#  Observations of $R$-process Stars in the Milky Way and Dwarf Galaxies
to appear in
Handbook of Nuclear Physics – Part III
Section 15 “Supernovae and Neutron Star Mergers”
by Springer Nature 2022

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 Evolution of the Elements
(JINA), East Lansing, MI 48824, USA

and

Alexander P. Ji

Department of Astronomy & Astrophysics, University of Chicago, 5640 S Ellis
Avenue, Chicago, IL 60637, USA

Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL
60637, USA

Joint Institute for Nuclear Astrophysics–Center for Evolution of the Elements
(JINA), East Lansing, MI 48824, USA

## Abstract

This chapter presents an overview of the recent progress on spectroscopic
observations of metal-poor stars with $r$-process element signatures found in
the Milky Way’s stellar halo and satellite dwarf galaxies. Major empirical
lessons related to the origins of the $r$-process are discussed, including the
universality of the observed $r$-process pattern and deviations from
universality among the light $r$-process elements and actinides. Different
astrophysical sites of the $r$-process based on theoretical expectations are
presented, including common and rare supernovae and neutron star mergers. A
major distinguishing factor between $r$-process sites is their delay time
distribution. The best constraints on the detailed $r$-process pattern come
from Galactic halo $r$-process stars, but these cannot provide information on
the environment of the stars’ birth gas clouds. Studying $r$-process
enrichment within dwarf galaxies can remedy the situation despite the fact
that high-resolution spectroscopic observations of individual stars in these
systems are very difficult to obtain. A general overview of dwarf galaxy
properties and chemical evolution expectations depending on their mass and
star formation duration is provided. The $r$-process trends depend on the
stellar mass and star formation durations of dwarf galaxies in a way that
clearly shows that the $r$-process is rare, prolific, and has both prompt and
delayed sources. This work complements ongoing theoretical heavy-element
nucleosynthesis explorations and experimental measurements of the properties
of $r$-process nuclei, such as with the Facility for Rare Isotope Beams.

##  1 Introduction

Astronomical observations of cosmic objects provide insight into a large range
of physics questions. One central question is that of the origin of the
chemical elements through a variety of nucleosynthesis processes that occur in
stars, supernova explosions, merging neutron stars and other objects.

This chapter presents an overview of recent astronomical observations of heavy
elements associated with $r$-process nucleosynthesis. The $r$-process (short
for “rapid neutron-capture process”) is responsible for synthesizing about
half of the isotopes of elements heavier than iron in the solar system. The
$s$-process (short for “slow neutron-capture process”) is responsible for the
other half. The elements synthesized by these and other nucleosynthetic
processes can be probed by studying the chemical composition of ancient, so-
called “metal-poor” stars. The elements preserved in these objects over
billions of years enable us to study abundance signatures that arose from just
a few (or even one) nucleosynthesis events that occurred prior to the star’s
birth in the early universe. This concept is often referred to as Stellar
Archaeology, and illustrated in Figure 1. Indeed, having the means to
observationally isolate a variety of clean nucleosynthesis signatures, and
interpreting them within the framework of nuclear astrophysics, is vital for
our understanding where and how the chemical elements were synthesized (Frebel
& Norris, 2015).

In this context, it is important to begin with a definition of metal-poor
stars. “Metal” refers in astronomy to all elements heavier than H and He.
“Metal-poor” refers to an amount of all heavy elements that is less than that
of the Sun, our reference star. Effectively that means, that the lower the
overall metallicity, the earlier the star must have formed due to ongoing
chemical enrichment events that only ever add new metals to the universe. With
spectroscopic observations, the chemical composition of stars can be obtained
to determine metallicity and abundances of individual elements. In most cases,
the iron abundance of the star (given as “[Fe/H]” in the bracket notation)
will be used to represent its overall metallicity, and used interchangeably.
Stellar chemical abundances of any two elements are then defined relative to
the respective abundances in the Sun (e.g., Asplund et al. 2009) as
[A/B]$=\log(N_{\rm A}/N_{\rm B})-\log(N_{\rm A}/N_{\rm B})_{\odot}$ where
$N_{\rm{A}}$ ($N_{\rm{B}}$) is the number of atoms of element A (B).
Consequently, the Sun will have a metallicity of $\mbox{[Fe/H]}=0.0$. Stars
with $\mbox{[Fe/H]}<-1.0$ are called “metal-poor” stars. Stars with
$\mbox{[Fe/H]}<-2.0$ are called “very metal-poor” stars. An “extremely metal-
poor” star would have $\mbox{[Fe/H]}<-3.0$, which corresponds to one
thousandth of the solar iron abundance. For better or for worse, the words
“very” and “extremely” have a specific technical meaning when studying metal-
poor stars. For a full classification, see table 1 in Frebel 2018.

Figure 1: Overview of the concepts of stellar and dwarf galaxy archaeology. In
both cases, observations of ancient stars in the Milky Way’s halo as well as
its orbiting dwarf satellite galaxies enable the reconstruction of the
physical and chemical conditions of stellar birth gas clouds present within
the earliest galactic systems that formed soon after the Big Bang as well as
over all of cosmic history. Comparisons with theoretical models allows testing
for specific sources and sites of nucleosynthesis and their effects on their
environment.

For nearly three decades by now, stellar archaeology has been carried out with
a group of rare, old, very and extremely metal-poor stars that display large
relative enhancements in heavy elements associated with the $r$-process. They
are found in the outskirts of the Milky Way, in the Galactic halo (Beers &
Christlieb, 2005; Sneden et al., 2008; Frebel, 2018). Astronomers distinguish
different $r$-process enhancement levels of these stars in the following way.
First, $r$-process stars need to fulfill the criterion of $\mbox{[Ba/Eu]}<0.0$
to ensure their neutron-capture element content does not originate with the
$s$-process. Mildly enhanced $r$-process stars are defined to have
$0.3\leq\mbox{[Eu/Fe]}\leq 0.7$ and are termed $r$-I stars. Strongly enhanced
$r$-process stars have $\mbox{[Eu/Fe]}>0.7$; they are the $r$-II stars. An
earlier definition had the transition from $r$-I to $r$-II at
$\mbox{[Eu/Fe]}=1.0$ but recent works shows a naturally occurring break at 0.7
in the distribution, with about 2/3 of the $r$-process stars having values of
$\mbox{[Eu/Fe]}<0.7$. Finally, the recent discovery of a star with
$\mbox{[Eu/Fe]}=2.3$ (Cain et al., 2020) led to the introduction of $r$-III
stars with exceedingly large Eu abundances of $\mbox{[Eu/Fe]}>+2.0$.

Metal-poor halo stars are thought to originate in small dwarf galaxies that
have been tidally disrupted by the Milky Way (Frebel & Norris, 2015). It was
mostly impossible to associate these halo stars with their birth environments,
but there are also intact dwarf satellite galaxies orbiting the Milky Way at
larger distances. Starting in the 2000s (e.g., Shetrone et al., 2001, 2003;
Koch et al., 2008) the advent of 6-10m diameter telescopes enabled direct
study of the chemical abundances of stars in these dwarf galaxies (see reviews
by Venn et al. 2004; Tolstoy et al. 2009; Frebel & Norris 2015; Simon 2019).
At first, very few stars were discovered with clear $r$-process-enhanced
nucleosynthetic signature outside the stellar halo (in the dwarf galaxy Ursa
Minor and the globular cluster M15; Otsuki et al. 2006; Aoki et al. 2007;
Cohen & Huang 2009).

It thus came as a surprise in 2016 when the dwarf galaxy Reticulum II (Ji et
al., 2016a; Roederer et al., 2016) turned out to be an entire “$r$-process
galaxy” when seven of nine stars observed showed the $r$-process pattern and
enhancement levels among the highest ever found. The existence of such stars
in a known and quantifiable dwarf galaxy environment provided a novel
constraint on the astrophysical production site of the $r$-process. Based on
an estimate for the mass of Reticulum II and together with the enhancement
level observed in the stars, it was concluded that likely a neutron star
merger had occurred to provide copious amounts of $r$-process elements in this
galaxy at very early times. Using entire dwarf galaxies as probes of chemical
enrichment events – and more broadly to constrain the physical and chemical
conditions of early galaxies – significantly builds on Stellar Archaeology,
since the birth environment of dwarf galaxy stars can be estimated and taken
into account. Accordingly, this is referred to as “dwarf galaxy archaeology”
and also shown in Figure 1.

Metal-poor halo stars and dwarf galaxies thus provide complementary ways to
observationally access information about the origin of the $r$-process
elements. Metal-poor halo stars are relatively nearby ($<5$ kpc), so it is
possible to directly study the detailed composition of $r$-process
nucleosynthesis across all the $r$-process peaks. This has led to many
exquisite results and findings, e.g., the universality of the $r$-process,
uranium measurements, actinide boost, second $r$-process peak abundances, that
have driven this line of observational exploration of $r$-process
nucleosynthesis. Dwarf galaxies are distant (30-200 kpc) making it challenging
to obtain stellar spectra from which to determine full $r$-process element
patterns (see Figure 2), but the known birth environment of the stars provides
the opportunity to understand the buildup of $r$-process material over time.
The many dwarf galaxies sample a wide range of formation histories, providing
a way to test the relative contributions of $r$-process sites with different
rates, yields, and delay time distributions. Ultimately, the goal is a unified
picture of the origin of $r$-process elements in the intact dwarf galaxies,
the tidally disrupted dwarf galaxies, and the Milky Way Galaxy itself. This
approach highlights the importance of nuclear astrophysics that brings
together results from astrophysics and nuclear physics in the quest to
understand the $r$-process. The work with $r$-process stars and dwarf galaxies
will thus provide information complementary to results to be obtained from
experimental facilities such as the Facility for Rare Isotope Beams (FRIB).

The rest of this Chapter first describes lessons about $r$-process
nucleosynthesis from Stellar Archaeology (Section 2) with metal-poor halo
stars. The next section briefly discusses different $r$-process sites and how
a primary distinguishing factor is not which elements are made, but when they
are made (Section 3). This motivates studying dwarf galaxies to understand the
$r$-process. General information about dwarf galaxies is reviewed in Section
4, and a discussion of lessons regarding the $r$-process origin from dwarf
galaxies is in Section 5. A summary and the path ahead is discussed in Section
6.

##  2 $R$-process Nucleosynthesis in the Cosmos

Starting in the mid 1990’s, astronomers began to occasionally find metal-poor
stars that would show an unusual, strong enhancement in $r$-process elements.
They would be located in the so-called halo of the Milky Way, depicting the
extensive spherical region that envelopes the Galaxy’s disk. The first such
star (with $\mbox{[Fe/H]}\sim-3.1$) was CS22892-052 (Sneden et al., 1994,
2003)) which eventually became one of the most well-studied metal-poor stars,
certainly in terms of number of elements. An impressive 57 elements were
measured based on high-resolution spectroscopic data taken with ground and
space based telescopes. Soon after, CS31082-001 was found (Cayrel et al.,
2001; Hill et al., 2002), another strongly $r$-process enhanced star which now
also enables Th and U measurement. However, this star appeared to be enhanced
in Th and U relative to other neutron-capture element abundances which lead to
negative values when attempting to age date this star (although the Th/U ratio
did deliver an age of $\sim$14 billion years). The actinide boost phenomenon
was found, leading to even more questions about $r$-process nucleosynthesis,
its astrophysical site, and frequency of occurrence. All these initial
observational findings of metal-poor halo stars enhanced in $r$-process
elements showed without a doubt that the $r$-process operated in the early
universe, and that clean nucleosynthesis signatures could be extracted from
stars through detailed chemical abundance analyses. It opened up a new branch
of nuclear astrophysics by enabling the collection of the observable
fingerprints of this process.

###  2.1 Discovering $R$-process Stars in the Milky Way Halo and their
Abundance Signatures

Astronomers began to systematically search for more metal-poor $r$-process
stars since it had become clear that they are out there – just not in large
numbers. In the early 2000’s, an extensive observational campaign, the HERES
survey (Christlieb et al., 2004; Barklem et al., 2005), was started that would
collect hundreds of so-called snapshot spectra of metal-poor red giants
allowing sifting through many stars to check for the presence of the strong Eu
absorption line at 4129 Å, the most prominent indicator for $r$-process
enhancement. Absorption line strength is temperature dependent where, at fixed
abundance, the cooler red giants will display a stronger, more easily to
detect line than warmer main-sequence star counterparts. Since 2017, the
$R$-Process Alliance (e.g., Sakari et al. 2018; Hansen et al. 2018b; Ezzeddine
et al. 2020; Holmbeck et al. 2020) has continued this work by conducting a
multi-year observational program with telescopes in both the Northern and
Southern hemisphere, with the goal of quadrupling the number of existing
$r$-process enhanced stars. Thus far, more than 2000 candidates have been
observed, of which $\sim$70 are strongly enhanced $r$-process stars with
$\mbox{[Eu/Fe]}>0.7$ discovered by the $R$-Process Alliance.

Detailed chemical abundance studies have by now been carried out for dozens of
$r$-process stars based on high-resolution, high $S/N$ spectra obtained with
telescopes such as the 8 meter ESO/VLT, 6.5 meter Magellan, and 8 meter Subaru
(Christlieb et al., 2004; Honda et al., 2005; Holmbeck et al., 2018; Placco et
al., 2020; Cain et al., 2020). A handful have even been studied with UV
spectra obtained with the Hubble Space Telescope and its STIS and COS
spectrographs to obtain measurements of additional elements with transition
only available in the UV spectral range (Roederer et al., 2012, 2014, 2018b).
The challenge with UV measurements is that stars must be rather bright, fairly
warm with respect to its surface temperature as to produce a larger relative
UV flux, and of course highly enhanced in $r$-process elements.

Figure 2: Portion of spectra of stars with different levels of neutron-capture
element enhancement around the strong Sr, Ba, and Eu absorption lines at 4215
Å, 6141 Å, and 4129 Å, respectively. Top panels: A limited-$r$ halo star (top,
J1812$-$4934), a mildly enhanced $r$-process halo star (middle, J1558$-$1224)
stars, and a strongly $-r$-process enhanced halo star (bottom, J0246$-$1518).
Figure taken from Hansen et al. (2018a). Bottom panels: Two stars from the
ultra-faint dwarf galaxy Reticulum II (Ji et al., 2016a). The top star is a
typical ultra-faint dwarf galaxy star completely lacking neutron-capture
element lines, while the bottom star is a strongly $r$-process enhanced star.
The halo stars were observed with a relatively small 2.5m diameter telescope
in 10-30 min, while the dwarf galaxy stars were observed with a 6.5m diameter
telescope for 1-3 hours. Despite the vast difference in telescope diameter and
exposure time, note the stark difference in signal-to-noise ratio of the
spectra between the halo stars and Reticulum II stars.

###  2.2 How Much $R$-process Material is Found in Old Halo Stars?

As part of the discovery process, candidate stars are identified by the Eu
line to obtain the stars’ Eu-to-Fe ratio. Moderate enhancement, termed $r$-I,
has been originally defined as $0.3<\mbox{[Eu/Fe]}<1.0$ (Beers & Christlieb,
2005) but more recently been changed to $0.3<\mbox{[Eu/Fe]}<0.7$ (Holmbeck et
al., 2020) to better reflect a naturally occurring break in the abundance
distribution. Regardless, $r$-I stars show ratios at least at a factor of 2 or
higher than the Eu/Fe ratio of the Sun. Strong enhancement, termed $r$-II, now
defined as $\mbox{[Eu/Fe]}>0.7$, a factor of at least 5 times higher compared
to the Sun’s ratio. By now, stars with much higher ratios has been found, up
to $\mbox{[Eu/Fe]}\sim 2.3$. Stars with $\mbox{[Eu/Fe]}>2.0$ have been termed
$r$-III stars (Cain et al., 2020; Ezzeddine et al., 2020). This is illustrated
in Figure 3. These $r$-III stars display more than a factor of 100 higher
Eu/Fe ratios than the Sun, providing evidence of significant contributions of
Eu to the stars’ early birth gas clouds, in relation to Fe contributions by
other sources and as compared to the pre-solar nebula’s enrichment history.
The $r$-III stars are especially interesting for setting constraints on the
maximum yield of potential $r$-process sites (e.g., Macias & Ramirez-Ruiz,
2018, 2019; Siegel et al., 2021)

In this context, it is also interesting to look at the “raw” abundance, log
$\epsilon(Eu)$ or [Eu/H] for a more direct comparison to the amount of Eu
present in the Sun (formed $\sim$9.2 billion years after the Big Bang). At
$\mbox{[Fe/H]}\sim-3.1$ and with $\mbox{[Eu/Fe]}\sim 1.5$ (Sneden et al.,
2000), CS22892-052 has still contains a significantly lower total Eu amount
than the Sun of $\mbox{[Eu/H]}\sim-1.6$, or a factor of 40 less than the Sun’s
value. Still, CS22892-052 is called a strongly enhanced $r$-process star
because the Eu amount relative to Fe is so unusual given it’s (supposed) early
formation time as indicated by the low [Fe/H] abundance (probably within the
first billion years or so). Compare this to another star. At
$\mbox{[Fe/H]}\sim-1.5$ and with $\mbox{[Eu/Fe]}\sim 1.3$ (Roederer et al.,
2018b), the $r$-II star HD 222925 has $\mbox{[Eu/H]}\sim-0.2$. This is very
close to the amount of Eu found in the Sun, and in fact the largest Eu amount
discovered in any of the $r$-process stars. Models incorporating $r$-process
nucleosynthesis, chemical evolution and star formation will need to reproduce
not just the observed $r$-process abundance signature of these stars but also
explain their total amounts of Eu and other heavy elements.

Figure 3: Logarithmic [Eu/Fe] and linear Eu-to-Fe ratio (relative to that of
the Sun) plotted against [Fe/H] for various $r$-process enhanced observed by
the $R$-Process Alliance. The adopted boundaries for $r$-I, $r$-II, and
$r$-III stars are shown at $\mbox{[Eu/Fe]}=0.7$ and 2.0. For educational
purposes, the older $r$-I-$r$-II boundary of $\mbox{[Eu/Fe]}=1.0$ that was
based on a smaller dataset is also shown. Data are from (Hansen et al., 2018b;
Sakari et al., 2018; Ezzeddine et al., 2020; Holmbeck et al., 2020). The
$r$-III star J1521$-$3538 is marked separately (Cain et al., 2020). Additional
$r$-II stars can be found in JINAbase (Abohalima & Frebel, 2018).

###  2.3 Frequency of $R$-process Stars in the Galactic Halo

While the Galactic halo contains relatively many ancient metal-poor stars, the
bulk of objects are much younger and metal-rich. This leaves metal-poor stars
to be rare objects that are difficult to identify (Beers & Christlieb, 2005;
Frebel & Norris, 2015). The $r$-process enhanced stars are exceedingly rare
and determining the occurrence rate has not been easy, especially when samples
were still small. For a long time, for stars with $\mbox{[Eu/Fe]}>1.0$, the
rate was about 5% among metal-poor stars with $\mbox{[Fe/H]}<-2.0$ (Barklem et
al., 2005). As of Spring 2022, hundreds of $r$-process are now known spanning
a large range of enhancement levels. Specifically, $r$-II stars with
$\mbox{[Eu/Fe]}>1.0$ found by the $R$-Process Alliance remain at 5% (27
stars), but numbers increase to 12% (70 stars) when taking
$\mbox{[Eu/Fe]}>0.7$ (Hansen et al., 2018a; Sakari et al., 2018; Ezzeddine et
al., 2020; Holmbeck et al., 2020). According to the JINAbase database
(Abohalima & Frebel, 2018) for metal-poor stars, 30 additional stars with
$\mbox{[Eu/Fe]}>1.0$ are known (3%) and 65 stars with $\mbox{[Eu/Fe]}>0.7$
(7%), all for $\mbox{[Fe/H]}<-1.5$. This brings the total of known $r$-process
halo metal-poor stars with $\mbox{[Eu/Fe]}>1.0$ to 57, and 135 with
$\mbox{[Eu/Fe]}>0.7$. Stars with Eu enhancement of $0.3<\mbox{[Eu/Fe]}<0.7$
are much more numerous, about 2-3 times as many of the strongly enhanced
$r$-process stars. Interestingly, no metallicity dependence has been observed
on these fractions (Holmbeck et al., 2020), although it should be noted that
hardly any of these stars have $\mbox{[Fe/H]}<-3.3$.

###  2.4 The Universality of the $R$-process between Barium and Platinum

Ever since the discovery of the first $r$-process star, CS22892-052, it has
been shown repeatedly that the derived abundance pattern of heavy neutron-
capture elements in all these stars shows a universal behavior; that is the
relative $\log\epsilon$(X) abundances (defined as $\log_{10}\epsilon$(X) =
$\log_{10}$($N_{\rm X}$/NH) + 12 $=\mbox{[X/H]}+\log\epsilon_{\odot}$(X)) for
elements barium and above always show the exact same distinct pattern. This is
illustrated in Figure 4 for the metal-poor $r$-process enhanced star HD 222925
(Roederer et al., 2022). For example, two stars with different metallicities
would not share the same level of enrichment (higher metallicity stars tend to
have higher overall abundances including those of neutron-capture abundances)
but they would share the same relative abundance pattern. This allows for
using e.g., the [Ba/Eu] ratio as an indicator for observationally identifying
$r$-process stars given that a value of $\mbox{[Ba/Eu]}=-0.8$ simply refers to
that underlying pattern (Sneden et al., 2008).

Figure 4: $R$-process pattern of the metal-poor red giant star HD 222925 which
has the most complete elemental abundance pattern of directly detected 42
$r$-process elements, based on ground-based and space-based spectroscopic
data. The three elemental $r$-process peaks at $Z\sim 34$, $54$, and $78$
correspond to the isotopic abundance peaks at $A\sim 80$, $130$, and $195$
that originate from the closed neutron shells at $N=28$, $50$, and $82$. The
match to the scaled solar $r$-process pattern is striking in the region from
Ba to Pt. HD 222925 does not appear to be an actinide boost star. Differences,
however, are found for several trans-Fe elements (Ga, Ge, As) and among the
lighter neutron-capture elements close to the second peak. Figure taken from
Roederer et al. (2022).

This universality of the heavy $r$-process elements, in fact, even extends to
the $r$-process residuals of the Sun – stars covering a range of metallicities
from $\mbox{[Fe/H]}\sim-1$ to $-3$ and the Sun show the same relative
abundance pattern despite having vastly different overall levels of heavy
element abundances. Note that the Sun’s $r$-process residual is obtained by
subtracting a theoretically derived $s$-process component from the Sun’s total
chemical abundance pattern (e.g., Goriely, 1999; Sneden et al., 2008; Bisterzo
et al., 2014; Prantzos et al., 2020). This is necessary because the Sun formed
from gas that experienced a variety of nucleosynthesis events over billions of
years, including $s$\- and $r$-process. As such, it is important to remember
that the Sun’s pattern is not a measured quantity as it is the case for the
$r$-process abundances patterns obtained from metal-poor stars. Still, the
universality seems to hold. Overall, the universality implies that no matter
where and when in the universe, the $r$-process production of heavy elements
of barium to the third peak elements appears to remains the same irrespective
of any astrophysical effects.

While the Sun’s $r$-process residual pattern is a derived quantity, it
uniquely has isotope abundances available in addition to element abundances.
As such, it has been the long-standing benchmark star for comparisons with
essentially all observational and theoretical results. However, recently, the
bright star HD 222925 was discovered to be $r$-process-enhanced. Using both
ground and spaced based observations it was possible to measure chemical
abundances of 42 heavy neutron-capture elements from 31 $\leq$ Z $\leq$ 90
(Roederer et al., 2022). This makes HD 222925 the star with the most elements
measured besides the Sun. Going forward, HD 222925 could be used as the
benchmark for all further comparisons related to testing the site of the
$r$-process, especially given the large deviations in the first $r$-process
peak. Table 1 provides multiple different determinations of the solar
$r$-process residual as well as the measurements of HD 222925 (Prantzos et
al., 2020; Roederer et al., 2022).

###  2.5 Variations of Light Neutron-Capture Element Abundance

The behavior of the lighter neutron-capture elements, from strontium to
barium, is not a universal pattern unlike what is found for the heavy
$r$-process elements. Instead, significant variations, of over a factor of 10,
are found in the ratio of these first $r$-process peak elements relative to
the universal pattern occurring above barium in $r$-process enhanced stars
(e.g., Sneden et al., 2008; Ji et al., 2016b; Ji & Frebel, 2018). This
behavior is shown in Figure 5, which displays the stellar $r$-process
residuals derived from subtracting off the solar $r$-process residuals (Burris
et al., 2000) from the stellar $\log\epsilon$(X) abundances. It can clearly be
seen that the scaled light neutron-capture element abundances (Sr, Y, Zr) vary
from being significantly lower than the bulk of the scaled heavy-element
pattern for some stars, to being much higher in other stars. In other words,
there is substantial scatter in the observed [Sr/Eu] ratio, where Sr and Eu
are representative elements for the light and heavy $r$-process elements,
respectively. Note that it is important to keep in mind that the benchmark for
comparisons, especially with theoretical predictions, has been the Sun’s
residual $r$-process pattern – but the body of metal-poor stellar data does in
fact not agree with the Sun among the lighter neutron-capture elements.

Figure 5: Residuals of stellar $r$-process element abundances subtracted from
the solar $r$-process pattern (Burris et al., 2000), for a variety of
$r$-process enhanced ($r$-II) stars in the halo, the brightest star in the
$r$-process dwarf galaxy Reticulum II (Ji & Frebel, 2018), and the $r$-process
star HD 222925 (Roederer et al., 2022). The residuals are calculated to
minimize the absolute deviation for $56\leq Z\leq 66$ (see Ji et al. 2016b).
The universality of the $r$-process is reflected in the small amount of
scatter of elements Ba to Yb, and when measurable in HD 222925 it extends up
to elements like Ir and Pt. On the contrary, the lighter neutron-capture
elements Sr, Y, and Z show significant variations compared to the solar
$r$-process pattern, with both higher and lower values. Variations in Th are
also relatively large and representative of the actinide boost and deficiency
phenomenon. Figure adapted and updated from Ji et al. (2016b).

There are at least two possible explanations for the observed variations in
the observed scatter among light neutron-capture element abundances. First,
the variation could result from the combination of two independent
astrophysical sites, each producing a characteristic but stable abundance
pattern in the first peak regime (e.g., Travaglio et al., 2004; Honda et al.,
2007; Montes et al., 2007; Siqueira Mello et al., 2014; Shibagaki et al.,
2016). Alternatively, the variation could be due to intrinsic variability in
$r$-process composition and yield within one astrophysical site, as is
commonly expected in theoretical calculations (e.g., Wanajo et al., 2014; Just
et al., 2015; Nishimura et al., 2015; Radice et al., 2016; Wu et al., 2016).
Mapping out these variations with more first peak elements in more $r$-process
enhanced stars is ultimately needed to gain a more complete picture of light
neutron-capture element production through the $r$-process.

An interesting future point of comparison could be multi-messenger
astrophysics, where the ratio of light to heavy $r$-process elements can be
observed directly through measuring detailed light curves of explosive
transients (Kilpatrick et al., 2017; Chornock et al., 2017; Tanaka et al.,
2017; Tanvir et al., 2017). Already, the one neutron star merger detected in
gravitational waves, GW170817, whose electromagnetic counterpart was observed
with telescopes has a composition inconsistent with the strongly enhanced
$r$-II stars (Ji et al., 2019a).

###  2.6 Actinide Element Variations and Nucleocosmochronometry

The measured abundances of the actinide elements, thorium and uranium, are
dominated by long-lived radioactive isotopes that decay over cosmic
timescales. The species 238U and 232Th have half-lives of 4.5 and 14 billion
years, respectively. Assuming metal-poor stars to be older than the Sun then
implies that the actinide abundances would be lower than the Sun’s values
compared to a stable heavy element such as Eu. This behavior principally
offers a way to age date old stars via this “cosmo-chronometry”, as long as
initial production ratios (yields) of the progenitor $r$-process are known and
reflective of the stars birth environment and conditions. This has so far
proven very challenging despite site-independent yield calculations (Schatz et
al., 2002; Hill et al., 2017) that have been utilized to age date a number of
metal-poor $r$-process stars (Cayrel et al., 2001; Frebel et al., 2007; Placco
et al., 2017). Another challenge is related to observational uncertainties
that quickly result in very large age uncertainties. Observational Th and U
measurements are very difficult to achieve for a variety of reasons (e.g.,
requiring strong lines, a very high resolution, very high signal-to-noise
spectrum, low stellar carbon abundance) but even reasonable uncertainties will
result in several billion year age uncertainty showing once again how
difficult cosmo-chronometry is observationally alone. Uncertainties in initial
production ratios, easily a multiple of the observed uncertainties, add to
this issue. See also Frebel (2018) for further details.

To complicate matters further, about a quarter of metal-poor star with
measurable Th (and U) abundances show a different behavior – their actinide
abundance are higher than those of the Sun’s pattern (Holmbeck et al., 2018).
This is illustrated in Figure 5. This phenomenon has been termed the “actinide
boost”. This additional amount of actinides must come from a second and/or
separate $r$-process or component that either occurred at a later time than
the main/first event, or there must be significant variations in actinide
production across $r$-processes and sites, perhaps due to fission cycling or
other environmentally driven details (Holmbeck et al., 2019). It has also been
found in a few individual stars in dwarf galaxies that there are actinide
deficient stars, with surprisingly low Th/Eu ratios (Ji & Frebel, 2018; Hansen
et al., 2021).

Generally, it would be of particular interest to measure actinide abundances
in dwarf galaxy stars and star clusters, as one can obtain independent age
measurements of these stellar systems from low-mass stellar evolution models.
This would provide one way forward to calibrate $r$-process yield and site
predictions in combination with an understanding of the gas mixing mass
involved. So far, thorium has been measured in a number of stars in several
dwarf galaxies: Reticulum II (Ji & Frebel, 2018), Ursa Minor (Aoki et al.,
2007), Fornax (Reichert et al., 2021), Sagittarius (Hansen et al., 2020), and
the disrupted dwarf galaxy Indus (Hansen et al., 2021). However, uranium
measurements will remain inaccessible due to the weakness of the strongest U
line at 3859 Å. The ages from cosmo-chronometry are consistent with the ages
of the dwarf galaxies, but the large uncertainties from cosmo-chronometry make
this comparison currently, unfortunately, fairly meaningless (Aoki et al.,
2007).

Z | El | L09 | G99 | S08 | B14 | P20 | R22
---|---|---|---|---|---|---|---
|  |  $\log\epsilon$(X)⊙ | $s$ | $r$ | [X/Eu] | $s$ | $r$ | [X/Eu] | $s$ | $r$ | [X/Eu] | $s$ | $r$ | [X/Eu] | $r$ | [X/Eu]
31 | Ga | $3.07$ | $2.96$ | $2.42$ | $-0.64$ | $2.83$ | $2.71$ | $-0.36$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | $2.93$ | $2.51$ | $-0.54$ | $1.26$ | $-1.69$
32 | Ge | $3.57$ | $3.41$ | $3.05$ | $-0.50$ | $3.29$ | $3.24$ | $-0.32$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | $3.37$ | $3.13$ | $-0.42$ | $1.46$ | $-1.99$
33 | As | $2.30$ | $1.88$ | $2.09$ | $-0.19$ | $1.63$ | $2.19$ | $-0.10$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | $2.06$ | $1.92$ | $-0.36$ | $1.01$ | $-1.16$
34 | Se | $3.34$ | $2.97$ | $3.09$ | $-0.23$ | $2.89$ | $3.14$ | $-0.19$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | $2.91$ | $3.13$ | $-0.18$ | $2.62$ | $-0.59$
35 | Br | $2.54$ | $1.77$ | $2.46$ | $-0.06$ | $1.53$ | $2.50$ | $-0.04$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | $1.96$ | $2.41$ | $-0.11$ |  $\cdots$ |  $\cdots$
36 | Kr | $3.26$ | $2.95$ | $2.96$ | $-0.28$ | $3.00$ | $2.91$ | $-0.34$ | $2.40$ | $3.19$ | $-0.04$ | $2.88$ | $3.02$ | $-0.21$ |  $\cdots$ |  $\cdots$
37 | Rb | $2.37$ | $2.12$ | $2.01$ | $-0.34$ | $1.99$ | $2.13$ | $-0.23$ | $1.63$ | $2.28$ | $-0.06$ | $2.08$ | $2.06$ | $-0.29$ |  $\cdots$ |  $\cdots$
38 | Sr | $2.87$ | $2.79$ | $2.12$ | $-0.73$ | $2.82$ | $1.91$ | $-0.95$ | $2.71$ | $2.36$ | $-0.48$ | $2.84$ | $1.78$ | $-1.07$ | $1.98$ | $-0.77$
39 | Y | $2.18$ | $2.06$ | $1.56$ | $-0.60$ | $2.03$ | $1.62$ | $-0.54$ | $2.03$ | $1.62$ | $-0.52$ | $2.07$ | $1.52$ | $-0.63$ | $1.04$ | $-1.01$
40 | Zr | $2.54$ | $2.41$ | $1.97$ | $-0.56$ | $2.45$ | $1.82$ | $-0.71$ | $2.36$ | $2.07$ | $-0.45$ | $2.46$ | $1.80$ | $-0.72$ | $1.74$ | $-0.68$
41 | Nb | $1.40$ | $1.34$ | $0.51$ | $-0.88$ | $1.23$ | $0.91$ | $-0.48$ | $1.15$ | $1.05$ | $-0.33$ | $1.22$ | $0.94$ | $-0.44$ | $0.71$ | $-0.57$
42 | Mo | $1.80$ | $1.66$ | $1.23$ | $-0.56$ | $1.62$ | $1.32$ | $-0.47$ | $1.50$ | $1.49$ | $-0.28$ | $1.61$ | $1.34$ | $-0.44$ | $1.36$ | $-0.32$
44 | Ru | $1.73$ | $1.26$ | $1.55$ | $-0.16$ | $1.28$ | $1.54$ | $-0.18$ | $1.22$ | $1.56$ | $-0.14$ | $1.30$ | $1.53$ | $-0.18$ | $1.32$ | $-0.28$
45 | Rh | $1.08$ | $0.37$ | $0.98$ | $-0.08$ | $0.28$ | $1.00$ | $-0.07$ | $0.15$ | $1.02$ | $-0.03$ | $0.16$ | $1.02$ | $-0.03$ | $0.64$ | $-0.31$
46 | Pd | $1.64$ | $1.31$ | $1.36$ | $-0.26$ | $1.28$ | $1.39$ | $-0.24$ | $1.20$ | $1.44$ | $-0.17$ | $1.30$ | $1.37$ | $-0.24$ | $1.05$ | $-0.46$
47 | Ag | $1.20$ | $0.54$ | $1.09$ | $-0.09$ | $0.53$ | $1.10$ | $-0.09$ | $0.24$ | $1.15$ | $-0.02$ | $0.52$ | $1.10$ | $-0.08$ | $0.44$ | $-0.64$
48 | Cd | $1.70$ | $1.42$ | $1.37$ | $-0.31$ | $1.41$ | $1.38$ | $-0.30$ | $1.37$ | $1.42$ | $-0.25$ | $1.45$ | $1.33$ | $-0.34$ | $0.34$ | $-1.23$
49 | In | $0.74$ | $0.28$ | $0.56$ | $-0.17$ | $0.25$ | $0.57$ | $-0.16$ | $0.21$ | $0.59$ | $-0.13$ | $0.33$ | $0.53$ | $-0.19$ | $0.51$ | $-0.11$
50 | Sn | $2.06$ | $1.89$ | $1.57$ | $-0.47$ | $1.94$ | $1.42$ | $-0.63$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | $1.91$ | $1.52$ | $-0.52$ | $1.39$ | $-0.55$
51 | Sb | $1.01$ | $0.58$ | $0.80$ | $-0.19$ | $0.23$ | $0.93$ | $-0.07$ | $0.30$ | $0.91$ | $-0.07$ | $0.40$ | $0.88$ | $-0.10$ | $0.37$ | $-0.51$
52 | Te | $2.18$ | $1.46$ | $2.09$ | $-0.07$ | $1.46$ | $2.09$ | $-0.08$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | $1.49$ | $2.08$ | $-0.08$ | $1.63$ | $-0.43$
53 | I | $1.55$ | $0.91$ | $1.44$ | $-0.10$ | $0.29$ | $1.53$ | $-0.02$ | $0.13$ | $1.53$ | $0.01$ | $0.06$ | $1.54$ | $0.01$ |  $\cdots$ |  $\cdots$
54 | Xe | $2.25$ | $1.85$ | $2.02$ | $-0.20$ | $1.55$ | $2.15$ | $-0.09$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | $1.51$ | $2.16$ | $-0.07$ |  $\cdots$ |  $\cdots$
55 | Cs | $1.08$ | $0.30$ | $1.00$ | $-0.06$ | $0.26$ | $1.01$ | $-0.06$ | $0.21$ | $1.02$ | $-0.04$ | $0.28$ | $1.01$ | $-0.05$ |  $\cdots$ |  $\cdots$
56 | Ba | $2.16$ | $2.09$ | $1.31$ | $-0.83$ | $2.09$ | $1.32$ | $-0.83$ | $2.09$ | $1.32$ | $-0.81$ | $2.11$ | $1.23$ | $-0.90$ | $1.26$ | $-0.78$
57 | La | $1.17$ | $0.99$ | $0.71$ | $-0.45$ | $1.05$ | $0.56$ | $-0.60$ | $1.05$ | $0.56$ | $-0.58$ | $1.07$ | $0.47$ | $-0.68$ | $0.51$ | $-0.54$
58 | Ce | $1.58$ | $1.49$ | $0.86$ | $-0.70$ | $1.49$ | $0.86$ | $-0.71$ | $1.50$ | $0.79$ | $-0.77$ | $1.51$ | $0.77$ | $-0.79$ | $0.85$ | $-0.61$
59 | Pr | $0.75$ | $0.30$ | $0.55$ | $-0.18$ | $0.44$ | $0.45$ | $-0.28$ | $0.44$ | $0.45$ | $-0.27$ | $0.47$ | $0.41$ | $-0.31$ | $0.22$ | $-0.40$
60 | Nd | $1.44$ | $1.20$ | $1.08$ | $-0.35$ | $1.20$ | $1.07$ | $-0.36$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | $1.22$ | $1.04$ | $-0.38$ | $0.88$ | $-0.44$
62 | Sm | $0.92$ | $0.39$ | $0.77$ | $-0.14$ | $0.40$ | $0.77$ | $-0.14$ | $0.44$ | $0.75$ | $-0.14$ | $0.44$ | $0.75$ | $-0.15$ | $0.62$ | $-0.18$
63 | Eu | $0.50$ | $-0.91$ | $0.49$ | $0.00$ | $-1.18$ | $0.49$ | $0.00$ | $-0.72$ | $0.48$ | $0.00$ | $-0.81$ | $0.48$ | $0.00$ | $0.38$ | $0.00$
64 | Gd | $1.07$ | $0.37$ | $0.97$ | $-0.08$ | $0.31$ | $0.98$ | $-0.07$ | $0.25$ | $0.99$ | $-0.04$ | $0.29$ | $0.98$ | $-0.06$ | $0.82$ | $-0.12$
65 | Tb | $0.31$ | $-0.97$ | $0.29$ | $-0.01$ | $-0.89$ | $0.28$ | $-0.02$ | $-0.78$ | $0.28$ | $-0.01$ | $-0.83$ | $0.28$ | $-0.01$ | $0.18$ | $-0.01$
66 | Dy | $1.12$ | $0.10$ | $1.07$ | $-0.03$ | $0.19$ | $1.06$ | $-0.05$ | $0.29$ | $1.05$ | $-0.04$ | $0.30$ | $1.04$ | $-0.05$ | $1.01$ | $0.02$
67 | Ho | $0.47$ | $-0.64$ | $0.43$ | $-0.02$ | $-0.70$ | $0.44$ | $-0.02$ | $-0.61$ | $0.43$ | $-0.01$ | $-0.66$ | $0.44$ | $-0.01$ | $0.12$ | $-0.23$
68 | Er | $0.92$ | $0.12$ | $0.85$ | $-0.06$ | $0.11$ | $0.85$ | $-0.06$ | $0.19$ | $0.83$ | $-0.06$ | $0.19$ | $0.83$ | $-0.07$ | $0.73$ | $-0.07$
69 | Tm | $0.12$ | $-0.67$ | $0.04$ | $-0.06$ | $-0.67$ | $0.04$ | $-0.07$ | $-0.92$ | $0.08$ | $-0.01$ | $-0.77$ | $0.06$ | $-0.04$ | $-0.09$ | $-0.09$
70 | Yb | $0.92$ | $0.46$ | $0.73$ | $-0.17$ | $0.42$ | $0.75$ | $-0.16$ | $0.53$ | $0.69$ | $-0.20$ | $0.55$ | $0.68$ | $-0.22$ | $0.55$ | $-0.24$
71 | Lu | $0.09$ | $-0.61$ | $-0.01$ | $-0.08$ | $-0.64$ | $0.00$ | $-0.08$ | $-0.59$ | $-0.01$ | $-0.07$ | $-0.61$ | $-0.01$ | $-0.08$ | $-0.04$ | $-0.01$
72 | Hf | $0.71$ | $0.45$ | $0.36$ | $-0.33$ | $0.39$ | $0.43$ | $-0.27$ | $0.49$ | $0.31$ | $-0.38$ | $0.48$ | $0.32$ | $-0.37$ | $0.32$ | $-0.27$
73 | Ta | $-0.17$ | $-0.47$ | $-0.46$ | $-0.28$ | $-0.56$ | $-0.40$ | $-0.22$ | $-0.50$ | $-0.44$ | $-0.25$ | $-0.47$ | $-0.47$ | $-0.28$ |  $\cdots$ |  $\cdots$
74 | W | $0.65$ | $0.42$ | $0.25$ | $-0.38$ | $0.37$ | $0.32$ | $-0.32$ | $0.44$ | $0.23$ | $-0.39$ | $0.43$ | $0.25$ | $-0.38$ | $0.02$ | $-0.50$
75 | Re | $0.27$ | $-0.44$ | $0.18$ | $-0.08$ | $-0.74$ | $0.23$ | $-0.04$ | $-0.53$ | $0.20$ | $-0.05$ | $-0.54$ | $0.20$ | $-0.05$ | $0.16$ | $0.01$
76 | Os | $1.34$ | $0.40$ | $1.29$ | $-0.04$ | $0.28$ | $1.30$ | $-0.03$ | $0.42$ | $1.29$ | $-0.03$ | $0.35$ | $1.29$ | $-0.03$ | $1.17$ | $-0.05$
77 | Ir | $1.34$ | $0.24$ | $1.30$ | $-0.02$ | $-0.59$ | $1.33$ | $0.00$ | $-0.46$ | $1.33$ | $0.02$ | $-0.61$ | $1.33$ | $0.02$ | $1.28$ | $0.07$
78 | Pt | $1.62$ | $-0.01$ | $1.60$ | $0.01$ | $0.33$ | $1.59$ | $-0.01$ | $0.40$ | $1.59$ | $-0.00$ | $0.51$ | $1.58$ | $-0.01$ | $1.45$ | $-0.04$
79 | Au | $0.80$ | $-0.88$ | $0.79$ | $0.01$ | $-0.47$ | $0.78$ | $-0.01$ | $-0.41$ | $0.77$ | $-0.00$ | $-0.44$ | $0.77$ | $-0.00$ | $0.53$ | $-0.15$
80 | Hg | $1.17$ | $0.98$ | $0.72$ | $-0.43$ | $0.93$ | $0.80$ | $-0.36$ | $0.88$ | $0.86$ | $-0.28$ | $0.92$ | $0.82$ | $-0.33$ |  $\cdots$ |  $\cdots$
81 | Tl | $0.77$ | $0.62$ | $0.23$ | $-0.52$ | $0.58$ | $0.32$ | $-0.44$ | $0.62$ | $0.24$ | $-0.51$ | $0.65$ | $0.15$ | $-0.60$ |  $\cdots$ |  $\cdots$
82 | Pb | $2.03$ | $1.98$ | $1.04$ | $-0.97$ | $1.93$ | $1.36$ | $-0.66$ | $1.97$ | $1.14$ | $-0.87$ | $1.95$ | $1.25$ | $-0.76$ | $1.14$ | $-0.77$
83 | Bi | $0.65$ | $0.45$ | $0.21$ | $-0.42$ | $0.20$ | $0.46$ | $-0.18$ | $-0.04$ | $0.55$ | $-0.07$ | $-0.02$ | $0.54$ | $-0.08$ |  $\cdots$ |  $\cdots$
90 | Th | $0.15$ |  $\cdots$ | $0.15$ | $0.02$ |  $\cdots$ | $0.15$ | $0.01$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | $0.15$ | $0.02$ | $-0.06$ | $-0.09$
92 | U | $-0.11$ |  $\cdots$ | $-0.11$ | $0.02$ |  $\cdots$ | $-0.11$ | $0.01$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | $-0.11$ | $0.02$ |  $\cdots$ |  $\cdots$
Table 1: Solar patterns for $s$-process and $r$-process from Goriely (1999)
(G99), Sneden et al. (2008) (S08), Bisterzo et al. (2014) (B14), and Prantzos
et al. (2020) (P20); along with the $r$-process pattern for HD 222925 from
Roederer et al. (2022) (R22). The solar abundance is adopted from Lodders et
al. (2009) meteoritic abundances (L09) but renormalized to $\log\epsilon$(X)
units using the Asplund et al. (2009) solar silicon abundance of
$\log\epsilon$(Si)${}_{\odot}=7.51$. The offset is because meteoritic
abundances are normalized to N(Si)$=6$ while the spectroscopist’s
$\log\epsilon$(X) values are normalized to N(H)$=12$. The $s$ and $r$ columns
are also given in $\log\epsilon$(X) units, while the [X/Eu] column indicates
the abundance of each element relative to solar in standard spectroscopist’s
notation. Note that even [Ba/Eu]r varies from $-0.78$ to $-0.90$ across these
five different $r$-process patterns despite using the same overall solar
isotopic abundance, which emphasizes the model-dependence of the solar
$r$-process residual.

##  3 Candidate Astrophysical Sites of the $r$-process

The fundamental question at hand is about the origin of heavy elements
synthesized in the rapid neutron-capture elements: What are possible
astrophysical sites, and what is their relative importance over cosmic
history? A number of sites have been proposed theoretically to explain the
operation of the $r$-process. Since $r$-process nucleosynthesis requires a
very high density of free neutrons, it can essentially only happen in events
associated with the birth and death of compact neutron stars.

Conditions for an $r$-process to operate must include a high neutron-to-seed
ratio. The most important quantity for describing the neutron-to-seed ratio is
the electron fraction $Y_{e}=n_{e}/n$. Since the ejecta is net neutral,
$Y_{e}$ is equal to the fraction of protons, and $1-Y_{e}$ is the fraction of
neutrons. Thus, a lower $Y_{e}$ means that the ejecta will be more neutron-
rich. A broad rule of thumb about $r$-process nucleosynthesis calculations is
that an electron fraction of $Y_{e}>0.25$ would result in the build up of
elements of the first peak region, $0.10<Y_{e}<0.25$ would lead to elements
partaking in the universal $r$-process pattern between the second and third
$r$-process peak as well as some actinide elements, and $Y_{e}<0.10$ would be
especially responsible for the production of the actinide elements (e.g.,
Lippuner & Roberts, 2015; Wu et al., 2016; Holmbeck et al., 2019). However,
there are many exceptions to this general rule due to the exact thermodynamic
properties of the ejecta (e.g., Farouqi et al., 2010; Wanajo et al., 2014;
Mumpower et al., 2016; Curtis et al., 2021). Note that when discussing the
origin of $r$-process elements, most people implicitly assume the question
concerns solely the origin of $r$-process elements beyond the second
$r$-process peak: The rare earth elements, the third $r$-process peak, and the
actinides. Focus on these heavier elements stems from the fact that elements
in the first $r$-process peak can also be produced in a much larger variety of
ways, such as the weak $s$-process or $\nu p$ process (Sukhbold et al., 2016;
Fröhlich et al., 2006).

Here, three broad categories of the most commonly invoked astrophysical sites
for the $r$-process to occur are considered (Cowan et al., 2021): Common core-
collapse supernovae (more than 1-10%), e.g., in neutrino-driven winds (e.g.,
Woosley & Hoffman, 1992; Woosley et al., 1994; Farouqi et al., 2010; Arcones &
Montes, 2011) or during electron-capture supernovae (Ning et al., 2007; Janka
et al., 2008; Wanajo et al., 2011); rare core-collapse supernovae (less than
1% occurrence rate), such as in magnetorotationally driven jets (Winteler et
al., 2012; Nishimura et al., 2015, 2017; Mösta et al., 2018) or in collapsar
disk winds (Pruet et al., 2004; Surman et al., 2011; Siegel et al., 2019;
Miller et al., 2020); and binary neutron star mergers, including both neutron
star-neutron star pairs and black hole-neutron star mergers (e.g., Lattimer &
Schramm, 1974, 1976; Lattimer et al., 1977; Surman et al., 2008; Hotokezaka et
al., 2013; Goriely et al., 2011, 2013; Rosswog et al., 2014; Wanajo et al.,
2014; Eichler et al., 2015; Just et al., 2015; Wu et al., 2016; Lippuner et
al., 2017; Curtis et al., 2021).

Below is a brief summary of the results of theoretical studies on four major
questions: How often does it occur – what is the event rate? How quickly does
it happen after star formation – what is the delay time distribution? How much
$r$-process material is made – What is the event yield? and What is the
distribution of elements made – What is the $r$-process composition?

###  3.1 Common core-collapse supernovae

Since Burbidge et al. (1957), core-collapse supernovae have been regarded as a
promising site for $r$-process nucleosynthesis. But it has also been clear
since McWilliam (1998) that supernovae could not all produce the same amount
of $r$-process elements. Yet a specific range of stellar masses, upon their
explosion, could principally be able to produce all the $r$-process elements
through the second and third peak. This would imply the operation of
$r$-process nucleosynthesis in a relatively large fraction (1-10%) of core-
collapse supernovae (e.g., Wanajo & Ishimaru, 2006).

Hypothetical mechanisms for producing the full slew of the $r$-process
elements include neutrino-driven winds emanating from the proto-neutron star
(e.g., Takahashi et al., 1994; Woosley & Hoffman, 1992; Woosley et al., 1994;
Qian & Woosley, 1996; Farouqi et al., 2010) and electron-capture supernovae of
$8-10M_{\odot}$ stars (e.g., Ning et al., 2007; Janka et al., 2008; Wanajo et
al., 2006). Due to the short lifetimes of their progenitor stars, these common
core-collapse supernovae would produce a small amount of $r$-process elements
essentially immediately after an episode of star formation from which they
originated. However, modern calculations show that these mechanisms tend not
to produce a full $r$-process, though they can produce a limited (weak)
$r$-process up to the first $r$-process peak (e.g., Arcones et al., 2007;
Arcones & Montes, 2011; Wanajo et al., 2011). Thus, theoretically such sites
are disfavored as the source of the heaviest $r$-process elements.

Note that there is evidence that such a limited $r$-process (also often called
the light element primary process, Travaglio et al. 2004; Montes et al. 2007;
Hansen et al. 2012) does exist in nature. A group of metal-poor stars, now
termed limited $r$-process stars (e.g., Frebel 2018; Hansen et al. 2018a),
qualitatively shows this type of abundance drop-off with increasing atomic
number, as expected for a limited (weak) $r$-process (Honda et al., 2004,
2007). Following the abundance definition for these limited-$r$ stars, they
need to fulfill $\mbox{[Eu/Fe]}<0.3$, $\mbox{[Sr/Ba]}>0.5$, and
$\mbox{[Sr/Eu]}>0.0$.

###  3.2 Rare core-collapse supernovae

Given the difficulties of the common core-collapse supernovae to produce a
full $r$-process, contemporary models of $r$-process nucleosynthesis in core-
collapse supernovae invoke extreme physical conditions that may occur rarely,
in less than 1% of core-collapse supernova explosions (if physical indeed).
Currently, the most popular models are collapsar disk winds (Pruet et al.,
2004; Surman et al., 2011; Siegel et al., 2019; Miller et al., 2020) and
magnetorotationally driven jet supernovae (Winteler et al., 2012; Nishimura et
al., 2015; Mösta et al., 2018; Halevi & Mösta, 2018), which both involve high
magnetic fields and very rapid rotation. Note these two mechanisms are not
mutually exclusive, and in principle both could happen in the same supernova.
Like the common core-collapse supernovae, it is currently rather uncertain
whether these rare core-collapse supernovae are even capable of synthesizing
the heaviest $r$-process elements, due to the complex physics involved (e.g.
neutrino transport, radiation magnetohydrodynamics, general relativity).
However, if suitable conditions for $r$-process production can be achieved,
the $r$-process yields can be relatively high ($0.01-1M_{\odot}$) and they
would also occur promptly after star formation due to the short lives of the
progenitors.

###  3.3 Neutron star mergers

Neutron star mergers result from the inspiraling of two compact objects that
have been orbiting each other and losing energy through gravitational waves.
The two subclasses are binary neutron star mergers (BNS) and black hole-
neutron star mergers (BHNS). The gravitational wave event GW170817 and its
associated electromagnetic kilonova counterpart AT2017gfo (Abbott et al.,
2017a, b) have provided conclusive evidence that binary neutron star mergers
can produce heavy $r$-process elements (Arcavi et al., 2017; Chornock et al.,
2017; Coulter et al., 2017; Cowperthwaite et al., 2017; Drout et al., 2017;
Evans et al., 2017; Kasliwal et al., 2017; Kilpatrick et al., 2017; McCully et
al., 2017; Nicholl et al., 2017; Pian et al., 2017; Shappee et al., 2017;
Smartt et al., 2017; Tanvir et al., 2017; Troja et al., 2017). This event
remains the only direct observation of $r$-process nucleosynthesis in the
cosmos, though only one individual element (strontium) was identified (Watson
et al., 2019). These neutron star mergers produce a moderately high amount of
$r$-process ($\sim 0.01M_{\odot}$) material, and it is expected that they will
produce a variable ratio of light and heavy $r$-process elements (e.g., Wu et
al., 2016; Lippuner et al., 2017; Ji et al., 2019a). Due to the time needed to
inspiral due to a continued loss of energy through gravitational radiation,
the actual merger events are expected to be delayed relative to star formation
episode that created their massive progenitor stars (e.g., Dominik et al.,
2012). Additionally, binary neutron stars can experience a substantial
velocity kick of a few hundred km/s during the formation of each of the
neutron stars (e.g., Willems & Kalogera, 2004; Dominik et al., 2012; Fong &
Berger, 2013; Beniamini et al., 2016a; Bramante & Linden, 2016).

While neutron star mergers are the only definite source of $r$-process
elements, it is still not clear how important they might be for the buildup of
$r$-process elements in the Galaxy, and in particular, for understanding the
composition of stars like our Sun. Reasons include that the delayed
$r$-process production may well occur only after most stars in a galaxy have
already formed, and/or that the enrichment in $r$-process elements may occur
far away from the original star-forming regions if the system experienced
strong velocity kicks.

One other important caveat is that there is currently significant debate about
how quickly neutron stars can actually merge. Most expectations are that a
typical merging time is distributed as $t_{\rm merge}\propto t^{-1}$ with a
minimum delay time of 10-100 Myr (e.g., Dominik et al., 2012; Belczynski et
al., 2018; Chruslinska et al., 2018; Neijssel et al., 2019), but several
authors have argued that a substantial fraction of neutron star binaries
should merge much faster, on the order of 1 Myr after both supernovae in the
binary system have exploded (e.g., Beniamini & Piran, 2019; Safarzadeh et al.,
2019).

###  3.4 Distinguishing factors

Comparing these three classes of sites, common core-collapse supernovae are
theoretically disfavored due to their inability to synthesize the heavy
$r$-process elements (as well as observationally ruled out by dwarf galaxies;
Section 5.1). The other two classes, rare core-collapse supernovae and neutron
star mergers, have very similar event rates and $r$-process yields. These rare
events have very few observational constraints, and if indeed physically
occurring in the universe, they operate under extreme multi-physics
circumstances. Given significant theoretical uncertainties in the predicted
electron fraction distributions, the uncertainties in nuclear experimental
data along the $r$-process path, and few direct observational constraints,
both of the rare $r$-process production sites should currently be considered
as able to reproduce the typical $r$-process pattern, certainly for elements
barium and above. Additional differences may be present on an isotopic level
but that unfortunately cannot be constrained with observations of metal-poor
stars.

Thus, the primary available distinguishing factor between rare core-collapse
supernovae and neutron star mergers as the primary source of $r$-process
elements in the universe is the _delay time distribution_ , i.e. how long it
takes after a burst of star formation in a given system for $r$-process
elements to be synthesized. Delay times for core-collapse supernovae are
simply the lifetimes of massive stars, which are extremely short (or
“prompt”), $10-20$ Myr. Delay times for neutron star mergers are typically
extended (or “delayed”), ranging from ${\sim}30$ Myr to several Gyr (e.g.,
Belczynski et al., 2018; Neijssel et al., 2019). The existence of $r$-process
enhanced metal-poor stars thus traditionally led astronomers to prefer a
prompt enrichment channel, such as core-collapse supernovae as the origin of
$r$-process elements (e.g., Qian, 2000; Argast et al., 2004; Wanajo &
Ishimaru, 2006).

However, it is important to recall that inferring the delay time distribution
is not independent of the astrophysical context in which an $r$-process event
occurs. As the most obvious example, the correspondence between metallicity
and time (often called the age-metallicity relation) varies substantially
depending on the mass of a galaxy that a star forms in (e.g., Ishimaru et al.,
2015; Ji et al., 2016a). Stars forming in low mass galaxies take much longer
to reach a level of even [Fe/H] $=-3$ compared to stars forming in high mass
galaxies. Furthermore, the detailed dynamics of how metals from an explosive
event mix into the surrounding interstellar gas (“metal mixing”) can introduce
inhomogeneities, such that coeval stars have in fact a range of metallicities,
or conversely, that a single metallicity corresponds to a range of ages (e.g.,
Webster et al., 2014; Emerick et al., 2019; Ji et al., 2022). Additionally,
the $r$-process elements are synthesized at high energy, and it takes time to
trap the material and cool it back down to star-forming gas in a galaxy’s
interstellar medium (Shen et al., 2015; Hirai et al., 2015; Naiman et al.,
2018; Schönrich & Weinberg, 2019; Côté et al., 2019; Naidu et al., 2022; Amend
et al., 2022; van de Voort et al., 2020, 2022) Thus, $r$-process enrichment
should vary across time and also between galaxies with properties and
environments that include different star formation histories and masses.
Unfortunately, the study of metal-poor Galactic halo stars limits the
exploration of these important issues; they cannot provide any information of
environment of host galaxy properties because these halo stars originate from
a variety of dwarf galaxies of different masses that were accreted by the
Milky Way. Other stars are needed to probe both $r$-process abundance
signatures as well as reveal environmental information about their birth
conditions.

##  4 Dwarf Galaxies: Nature’s Best $R$-process Laboratories

The Milky Way’s dwarf satellite galaxies have been extensively studied over
the past half century (see e.g. Tolstoy et al. 2009 for a comprehensive
summary, and also Simon 2019 for more recent results). Given the specific
focus here on $r$-process observations in dwarf galaxies, here is a brief
summary of the state of the art, including providing information on the basic
properties of dwarf galaxies as understanding dwarf galaxy environments has
become increasingly important for learning about the site and operation of the
$r$-process.

There are currently ${\sim 60}$ dwarf galaxy satellites of the Milky Way
(Simon, 2019). Their basic properties are tabulated in Table 2 and show some
important quantities in Figure 6. Only two of these galaxies contain gas and
are star-forming (the Large and Small Magellanic Clouds, LMC and SMC). All of
the other galaxies are so-called dwarf spheroidal (dSph) galaxies, which
contain no neutral gas and look morphologically like a diffuse cloud of stars.
It is thus useful here to define “galaxy,” as opposed to other gravitationally
bound stellar systems such as star clusters (Willman & Strader, 2012). A
galaxy forms at the center of a dark matter halo, so its gravitational mass is
10-100 times higher than its stellar mass. Even galaxies with only a few
thousand solar masses of stars have their own extensive dark halo and thus
represent the lower mass end of galaxy formation. On the contrary, a star
cluster is not embedded in a dark halo, even the most massive ones containing
several million solar masses of stars. Twelve of the Milky Way satellites are
still candidate galaxies at the time of writing, meaning that there is not yet
enough data to conclusively distinguish them from star clusters.

Some confusing naming conventions should also be clarified. Dwarf galaxies are
typically named after the International Astronomical Union-defined
constellation where they were originally discovered, followed by a roman
numeral if multiple galaxies or candidate galaxies or structures are in the
same constellation on the sky. For example, Reticulum II is the 2nd galaxy-
like structure found within the Reticulum constellation. The first galaxy
discovered typically has the roman numeral dropped (e.g., Carina I = Carina)
as is especially the case with the longer known systems. However, upon initial
discovery, it can be unclear if a system is ultimately confirmed to be a
galaxy or rather a star cluster, as the structure needs to be followed up with
spectroscopy to confirm a high mass-to-light ratio and metallicity dispersion.
As a result, galaxy names do not always follow this rule. For example, Segue 1
and 2 were named after the SEGUE survey, instead of a constellation, and were
only later confirmed to actually be galaxies. Reticulum I has been shown to be
a globular cluster, but Reticulum II is a dwarf galaxy. Once names are given,
they are typically kept.

###  4.1 The Need to Study Dwarf Galaxies to Learn about the $R$-process

Contrary to the availability of relatively bright and close-by halo stars with
observable $r$-process enhancements, stars in dwarf galaxies are much, much
fainter. This is mostly due to the large distances of often up to 250 kpc of
these system, leaving only the brightest red giant stars available for
detailed spectroscopic observations. These brightest stars are of 16th to 19th
magnitude, where 19th magnitude is at the edge of what is technically possible
to observe with high-resolution spectroscopy even with the largest telescopes.
Every single star thus takes at least several hours if not an entire night or
more to observe.

However, stars in dwarf galaxies provide a powerful advantage over Galactic
halo stars: A dwarf galaxy provide a collection of stars with a known common
and correlated formation history. This includes environmental information
related to metal mixing, gas dilution mass, and star formation history. The
observed stars are still within their birth environment, which means that the
chemical enrichment that took place prior to their birth can be reconstructed
more quantitatively. Knowing about the environment helps to break degeneracies
of galaxy evolution. At fixed [X/H], the number of enriching sources is
completely degenerate with the gas mass of the system. But within the same
galaxy, the gas mass is constant, thus offering a way to constrain the
enrichment history. This is essential when trying to understand the signature
and origin scenarios of different nucleosynthesis processes. Since the
Galactic halo formed from a combination of dissolved dwarf galaxies as part of
the hierarchical assembly of the Milky Way, any given halo star likely did not
originate from within the Galaxy but in a small dwarf galaxy long ago. Hence,
any information on the birth gas cloud conditions was lost upon the accretion
of the erstwhile host galaxy.

While element nucleosynthesis is entirely governed by nuclear physics
processes, the initial conditions for it to occur are determined by the
astrophysical site and associated environmental situation at the time of the
event. On one hand, this complicates the interpretation of the observed
signatures, but on the other hand, it also provides an opportunity to obtain
information that might provide insight into the astrophysical site and
conditions.

Regarding $r$-process nucleosynthesis, stars located in dwarf galaxies are
ideally suited for studying individual, clean nucleosynthesis processes, since
they still reside in the environment in which the $r$-process event occurred.
Besides the yield constraints, the dwarf galaxy environment specifically
provides means to constrain different production sites in terms of their
astrophysics delay times and and type of yields. With chemical evolution
models, varying delay times can be taken into account when predicting observed
trends and abundance ratios pertaining to contributions by prompt and delayed
sources. However, the sites associated with those timescales remain
indistinguishable at present. More data, likely to come in the next decades,
will hopefully shed more light on these questions.

###  4.2 $R$-process Observables in Dwarf Galaxies

Of all the neutron-capture elements, only three are usually available to
measure in dwarf galaxies: strontium (Sr), barium (Ba), and europium (Eu),
which trace the first $r$-process peak, the second $r$-process peak, and the
rare earth elements, respectively. This is because in low-metallicity stars
($\mbox{[Fe/H]}<-2$), the absorption lines of other neutron-capture elements
are intrinsically much weaker and as such usually undetectable in spectrum of
low or moderate quality. At metallicities of $\mbox{[Fe/H]}\gtrsim-2.0$,
yttrium (Y) becomes measurable in place of Sr, and lanthanum (La) in place of
Ba. With increasing [Fe/H] many other elements also become measurable
(especially Zr, Ce, Nd, Dy), especially if their abundances are enhanced.
Indeed, in a few rare cases of highly $r$-process enhanced stars, it has been
possible to measure the actinide element thorium (Th) (Aoki et al., 2007; Ji &
Frebel, 2018; Hansen et al., 2018a, 2021; Reichert et al., 2021).

Still, measuring neutron-capture element abundances in dwarf galaxies is hard.
Since dwarf galaxies are at least 20 kiloparsecs away, it is currently only
feasible to study red giant stars, and unfortunately most neutron-capture
element absorption lines occur at relatively low (blue) wavelengths where
these stars produce little flux and spectrograph detectors have poor quantum
efficiency. Additionally, moderately high spectral resolution
($R=\lambda/\Delta\lambda\gtrsim 25,000$) is required to detect any of the
intrinsically weak $r$-process element absorption lines. This generally limits
observations to the available brighter stars with $V<19$, and requires,
despite the above challenges, reaching down to wavelengths of 4000 Å to
measure at least Sr (4077 Å and 4215 Å) and Eu (4129 Å and other lines further
to the blue and red). The easiest of the three element to measure is Ba
because has multiple strong lines at relatively red wavelengths (4554-6497 Å).
Recently, it has been shown that Ba can be accurately measured at lower
spectral resolutions of $R\sim 6000$ by simultaneously fitting all the Ba
lines (Duggan et al., 2018). Thus, in many dwarf galaxy studies, Ba is the
only neutron-capture element available.

In general, dwarf galaxies are enriched by a combination of the $r$-process
and $s$-process. Before studying $r$-process nucleosynthesis and its history,
the $s$-process component must be removed. This is typically accomplished by
measuring both Ba and Eu abundances, then assuming that the solar $r$-process
pattern is universal from the second to the third peak ([Ba/Eu] $=-0.8$,
Sneden et al. 2008), and that any excess Ba is due to the $s$-process (e.g.,
Duggan et al., 2018; Skúladóttir et al., 2019; de los Reyes et al., 2022). In
principle, this fundamentally limits our ability to use dwarf galaxies to
study variations in the $r$-process composition. However, the most metal-poor
stars in the least massive dwarf galaxies can be assumed to have formed early
enough that $s$-process contamination of the system is unlikely. Measurements
made for some of these stars have confirmed that deviations from the universal
$r$-process pattern are at the same level as measurement uncertainties. Thus,
when considering average abundance trends, it is a reasonable procedure to do
this subtraction, though it precludes studying variations in the detailed
$r$-process composition.

Overall, it is thus possible to study the (more) detailed $r$-process patterns
of dwarf galaxy stars only in the rare cases where the stars are unusually
close, and only with a very large investment of telescope time (e.g., Ji &
Frebel, 2018; Hansen et al., 2021). However bulk distributions of a few
element ratios are currently achievable, such as [Ba/Eu] and [Sr/Eu].

###  4.3 General Properties of Dwarf Galaxies

Galaxy Name | R.A. | Decl. | $M_{V}$ | [Fe/H] | $t_{\rm SF}$ | References
---|---|---|---|---|---|---
Large Magellanic Cloud | 05:23:34.6 |  $-$69:45:22 | $-18.12$ | $-0.50$ | $13.8$ | 33,33,33,NA
Small Magellanic Cloud | 00:52:44.8 |  $-$72:49:43 | $-16.83$ | $-1.00$ | $13.8$ | 33,33,33,NA
Sagittarius | 18:54:59.2 |  $-$30:27:38 | $-13.50$ | $-0.53$ | $10.4$ | 31,31,34,47
Fornax | 02:39:50.0 |  $-$34:29:59 | $-13.34$ | $-1.07$ | $11.6$ | 35,35,21,47
Leo I | 10:08:27.5 |  $+$12:18:21 | $-11.78$ | $-1.48$ | $12.1$ | 35,35,21,47
Sculptor | 01:00:04.4 |  $-$33:43:07 | $-10.82$ | $-1.73$ | $3.1$ | 35,35,21,47
Antlia II | 09:35:13.9 |  $-$36:41:56 | $-9.86$ | $-1.90$ |  $\cdots$ | 18,18,18,NA
Leo II | 11:13:27.0 |  $+$22:09:10 | $-9.74$ | $-1.68$ | $7.4$ | 35,35,21,47
Carina | 06:41:37.6 |  $-$50:57:33 | $-9.45$ | $-1.80$ | $11.6$ | 35,35,11,47
Ursa Minor | 15:08:58.1 |  $+$67:13:20 | $-9.03$ | $-2.12$ | $4.7$ | 35,35,21,47
Sextans | 10:13:03.1 |  $-$01:36:48 | $-8.94$ | $-1.97$ | $1.8$ | 35,35,21,27
Draco | 17:20:16.4 |  $+$57:55:07 | $-8.88$ | $-2.00$ | $3.6$ | 35,35,21,47
Canes Venatici I | 13:28:02.2 |  $+$33:33:08 | $-8.73$ | $-1.91$ | $5.5$ | 35,35,21,47
Crater II | 11:49:14.4 |  $-$18:24:47 | $-8.20$ | $-2.16$ | $3.3$ | 43,43,18,46
Leo T | 09:34:55.0 |  $+$17:02:54 | $-7.56$ | $-1.91$ | $12.2$ | 35,35,21,47
Eridanus II | 03:44:20.1 |  $-$43:32:02 | $-7.10$ | $-2.38$ | $2.0$ | 8,8,28,42
Bootes I | 14:00:04.8 |  $+$14:30:49 | $-6.02$ | $-2.34$ | $1.1$ | 35,35,15,2
Hercules | 16:31:05.3 |  $+$12:47:07 | $-5.83$ | $-2.47$ | $1.8$ | 35,35,21,2
Centaurus I | 12:38:20.4 |  $-$40:54:07 | $-5.55$ |  $\cdots$ | $0.9$ | 32,32,NA,32
Canes Venatici II | 12:57:10.2 |  $+$34:19:21 | $-5.17$ | $-2.35$ | $1.1$ | 35,35,21,2
Ursa Major I | 10:34:44.4 |  $+$51:55:34 | $-5.13$ | $-2.16$ | $2.5$ | 37,35,21,2
Leo IV | 11:32:57.7 |  $-$00:32:43 | $-4.99$ | $-2.48$ | $1.6$ | 35,35,15,2
Hydra II | 12:21:42.0 |  $-$31:59:10 | $-4.86$ | $-2.02$ | $2.2$ | 35,35,22,38
Hydrus I | 02:29:33.4 |  $-$79:18:32 | $-4.71$ | $-2.52$ |  $\cdots$ | 25,25,25,NA
Eridanus IV | 05:05:45.1 |  $-$09:30:54 | $-4.70$ |  $\cdots$ | $0.8$ | 4,4,NA,4
Carina II | 07:36:25.6 |  $-$57:59:57 | $-4.50$ | $-2.44$ |  $\cdots$ | 45,45,29,NA
Ursa Major II | 08:51:29.4 |  $+$63:08:01 | $-4.43$ | $-2.23$ |  $\cdots$ | 35,35,21,NA
Aquarius II | 22:33:55.5 |  $-$09:19:39 | $-4.36$ | $-2.30$ |  $\cdots$ | 44,44,44,NA
Indus II | 20:38:52.8 |  $-$46:09:36 | $-4.30$ |  $\cdots$ |  $\cdots$ | 9,9,NA,NA
Leo V | 11:31:08.6 |  $+$02:13:10 | $-4.29$ | $-2.29$ |  $\cdots$ | 35,35,15,NA
Coma Berenices | 12:26:58.9 |  $+$23:54:25 | $-4.28$ | $-2.43$ | $0.8$ | 35,35,21,2
Pegasus IV | 21:54:09.4 |  $+$26:37:12 | $-4.25$ | $-2.67$ | $1.3$ | 5,5,5,5
Pisces II | 22:58:32.3 |  $+$05:57:09 | $-4.23$ | $-2.45$ |  $\cdots$ | 35,35,22,NA
Columba I | 05:31:25.7 |  $-$28:02:33 | $-4.20$ |  $\cdots$ |  $\cdots$ | 3,3,NA,NA
Pegasus III | 22:24:22.6 |  $+$05:25:12 | $-4.10$ | $-2.40$ |  $\cdots$ | 19,19,20,NA
Tucana II | 22:52:14.4 |  $-$58:34:12 | $-3.90$ | $-2.90$ | $1.0$ | 1,1,6,38
Grus II | 22:04:04.8 |  $-$46:26:24 | $-3.90$ | $-2.51$ |  $\cdots$ | 9,9,41,NA
Reticulum II | 03:35:40.9 |  $-$54:03:05 | $-3.88$ | $-2.65$ | $1.5$ | 35,35,39,38
Horologium I | 02:55:31.5 |  $-$54:06:58 | $-3.76$ | $-2.76$ | $2.3$ | 35,35,24,38
Pictor I | 04:43:47.8 |  $-$50:17:07 | $-3.67$ |  $\cdots$ |  $\cdots$ | 35,35,NA,NA
Tucana IV | 00:02:55.2 |  $-$60:51:00 | $-3.50$ | $-2.49$ |  $\cdots$ | 9,9,41,NA
Grus I | 22:56:43.1 |  $-$50:10:48 | $-3.47$ | $-2.50$ |  $\cdots$ | 35,35,7,NA
Reticulum III | 03:45:26.4 |  $-$60:27:00 | $-3.30$ |  $\cdots$ |  $\cdots$ | 9,9,NA,NA
Pictor II | 06:44:43.2 |  $-$59:53:49 | $-3.20$ |  $\cdots$ |  $\cdots$ | 10,10,NA,NA
Bootes II | 13:58:03.4 |  $+$12:51:19 | $-2.94$ | $-2.79$ |  $\cdots$ | 35,35,16,NA
Willman 1 | 10:49:22.5 |  $+$51:03:00 | $-2.90$ | $-2.19$ |  $\cdots$ | 35,35,48,NA
Phoenix II | 23:39:58.3 |  $-$54:24:18 | $-2.70$ |  $\cdots$ | $1.3$ | 36,36,NA,38
Cetus III | 02:05:19.4 |  $-$04:16:12 | $-2.45$ |  $\cdots$ |  $\cdots$ | 14,14,NA,NA
Carina III | 07:38:31.2 |  $-$57:53:59 | $-2.40$ | $-2.65$ |  $\cdots$ | 45,45,17,NA
Segue 2 | 02:19:17.4 |  $+$20:09:45 | $-1.98$ | $-2.14$ |  $\cdots$ | 35,35,21,NA
Tucana V | 23:37:24.0 |  $-$63:16:12 | $-1.60$ | $-2.17$ |  $\cdots$ | 9,9,41,NA
Triangulum II | 02:13:18.0 |  $+$36:10:13 | $-1.60$ | $-2.24$ | $0.9$ | 35,35,23,38
Horologium II | 03:16:25.8 |  $-$50:02:55 | $-1.56$ |  $\cdots$ |  $\cdots$ | 35,35,NA,NA
Tucana III | 23:56:25.8 |  $-$59:35:00 | $-1.49$ | $-2.42$ |  $\cdots$ | 36,36,40,NA
Segue 1 | 10:07:00.1 |  $+$16:04:32 | $-1.30$ | $-2.71$ |  $\cdots$ | 35,35,12,NA
Draco II | 15:52:47.6 |  $+$64:33:55 | $-0.80$ | $-2.70$ |  $\cdots$ | 26,30,30,NA
Virgo I | 12:00:09.6 |  $-$00:40:48 | $-0.80$ |  $\cdots$ |  $\cdots$ | 13,13,NA,NA
Cetus II | 01:17:52.8 |  $-$17:25:12 | $+0.00$ |  $\cdots$ |  $\cdots$ | 9,9,NA,NA
Table 2: Milky Way Dwarf Galaxy Satellite Basic Properties, sorted by absolute
magnitude $M_{V}$. Table based on Simon (2019) with recent updates. Reference
column indicates references for coordinates, $M_{V}$, [Fe/H], and $t_{\rm SF}$
separated by commas, with NA indicating no value for that data. The LMC and
SMC are still star forming so $t_{\rm SF}$ is set to the age of the universe
today. Reference numbers are 1: Bechtol et al. (2015), 2: Brown et al. (2014),
3: Carlin et al. (2017), 4: Cerny et al. (2021), 5: Cerny et al. (2022), 6:
Chiti et al. (2018), 7: Chiti et al. (2022), 8: Crnojević et al. (2016), 9:
Drlica-Wagner et al. (2015), 10: Drlica-Wagner et al. (2016), 11: Fabrizio et
al. (2012), 12: Frebel et al. (2014), 13: Homma et al. (2016), 14: Homma et
al. (2018), 15: Jenkins et al. (2021), 16: Ji et al. (2016a), 17: Ji et al.
(2020a), 18: Ji et al. (2021), 19: Kim et al. (2015), 20: Kim et al. (2016),
21: Kirby et al. (2013), 22: Kirby et al. (2015), 23: Kirby et al. (2017), 24:
Koposov et al. (2015), 25: Koposov et al. (2018), 26: Laevens et al. (2015),
27: Lee et al. (2009), 28: Li et al. (2017), 29: Li et al. (2018), 30:
Longeard et al. (2018), 31: Majewski et al. (2003), 32: Mau et al. (2020), 33:
McConnachie (2012), 34: Mucciarelli et al. (2017), 35: Muñoz et al. (2018),
36: Mutlu-Pakdil et al. (2018), 37: Okamoto et al. (2008), 38: Sacchi et al.
(2021), 39: Simon et al. (2015), 40: Simon et al. (2017), 41: Simon et al.
(2020), 42: Simon et al. (2021), 43: Torrealba et al. (2016a), 44: Torrealba
et al. (2016b), 45: Torrealba et al. (2018), 46: Walker et al. (2019), 47:
Weisz et al. (2014), 48: Willman et al. (2011)

The most important parameter describing a dwarf galaxy is its stellar mass,
which spans 7 orders of magnitude ($10^{3}-10^{10}\,M_{\odot}$). The stellar
mass is inferred from a galaxy’s observed luminosity which is typically given
in absolute $V$-band magnitudes ($M_{V}$) and can be converted using

$M_{\star}=\eta\,10^{0.4(4.83-M_{V})}$ (1)

where $\eta$ is the mass-to-light ratio and is $\approx 2.2$ for old, metal-
poor stellar populations (Ji et al., 2016a). $\eta$ decreases to $1.0-1.5$ for
younger stellar populations (Kirby et al., 2013). The constant 4.83 is the
absolute $V$ magnitude of the Sun. Because of the large dynamic range, it is
common to divide the dwarf galaxies into high- and low-mass galaxies, with a
typical threshold that relatively luminous dwarf galaxies with $M_{V}<-7.7$
($M_{\star}\gtrsim 2\times 10^{5}\,M_{\odot}$) are called “classical dwarf
spheroidal” (dSph) galaxies, while galaxies with luminosity $M_{V}>-7.7$ are
deemed “ultra-faint” dwarf galaxies (UFDs).

The top panel of Figure 6 shows the galaxy “luminosity-metallicity relation”
(often abbreviated LZR, where Z is a common symbol representing metallicity;
or MZR for the “mass-metallicity relation”). The y-axis
$\langle\mbox{[Fe/H]}\rangle$ is the mean of individual star [Fe/H]
measurements, so it is best thought of as the median metallicity of the whole
galaxy (due to the $\log_{10}$ in the definition of [Fe/H]). It is clear that
there is an overall scaling where more massive galaxies have higher median
metallicities. This relation extends continuously to higher mass galaxies and
appears to be present independent of a galaxy’s large-scale environment (Kirby
et al., 2013). However, it is important to remember that metal-poor stars are
in fact present in all galaxies, though they are a small fraction of the stars
in metal-rich galaxies (e.g., Frebel et al., 2010; Chiti et al., 2018;
Reggiani et al., 2021).

In the Figure, galaxies with high-resolution spectroscopic abundances are
highlighted as larger black points. These are the only galaxies in which some
$r$-process element abundances can be measured. Only about 50% of the known
Milky Way dwarf galaxies have been studied with high-resolution spectroscopy,
though current studies span the entire range of masses and metallicities.
Three of the ultra-faint dwarf galaxies (Ret II, Tuc III, Gru II) are
highlighted in red as $r$-process ultra-faint dwarf galaxies, which will be
discussed in Section 5.1.

Figure 6:  Summary of bulk dwarf galaxy properties. In both panels, the large
black points indicate galaxies for which high-resolution spectroscopic data
has been obtained, and thus the potential to measure abundances of the
$r$-process elements. The small black points indicate galaxies with no high-
resolution spectroscopy. The dotted black vertical line shows the division
between Ultra-Faint Dwarf Galaxies and Classical Dwarf Galaxies. _Top panel:_
Absolute magnitude $M_{V}$ vs. mean metallicity $\langle\mbox{[Fe/H]}\rangle$.
The top axis indicates the approximate stellar mass corresponding to each
magnitude, assuming a mass-to-light ratio of 2.2 in Equation 1. This
overestimates the mass of high luminosity galaxies, where the mass-to-light
ratio can decrease to $1.0-1.6$ (Kirby et al., 2013). In general, more massive
dwarf galaxies have higher median metallicities. _Bottom panel:_ Absolute
magnitude $M_{V}$ vs the star formation duration (in Gyr). The star formation
duration is defined to be the time to form ${\approx}90\%$ of a galaxy’s
stars. The shaded pink region at the bottom indicates the range of ages where
current galaxy age determinations are not sufficiently precise to robustly
distinguish between different ages, i.e. galaxies in that range should be
thought of as having essentially identical star formation durations. Galaxies
with stellar masses below ${\approx}10^{5}M_{\odot}$ uniformly formed in the
first 1-2 billion years, while more massive galaxies are able to form stars
for longer times. The original references for data in this figure are given in
Table 2.

The bottom panel of Figure 6 shows the primary reason to divide galaxies by
mass which corresponds to their fundamentally different formation histories.
The $y-$axis of that panel is the star formation duration, defined as the time
it takes for the galaxy to form ${\approx}90\%$ of its present-day stellar
mass. Low-mass dwarf galaxies occupy low-mass dark matter halos with present-
day total masses of $M_{\rm halo}\lesssim 10^{9}\,M_{\odot}$. These halos are
not massive enough to accrete gas from the intergalactic medium after cosmic
reionization occurred at $z\approx 6$. Thus, the ultra-faint dwarf galaxies
have their star formation halted by reionization, and their star formation
histories appear to uniformly terminate somewhere between $z=2-6$,
corresponding to 1-2 Gyr after the Big Bang (Weisz et al., 2014; Brown et al.,
2014; Rodriguez Wimberly et al., 2019). In contrast, more massive galaxies can
continue to accrete gas and form stars after $z=6$, likely only quenching when
they interact with a more massive galaxy (Geha et al., 2012; Fillingham et
al., 2019). Of the Milky Way’s known satellite galaxy population (i.e. within
its 300 kpc dark matter halo virial radius), only the Large and Small
Magellanic Clouds (the most massive satellites and orbiting for only 1-2 Gyr
around the Milky Way, Besla et al. 2007; Kallivayalil et al. 2013) have
retained any gas and are still forming stars. However, even low-mass dwarf
galaxies outside the virial radius (e.g., the distant dwarf galaxy Leo T at
400 kpc away) can still retain gas and actively form stars.

###  4.4 Chemical Enrichment and Evolution of Non-$r$-process Elements in
Dwarf Galaxies

Before describing the observed $r$-process signatures in dwarf galaxies in
Section 5, first consider a brief overview of the chemical evolution in dwarf
galaxies.

Chemical element abundances are best derived from high-resolution spectrum,
but only half of the ${\sim}60$ dwarf galaxy satellites of the Milky Way have
even a single star observed with the high-resolution spectroscopy. The
elements measurable with stellar spectroscopy are generally grouped into four
categories: The $\alpha$-elements (e.g., O, Mg, Ca, Ti) that are made
predominantly in core-collapse supernovae; the iron-peak elements (e.g., Mn,
Fe, Ni, Zn) that are produced predominantly in thermonuclear (Type Ia)
supernovae; the $s$-process elements that are synthesized predominantly in
evolved, low and intermediate mass Asymptotic Giant Branch (AGB) stars; and
the $r$-process elements whose origin remains uncertain. Recall that element
sources occurring shortly after a burst of star formation are regarded
“prompt” (e.g., core-collapse supernovae following the deaths of massive
stars), and element sources occurring longer after a burst of star formation
are “delayed” (e.g., Type Ia SNe, low mass AGB stars, and neutron star
mergers).

The first and most important feature of dwarf galaxy chemical evolution is the
fact that metallicity increases at different rates in different dwarf
galaxies. Gas in lower-mass galaxies increases its metallicity at a slower
rate than gas in higher-mass galaxies, for two reasons. First, the lower
gravitational potential well of low-mass galaxies means that it is easier to
directly expel metals out of low mass dwarf galaxies (e.g., Dekel & Woo, 2003;
Kirby et al., 2011; Brauer et al., 2021). Second, stellar feedback is more
efficient at preventing star formation in low-mass galaxies, so the overall
star formation efficiency, and thus metal production rate, is lower (e.g.,
Ishimaru et al., 2015; Ji et al., 2016a). Together, these effects mean that
the expected age of a metal-poor star depends strongly on the galactic
environment that it forms in. Metallicities can thus reasonably be interpreted
as relative ages in dwarf galaxies, but this does not applied to stars or
stellar samples from the Milky Way stellar halo.

The next most important feature of chemical evolution is the so-called
“$\alpha$-plateau and knee” (Tinsley, 1980; Matteucci & Brocato, 1990; Tolstoy
et al., 2009), shown in the top-left panel of Figure 7. These panels compare
an $\alpha$-element like Mg, produced only in core-collapse supernovae, to an
iron-peak element such as Fe, produced in both core-collapse supernovae and
Type Ia supernovae. In every galaxy, the low-metallicity stars (those forming
earlier in a dwarf galaxy’s life) tend to have enhanced ratios of [Mg/Fe]
$\gtrsim 0.3$ (i.e., more Mg than Fe relative to the solar composition for
which the ratio is zero). At some metallicity, that ratio begins to decrease,
and the more metal-rich stars (those forming later in a dwarf galaxy’s
evolution) end up with progressively lower ratios of [Mg/Fe] all the way to
${\lesssim}0$. The interpretation here is that early in a galaxy’s history, it
is predominantly enriched by core-collapse supernovae which produce a large
amount of $\alpha$-elements compared to the solar composition. At some point,
the delayed Type Ia supernovae begin to dominate, synthesizing enough Fe to
reduce the [$\alpha$/Fe] ratio, and thus producing a “kink” or “knee” in the
[$\alpha$/Fe] vs. [Fe/H] chemical abundance trend. Because the timing of the
onset of Type Ia supernovae is a property of the underlying stellar
populations, galaxies with efficient metal production will have their
$\alpha$-knee located at a _higher_ metallicity, while galaxies with
inefficient metal production will have their $\alpha$-knee located at a
_lower_ metallicity. Since galaxies of higher mass tend to produce stars and
metals more efficiently, the metallicity location of the $\alpha$-knee is thus
positively correlated with stellar mass. One major exception is galaxies that
form so quickly that they never experience enrichment by Type Ia supernovae,
leaving a flat [$\alpha$/Fe] trend over their entire metallicity range (Frebel
& Bromm, 2012). So far, only the Segue 1 ultra-faint dwarf galaxy displays
this signature (Frebel et al., 2014).

Note that the above simple picture explains the overall evolution in most
galaxies and the overall trend with galaxy mass, but it is not correct in
detail. In particular, a common misconception is that the $\alpha$-knee
indicates the exact time that the first Type Ia supernovae “turn on” (e.g.,
${\approx}100$ Myr after the first burst of star formation, Maoz & Mannucci
2012). However, in fact it occurs when Type Ia supernovae ejecta _dominate_
over core-collapse supernovae, which can happen much later (e.g., Maoz &
Graur, 2017). Theler et al. (2020) and Kirby et al. (2020) have recently both
advocated that the _slope_ of the [$\alpha$/Fe] vs. [Fe/H] decline is a more
meaningful tracer indicator than the knee location. This would naturally
explain why the Large and Small Magellanic Clouds, the most massive dwarf
galaxies around the Milky Way, have some of the lowest metallicity
$\alpha$-knees (Nidever et al., 2020).

A third important feature is the “rise of the $s$-process” (e.g., Simmerer et
al., 2004; Venn et al., 2004). The bottom-left panel of Figure 7 shows the
[Ba/Eu] ratio vs metallicity [Fe/H]. Assuming the solar $r$-process pattern is
universal, the $r$-process intrinsically produces a fixed ratio of [Ba/Eu] =
$-0.9$ to $-0.7$ (Sneden et al., 2008). It is empirically observed that the
most metal-poor stars in a galaxy cluster around this intrinsic value, while
the more metal-rich stars have higher [Ba/Eu], which is interpreted as delayed
$s$-process enrichment from AGB stars. The different [Ba/Y] ratio in dwarf
galaxies is interpreted as being due to enrichment by the $s$-process
operating in metal-poor AGB stars where the metal-poor $s$-process produces
less Y than Ba compared to metal-rich AGB stars, due to the lower neutron-to-
seed ratio in metal-poor AGB stars (e.g., Venn et al., 2004; Lugaro et al.,
2012) leading to a larger relative production of the heavier elements.

Finally, an important distinction between chemical _enrichment_ and chemical
_evolution_ in dwarf galaxies needs to be made. Chemical enrichment is the
phase where metal production and observed stellar abundances can be linked to
discrete enrichment sites (e.g., individual core-collapse supernovae).
Chemical evolution is the long-term average evolution of the galaxy
composition, once it is no longer possible to distinguish between individual
sources of elements. For most dwarf galaxies, the chemical enrichment phase is
restricted to the earliest times and as such only reflected in the abundances
of the most metal-poor stars in the system. However, the lowest mass dwarf
galaxies may never form enough stars to exit the chemical enrichment phase.
This can be seen in Figure 7 on all panels, where the scatter in metal ratios
at low [Fe/H] is generally larger than that at higher [Fe/H].

Figure 7: Chemical evolution in dwarf galaxies. Each point represents the
chemical abundances of one star, with colors and shapes indicating the
formation site of a star. Data with upper limits have not been plotted. Grey
points are stars in the Milky Way’s stellar halo (Abohalima & Frebel, 2018).
Light blue points are stars from the relatively massive
$10^{6}-10^{7}M_{\odot}$ Fornax and Sculptor dSph galaxies (Letarte et al.,
2010; Hill et al., 2019). Purple points are stars from the lower mass
$10^{6}M_{\odot}$ Carina (Venn et al., 2012; Lemasle et al., 2012; Norris et
al., 2017), Draco (Cohen & Huang, 2009; Tsujimoto et al., 2017), and Ursa
Minor (Cohen & Huang, 2010; Kirby & Cohen, 2012; Ural et al., 2015) dSph
galaxies. Yellow points are stars from ultra-faint dwarf galaxies (UFDs,
$<10^{5}M_{\odot}$), using the literature compilation in Ji et al. 2020a)
displaying low neutron-capture element abundances. Bootes I is plotted
separately as it shows a rise in $s$-process at high metallicity, contrasting
with other UFDs (Frebel et al., 2016). Red points are stars from $r$-process
enhanced UFDs, where larger points are from the highly $r$-process enhanced
galaxy Reticulum II and smaller points are the other two UFDs (Ji et al.,
2016b; Marshall et al., 2019; Hansen et al., 2021). _Top left:_ [Mg/Fe] vs
[Fe/H], which indicates the relative enrichment of Type Ia and core-collapse
supernovae. An approximate plateau at $\mbox{[Mg/Fe]}\sim 0.4$ exists at low
metallicity for all systems (shown as shaded grey bar), but transitions to
lower [Mg/Fe] at an [Fe/H] that broadly depends on galaxy mass. _Bottom left:_
[Ba/Eu] vs [Fe/H], which indicates the relative amount of $s$-process vs
$r$-process enhancement. The shaded grey bar shows $\mbox{[Ba/Eu]}\sim-0.8$,
which is the universal value found in the solar $r$-process residual and in
$r$-process enhanced stars. At higher metallicities, the onset of delayed
$s$-process enrichment from AGB stars adds a lot of barium relative to
europium, resulting in a gradual increase in [Ba/Eu] with metallicity. There
is one UFD star with high [Ba/Eu] that is the result of $s$-process from AGB
mass transfer. _Top right:_ [Ba/Mg] vs [Fe/H]. The origin of Ba depends on
metallicity and environment. At high metallicities, [Ba/Mg] shows the rise of
the $s$-process by comparing delayed AGB to prompt core-collapse supernovae
enrichment. At low metallicities, Ba is predominantly from $r$-process, where
the UFDs show a very large scatter due to stochastic early $r$-process
enrichment. Note that all stars with sufficient data quality to detect
$\mbox{[Ba/H]}>-4$ have successfully detected Ba (Roederer, 2013). _Bottom
right:_ [Eu/Mg] vs [Fe/H], which compares the relative delay times of the
$r$-process source compared to core-collapse supernovae. It is clear that
dwarf galaxies of different masses have different overall [Eu/Mg] (especially
comparing Fornax to Sculptor), which is strong evidence for the existence of
delayed $r$-process enrichment.

##  5 $R$-process Signatures in Dwarf Galaxies

This section gives a general summary of all existing $r$-process chemical
evolution trends in dwarf galaxies, as well as specifics about important
individual dwarf galaxies. Dwarf galaxies are grouped into three categories:
The ultra-faint dwarf galaxies which are dominated by stochastic $r$-process
enrichment (Section 5.1); the large intact dwarf galaxies which display a
transition from $r$-process enrichment to $r$-process element evolution
(Section 5.2); and the tidally disrupted dwarf galaxies now observable as
stellar streams and kinematic structures in the stellar halo (Section 5.3).

###  5.1 Stochastic $R$-process Events in Ultra-Faint Dwarf Galaxies

Ultra-faint dwarf galaxies typically have masses of $M_{\star}\lesssim 2\times
10^{5}M_{\odot}$; systems more massive that this are the classical dwarf
spheroidal galaxies. Note that this dividing mass is somewhat arbitrary and
more reflects the history of their relatively recent discoveries than any
underlying physical properties. However, $2\times 10^{5}M_{\odot}$ roughly
corresponds to galaxies insufficiently massive to form stars after
reionization at $z\sim 6$ (Simon, 2019). There are ${\sim}50$ known ultra-
faint dwarf galaxies, of which ${\sim}20$ have high-resolution spectroscopy
available of at least one star and in which neutron-capture elements could in
principle be detected.

The vast majority of ultra-faint dwarf galaxies display unusually low neutron-
capture elements – so low that it is not even possible to identify whether the
neutron-capture source is $r$-process or $s$-process as only Sr and Ba can be
measured (Frebel & Norris, 2015; Ji et al., 2019b). The fundamental
explanation is the low stellar mass of ultra-faint dwarf galaxies. For
example, if the average rate of $r$-process production is about one
$r$-process event per ${\sim}$1,000 core-collapse supernovae, it takes
${\sim}10^{5}M_{\odot}$ of stellar mass formed in order to produce one single
$r$-process event. Thus, individual ultra-faint dwarf galaxies are unlikely to
display evidence of $r$-process enrichment; but as a population, a few UFDs
should be $r$-process-rich galaxies.

This line of reasoning was brought about by the discovery that the ultra-faint
dwarf galaxy Reticulum II is $r$-process enhanced, with over 2/3 of its stars
having $\mbox{[Eu/Fe]}\sim 1.7$ (Ret II; Ji et al. 2016a; Roederer et al.
2016; see Figure 8 for updated data). Ret II has $r$-process abundances over
$10-100{\times}$ higher than what is found in other ultra-faint dwarf
galaxies, indicating that it preserves the chemical abundance signature of a
single $r$-process event. By considering the 10 ultra-faint dwarf galaxies
available at that time, Ji et al. (2016a) derived strong $r$-process
production constraints from inferring that the event produced
$10^{-5.5}-10^{-3.5}M_{\odot}$ of europium, and that the relative rate of
$r$-process events across the ultra-faint dwarf population was 1 $r$-process
event for every 1,000-2,000 core-collapse supernovae (also see Beniamini et
al. 2016b). These properties were consistent with theoretical expectations for
neutron star mergers (Goriely et al., 2011; Dominik et al., 2012), and the
theoretical values have since been validated by multi-messenger observations
of the neutron star merger GW170817 and its kilonova (e.g., Côté et al.,
2018). An immediate major concern with neutron star mergers is the fact that
neutron star binaries typically get a velocity kick upon formation, which
would cause them to be unbound from such a low-mass galaxy, in which case the
$r$-process elements would not be captured by later generations of star
formation (Bramante & Linden, 2016; Bonetti et al., 2019). This scenario can
be avoided if the binary merges sufficiently quickly, and it is an open
question whether binary neutron stars can merge sufficiently quickly to
deposit their $r$-process elements in ultra-faint dwarf galaxies (Beniamini et
al., 2016a; Safarzadeh et al., 2019). An alternate likely possibility is that
a rare core-collapse supernovae would produce a large amount of $r$-process,
perhaps through strong magnetorotationally driven jets or disk winds from
collapsars (see Section 3).

The most recent study of Ret II finds that 70% of its stars are $r$-process
enhanced, and in those stars the $r$-process material is very homogeneously
distributed (Ji et al., 2022). Current theoretical expectations for galaxies
of Ret II’s mass are that the stars without $r$-process enhancement should be
born in the same galaxy rather than accreted (Griffen et al., 2018). Based on
metal mixing simulations, this suggests that ${\gtrsim}100$ Myr must have
elapsed between the _production_ of $r$-process material and the formation of
the first 30% of Ret II stars (Tarumi et al., 2020). This suggests a very
prompt source of $r$-process elements and a relatively large $r$-process yield
of $M_{r}\gtrsim 10^{-1.5}M_{\odot}$.

Since the discovery of Ret II, two other ultra-faint dwarf galaxies or galaxy
candidates have been clearly shown to contain $r$-process enhancements: Tucana
III (Hansen et al., 2017) and Grus II (Hansen et al., 2020). Unlike Ret II,
these two systems have moderate $r$-process enhancements [Eu/Fe] $\sim+0.5$,
which can either be explained by dilution into different gas mass reservoirs
(Safarzadeh & Scannapieco, 2017; Tarumi et al., 2020) or variable $r$-process
yields (Ji et al., 2019a). Gru II is clearly a bona fide dwarf galaxy, and
like Ret II it shows a transition from metal-poor $r$-process-free stars to
(relatively) metal-rich rich $r$-process-enhanced stars. In contrast, there is
still debate whether Tuc III is a ultra-faint dwarf galaxy or a globular
cluster, though the current evidence suggests it is more likely an ultra-faint
dwarf galaxy (Marshall et al., 2019). There have not yet been more detailed
studies using all galaxies that could result in more precise (but more model-
dependent) determinations of the $r$-process yield and rate from ultra-faint
dwarf galaxies.

An important question is whether all the $r$-process enhanced stars in the
Milky Way halo could be attributed to tidally disrupted UFDs (Tsujimoto &
Shigeyama, 2014; Ishimaru et al., 2015; Ji et al., 2016b; Ojima et al., 2018).
Brauer et al. (2019) modeled the assembly of a Milky Way stellar halo, finding
that typically 50% of the metal-poor $r$-II stars originate from UFDs, though
this fraction varies from 20% to 100% depending on the specific Milky Way
accretion history. Other, similar studies find fractions close to 100% as well
(Hirai et al., 2022). The other $r$-II stars thus likely originate from more
massive dwarf galaxies, such as the $r$-process enhanced stars found in Ursa
Minor (Cohen & Huang, 2010) or Fornax (Reichert et al., 2021).

Figure 8: Neutron-capture elements in dwarf galaxies depending on their
stellar mass. Blue circles are relatively massive classical dSphs, purple
squares are intermediate mass classical dSphs, yellow diamonds are ultra-faint
dwarf galaxies with no indication of $r$-process elements, red circles are the
three ultra-faint dwarf galaxies with some enhancement in $r$-process
elements. Ret II is shown as larger symbols to emphasize its higher [Eu/Fe]
compared to Tuc III and Gru II. Open symbols with downward pointing arrows are
upper limits, i.e. no detection of that element was possible. Most ultra-faint
dwarf galaxies have low neutron-capture abundances compared to classical
dSphs, including in the range $-3<\mbox{[Fe/H]}<-2$, except for the rare
$r$-process enhanced ultra-faint dwarf galaxies. Note that the upper limits
for Sr and Ba are quantitatively meaningful in many cases, but the upper
limits for the $r$-process tracer Eu just indicate that Eu is difficult to
detect at low abundances. The increase in Ba for classical dSphs and a few
ultra-faint dwarf galaxies at [Fe/H] $\gtrsim-2$ indicates the onset of
significant $s$-process enrichment.

###  5.2 The Rise of the $R$-process: From Enrichment to Evolution

Galaxies with stellar mass exceeding ${\sim}10^{6}M_{\odot}$ will experience
$\gtrsim 10$ $r$-process enrichment events over the course of their lives. The
larger number of $r$-process events induces a transition from _chemical
enrichment_ to _chemical evolution_ : Rather than being dominated by
individual stochastic $r$-process enrichment events, instead the galaxy’s
$r$-process composition can reasonably be described as continuous chemical
evolution. To estimate how many $r$-process events are required for this
transition to occur, note that an unresolvable $r$-process abundance scatter
would be 0.1-0.2 dex scatter (a typical systematic uncertainty on [Eu/Fe]
measurements in dwarf galaxies). This translates to 25%-60% relative
$r$-process scatter, or equivalently the Poisson scatter of $r$-process yields
from 3-15 $r$-process events.

The bottom right panel of Figure 7 shows $r$-process chemical evolution in
dwarf galaxies as measured by [Eu/Mg] vs [Fe/H]. Each point on the plot
indicates the chemical abundances of a single star in a dwarf galaxy, and the
points have been color-coded according to the typical mass of the galaxy (with
different symbols representing individual dwarf galaxies). Traditionally, the
literature has focused on the [Eu/Fe] vs [Fe/H] evolution plane, because Fe is
the easiest-to-measure and most precise stellar metallicity indicator.
However, it was emphasized in Tolstoy et al. (2009) and more recently by
Skúladóttir et al. (2019) that Fe may not be a simple reference element to
study dwarf galaxy chemical evolution, because it is produced in both core-
collapse supernovae and Type Ia supernovae. An empirical way to address this
is using Mg instead of Fe as a reference element, as Mg is only produced in
core-collapse supernovae. It can also be addressed with chemical evolution
modeling, e.g. by simultaneously fitting [Mg/Fe] observations (e.g., Molero et
al., 2021; de los Reyes et al., 2022) or calculating the Ia contribution with
[Mg/Fe] (e.g., Kirby et al., 2019).

The dwarf galaxies Draco, Ursa Minor, Sextans, and Carina have present-day
stellar masses $\sim 10^{6}M_{\odot}$, so they should display a transition
from discrete $r$-process enrichment at the low-metallicity end to continuous
$r$-process trends at high-metallicity (Duggan et al., 2018; Skúladóttir et
al., 2019). Draco is the clearest example of this, as it shows multiple
distinct [Eu/H] plateaus that may correspond to discrete $r$-process
enrichment events, though its neutron-capture elements are dominated by
$s$-process enrichment (Cohen & Huang, 2009; Tsujimoto et al., 2015, 2017).
Ursa Minor is dominated by $r$-process enrichment, but it has unusual Eu
trends and large scatter that likely suggest it is still dominated by
stochastic $r$-process enrichment (Cohen & Huang, 2010; McWilliam et al.,
2018). Sextans unfortunately currently has only limited $r$-process
measurements (Theler et al., 2020; Reichert et al., 2020), but at the high-
metallicity end it currently appears to have low Eu scatter indicating a
transition to continuous chemical evolution. Carina is a strange case as its
star formation history has at least three distinct bursts (Hurley-Keller et
al., 1998; Weisz et al., 2014). Its early history seems to have clear
indications of inhomogeneous $r$-process abundances (Venn et al., 2012), and
its later history has more continuous Eu evolution (Lemasle et al., 2012;
Norris et al., 2017).

Sculptor, Fornax, and Sagittarius are sufficiently massive that they should be
dominated by chemical evolution rather than enrichment. Sculptor is one of the
best-studied dwarf galaxies with a very simple star formation history and
smooth $r$-process chemical evolution (Duggan et al., 2018; Hill et al., 2019;
Skúladóttir et al., 2019; Molero et al., 2021; de los Reyes et al., 2022).
There is still debate about the relative importance of prompt vs delayed
$r$-process sources in Sculptor, but it clearly has reached the point of
continuous chemical evolution with [Eu/Mg] ${\approx}0$. Fornax (Letarte et
al., 2010; Lemasle et al., 2014) and Sagittarius (Bonifacio et al., 2000;
McWilliam et al., 2013; Hansen et al., 2018a) are two of the more massive
dwarf spheroidal galaxies with $r$-process elements, both with enhanced
[Eu/Mg] $\sim 0.4$. These indicate that Fornax and Sagittarius have a
relatively large contribution from delayed sources of $r$-process elements
compared to Sculptor, which matches the difference in star formation durations
seen in the bottom panel of Figure 6. Note that there is clearly some
inhomogeneous $r$-process enrichment in Fornax, as some of its most metal-rich
stars have extreme Eu enhancements (Reichert et al., 2021).

The Large and Small Magellanic Clouds (LMC, SMC) are the only gas-rich and
actively star-forming dwarf galaxy satellites of the Milky Way. The most
comprehensive recent study of the LMC and SMC is by Nidever et al. (2020).
They were unable to study $r$-process chemical evolution, but they did show
that the LMC and SMC have an inefficient star formation history, such that it
should be dominated by delayed-enrichment sources even at relatively low
metallicity. This is consistent with the findings of Reggiani et al. (2021),
who measured $r$-process abundances of metal-poor stars
($-2.5\lesssim\mbox{[Fe/H]}\lesssim-1.5$) in the LMC and SMC, finding they
were unusually enhanced and thus favoring delayed sources of $r$-process
production. At higher metallicities, there is also evidence of enhanced
[Eu/Mg] implying delayed $r$-process enrichment (Naidu et al., 2022), though
also higher levels of contamination by the $s$-process in AGB stars (Van der
Swaelmen et al., 2013). Unlike the simpler dSph galaxies, the LMC and SMC have
distinct physical components (e.g. disk, bar, halo) with their own formation
histories, and thus it is wise to separate chemical abundance interpretations
based on the component being studied (e.g., Pompéia et al., 2008; Van der
Swaelmen et al., 2013; Reggiani et al., 2021).

###  5.3 Tidally Disrupted Dwarf Galaxies: Stellar Streams and Dissolved
Galaxies

Dwarf galaxies that accreted very early on into the Milky Way will be tidally
disrupted by the Milky Way’s gravitational potential. Their stars will be
strewn throughout the Milky Way’s stellar halo, but the stars will still
retain their chemical compositions and some conserved kinematic quantities
(e.g. energy, angular momentum, and actions). The advent of all-sky astrometry
from the _Gaia_ space mission (Gaia Collaboration et al., 2016) has recently
enabled detailed calculations of the kinematics, and has ushered in a new era
of discovery and chemically characterization of such tidally disrupted dwarf
galaxies. These galaxies can differ from the intact galaxies discussed
previously, because they stop forming stars when they interact with the Milky
Way (e.g., Johnston et al., 2008; Fillingham et al., 2019).

The task of breaking apart the stellar halo into discrete accreted dwarf
galaxies is still ongoing, but there should only be a few massive dwarf galaxy
accretions (e.g., Deason et al., 2016; Brauer et al., 2019). The broad picture
of the massive Milky Way mergers is now largely in place (e.g., Naidu et al.,
2020; Kruijssen et al., 2020). The most significant dwarf galaxy merger is
Gaia-Sausage-Enceladus (or GSE, Belokurov et al., 2018; Helmi et al., 2018),
which makes up over 50% of the halo stars in the solar neighborhood (though a
smaller fraction of the metal-poor stars). This galaxy had a stellar mass of
${\approx}10^{8}M_{\odot}$ when it merged into the Milky Way $10-12$ billion
years ago. Several studies have shown that the metal-rich GSE stars have a
high [Eu/Mg], indicating a preference for enrichment by delayed $r$-process
sources (Matsuno et al., 2021a; Aguado et al., 2021; Naidu et al., 2022).
Another significant merger is the Kraken or Heracles galaxy (Kruijssen et al.,
2020; Horta et al., 2021), which is confined to the inner 5 kpc of the Milky
Way and thus merged with the Milky Way before GSE. Naidu et al. (2022) showed
that Kraken stars display a low [Eu/Mg] enhancement, so it may be dominated by
prompt $r$-process sources. A third likely dwarf galaxy merger is the Sequoia
galaxy (Matsuno et al., 2019; Myeong et al., 2019), which is substantially
more metal-poor and chemically distinct (Matsuno et al., 2021b) but does not
yet have detailed $r$-process studies. There should be many more tidally
disrupted low-mass dwarf galaxies that can be identified in the Milky Way, and
searches are ongoing to discover and characterize their nature (e.g., Roederer
et al., 2018a; Naidu et al., 2020; Yuan et al., 2020; Gudin et al., 2021;
Shank et al., 2022; Brauer et al., 2022; Mardini et al., 2022).

Dwarf galaxies accreted more recently onto the Milky Way can be found as
tidally unbound but still spatially coherent structures known as stellar
streams. Streams are very low surface brightness, and they are discovered
through a combination of deep imaging and Gaia astrometry (e.g., Belokurov et
al., 2006; Grillmair, 2009; Shipp et al., 2018; Ibata et al., 2019). The most
spectacular stellar stream is the Sagittarius stream, which is caused by the
active tidal disruption of the Sagittarius dwarf galaxy (Majewski et al.,
2004); but many stellar streams have no apparent progenitor system. Streams
with unknown progenitors require spectroscopic followup to confirm whether
they are dwarf galaxies or globular clusters (e.g., Li et al., 2021). There
are now several spectroscopic studies of stellar streams that are producing
$r$-process constraints (e.g., Roederer et al., 2010; Casey et al., 2014; Ji
et al., 2020b; Hansen et al., 2021; Gull et al., 2021; Limberg et al., 2021).
Currently the data are still limited, but there are already as many dwarf
galaxy streams as intact dwarf galaxies in the intermediate mass range of
$10^{5}-10^{6}M_{\odot}$, and it is likely many more will be discovered in the
future.

The immense promise of the tidally disrupted dwarf galaxies for the
$r$-process is that they could be the best of both worlds, containing stars
close enough to obtain extremely high quality spectra for full $r$-process
patterns while also having a galactic environment to interpret (e.g., Naidu et
al., 2022). However, a general challenge with interpreting the $r$-process
content of tidally disrupted systems is ensuring the purity of stars studied
(e.g., Limberg et al., 2021). Unlike intact dwarf galaxies, where a spatial
cut clearly selects galaxy member stars, a tidally disrupted system can
overlap with multiple other structures in position and velocity space.
Membership in these systems must be probabilistic. It is thus difficult to
study intrinsic scatter in abundances in tidally disrupted systems, but it is
still useful to study mean chemical abundance trends.

##  6 State of the Art and Path Ahead

The many discoveries and observations of $r$-process signatures in halo and
dwarf galaxies confirm the existence of the $r$-process within early star
forming environments as well as within dwarf galaxies at various times since
the Big Bang. Still, information remains limited with regards to details on
the astrophysical site and environment as well as other parameters that
describe the operation of this nucleosynthesis process.

The following open questions will eventually need to be answered to fully
understand the origin of $r$-process elements:

  * •

How many astrophysical sites can be identified? If more than one, what is
their relative importance in different environments and over cosmic time?

  * •

What is the average rate of $r$-process events? When did the first $r$-process
events occur? How quickly does $r$-process production occur after star
formation?

  * •

What is the $r$-process yield? Is it variable per site? How do yields for
light and heavy $r$-process elements, as well as actinides, compare?

  * •

How much does $r$-process material get diluted and how quickly does it
reincorporated into stars? What is the explosion energy associated with
$r$-process events? How does this depend on galactic environment?

Current data have begun to provide answers while future photometric and
spectroscopic sky surveys as well as new instruments and telescopes will
hopefully provide additional insight over the coming decades. The current
state of the art is laid out in this section, which offers a glimpse of what
is to come in terms of new data and telescopes.

###  6.1 Observational Constraints on the $R$-process

Despite the above questions about the nature and origin of the $r$-process,
the body of data has, over the last decade, finally begun to reveal a number
of important findings, constraints, anecdotes, and partial answers. Table 3
summarizes these results, which represents the state of the art of
observational results regarding the astrophysical $r$-process from metal-poor
halo stars and dwarf galaxies. Overall, it is clear that compositional
information is best derived from the closer halo stars, while questions
relying on the galactic environment benefit most from the dwarf galaxies.

Property |  Evidence from Metal-Poor Halo Stars |  Evidence from Dwarf Galaxies
---|---|---
Rate |  Rare: large [Eu/Fe] scatter |  Rare: fraction of ultra-faint dwarf galaxies with $r$-process; ${\sim}10^{-3}$ that of core-collapse supernovae
Yield |  Ambiguous due to unknown dilution mass and metal-poor star formation site |  At least one prolific $r$-process site $M_{r}\gtrsim 10^{-2}M_{\odot}$
Delay Time |  Likely have prompt sources and may have delayed sources |  Must have both prompt and delayed sources
Composition |  Universal pattern from 2nd to 3rd peak Variations in relative abundance of 1st peak and actinides |  Consistent with halo stars
Table 3:  Summary of Evidence for $R$-process Site(s)

In more detail:

  * •

There are large variations in the absolute level of observed $r$-process
enhancements between stars, indicating either variable yields, or that the gas
mass in which yields were diluted were very different, or both.

  * •

There are significant variations in the detailed elemental composition of
$r$-process-enhanced stars. There is a universal pattern from the 2nd to 3rd
$r$-process peak between the solar system $r$-process residuals, but the
relative amount of first peak and actinide elements changes from star to star.
Future observations should be able to quantitatively investigate these
variations in metal-poor halo stars.

  * •

Some low-mass dwarf galaxies (e.g. Reticulum II) show $r$-process enhancement
while most others do not, indicating early $r$-process enrichment is
stochastic. Thus, the observed large $r$-process scatter in metal-poor halo
stars is likely due to accreting dwarf galaxies of different masses, rather
than inhomogeneous scatter within a single source of metal-poor stars.

  * •

In higher-mass dwarf galaxies, very few (if any) of the most metal-poor stars
appear to be completely free of $r$-process material, indicating that some
$r$-process element enrichment is rare but not delayed, i.e. it is ubiquitous
after a certain amount of stellar mass has been achieved in any given system.
However, the most metal-rich stars in these dwarf galaxies have differing
amounts of $r$-process relative to core-collapse supernovae ([Eu/Mg]), showing
that delayed sources eventually dominate.

  * •

Taken together, $r$-process dwarf galaxies and metal-poor $r$-process halo
stars point to a requirement for both prompt and delayed sources of
$r$-process elements.

###  6.2 New Surveys and New Dwarf Galaxies

The majority of results so far have come from studying the Milky Way stellar
halo and intact dwarf galaxies. The next decade will bring a number of
exciting spectroscopic and deep photometric surveys that will push this field
to new levels. Over the coming years, the community can thus anticipate the
discovery of many more dwarf galaxies whose varying properties will reveal
more information about the nature of the $r$-process.

New intact dwarf galaxies to be found in large photometric surveys: Given
current sky coverage, it is unlikely (though not impossible) that many new
intact dwarf galaxies will be found around the Milky Way with
$M_{\star}\gtrsim 10^{6}M_{\odot}$ in the coming years. However, it is
extremely likely that over 100 ultra-faint dwarf galaxies with
$M_{\star}\lesssim 10^{5}M_{\odot}$ will be found (Hargis et al., 2014;
Manwadkar & Kravtsov, 2021), especially with the Vera Rubin Observatory’s
Legacy Survey of Space and Time (Ivezić et al., 2019). With spectroscopic
followup, this should lead to a much better mapping of and understanding about
early stochastic $r$-process enrichment.

Tidally disrupted galaxies discovered with Gaia and spectroscopic surveys: In
principle, metal-poor stars in the halo all come from tidally disrupted dwarf
galaxies, and it is starting to be possible to associate them with erstwhile
dwarf galaxies. Likely only the surface has been scratched of discovering
tidally disrupted dwarf galaxy streams and halo structures with _Gaia_ and
spectroscopic surveys. Hence, the chemical study of such systems is still in
relative infancy (Roederer et al., 2010; Ji et al., 2020b; Hansen et al.,
2021; Aguado et al., 2021; Matsuno et al., 2021a, b). In the near future,
major spectroscopic surveys with the capability to directly measure
$r$-process abundances are WEAVE and 4MOST (Dalton et al., 2012; Feltzing et
al., 2018). The surveys SDSS-V and DESI are lower spectral resolution and do
not have the capability to measure $r$-process elements, but they will help
discover structures that can then be followed up with other facilities. There
are many nascent plans to build other wide-field spectroscopic facilities that
could potentially benefit $r$-process studies in both intact and tidally
disrupted dwarf galaxies, such as the Mauna Kea Spectroscopic Explorer (MSE;
The MSE Science Team et al. 2019). These tidally disrupted dwarf galaxies
should help fill out the range of dwarf galaxy masses and star formation
durations (Figure 6), enabling testing different chemical evolution
predictions on a larger sample of $r$-process abundance measurements.

###  6.3 New Instrumentation and Observational and Experimental Facilities

Ultraviolet spectroscopy: Many of the most important $r$-process elements can
only be measured at ultraviolet wavelengths, but it is currently difficult to
study even the brightest most nearby stars (Roederer et al., 2012, 2022) this
way. The United States 2020 Astronomy Decadal Survey identified a large IR-O-
UV space telescope as a priority for future development, and a high-resolution
UV spectrograph would help expand on existing, very limited stellar UV
datasets. However, it is unlikely that even future UV spectrographs will have
enough light-collecting power to study stars in distant dwarf galaxies.

Infrared spectroscopy: Other than ultra-violet, one technological development
in the past years is the development of high quality infrared detectors and
high-resolution spectrographs. The promise of this for $r$-process studies is
not yet clear because absorption lines in the infrared tend to be weaker than
the optical. However, lines have been identified for Sr, Y, Zr, Ba, Sm, Ce,
Nd, Eu, Dy, and Yb (Matsunaga et al., 2020; Smith et al., 2021)) in metal-
rich, solar-type disk stars.

Extremely Large Telescopes: The vast majority of spectroscopic observations of
dwarf galaxies are currently done on telescopes with effective mirror
diameters of 6.5 m to 10 m (e.g., the Magellan telescopes, the Very Large
Telescopes, the Subaru Telescope, the Keck Telescopes). A major endeavor of
the next decade is three projects aiming to build telescopes with effective
mirror diameters of $25-40$ meters: the Giant Magellan Telescope (GMT), the
Thirty Meter Telescope (TMT), and the European Extremely Large Telescope
(E-ELT). Tripling the telescope diameter effectively triples the distance out
to which dwarf galaxies can be studied while also enabling much larger numbers
of stars to be studied in individual galaxies. It also enables much higher
signal-to-noise spectra of existing stars, which will likely enable the
detection of additional elements, especially thorium.

New Experimental Facilities: Currently, theoretical calculations of
$r$-process nucleosynthesis rely on extensive models of nuclear masses and
reactions. The nuclear data uncertainties significantly limit many predictions
of astrophysical $r$-process calculations (e.g., Eichler et al., 2015;
Mendoza-Temis et al., 2015; Mumpower et al., 2016; Surman et al., 2017; Barnes
et al., 2021). However, upcoming experimental facilities like the Facility for
Rare Isotope Beams (FRIB), the Radioactive Isotope Beam Factor (RIBF), the
International Facility for Antiproton and Ion Research (FAIR), the Advanced
Rare IsotopE Laboratory (ARIEL), and the $N=126$ Factory at Argonne will
fundamentally transform this landscape (Horowitz et al., 2019). In the future,
small elemental and isotopic abundance deviations currently deemed consistent
will likely become major areas of research.

The next decades thus promise important advances in the field of nuclear
astrophysics, especially the study of the $r$-process and its astrophysical
site. Combining results from metal-poor $r$-process enhanced stars in the
Galactic halo and dwarf galaxies with other observations, such as
gravitational wave events from neutron star mergers, deep sea radioactive
isotope measurements of recent, local $r$-process events, as well as
experimental measurements of nuclei and reaction rates and theoretical
predictions for supernovae and neutron star merger yields has the potential to
provide a unified picture of the origin of $r$-process elements across cosmic
time.

## Acknowledgments

We thank our colleagues in the field of nuclear astrophysics for many years of
fruitful and enjoyable discussions about $r$-process topics, both
observationally and theoretically, and seeing the field grow from individual
stellar abundance patterns to large samples, including observations of stars
in dwarf galaxies. Specifically, we warmly thank our collaborators Tim Beers,
Rana Ezzeddine, Terese Hansen, Erika Holmbeck, Evan Kirby, Ting Li, Gail
McLaughlin, Andy McWilliam, Rohan Naidu, Brian O’Shea, Vinicius Placco, Ian
Roederer, Charli Sakari, Joshua Simon, and Rebecca Surman for sharing our
excitement about nuclear astrophysics. We are grateful to the Joint Institute
for Nuclear Astrophysics (JINA) for facilitating many of these interactions
over the last 20 years. We acknowledge support awarded by the U.S. National
Science Foundation (NSF): AST 1716251 and PHY 14-30152; Physics Frontier
Center/JINA Center for the Evolution of the Elements (JINA-CEE).

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