference,
Figure 1 shows the abundance pattern of HD 222925 compared to the Solar _s_ \-
and _r_ -process abundances, scaled to the abundance of Ba.

Figure 1: Abundance patterns of HD 222925 (black points) compared to the Solar
_r_ and _s_ -process components (gray lines) and weak _s_ -process models from
Banerjee et al. (2018) (green lines). The Solar neutron-capture patterns and
the 40-M⊙ _s_ -process model are scaled to Ba, while the 12-M⊙ model is scaled
to Se.

###  2.1 Se and the _s_ -process

In the lightest portion of its heavy-element abundance pattern, HD 222925’s
high Se abundance relative to its neighbors stands out. This element is
dominated by the _r_ -process in the Solar system; however, it is worth noting
that Se can be produced by a low-metallicity, weak _s_ -process. We show in
Figure 1 two weak _s_ -process models: progenitors of mass 12 and 40 M⊙ with
$[\textrm{Fe/H}]=-3$ and $[\textrm{CNO/H}]=0$ from Banerjee et al. (2018).
Although a limited _s_ -process could account for the high abundances of
elements such as Se and Sn, such weak _s_ -process models tend to overproduce
elements lighter than Se (e.g., Zn through As, $30\leq Z\leq 33$), as shown by
the dark green (12 M⊙) line. Attempts to mitigate the overproduction of the
lighter elements with different _s_ -process models underproduces Se by an
order of magnitude at the cost of overproducing Ba, shown by the light green
(40 M⊙) line. Similarly, models that can reproduce the high Sn are an
otherwise poor match to the other elements in HD 222925. We support the claim
made in Roederer et al. (2022a) that HD 222925 is not so significantly _s_
-process enriched as to account for a significant production of the lighter
elements like Se and Sn and attribute the majority of their origin to the _r_
-process.

We note that the abundance of Se was derived from one absorption feature in
the UV; however, the absorption feature is strong, well-isolated, and not
suspected to greatly suffer from hyperfine-splitting effects, isotopic shifts,
or assumptions about non-local thermodynamic equilibrium (Roederer & Lawler,
2012; Peterson et al., 2020). Our initial ADM model will not use Se as a
constraint (since this model did not sample enough parameter space for our _r_
-process models to robustly produce it), but we will enforce Se production in
a more complex model (see Section 3.4) as a noteworthy feature in need of
explanation.

###  2.2 Zr to Te

Figure 2: Combined abundance patterns (left) and $Y_{e}$ distributions of
ejecta (right) predicted by the model when two (gray), three (teal), and five
(green filled) elemental ratios are used. The individual nucleosynthesis
calculations use the FRLDM fission fragment distribution for actinide-
producing conditions ($Y_{e}\lesssim 0.25$).

Perhaps the most intriguing feature in the abundance pattern of HD 222925 is
the rapid departure from the Solar _r_ -process pattern for the $40\leq Z\leq
48$ elements, followed by an agreement with Solar at In and Sn ($Z=49$ and 50,
respectively) and lower abundances again for the next two elements, Sb and Te.
Also note that the Solar _r_ -process component has not been scaled; the _r_
-process enhancement of HD 222925 is so significant that its absolute
abundances are on par with that of the Solar system (Roederer et al., 2018).
The abundances for the four elements with $Z=48$–51 were derived from only one
spectral feature each, and thus large uncertainties accompany their adopted
abundance values. While we do not invoke their uncertainties to dismiss these
measurements, we place less importance on explaining their trends than the
other elements in this region. In particular, we will focus on the
relationship between Zr, Ru, Pd, Ag, and Te, as well as their overall co-
production with the main _r_ -process pattern ($Z\geq 56$).

###  2.3 Ba to Th

In order to investigate whether one _r_ -process source can synthesize the
entire range of abundances in HD22295, we will also require our model to
produce lanthanide and actinide abundances (represented by Dy and Th,
respectively, as per the original ADM model) commensurate with those derived
for the star. We focus less on fitting the element-by-element details of this
main _r_ -process component since nuclear uncertainties dominate in this
region and might lead to overfitting. As in Holmbeck et al. (2019), we assume
the Th abundance at 1 Gyr post-event was 0.2 dex greater than the modern-day
Th abundance derived for the star in order to account for roughly 10 Gyr of
radioactive decay, commensurate with its low metallicity.

##  3 _r_ -process sites

###  3.1 The base model

To reproduce the abundance trends of HD 222925, we first run a calculation
based on the ADM model of Holmbeck et al. (2019). In this model, we randomly
sample nucleosynthesis simulation output for a set of initial astrophysical
conditions (entropy and density) with different starting compositions
(calculated from nuclear statistical equilibrium at 10 GK with varying initial
$Y_{e}$). This variation provides a conceptual insight for the distribution of
_r_ -process ejecta from an astrophysical site that could explain the observed
abundance trends, and the $Y_{e}$ distribution constructed by previous
applications of the ADM model has demonstrated agreement with those from
robust hydrodynamical simulations. We start with our base, two-ratio model
that uses the Zr/Dy and Th/Dy abundance ratios and will only add complexities
later as needed to explain the data.

First we test a combination of ejecta with two distinct entropies. We run a
suite of nucleosynthesis calculations that follow one of two of the same
astrophysical trajectories (temperature and density evolution over time), but
vary the initial composition. All nucleosynthesis simulations are run with the
nuclear reaction network code Portable Routines for Integrated nucleoSynthesis
Modeling (PRISM; Sprouse, 2020) and use nuclear masses from the Finite Range
Droplet Model (FRDM2012; Möller et al., 2012, 2016) and $\beta$-decay rates
from Möller et al. (2019). Laboratory-measured nuclear masses from the 2020
compilation of the Atomic Mass Evaluation (AME2020; Wang et al., 2021) and
decay rates from the 2020 NUBASE evaluation (Kondev et al., 2021) are used
instead of the theoretical values wherever available. For astrophysical
conditions, we choose a very low-entropy ($s\sim 8~{}k_{b}/{\rm baryon}$)
trajectory characteristic of dynamical ejecta from a neutron star merger and a
moderately low entropy ($s\sim 40~{}k_{b}/{\rm baryon}$) trajectory
representing disk-wind-like conditions. In the lower entropy case, we vary the
$Y_{e}$ up to 0.25. The $Y_{e}$ for the wind-like trajectory is allowed to
vary between 0.25 and 0.5. A separation at $Y_{e}=0.25$ was chosen since, for
these entropies, this $Y_{e}$ is approximately the transition point at which
lanthanides and actinides are synthesized in the _r_ -process. We use a broad
fission fragment distribution based on the Finite Range Liquid Droplet Model
(FRLDM) of Möller et al. (2015); Mumpower et al. (2020), as employed by Vassh
et al. (2020). Note that at the entropies considered here, only the most
neutron-rich conditions ($Y_{e}\lesssim 0.20$) will achieve fission; in other
words, only the “dynamical-like” conditions will allow fission cycling for
this subset of nucleosynthesis simulations.

The ADM model randomly samples output from the above trajectories in their
allowed $Y_{e}$ ranges and finds the combination of 15 samples whose total
abundance ratios are within given tolerances (typically about 0.1 dex). All
ratios must be simultaneously be within acceptable tolerances for the 15
samples to be considered a match. For the base model, we use the abundance
ratios of Zr/Dy and Th/Dy, as in the original ADM application. The gray line
in Figure 2 shows the result of the ADM model compared to HD 222925 using
these two constraints. As constrained by the model, the lighter _r_ -process
elements (Zr), lanthanides (Dy), and actinides (Th) are overall a decent match
to the stellar data, and the $Y_{e}$ distribution is overall continuous,
agreeing roughly with previous applications (Holmbeck et al., 2019).111The gap
in the distribution at $Y_{e}\approx 0.12$ is due to an (unfavorable) excess
of actinide abundance, as described in Holmbeck et al. (2019) (see also
Eichler et al., 2019). This baseline ADM application finds remarkable success
with effectively only three elements; however, there are a few regions in
which the ADM result departs from observational data. For example, the region
between Pd and Te is significantly overproduced by the base model, suggesting
that the $Y_{e}$ distribution in Figure 2 is not representative of the
“canonical” _r_ -process site that produced the heavy elements in HD 222925.
The overproduction in this region was not noteworthy in Holmbeck et al. (2019)
since none of the stars considered in that sample had abundance derivations
for the elements in this region. Now, however, our model must account for the
new data in this region. It should also be noted that when this exercise was
repeated with the Solar _r_ -process abundances, the reconstructed $Y_{e}$
distribution was similarly continuous as in the “base” case in Figure 2. Note
again that Se also does not match with our ADM model, and none of the $Y_{e}$
variations for the two entropy cases produces sufficiently high Se in order to
obtain such a match. With the current model parameters, it is possible that Se
could be produced at $Y_{e}>0.5$ by, e.g., the $\nu p$-process or a very weak
_r_ -process (Psaltis et al., 2022). Se aside, it is clear we can invoke more
constraints to obtain a better fit to the HD 222925 abundance pattern,
especially in the light _r_ -process-element region: $44\lesssim Z\lesssim
52$.

###  3.2 Adding more constraints

Since the region from Pd to Te is overproduced by the baseline ADM model, we
expand the model by adding more constraints in addition to the original Zr,
Dy, and Th in order to find the conditions of the canonical site responsible
for the _r_ -process pattern of HD 222925. For this exercise, we add Te, Ru,
and Pd as additional constraints to the model. In practice, we use the
abundance ratios Zr/Te, Zr/Pd, Pd/Ru, Te/Dy, and Th/Dy from HD 222925 in order
to capture the downward trend of the elements between Zr and Te. There are
regions in the heavy _r_ -process-element ($Z\geq 56$) abundance pattern that
are also a less-than-ideal fit: for example, the underproduction of elements
to the right of the second _r_ -process peak at $57\leq Z\leq 63$. In
addition, the overall shape and location of the third _r_ -process peak could
also be affected by late-time neutron captures (Surman & Engel, 2001; Eichler
et al., 2015). We do not add more constraints to this portion of the abundance
pattern, however, since we use this work to focus on the light _r_ -process
region where the abundance pattern of HD 222925 significantly diverges from
the Solar _r_ -process component.

The green line and shaded region in the left panel of Figure 2 shows the total
abundance results when more constraints are added to the base set: first only
Te (in the form of Zr/Te), then with the addition of Ru and Pd, respectively.
Note that the abundances of Zr, Dy, and Th (the “base” set) are still being
used by the model. Even adding the additional Te ratio (solid green line)
begins to capture the downward trend of Pd, Ag, and Cd. (For the Solar case,
adding Te did not significantly change the $Y_{e}$ distribution.) Adding even
more constraints (shaded region) lowers this region even further for near-
perfect agreement with Ag and Cd. We cannot replicate the high abundances of
In, Sn, and Sb, and many of the elements between Ba and Gd are similarly still
underproduced. However, seeing as how the uncertainties on the abundance
derivations of In, Sn, and Sb are large, we count these fits as overall
successes.

The right panel of Figure 2 shows a histogram of the $Y_{e}$ combinations that
contributed to the overall matching abundance ratios. Unlike the mostly
continuous $Y_{e}$ distribution in the base model, requiring the model to fit
more elements leads to a more constrained $Y_{e}$ distribution. With the
addition of just one more element (Te), the $Y_{e}$ distribution begins to
disfavor $Y_{e}\approx 0.25$ and $0.30$ (compare the gray shaded histogram
with the green outlined one). Adding two more elements for matching yields an
even more constrained distribution that shows preference for four specific
values of initial $Y_{e}$: $\sim$0.09, $\sim$0.17, $\sim$0.27, and $\sim$0.45.
(Recall that for $0\leq Y_{e}\leq 0.25$, the $s\sim 8~{}k_{b}/{\rm baryon}$
were used, and $s\sim 40~{}k_{b}/{\rm baryon}$ for $Y_{e}\geq 0.25$.)

Figure 3: Abundance patterns corresponding to individual initial $Y_{e}$
values. The lowest values ($Y_{e}=0.09$ and 0.17) use very low entropy
“dynamical” conditions with FRLDM fission yields, and the rest ($Y_{e}=0.27$,
0.45, and 0.34) use the moderately low entropy “wind” conditions.

Figure 3 illustrates why these $Y_{e}$ values are preferred; the fission
fragments from low-entropy, low-$Y_{e}$ conditions contribute most of the Pd
abundance, and some can produce sufficiently high lanthanides without
overproducing the actinides or Pd by fission deposition; compare the two green
lines for $Y_{e}=0.09$ and 0.17. Higher-$Y_{e}$ conditions contribute most of
the Zr and Te abundance, as shown by the pink lines for $Y_{e}=0.27$ and 0.45.
Figure 3 also begins to show why Se cannot be used as a constraint for these
initial models; the entropies and $Y_{e}$ values that the model samples from
is simply not sufficient to produce Se. We will return to Se in the next
section by considering an astrophysical trajectory that does produce it.

Intriguingly, Zr and Te production appear decoupled from one another; there is
a specific component that produces Zr and essentially none of the other
elements ($Y_{e}\approx 0.45$), while Te can be produced by a variety of
initial $Y_{e}$ values, but notably at $Y_{e}\approx 0.27$. This separation
contradicts recent evidence in metal-poor stars that Zr and Te are in fact
correlated (Roederer et al., 2022b). Moreover, this separation occurs at
$Y_{e}\approx 0.34$ (orange line). At these values of $Y_{e}$, Zr and Te are
coproduced, but this model disfavors such coproduction as an explanation for
HD 222925 due to the extreme overabundance of elements like Pd that also
occurs at this $Y_{e}$.

In principle the preference for certain conditions (here, entropy and $Y_{e}$)
is unsurprising; additional distinct conditions are necessary to fit more
abundance features in the same way early _r_ -process studies necessarily
invoked separate astrophysical conditions to explain the three _r_ -process
peaks in the Solar abundance pattern (e.g., Kratz et al., 1993). However, in
the case of the Sun, it can be argued that the need for a variety of
conditions is evidence for multiple _r_ -process sites contributing to the
heavy-element abundances in the Solar system. If the progenitor site of HD
222925 is to be canonical of progenitors of _r_ -process-enhanced stars, then
the logical assumption is that the $Y_{e}$ distribution in Figure 2 describes
a single _r_ -process site, not multiple. With this in mind, we discuss four
ways to interpret the $Y_{e}$ distribution for the most constrained case in
Figure 2 (green shaded region):

  1. 1.

At face value: the ejecta responsible for the _r_ -process enrichment of HD
222925 did not have a continuous distribution of conditions, and specifically
$s\approx 40$ with $Y_{e}\approx 0.34$ conditions were not or could not be
achieved in the ejecta.

  2. 2.

As evidence for at least two astrophysical sites: one in which conditions
produce ejecta with $Y_{e}\gtrsim 0.35$ and another with $Y_{e}\lesssim 0.30$.

  3. 3.

As a challenge to one of the basic assumptions of our ADM model: that we can
represent the entirely of the ejecta with only two values of initial entropy.

  4. 4.

As a call for new laboratory studies of the nuclear data that shapes the
abundance pattern features between the first and second _r_ -process peaks.

If the first case is correct, a precise balance in ejecta $Y_{e}$ would be
needed in order to reproduce the main features of the abundance pattern of HD
222925, with sufficient $Y_{e}\approx 0.40$ for Zr, and no ejecta with
$Y_{e}\approx 0.34$. While possible, such a constraint seems unlikely; not
only do many detailed NSM simulations easily predict ejected material with
0.34, but the distributions of $Y_{e}$ in the simulated ejecta are typically
smooth in general with no such abrupt gaps, similar to the baseline
distribution shown in Figure 2 in gray.

Figure 4: Combined abundance patterns (left) and $Y_{e}$ distributions of
ejecta (right) predicted by the model when two (gray), three (teal), and five
(green filled) elemental ratios are used. The individual nucleosynthesis
calculations use the 50/50 fission fragment distribution for actinide-
producing conditions ($Y_{e}\lesssim 0.25$).

The trend in the light elements ($38\leq Z\leq 52$) in HD 222925 appears to
effectively require at least two _r_ -process environments, supporting the
second case: that one component produces up to (and effectively nothing
beyond) Zr, and at least one component produces the main _r_ -process pattern.
This separation in $Y_{e}$ suggests a decoupling of the environments that
produce Zr and the main _r_ -process pattern. While possible, this decoupling
also seems unlikely. If Zr and the main _r_ -process pattern are produced in
decoupled sites, one might expect to find an _r_ -process-enhanced star
lacking in Sr. However, there are no such _r_ -process-enhanced stars known
(Roederer, 2013) Furthermore, the variation between the light elements and the
main _r_ -process elements, while present, is much less than what might be
expected if these elements were produced in different _r_ -process sites
(Roederer et al., 2022b). Alternatively, these two sites may still inherently
be from the same source (e.g., the dynamical and wind ejecta of NSMs) wherein
they would always be produced, but perhaps in different relative amounts. This
explanation seems likely, provided there exists a clear separation between the
$Y_{e}$ distribution of dynamical ejecta and that of wind ejecta (specifically
at $Y_{e}\approx 0.34$), though current simulations do not support such a
clear separation.

While either of the first two cases _may_ be possible, there is no strong
evidence in support of either one. It is far more likely (and scientifically
interesting) that our baseline model could benefit from additional complexity,
particularly as when it comes to whether the abundance pattern of HD 222925
(especially the lighter _r_ -process elements) could be reproduced by a
specific combination of parameterized astrophysical conditions. In the next
sections, we search for variations on our model that are not only a good match
to the _r_ -process abundance pattern of HD 222925, but also yield a
reasonable (i.e., not highly constrained) ejecta profile. Specifically, we
will increase the complexity of our ADM model to see if a different fission
fragment distribution or a smooth distribution of merger ejecta can be
achieved in non-parameterized trajectories. If we still find that highly
constrained ejecta is needed to reproduce the abundances derived for HD
222925, we are left with the last option: to challenge the nuclear data far
from stability between the $N=50$ and $N=82$ closed shells.

###  3.3 Fission fragments

The fission fragment distribution employed in the initial application of the
ADM model in Holmbeck et al. (2019) uses a “50/50” deposition scheme in which
a fissioning parent nucleus produces two daughter products of identical mass
and charge: $(Z,A)\rightarrow(Z/2,A/2)+(Z/2,A/2)$. This choice is simple, as
robust fission studies can vary from being symmetric about $(Z/2,A/2)$ to wide
and asymmetric, even depositing in the Sr region (e.g., Vassh et al., 2019,
2021). This increase in maturity of fission studies is what motivated our
decision to use FRLDM fission fragment yield for our baseline case. However,
this fission fragment distribution is broad enough to deposit in the Pd–Te
region instead of being localized near the heavier side of second _r_ -process
peak (Ba), where the 50/50 fission fragments typically deposit in low-entropy
conditions. Is the overproduction of the Pd–Te region and the disfavor of
$Y_{e}\approx 0.34$ simply a product of broad fission yields? For this study,
we repeat the previous nucleosynthesis and ADM calculations, but instead
revert back to the 50/50 fission fragment distribution to test the sensitivity
of the gap at $Y_{e}\approx 0.34$ to fission fragment deposition.

We test both the initial baseline, two-component (Zr/Dy and Th/Dy) model as
well as the more complex models which use one and three additional elements
(see the previous section for details). The results for these cases are shown
in Figure 4. As in the previous case that uses FRLDM fission yields, the
elements between Pd and Te are still over-produced in the base model (gray)
line, though not as egregiously (compare especially $Z=50$ in Figures 2 and
4). In addition, a better fit to the abundance pattern is again obtained with
more constraints. However, the better fit still comes with a more constrained
$Y_{e}$ distribution: the same effect (and at the same $Y_{e}$) as we saw in
the baseline case that used FRLDM fission fragments. The dearth of ejecta with
$Y_{e}\approx 0.34$ is clearly robust to fission fragment considerations and
indicates that the FRLDM fission yields are not causing the model to
artificially disfavor $Y_{e}\approx 0.34$. The $Y_{e}$ distribution for our
“canonical” astrophysical site is still highly constrained. Therefore, fission
fragment deposition is likely not the solution to obtaining a smoother
distribution of ejecta $Y_{e}$.

###  3.4 Rapidly expanding ejecta

Changing the fission model or the abundance ratios are not the only ways in
which the ADM model can be improved. Perhaps it is our simple two-entropy
baseline for the astrophysical trajectories that needs added complexity. Since
elemental production is sensitive to not only the initial $Y_{e}$ and entropy,
but also the _evolution_ of entropy (related to temperature through the
equation of state) over time, the gaps in the $Y_{e}$ distribution may be
effectively filled by astrophysical trajectories which treat the temperature
evolution differently than in our two parameterized cases. For this test, we
continue exploring alternatives to our baseline model by considering a
modification to the temperature evolution in our astrophysical trajectories
for the _r_ -process ejecta. In addition, we have shown that adding Te as a
constraint produces a better fit to the abundance pattern of HD 222925. While
continuing to add more abundance ratios (e.g., Ru and Pd) produces an even
better fit, the fit is not so much increased as to justify the increase in
computational time needed for the model to converge, and similar conclusions
can be drawn about the ejecta without these additional constraints. For the
following tests, unless otherwise noted, we use Zr/Dy, Th/Dy, and Zr/Te as the
default set of model constraints supplied to the ADM model.

All of the network simulations that form the basis of our ADM models in this
work include nuclear reheating; the decay of _r_ -process nuclei in the ejecta
will add energy in the form of heat to the environment and thus affect the
(temperature-dependent) reaction rates at play during the _r_ -process. In our
network simulations, the amount of reheating is self-consistently modified
such that the amount by which the temperature changes throughout its evolution
depends on the initial $Y_{e}$ (and evolving composition) for the same
thermodynamic trajectory. At low entropy and low-$Y_{e}$, the effect of
reheating can govern the entire thermodynamic evolution of the trajectory and
produce an abundance pattern drastically different from the case in which
nuclear reheating is neglected. For example, Figure 5 shows a collection of
nucleosynthesis output with and without nuclear reheating. Even at the same
$Y_{e}$, the inclusion of nuclear reheating can produce a completely different
abundance pattern (compare the teal and orange lines at $Y_{e}=0.25$). Some
non-reheated cases succeed at co-producing Zr and Te, while allowing Pd, Ag,
and Cd to remain extremely low (light pink line at $Y_{e}=0.36$). Notably, the
“cold” trajectories produce Se at moderately low $Y_{e}$ ranges, some with
ejecta that is almost entirely Se (dark pink line at $Y_{e}=0.37$).

Figure 5: Abundance patterns of “cold” (without nuclear reheating)
trajectories at different initial $Y_{e}$ values. The teal line at
$Y_{e}=0.25$ is an output from one of the original trajectories that uses
reheating.

Figure 6: Combined abundance patterns (left) and $Y_{e}$ distributions of
ejecta (right) predicted by the model when using a Te (gray) or a Se (orange
line) constraint in addition to the constraints on Zr, Dy, Th (gray) and when
both Te and Se are used (orange filled).

We perform a simple test wherein the low-entropy trajectories are run through
PRISM without nuclear reheating included, then run the ADM model with these
“cold” trajectories at $0.35\leq Y_{e}\leq 0.40$ in additional to the original
(nuclear-reheated) ones at $Y_{e}\leq 0.25$. We still include the medium-
entropy set for the model to randomly sample in range $0.25\leq Y_{e}\leq
0.50$. Figure 6 shows the ADM results for this case (gray line) and the
$Y_{e}$ histogram when the low-entropy, cold (i.e., non-reheated) trajectories
are included. Note that Te is used as a constraint in addition to the baseline
Zr, Dy, and Th. The $Y_{e}$ distribution in gray is nearly identical to the
teal histogram in Figure 2. This agreement is unsurprising; the teal line uses
the same elements as constraints. In this case, the non-reheated trajectories
do not need to (and barely do) contribute since a decent match can be found to
the abundance pattern of HD 222925 without them.

However, Figure 5 shows that the cold trajectories are able to produce
abundant Se. Therefore, we also test how using Se as an additional constraint
(in the form of the Se/Zr ratio) affects the fit and the distribution. We test
both the case where Se is used in addition to the original Zr, Dy, and Th
(i.e., replacing the use of Te) and one in which both Te and Se are used. The
case with Se (and not Te) is shown by the orange line in Figure 6. Since the
constraint on Te was released, the Pd to Te region is again overproduced, as
we saw in the original ADM application. However, Se is a good match to HD
222925 and the $Y_{e}$ distribution for the case with Se is relatively
continuous.

The case in which both Te and Se are used as constraints is shown by the
orange filled region in Figure 6. There are two noteworthy features about this
distribution. First, compared to the case with only Te, the distribution
appears perhaps slightly less constrained, but with more production at
$Y_{e}\approx 0.30$ and 0.37. At these values of initial $Y_{e}$, the non-
reheated nucleosynthesis calculations contribute, filling in some of the gaps
produced when the model is run without them. The second noteworthy feature is
that there is no material at $Y_{e}<0.15$ in this distribution. In this case,
the combination of heated and non-heated ejecta produces a sufficiently robust
main _r_ -process pattern that no very low-$Y_{e}$ ($\lesssim 0.1$) ejecta is
necessary, which further suggests that the abundance pattern of HD 222925 does
not require such extremely neutron-rich conditions.

Since the “cold” case (with Se and Te as added constraints) leads to a
somewhat less-constrained $Y_{e}$ distribution, we interpret this solution as
a possible canonical _r_ -process site: that is, that _r_ -process sites at
low metallicity included a significant ejecta component that did not undergo
nuclear reheating. To achieve a non-reheated case, the ejecta would have to
expand very rapidly such that a sudden decrease in density effectively
suppresses reheating efficiency. For the case in Figure 6 to be the solution
to HD 222925, there may need to be a correlation of $Y_{e}$ with ejecta
velocity, with higher-$Y_{e}$ ejecta expanding faster than lower-$Y_{e}$
ejecta. Indeed, as one example, the collapsar disk models of Miller et al.
(2020) appear to show a high-velocity component at $Y_{e}\approx 0.35$. The
abundance pattern of HD 222925 could be the result of an _r_ -process event
(such as an NSM) with a low-entropy component of sufficiently high velocity to
suppress nuclear reheating and produce both the high Se and Te as well as the
downward trend between Zr and Te. However, low-entropy, rapidly expanding
ejecta without nuclear reheating is uncommon in NSM simulations; shock-
interface ejecta, which is ejected quickly and at $Y_{e}\approx 0.2$–0.4
(Hotokezaka & Piran, 2015), typically has higher entropy than the very low-
entropy case considered here. Many unknowns still exist in our understanding
of NSM ejecta. Perhaps low-entropy, high-velocity ejecta that does not undergo
nuclear reheating comprises a substantial fraction of the total NSM outflows.
Further studies on the theory side, especially in neutrino physics, are
necessary to understand the complexities of merger ejecta to test whether a
high-mass, non-reheated component is viable in NSM sites. We continue to
explore other possibilities and next test if a smoother entropy range can
remove the gap at $Y_{e}\approx 0.34$.

###  3.5 A smooth entropy range

Figure 7: Combined abundance patterns (left) and $Y_{e}$-entropy distribution
of ejecta (right) predicted by the ADM model (blue) compared to the original
simulation (gray). The light-blue shaded abundance pattern in the left panel
shows the average of subset of trajectories that start with a $Y_{e}\approx
0.2$, corresponding to the range highlighted in the right panel.

Rather than sampling from a variety of $Y_{e}$’s but only two entropies we
instead sample from the hydrodynamic simulation output of Metzger & Fernández
(2014). Although initial $Y_{e}$ and specific entropy of the trajectories in
the simulation output do not evenly populate a regular grid, they nevertheless
span a range that should be more or less in agreement with other theoretical
predictions. This sampling allows us to try not only different $Y_{e}$-entropy
combinations, but also different dynamical timescales (essentially expansion
velocities). In addition, sampling from a simulation will also be able to
capture any correlation effects between astrophysical conditions. We take the
trajectories from the 100-ms-lived hyper-massive neutron star case in Metzger
& Fernández (2014) and randomly sample ten output abundance patterns from
previously performed calculations (Holmbeck et al., 2021) to test if the
randomly sampled combination is a reasonable subset of the total. For this
exercise, we use both the Se and Te constraints, as in the orange shaded case
in Figure 6.

Figure 7 shows the results when, instead of randomly sampling a range of
$Y_{e}$’s for a small handful of entropies, an entire distribution of
entropy-$Y_{e}$ space is sampled, based on simulation data for NSMs. The total
abundance pattern and selected entropy-$Y_{e}$ combinations are shown from ADM
(blue) compared to the original full set of trajectories (gray). As can be
seen in the left panel of Figure 7, the main trends (high Se, low Pd, and
Solar lanthanide-to-actinide ratios) are well-reproduced by the ADM
combination. The right panel of Figure 7 shows that, for the most part, the
ADM-selected trajectories are indeed a reasonable subset of the total
distribution.

However, there are two important differences; first, there is a preference for
low $Y_{e}$ ($\lesssim 0.18$), dominating over the original distribution. The
preference for low $Y_{e}$ can be explained by comparing the blue and gray
abundance patterns in the left panel of the figure. The full set has lower
overall main _r_ -process abundances. For a star like HD 222925, which is
enhanced in these elements, a higher contribution of the conditions that
produce the main _r_ -process (low-$Y_{e}$, low-entropy) is preferred.

Secondly, there is a gap at $Y_{e}\approx 0.2$. The light-blue shaded
abundance pattern shows the average of all trajectories in the original sample
with initial $Y_{e}\approx 0.2$, about 2% of all the simulation data. From
this abundance pattern, it is clear why there is a lack of material at this
$Y_{e}$; the Te region is overproduced, similarly to what occurred at
$Y_{e}\approx 0.34$ in the ADM cases from the previous sections. Because Te is
used as one of the constraints for the ADM fit, it is natural that the model
gravitates away from this subset of simulation output.

We have explored many astrophysical variations—and one nuclear one—and
conclude that the puzzle of the $Y_{e}$ gap first seen in Figure 4 cannot be
solved by considering a more complex model, a smooth entropy range, or a
different fission fragment distribution. (A non-heated, rapidly expanding
ejecta case remains a possibility.) In terms of astrophysics, the persistence
of a highly constrained ejecta profile no matter what variations we make to
the model forces us back to the original first two possibilities presented in
Section 3.1: that the ejecta for the canonical _r_ -process site is indeed
highly constrained, or that more than one site is needed. While there remains
still a broad range of astrophysical parameter space to explore, we consider
an alternate option outside of the realm of astrophysics: that the nuclear
data responsible for shaping the abundance pattern between the first and
second _r_ -process peaks needs to be revisited (Mumpower et al., 2016).

##  4 Nuclear data revisited

If the abundance pattern of HD 222925 cannot be straightforwardly explained by
increasing model complexity or a continuum of astrophysical _r_ -process
conditions (nor readily by _s_ -process models), then it may be that the
highly constrained and possibly artificial ejecta distributions are a result
of uncertain nuclear physics. Here we examine the nuclear physics inputs used
in our models, particularly the neutron-rich species between the $N=50$ and
$N=82$ shell closures that shape the pattern of $44\leq Z\leq 48$ elements in
HD 222925 that fall well below that of the scaled Solar residuals.

Since $Y_{e}\approx 0.34$ was heavily disfavored in our initial ejecta
distribution models, we investigate the specific production at this $Y_{e}$
with a range of nuclear mass models. For this study, we change the separation
energies, neutron-capture rates, and $\beta$-decay rates as self-consistently
as possible within each mass model using state-of-the-art calculations
(Mumpower et al., 2015). (Fission and $\alpha$-decay rates are also changed
for completeness, though the heaviest elements that undergo these processes
are not produced in any significant amounts for these astrophysical
conditions.) In all nucleosynthesis calculations, laboratory-measured nuclear
masses and decay rates were used for nuclei for which these data exist. In
other words, reaction and decay rates using different theoretical nuclear mass
models only change data for which laboratory measurements do not exist, which
typically means data for nuclei very far from stability.

Figure 8: Abundance patterns for $Y_{e}=0.34$ cases with different nuclear
mass models. Gray shading represents the full range spanned for each element
across the mass models.

Figure 8 shows the results from the PRISM nuclear reaction network code for
each change of nuclear mass model: UNEDF0 (Kortelainen et al., 2010), UNEDF1
(Kortelainen et al., 2010), FRDM1995 (Möller et al., 1995), HFB17 (Goriely et
al., 2009), HFB24 and HFB27 (Goriely et al., 2013), DZ (Duflo & Zuker, 1995),
WS3 and WS4 (Liu et al., 2011; Wang et al., 2014; Zhang et al., 2014), KTUY
(Koura et al., 2005), and ETFSI (Aboussir et al., 1995). Our baseline case,
FRDM2012, performs the worst in the $46\leq Z\leq 50$ region, overproducing Pd
and Ag and underproducing Sn. This difference highlights why the ADM model
results disfavor $Y_{e}\approx 0.34$ (and $\approx$0.2 in the smooth-entropy
case); including those conditions does not satisfy the elemental ratio
constraints supplied to the model. Note that some models like UNEDF0 fare
slightly better, producing a steeper Pd-Ag-Cd trend commensurate with HD
222925’s elemental trend as well as a slightly higher Sn abundance.

For a simple study, we use our baseline, two-component results (gray line in
Figure 2) and replace all simulations that use $0.30\leq Y_{e}\leq 0.38$ with
the UNEDF0 calculations at $Y_{e}\approx 0.34$. We did not rerun the ADM
model, but rather use the output from Figure 2 and exchanged the original
(FRDM2012) output abundances with equivalent UNEDF0 abundances. The $Y_{e}$
distribution, therefore, would be the same as the gray region in Figure 2.
Figure 9 shows the total abundance pattern after this swap. The overproduction
originally displayed by the FRDM2012 result (and shown in Kratz et al. 2014)
can be effectively suppressed by an exchange of nuclear mass model. The Zr and
Te abundances are slightly overproduced, but the Pd, Ag, and Cd abundances are
much lower than in the FRDM2012-only case. Without altering the astrophysics
at all, changing the nuclear physics baseline leads to a case in which the
main interesting features of the abundance pattern of HD 222925 are replicated
while simultaneously producing a $Y_{e}$ ejecta distribution that
qualitatively agrees with NSM outflows from more rigorous simulations (e.g.,
Fernández et al., 2015; Radice et al., 2018; Fujibayashi et al., 2022). With a
small modification to the nuclear physics, the baseline (gray) distribution
could be descriptive of the canonical _r_ -process site for metal-poor stars.

The dramatic effect of the underlying mass model on abundance predictions is
perhaps surprising, given the experimental advances in studies of nuclei near
the second _r_ -process peak (e.g.,Kozub et al. (2012); Van Schelt et al.
(2013); Lorusso et al. (2015)). Consequently, we did not anticipate that the
choice of nuclear mass model would affect this region so significantly.
Clearly, nuclei outside of current laboratory measurements continue to drive
the uncertainties on the _r_ -process, even at these lower-mass nuclei. The
projected reach of current and next-generation accelerators for nuclear
physics (such as the Facility for Rare Isotope Beams, FRIB) are able to
explore this region and contribute significantly more new data, even
approaching the neutron dripline near $Z=40$. More uncertainties remain at
even higher-mass nuclei, but our investigation of HD 222925 demonstrates that
understanding the second-peak region is still a high priority for the _r_
-process.

Figure 9: Gray: combined abundance pattern for the baseline case using
FRDM2012 and constraints from two elemental ratios to match HD222295: Zr/Dy
and Th/Dy. This pattern is the same as in Figure 2. Brown: the same output
results as in the baseline (gray) case, but with the original FRDM2012 output
around $Y_{e}=0.34$ replaced by calculations that use UNEDF0.

##  5 Summary and discussion

HD 222925 is second only to our Solar System for the most complete neutron-
capture-element abundance pattern. Unlike the Sun though, its low metallicity
argues for a single _r_ -process progenitor site that created those elements.
Since HD 222925 represents possibly a new _r_ -process template for metal-poor
stars, the progenitor astrophysical site of its neutron-capture elements could
be the canonical site for _r_ -process-enhanced, metal-poor stars. This goal
was the motivation for the present study: to define and characterize the
canonical _r_ -process site for metal-poor stars as a function of its ejecta
$Y_{e}$ distribution. The model-reconstructed distribution of the $Y_{e}$ of
the ejecta can then hint at what conditions are necessary to reproduce the
elemental abundances in HD 222925, for example, the ratio of wind to dynamical
ejecta for an NSM case.

We found that starting with our baseline two-component, two-ratio model
produced a poor fit to the elemental abundance pattern of HD 222925 between Pd
and Te, where the elemental abundance pattern is uniquely complete. We
attempted to improve the fit by adding more constraints to the model. While
adding additional constraints indeed produced a better elemental fit to this
region, it came at the cost of a highly—artificially—constrained $Y_{e}$
distribution, with a notable gap at $Y_{e}\approx 0.34$. Although a highly
constrained ejecta distribution could explain the origin of the elements in HD
222925, we explore other options to test if the gap is indeed artificial:
perhaps as a result of our simplified astrophysical model or the nuclear
physics basis used for the nucleosynthesis simulations.

Increasing the model complexity by considering a more robust sampling of
astrophysical trajectories did not remove the gap in the $Y_{e}$ distribution.
Neither did changing the fission fragment distribution (with fragment
deposition in the Zr to Te region) mitigate this gap. We found a possible
solution for a case in which the _r_ -process material is ejected in such a
way that it is not reheated by energy from the decay of its own heavy nuclei.
This case argues for a site in which the $Y_{e}$ of the ejecta is correlated
with velocity—a situation in which the third _r_ -process peak could also be
affected by spallation (Wang et al., 2020). Furthermore, a site with low
entropy and no nuclear reheating is exotic in terms of current NSM
simulations. For this site to be the _canonical_ source of _r_ -process
material in metal-poor stars, it would have to be fairly common and/or high-
yield. It is possible that an exotic site like this is indeed the progenitor
of HD 222925 and that this star is not canonical at all. Alternatively, this
exotic site could hint at our limited understanding of NSM ejecta; it could be
that all compact binary mergers have such a low-entropy, high-velocity
component (and little to no $Y_{e}\lesssim 0.18$ ejecta). Either way, further
studies are necessary to explore what conditions (more realistic and physics-
based than our artificial study) can achieve low-entropy ejecta that also
doesn’t undergo nuclear reheating and if an NSM is a viable explanation for HD
222925.

Next, we continued to explore if the gap at $Y_{e}\approx 0.34$ could be an
effect from the underlying nuclear physics mass model instead of requiring an
exotic ejecta distribution to favor conditions that do not overproduce the Pd
to Te region. We found that at $Y_{e}=0.34$, our baseline nuclear mass model,
FRDM2012, overproduces the Pd-Ag-Cd region compared to nearly all other mass
models for the astrophysical conditions we consider. Running a simple test
wherein we replace the $Y_{e}\approx 0.34$ output in the baseline case that
uses FRDM2012 with equivalent calculations that use UNEDF0 resulted in a
better fit to the abundance pattern of HD 222925 without the need for a highly
constrained $Y_{e}$ ejecta distribution. A sensitivity study on the second _r_
-process peak region is necessary to pinpoint which nuclei most affect the Pd,
Ag, and Cd abundances in order to guide studies with next-generation
accelerators such as FRIB. For example, recent work has explored $(\alpha,xn)$
reactions and their effect on observationally derived abundance ratios between
the first and second _r_ -process peaks (Psaltis et al., 2022).

Our main conclusions are as follows:

  * •

A basic attempt to reproduce the abundance pattern of HD 222925 leads to
highly constrained ejecta that suggests at least two _r_ -process progenitor
sites: one that produces light _r_ -process elements with $Z\lesssim 50$ and
one that produces the main _r_ -process pattern with $Z\gtrsim 52$. This
explanation is possible, but unlikely considering the observational variation
between the light and heavy _r_ -process elements does not reflect the
variation expected if these two elemental regions were not co-produced. More
UV observations of _r_ -process-rich, metal-poor stars to determine abundances
in the $46\lesssim Z\lesssim 52$ region are necessary to investigate whether
HD 222925 is indeed typical of its class.

  * •

NSM ejecta with low entropy and high velocity to suppress nuclear reheating
could explain the abundance pattern of HD 222925. Assuming this star and its
elemental origin is representative of metal-poor, _r_ -process-enhanced
stars—and if NSMs are to be considered the primary source of heavy elements at
low metallicities—models of NSMs must accommodate a high-mass component that
can achieve low entropy, free from nuclear reheating.

  * •

One last explanation for the elemental abundances of HD 222925 and the failure
of our models is that we are still limited by our need to use theoretical
nuclear data. New laboratory measurements of nuclear masses and $\beta$-decay
rates near the second _r_ -process peak are essential to guiding the
astrophysical interpretation of our results. For example, our model shows some
success with different nuclear data, possibly rendering the previous two
explanations for HD 222925 moot.

We look forward to advances in observational astronomy, computational
astrophysics, nuclear theory, and nuclear experiment to study the _r_ -process
in light of the new, nearly complete abundance pattern of HD 222925.

We thank Matthew R. Mumpower and Trevor M. Sprouse for their helpful comments
and PRISM support. Support for this work was provided by NASA through the NASA
Hubble Fellowship grant HST-HF2-51481.001 awarded by the Space Telescope
Science Institute, which is operated by the Association of Universities for
Research in Astronomy, Inc., for NASA, under contract NAS5-26555. This work
was partially enabled by the National Science Foundation (NSF) grant No.
PHY-1430152 (Joint Institute for Nuclear Astrophysics Center for the Evolution
of the Elements). IUR acknowledges support from NSF grants AST 1815403, AST
1815767, and AST 2205847; the NASA Astrophysics Data Analysis Program (grant
80NSSC21K0627); and NASA grants HST-GO-15657 and HST-GO-15951 from the Space
Telescope Science Institute. AF acknowledges support from NSF CAREER grant
AST-1255160 and NSF grant AST-1716251. We also acknowledge support from the US
Department of Energy (DOE) under contracts DE-FG02-02ER41216 (GCM), DE-
FG02-95-ER40934 (RS), and LA22-ML-DE-FOA-2440 (GCM, RS). RS and GCM
acknowledge additional support from the NSF under grant No. PHY-2020275
(Network for Neutrinos, Astrophysics, and Symmetries) and the Heising-Simons
foundation under grant No. 2017-228 and the Fission In R-process Elements
(FIRE) topical collaboration in nuclear theory, funded by the DOE.

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