fission products produced from the proton-induced fission of Thorium. Fission
products were swept away by a Helium gas jet system into a double Penning trap
system that acts as a mass separator, resulting in a relatively pure beam of
$\beta$-decaying products. The transport system takes some time, on the order
of a few hundred milliseconds and imposes a limitation on the lifetimes that
can be studied. The BELEN detector is soon to become a part of the largest
ever neutron detector of its kind as a part of a 160 3He counter arrangement
being built by the BRIKEN collaboration for measurements of exotic nuclei at
RIKEN. The challenges that remain are the trade-offs between the highest
efficiencies and the best energy resolutions for the detection of neutrons.
First, measurements at the GSI fragment separator focused on the study of
massive radioactive nuclei of the N=126 closed shell in the Au to Rn range, in
order to determine the half-lives of these isotopes, the $\beta$-delayed
neutron emission probabilities, and the $P_{n}$-values, to compare with
theoretical model predictions Caballero-Folch  _et al._ (2016). This work
demonstrated that the FRDM+QRPA predictions typically used in r-process
simulations differ sometimes by up to an order of magnitude from the
experimental values. These discrepancies between theoretical predictions and
experimental result underline the importance of these kind of studies for
exploring the evolution of nuclear structure towards the r-process path and
beyond.

Recently, a new technique was demonstrated in which the challenges of neutron
detection are circumvented by measuring the nuclear recoil Yee  _et al._
(2013) instead of the neutron energy using traps. The traps can confine a
radioactive ion and basically $\beta$-decay at rest. The emitted radiation
emerges with minimal scattering, allowing the measurement of the ion recoil.
The $\beta$ is measured in coincidence with the ion recoiling as a result of
neutron emission resulting in a time of flight spectrum. The proof of
principle was demonstrated using a fission source of 252Cf, where fission
fragments are thermalized in a large volume gas catcher, extracted, bunched,
trapped and mass separated in a Penning trap, then delivered into a
$\beta$-decay Paul Trap (BPT). The $\beta$-particles are detected in a
$\Delta$E-E plastic scintillator while the recoil ions are detected in a
microchannel plate detector. The technique allows the measurements of exotic
isotopes with half-lives as short as 50 ms while avoiding some of the
complications of neutron measurements.

###  IV.3 Experiments towards Neutron Capture Rates

For a long time, the determination of neutron capture rates on neutron-rich
nuclei has been considered of secondary relevance for the simulation of
r-process nucleosynthesis and scenarios. This is due to the fact that the r
process is governed by an $(n,\gamma)\rightleftarrows(\gamma,n)$ equilibrium,
where the actual reaction rates cancel out as described earlier. However,
after freeze-out the equilibrium is no longer maintained and neutron capture
reactions on the neutron-rich r-process reaction products may well shift the
abundance distribution towards heavier nuclei. Sensitivity studies with
variations of the neutron capture rates by factors of ten result in
significant variations in the resulting abundances of the heavy elements as a
function of the astrophysical trajectories that are used (Mumpower  _et al._ ,
2015), but the experimental measurements of neutron capture on exotic beams
pose significant challenges, both in the production of the exotic nuclei as
well as the neutrons and in turn the measurements of the reaction rates.

While the direct measurement of neutron capture reactions on stable and even
long-lived radioactive for the s process has been very successful Guerrero
_et al._ (2017), a similar approach to study neutron capture on short-lived
neutron rich isotopes provides considerable challenges. Most of the r-process
neutron capture rates rely on theoretical predictions based on the Hauser-
Feshbach statistical model formalism Rauscher  _et al._ (1997); Goriely
(1998). To test and verify these predictions a number of indirect methods have
been developed over the last decade as a first step towards this goal. This
includes the so-called Oslo method Guttormsen  _et al._ (1987) as well as the
surrogate reaction technique Escher  _et al._ (2012), while new methods are
being envisioned towards a direct experimental approach.

####  IV.3.1 Neutron Capture on neutron rich nuclei: $\beta$-Oslo method

The Oslo method involves the extraction of level densities and $\gamma$-ray
strength functions by the measurements of the total de-excitation of a nucleus
as a function of energy. The different excitation ranges to be studied are
populated by different nuclear reaction modes that can range from light ion
transfer reaction to inelastic scattering techniques. This approach requires
high intensity beams and the direct measurements of cross sections Guttormsen
_et al._ (1987) to obtain the level density and strength function data with
sufficient statistics for extracting neutron capture cross sections. The
recent adaptation of the Oslo method has been demonstrated in the $\beta$-Oslo
method in which the $\beta$-decay of a neutron-rich nucleus populates the
levels at high excitation range and the subsequent $\gamma$-decay is measured
using total absorption spectroscopy Spyrou  _et al._ (2017). A first version
of this approach was developed on the basis of $\beta$-decay data obtained at
the ILL Grenoble and at ISOLDE at CERN (Kratz  _et al._ , 1983; Leist  _et
al._ , 1985). A benchmark test for quantifying the method was the successful
comparison between the level density analysis from the study of
87Br$(\beta^{-}n){}^{86}$Kr through neutron unbound states in 87Kr and the
direct 86Kr$(n,\gamma){}^{87}$Kr resonant neutron capture data (Raman  _et
al._ , 1983). An important aspect in this work is the fact that the extracted
level density is based on the analysis of the neutron decay data and not on
the $\gamma$-decay analysis.

The present approach, the so-called $\beta$-Oslo method, however, rests mostly
on the analysis $\gamma$-decay of highly excited states. Neutron unbound
states, populated by the $\beta$-decay are less likely to be observed because
they primarily decay into the particle rather than the $\gamma$ channel as
observed in the early studies Raman  _et al._ (1983). Nevertheless, the study
of the $\beta$-delayed $\gamma$-decay is a useful tool for determining level
densities up to the threshold. The new approach relies on the use of a 4$\pi$
summing detector device instead of a single Ge detector to analyze the
$\gamma$-decay pattern. The spectra are then unfolded as a function of
excitation energy in order to determine the nuclear level density and the
$\gamma$-strength function. The neutron capture cross section is derived by
folding the level density and $\gamma$-ray strength function with a nucleon-
nucleus optical model potential, adopting statistical asumptions for the
neutron transmission channels. The analysis depends critically on a number of
assumptions with respect to level density normalization and the optical
potential, which possibly introduces systematic uncertainties. However, the
largest uncertainty is in the assumption of the density of neutron unbound
states above the threshold and the associated neutron strength distribution.
This is typically determined from systematics and statistical model
simulations. It works well near the stability where the level density above
the neutron threshold is high. It becomes more questionable when the method is
applied to nuclei at the r-process path, where the neutron thresholds and
therefore the level density are much lower. A number of measurements have been
performed and the extracted results agree well with the predictions of Hauser-
Feshbach simulations (Spyrou  _et al._ , 2014) and the uncertainty range in
the prediction is claimed to be significantly reduced (Liddick  _et al._ ,
2016). The approach suggests a certain redundancy since the experimental data
do not consider the neutron strength function above the threshold, but adopt
the one predicted by the same statistical model against which the predicted
reaction rates are being tested. A study of the systematic uncertainties by
Spyrou  _et al._ (2017) suggests that the overall uncertainty in the rates
obtained by the $\beta$-Oslo method is within a factor of $\sim 3$ which is
comparable to the uncertainty range of case-optimized Hauser Feshbach
calculations (Beard  _et al._ , 2014).

####  IV.3.2 Neutron capture by $(d,p)$ surrogate reactions

Single particle transfer reactions such as $(d,p)$ have emerged as a powerful
tool for probing the single particle structure of neutron-rich nuclei near the
r-process path. First $(d,p)$ transfer measurements, using radioactive
130,132Sn beams on CD2 (deuterated polyethylene) targets at the Holifield
Radioactive Ion Beam Facility (HRIBF) radioactive beam facility in Oak Ridge
National Laboratory, led to a better understanding of the single particle
structure of bound states in 131,133Sn Kozub  _et al._ (2012); Jones  _et al._
(2010). The extracted single particle spectroscopic factors allowed
calculating the direct reaction components for neutron capture reactions.
Higher energy unbound states were not observed. The observation of such states
is critical for extracting reliably the single resonant or statistical
resonant contributions expected for high level density compound nuclei in
$(n,\gamma)$ reactions.

The study of the unbound regions of neutron-rich compound nuclei in
$(n,\gamma)$ reactions near the r-process path is the primary goal of the
surrogate reaction approach where single particle transfer reactions are
utilized to bypass the challenges of measuring neutron capture cross sections
on short lived nuclei. Neutron transfer reactions such as $(d,p)$ or
$(d,p\gamma)$ are frequently highlighted as surrogates for direct neutron
capture studies Escher  _et al._ (2012). In surrogate reactions the neutron is
carried within a “trojan” projectile and brought to react with the target. The
neutron-capture cross sections on the target nucleus can be extracted by
measuring the proton in the final stage Escher and Dietrich (2006); Forssén
_et al._ (2007). First benchmark experiments have been performed at the
88-inch cyclotron at Lawrence Berkeley National Laboratory probing the
171,173Yb$(n,\gamma)$ cross section via the surrogate reaction
171,173Yb$(d,p\gamma)$, using a high intensity deuterium beam Hatarik  _et
al._ (2010). The extracted neutron capture cross sections agreed within 15%
with direct measurements Wisshak  _et al._ (2000) at energies above 90 keV. At
lower energies corresponding to the stellar energy range considerably larger
discrepancies are observed.

In the case of neutron capture on short-lived nuclei, inverse kinematics
techniques will be necessary with short-lived radioactive beams interacting
with a deuterium target. Neutron-transfer measurement on a radioactive
r-process nucleus needs large area silicon detector arrays at backward angles
in coincidence with an ionization counter at forward angles to detect the
beam-like recoils to reduce the beam induced background. Such a system was
developed as the Oak Ridge - Rutgers University Barrel Array (ORRUBA) Pain
_et al._ (2007). The ORRUBA detector has been used in the center of the
Gammasphere Ge-array in a combination called Gammasphere Orruba Dual DEtectors
for $(d,p\gamma)$ studies using stable 95Mo beams Cizewski  _et al._ (2018)
but no conclusive results have been presented. Extracting the neutron capture
cross section out of the surrogate reaction measurements offers its own
challenges since it requires proper treatment of nuclear model parameters.
Deviations between the results of direct measurements and surrogate reaction
studies may reflect insufficient treatment and separation between different
reaction mechanisms, such as direct transfer and break-up components Avrigeanu
and Avrigeanu (2016). While promising as a method, a deeper understanding of
the reaction mechanism seems necessary Potel  _et al._ (2015).

####  IV.3.3 n-capture in ring experiments

Recently a new method has been proposed for the direct study of neutron
capture on short-lived nuclei, using high intensity radioactive beams in a
storage ring on a thermalized neutron target gas produced on-line by proton-
induced spallation reactions. Reifarth  _et al._ (2017). The cross section of
the neutron capture reactions would be measured in inverse kinematics,
detecting the heavy ion recoils in the ring, using for example the Schottky
method developed at the GSI storage ring facilities Nolden  _et al._ (2011).
This concept is an expansion of earlier work that proposed the use of the high
neutron flux in a reactor core as possible target environment with the
radioactive beam passing through the reactor core in a storage ring Reifarth
and Litvinov (2014). A number of simulations demonstrate that both methods
seems feasible albeit technically challenging, since it requires the
combination of a storage ring facility with either a spallation or fission
neutron source. There is a half-life limit that is mostly determined by the
production rate at the radioactive ion facility or the beam intensity and the
beam losses due to interactions with the rest gas in the ring. Yet, such a
facility would allow for the first time to address the challenges of neutron
capture reaction measurements on neutron rich radioactive isotopes with half
lives less than a minute in the decay products of r-process neutron-rich
nuclei.

##  V Nuclear modeling of r-process input

###  V.1 Nuclear masses

Table 1: Comparison of the root mean square deviation, in keV, for the mass models FRDM-1992 (Möller  _et al._ , 1995), HFB-21 (Goriely  _et al._ , 2010), DZ10, DZ31 (Duflo and Zuker, 1995), and WS3 (Liu  _et al._ , 2011) with experimental taken from the 2003 (Audi  _et al._ , 2003) and 2012 (Wang  _et al._ , 2012). The columns labeled “full” consider all masses present in each evaluation while the column labeled “new” includes only masses found in AME-2012 but not in AME-2003.  Model | AME-2003 | AME-2012 (new) | AME-2012
---|---|---|---
| (full) | (new) | (full)
FRDM-1992 | 655 | 765 | 666
HFB-21 | 576 | 646 | 584
WS3 | 336 | 424 | 345
DZ10 | 551 | 880 | 588
DZ31 | 363 | 665 | 400
Figure 24: Differences, in MeV, between experimental, taken from the 2012
version of the atomic mass evaluation AME12 (Wang  _et al._ , 2012), and
theoretical binding energies (left panels) and two-neutron separation energies
(right panels). The following mass models are shown: (FRDM-1992 Möller  _et
al._ , 1995, a, b), (HFB-21 Goriely  _et al._ , 2010, c, d), (DZ10 Duflo and
Zuker, 1995, e, f), (DZ31 Duflo and Zuker, 1995, g, h), (WS3 Liu  _et al._ ,
2011, i, j). (Figure from Mendoza-Temis, 2017).

The most basic nuclear property for any r-process calculation is the mass of
the nuclei involved. It determines the threshold energy for the main reactions
during the r process: $\beta$ decay, neutron capture and photo-dissociation.
Neutron separation energies, $S_{n}$, are particularly important if the r
process proceeds in $(n,\gamma)\rightleftarrows(\gamma,n)$ equilibrium, as the
reaction path is then fixed at a constant value of $S_{n}$, for given values
of neutron density and temperature of the astrophysical environment. The most
commonly used mass tabulations can be grouped in three different approaches:
a) microscopic-macroscopic models like the finite-range droplet model (FRDM)
approach Möller  _et al._ (1995, 2012a, 2012b, 2015, 2016), the Extended
Thomas-Fermi model with Strutinski Integral (ETFSI) approach Aboussir  _et
al._ (1995), the extended Bethe-Weizsäcker formula Kirson (2008) and the
Weizsäcker-Skyrme mass models Wang  _et al._ (2010); Liu  _et al._ (2011); b)
a microscopically inspired parametrization based on the averaged mean field
extracted from the shell model and extended by Coulomb, pairing and symmetry
energies Duflo and Zuker (1995); and c) microscopic models based on the non-
relativistic Goriely  _et al._ (2016) or relativistic Sun and Meng (2008)
mean-field models.

All mass models have in common that, by fitting a certain set of parameters to
known experimental data, they are then being used to predict the properties of
all nuclei in the nuclear landscape. The models reproduce the experimentally
known masses quite well, with mean deviations between 350 keV and 600 keV (see
Table 1). It is quite satisfying to see that, when in 2012 a new atomic mass
evaluation (AME) Wang  _et al._ (2012), including 219 new experimental masses,
became available the agreement with data worsened only slightly compared to
the comparison with the previous AME. However, when considering only the new
experimental masses found in AME-2012 the agreement deteriorates. As the new
masses typically involve more exotic nuclei than those found in a previous
evaluation, they provide a measure of the capabilities of each model to
extrapolate to regions far from stability. This is in general one the most
challenging aspects to determine when using a given mass model in r-process
calculations. Neufcourt  _et al._ (2018) has recently applied Bayesian
machine-learning techniques to assess the predictive power of global mass
models towards more unstable neutron-rich nuclei and provide uncertainty
quantification of predictions. Nevertheless, deviations between model and data
for neutron-rich nuclei are typically related to bulk properties that may not
dramatically affect the abundance predictions, e.g. the symmetry energy whose
value is known with an uncertainty 3.8 MeV to be the range 29.7–33.5 MeV
(Hebeler  _et al._ , 2013).

Fig. 24 provides a closer comparison between models and data. One notices
systematic deviations between models and data, i.e. for neutron numbers around
$N\sim 90$ and 130 just above the neutron shell closures at $N=82$ and 126
(Fig. 24). These mass regions are known as ‘transitional regions’ where
nuclear shapes change from spherical to deformed configurations, accompanied
by a sudden drop in neutron separation energies. The description of these
shape changes is very sensitive to correlations which are not fully accounted
for in the current mass models. Noticeable differences among the various mass
models, and the data, are also observed in the differences of neutron
separation energies for odd-A and odd-odd nuclei Arzhanov (2017), likely
pointing to the need for an improved description of neutron-proton
correlations. A better description, in particular of the transitional region,
requires beyond-mean-field techniques. A first attempt has been presented in
Rodríguez  _et al._ (2015), based on the Generator Coordinator Method which
considers superpositions of different shapes and restores the breaking of
particle number and angular momentum as inherent in the Hartree-Fock-
Bogoliubov (HFB) approach. However, first calculations of nuclear masses show
only rather slight effects for nuclei in the $N\sim 90$ range.

Although the differences in the transitional regions at $N\sim 90$ and 130
between the various mass models might be rather minute, they can have
noticeable impact in r-process simulations. The FRDM (Möller  _et al._ , 1995)
and version 21 of the Brussels Hartree-Fock-Bogoliubov mass model (HFB21
Goriely  _et al._ , 2010) predict noticeably smaller neutron separation
energies than the Duflo-Zuker (Duflo and Zuker, 1995) or the Weizsäcker-Skyrme
(WS3 Wang  _et al._ , 2010; Liu  _et al._ , 2011) models in the $N\sim 130$
mass range. As a consequence, for the former two mass tabulations, these
nuclei act as obstacles in the r-process mass flow and produce a third
r-process abundance peak which is narrower in width, overestimated in height,
slightly shifted to larger mass numbers and followed by an abundance trough
just above the peak if compared to simulations using the Duflo-Zuker and WS3
masses (and to data) (see Fig. 25). At $N\sim 90$ the FRDM predicts very low
neutron separation energies, in contrast to the other mass models! Arcones and
Martínez-Pinedo (2011). As is discussed in Mendoza-Temis  _et al._ (2015)
these low $S_{n}$ values have consequences for the matter flow between the
second and third r-process peaks and result in a narrow peak around $A\sim
136$ in the r-process abundances at freeze-out, which is, however, washed out
at later times due to continuous productions of material in this region by
fission. Similar effects have also been observed in Martin  _et al._ (2016)
using masses derived from Skyrme energy density functionals based on different
optimization protocols. This allows for systematic studies of uncertainty
bands under the same underlying physical model for the description of nuclear
masses.

Figure 25: Final mass-integrated r-process abundances obtained in a neutron-
star merger simulation using four different mass models (adopted from Mendoza-
Temis  _et al._ , 2015) Figure 26: Comparison of experimental (Pfeiffer  _et
al._ , 2001; Dillmann  _et al._ , 2003; Fogelberg  _et al._ , 2004; Lorusso
_et al._ , 2015) and shell-model halflives (Zhi  _et al._ , 2013) for $N=82$
r-process nuclei

###  V.2 Beta half lives

Nuclear beta decays, which change a neutron into a proton, are responsible for
the mass flow to elements with increasingly heavier $Z$-number. As the r
process occurs in a dynamical environment, the time, which is needed for the
succession of beta decays to produce thorium and uranium from the seed nuclei
available after freeze-out of charged-particle fusion reactions, is competing
with the dynamical timescale of the explosion, which transports matter to
larger radii (and lower densities), thus suppressing the neutron number
density required for the mass flow to heavier nuclei by neutron captures.
Particularly important are beta decays of nuclei with magic neutron numbers
$N_{\rm mag}$, as the matter flow is hindered by the reduced neutron
separation energies of the nuclei with $N_{\rm mag}+1$. Furthermore, due to
the extra binding of the magic nuclei, the $Q$-value of their beta decays is
relatively reduced, resulting in longer lifetimes.

Calculations of beta decays require two ingredients: the relative energy scale
between parent and daughter nuclei (Q value) and the transition strength
distribution in the daughter nucleus. We note that the $Q$ values are large
for r-process nuclei due to the extreme neutron excess. As a consequence
uncertainties in this quantity (usually of order 0.5–1 MeV) have a mild effect
on the half lifes, despite the strong energy dependence of the involved phase
space ($E^{5}$ for allowed Gamow-Teller transition, and even higher powers for
forbidden transitions). However, this strong energy dependence makes the half
life sensitive to the detailed low-lying strength distribution, which is also
crucial to determine whether the beta decay is accompanied by the emission of
neutrons, i.e. whether the transition proceeds to states in the daughter
nucleus above or below the neutron threshold (which is only 2–3 MeV in
r-process nuclei). This so-called $\beta$-delayed neutron emission is a source
of free neutrons and plays an important role in determining the final
r-process abundances during the freeze-out of neutron captures Arcones and
Martínez-Pinedo (2011).

Nucleon-nucleon correlations are responsible for the strong fragmentation of
the transition strengths and for its suppression compared to the Independent
Particle Model. These correlations are accounted for in the interacting shell
model Caurier  _et al._ (2005), and in fact large-scale shell model
calculations have been proven as the appropriate tool to describe nuclear
Gamow-Teller distributions Caurier  _et al._ (1999); Cole  _et al._ (2012) for
stellar weak interaction processes Langanke and Martínez-Pinedo (2000, 2003).
Shell-model calculations proved also very valuable for the calculation of the
half lives of r-process key-nuclei with magic neutron numbers. For 78Ni the
shell model predicted a half life of 127 ms (Langanke and Martínez-Pinedo,
2003), which was significantly shorter than the value estimated by global
models at the time, and was subsequently experimentally verified ($110\pm 40$
ms, Hosmer  _et al._ , 2005). As is shown in Fig. 26, the half lives for the
$N=82$ r-process nuclei recently measured at RIKEN Lorusso  _et al._ (2015)
agree very well with the earlier shell model values Zhi  _et al._ (2013), once
the quenching of GT transitions is adjusted to the new 130Cd half-live. The
shell model calculations imply that the half lives for the $N=50$ and 82
r-process nuclei are dominated by Gamow-Teller transitions and forbidden
strengths contribute only on the few-percent level. This is different for the
$N=126$ r-process waiting points. Here two independent large-scale shell model
calculations Suzuki  _et al._ (2012); Zhi  _et al._ (2013) give evidence that,
due to the presence of intruder states with different parity, forbidden
transitions contribute significantly and make the half lives about a factor of
2 shorter than estimated for pure allowed transitions. In turn, the shorter
half lives allow for a faster mass flow through the $N=126$ waiting points. We
note that the relevant forbidden transitions are at low excitation energies,
where due to their enhanced phase space energy dependence they can compete
with allowed transitions, and hence they have a strong impact on the
$\beta$-delayed neutron emission probability.

The shell model is the method-of-choice for $\beta$-decay calculations.
However, due to the model spaces involved, calculations are only possible for
r-process nuclei near closed neutron shells. Thus, the global beta decay rates
for r-process simulations have to be modelled by less sophisticated many-body
models. Traditionally these studies were performed by calculation of the
Gamow-Teller strength distributions within the Quasiparticle Random Phase
Approximation on the basis of the Finite Range Droplet Model Möller  _et al._
(1997) or the ETFSI approach (Extended Thomas Fermi Model with Strutinsky
Integral, Borzov and Goriely, 2000). Experimental data for half-lives of
r-process nuclei around $N=50$ and 82 Pfeiffer  _et al._ (2001); Lorusso  _et
al._ (2015) showed that these estimates were systematically too long. The
FRDM+QRPA model was subsequently extended to include forbidden transitions
within the phenomenological “gross theory” Möller  _et al._ (2003). A new
promising road towards globally calculating half lives for r-process nuclei
has recently been developed by performing QRPA studies on top of the self-
consistent Hartree-Fock-Bogoliubov (HFB+QRPA, Engel  _et al._ , 1999) method
or density functionals either non-relativistic (Borzov, 2003) or relativistic
(Marketin  _et al._ , 2007). Recent covariant density functional theory
(D3C∗+QRPA Marketin  _et al._ , 2016a) and Skyrme finite-amplitude Mustonen
and Engel (2016); Shafer  _et al._ (2016) studies, which accounted for allowed
and forbidden transitions, yielded noticeably shorter half lives for medium
and heavy nuclei than obtained by the FRDM+QRPA approach.

Shorter half lives for r-process nuclei with $Z>80$ have a strong impact on
the position of the third r-process peak Eichler  _et al._ (2015) and enhance
the mass flow through the $N=126$ waiting points Mendoza-Temis  _et al._
(2015). The latter implies more material available for fission, thus affecting
the abundances of the second r-process peak, and the late-time $\alpha$ decays
from the decaying r-process matter in a neutron star merger event (Wu  _et
al._ , 2018). Studies of the influence on beta decays on the r-process
abundances for different astrophysical sites have been reported in Mumpower
_et al._ (2016); Shafer  _et al._ (2016); Kajino and Mathews (2017).

In principle, the transformation of neutrons into protons can also be achieved
by charged-current ($\nu_{e},e^{-}$) reactions. In fact, there have been
various suggestions how neutrino-induced reactions on nuclei might affect
r-process nucleosynthesis (e.g. Qian  _et al._ , 1997; Haxton  _et al._ ,
1997; Meyer  _et al._ , 1998; Otsuki  _et al._ , 2000; Terasawa  _et al._ ,
2004). All these studies were based on the assumption that the r-process
operates in the neutrino-driven wind scenario in the presence of strong
neutrino fluxes. These assumptions are not supported by modern supernova
simulations. In the neutron star merger scenario neutrino fluxes once the
r-process operates are too low to substantially influence the abundances by
charged-current reactions (Roberts  _et al._ , 2017). However, the initial
proton-to-neutron ratio of the matter ejected in neutron star mergers and its
spatial and time dependence is set by neutrino reactions on free nucleons (see
section VI)

###  V.3 Neutron captures

During the r-process phase, in which the temperature is large enough
($T\gtrsim 1$ GK), neutron captures and its inverse reaction, photo-
dissociation, are in equilibrium. The rates become, however, relevant once the
nucleosynthesis process drops out of this equilibrium. As the temperature is
cooler during this period, it is mainly neutron capture that matters.

The neutron capture and photo-dissociation rates for r-process nuclei (the
latter can be derived by detailed balance from the former) are traditionally
determined within the statistical model. This assumes a sufficiently high
density of states in the daughter nucleus at the relevant capture energies
just above the neutron threshold which is not given for the most neutron-rich
nuclei close to the neutron dripline. A systematic estimate about the range of
nuclei for which the statistical model is applicable to calculate neutron
capture rates is given in Rauscher  _et al._ (1997). It has been proposed that
for the most neutron-rich nuclei the capture rates should be calculated within
a direct-capture approach based on a potential Mathews  _et al._ (1983);
Otsuki  _et al._ (2010); Xu and Goriely (2012); Xu  _et al._ (2014). In such
an approach the rate is often determined by a single resonance in the Gamow
window Loens  _et al._ (2012). This makes rate predictions quite uncertain, as
nuclear models are not capable to predict the resonance energies with
sufficient accuracy. It has therefore been suggested to describe the final
states by a level density rather than by discrete levels Goriely (1997);
Ejnisman  _et al._ (1998). Calculations of neutron capture rates which include
a statistical component and a direct contribution are reported in Mocelj  _et
al._ (2007).

The main ingredients of statistical model calculations within the Hauser-
Feshbach approach are the nuclear level density, the $\gamma$-strength
function for the decay of the compound state, and various light-particle
potentials. The $\gamma$ transition can occur with different multipolarities
requiring either different ($E1$) or equal parities ($M1$, $E2$) between the
involved states. To additionally fulfil the angular momentum selection rules,
requires the knowledge of parity- and angular-momentum-dependent level
densities.

There has been significant progress in modelling nuclear level densities in
recent years. With the Shell Model Monte Carlo approach (SMMC) Johnson  _et
al._ (1992); Koonin  _et al._ (1997) a tool became available which allowed
level densities in unprecedently large model spaces. The method to derive
level densities within the SMMC was presented in Ormand (1997); Nakada and
Alhassid (1997); Langanke (1998) and then systematically extended to explore
the parity-dependence Alhassid  _et al._ (1999) and angular-momentum-
dependence Alhassid  _et al._ (2007). In Özen  _et al._ (2015) the collective
vibrational and rotational enhancement factors have been explored, finding
that the decay of these enhancement factors is correlated with the pairing and
shape phase transitions. The vanishing of pairing and its effect on the level
density has been studied in Langanke (2006). In the Bethe Fermi Gas (BFG)
level density formula this vanishing has been described by a temperature-
dependent pairing parameter Mustafa  _et al._ (1992); Junghans  _et al._
(1998) for which Langanke (2006) gives a parametrization on the basis of the
SMMC calculations. SMMC calculations have been performed for many mid-mass and
heavy nuclei. These include even-even, odd-A and odd-odd nuclei, allowing to
microscopically test the standard presription in the BFG level density to
describe the systematic differences in these nuclei due to the pairing effect
by a pairing shift parameter (e.g. Cowan  _et al._ , 1991; Rauscher and
Thielemann, 2000).

Despite these advances, a calculation of level densities for all nuclei
involved in r-process nucleosynthesis is out of scope. However, these
calculations have initiated and guided attempts to extend a microscopically
derived parity dependence into phenomenological level density formulae like
the BFG approach. This is achieved by deriving the excitation-energy dependent
parity ratio in the level density by the assumption of Poisson distributed
independent quasi-particles combined occupation numbers obtained from the BCS
(Bardeen-Cooper-Schrieffer) model, in this way including pairing (Alhassid
_et al._ , 2000). In Mocelj  _et al._ (2007) this approach has been applied to
the large set of r-process nuclei (incorporating also a temperature-dependent
pairing parameter suggested from SMMC studies) and its effects on
astrophysically relevant reaction rates was studied in Loens  _et al._ (2008).
This improved level density description is part of the statistical model
packages NON-SMOKER and SMARAGD developed by Rauscher Rauscher and Thielemann
(2001); Rauscher (2011).

A different path to derive parity- and angular-momentum-dependent level
densities has been followed by Goriely and co-workers, based on a
combinatorial approach within HFB calculations. Also this approach has been
incorporated into a statistical model package and applied to the calculation
of neutron capture rates for r-process nuclei within the Brussels Nuclear
Library for Astrophysics Applications
(BRUSLIB)666http://www.astro.ulb.ac.be/bruslib data compilation Koning  _et
al._ (2008); Goriely  _et al._ (2008); Hilaire  _et al._ (2010); Goriely  _et
al._ (2012).

Traditionally the different $\gamma$-strength functions have been described by
global parametrizations Cowan  _et al._ (1991) which were adjusted to photo-
dissociation for $E1$ transitions or electron scattering data for $M1$
transitions (e.g. Cowan  _et al._ , 1991). Recently $E1$ strength functions
became available which were microscopically calculated for individual nuclei
within the framework of the HFB model Goriely and Khan (2002); Goriely  _et
al._ (2004) or based on the relativistic mean field model Litvinova  _et al._
(2009). These calculations support the presence of enhanced dipole strength at
energies just above the neutron threshold. Experimentally such enhanced
strength is observed as ‘pygmy dipole strength’ in nuclei with large neutron
excess, like those involved in r-process nucleosynthesis Adrich  _et al._
(2005). As shown in Goriely (1998) this enhanced dipole strength can have
significant impact on neutron capture cross sections.

Dipole $\gamma$-strength functions determined from particle-$\gamma$
coincidence data in neutron pick-up and inelastic scattering data for several
mid-mass nuclei exhibit a remarkable upbend of the strength towards
$E_{\gamma}=0$ (e.g. Guttormsen  _et al._ , 2005; Larsen  _et al._ , 2006,
2007). The data also allow for the derivation of the nuclear level density,
making a few assumptions (the Oslo method, Schiller  _et al._ , 2000) (see
section IV.3.1). The impact of this upbend on neutron capture rates for
r-process nuclei has been studied in Larsen and Goriely (2010); Larsen  _et
al._ (2015) and a potential increase of the capture rate by up to two orders
of magnitude has been calculated. The origin of the low-energy upbend has yet
not been completely identified. Coherent adding of magnetic moments of
high-$j$ orbitals has been suggested as a possible mechanism for low-energy
$M1$ enhancement Schwengner  _et al._ (2013); Brown and Larsen (2014);
Schwengner  _et al._ (2017), while a low-energy upbend in the $E1$ strength
was obtained within finite-temperature relativistic QRPA calculations
Litvinova and Belov (2013). An upbend in the $M1$ strength function has also
been found in large-scale shell model calculations for selected $pf$-shell
nuclei Sieja (2017) and $A\gtrsim 100$ Sieja (2018). Goriely  _et al._ (2018)
have performed large scale calculations of $E1$ and $M1$ strength functions by
a combination of shell-model and Gogny-HFB+QRPA calculations.

Several general questions regarding basic assumptions made in statistical
model evaluations of capture rates have been addressed in large-scale shell
model calculations of the $M1$ strength functions for several mid-mass nuclei
(similar studies for $E1$ transitions are yet prohibited by computing
limitations as they require the inclusion of two major shells, Loens  _et al._
, 2012). The results are briefly summarized as: a) The shell-model $M1$
strength functions turned out to give smaller cross sections than the usually
adopted parametrizations; b) the scissors mode, a fundamental orbital $M1$
excitation observed in deformed nuclei at low energies Bohle  _et al._ (1984),
might lead to a noticeable enhancement of the capture rates; c) the assumption
of the Brink hypothesis, i.e. the strength function is the same for all
nuclear states Brink (1955, 1957) is only valid with moderate accuracy; and d)
the cross section calculated microscopically by a state-by-state approach had
the largest contribution from a single state with $M1$ excitations just in the
Gamow window. Such a nuclear structure effect cannot be caught by any global
parametrization. The potential impact of the $M1$ scissors mode on r-process
neutron capture cross sections has subsequently been revisited by Mumpower
_et al._ (2017a).

The transmission coefficients required in statistical model calculations of
astrophysical rates Cowan  _et al._ (1991); Rauscher and Thielemann (2000) are
calculated on the basis of global optical potentials. For the proton and
neutron potentials several rather reliable potentials exist (e.g., Jeukenne
_et al._ , 1977; Bauge  _et al._ , 2001; Koning and Delaroche, 2003; Goriely
and Delaroche, 2007). The situation is different for the $\alpha$-optical
potential. Although several global potentials exist (e.g., McFadden and
Satchler, 1966; Demetriou  _et al._ , 2002, 2003; Kiss  _et al._ , 2009; Mohr
_et al._ , 2013), none of them is able to consistently describe the existing
data at low energies in statistical model approaches. Using 64Zn as an
example, Mohr  _et al._ (2017) explores the sensitivity of the
$\alpha$-induced reaction cross section to the variation of different alpha
optical potential (and other parameters in the statistical model). Attempts
have been made to cure the problem. Rauscher suggested that the consideration
of Coulomb excitation leads to a better agreement with data Rauscher (2013).
In Demetriou  _et al._ (2002) it was shown that a modified imaginary part of
the optical potential can improve the reproduction of experimental reaction
data at low energies. Based on a large set of $\alpha$-induced reaction data
at sub-Coulomb energies Avrigeanu  _et al._ (2014); Avrigeanu and Avrigeanu
(2015) have presented a global $\alpha$-optical potential for nuclei in the
mass range $45\leq A\leq 209$.

###  V.4 Fission

Fission plays an important role in the r process, in particular within the NS-
NS merger scenario. Fission determines the region of the nuclear chart at
which the flow of neutron captures and beta decays stop Thielemann  _et al._
(1983); Petermann  _et al._ (2012); Giuliani  _et al._ (2018). In the
particular case of dynamic cold ejecta from mergers, several fission cycles
are expected to operate before all neutrons are used Korobkin  _et al._
(2012); Goriely (2015); Goriely and Martínez-Pinedo (2015). Fission has been
suggested to be responsible for producing a robust r-process pattern Korobkin
_et al._ (2012); Rosswog  _et al._ (2014); Goriely (2015), in which the
abundances of nuclei with $A\lesssim 140$ are determined during the r-process
freeze-out from the fission yields of nuclei with $A\lesssim 280$ (see
Mendoza-Temis  _et al._ , 2015, and Fig. 19).

The description of fission for r-process nuclei is very challenging as it
sensitively depends on the knowledge of the fission barriers for a broad range
of very neutron-rich nuclei. In addition, the evolution of the shell structure
as function of neutron excess is very uncertain. Several competing reaction
channels need to be modelled, including neutron capture, neutron-induced
fission, beta decay, $\beta$-delayed fission, spontaneous fission, alpha decay
and gamma-induced fission. Hence, parallel to the calculation of fission
barriers one has to develop models for all these different reaction channels.
Several studies have computed barriers for r-process nuclei Howard and Möller
(1980); Myers and Świaţecki (1999); Mamdouh  _et al._ (2001); Goriely  _et
al._ (2009); Erler  _et al._ (2012); Möller  _et al._ (2015). It has been
shown that the dominating fission channel during r-process nucleosynthesis is
neutron-induced fission (Panov  _et al._ , 2005; Martínez-Pinedo  _et al._ ,
2007; Petermann  _et al._ , 2012). However, the necessary reaction rates have
been computed for a strongly limited set of barriers Thielemann  _et al._
(1989); Panov  _et al._ (2005); Goriely  _et al._ (2009); Panov  _et al._
(2010). This hinders studies of the sensitivity of the r-process abundances to
the fission barriers. Due to the dominance of neutron-induced fission, the
fission barrier itself is the most important quantity for the determination of
reliable fission rates, as the fission process occurs at energies just above
the fission barrier. In this case, the inertial mass parameter plays a minor
role as tunneling through the barrier has only a negligible contribution. This
fact, however, simplifies calculations considerably as the calculation of the
inertial mass parameter is rather challenging Sadhukhan  _et al._ (2013);
Giuliani  _et al._ (2014, 2018).

In addition to the description of the different fission reaction channels,
also the corresponding fission yields, which depend on the excitation energies
of the compound nucleus Kelic  _et al._ (2008, 2009); Schmidt  _et al._
(2016); Sadhukhan  _et al._ (2016); Zhang  _et al._ (2016); Schmitt  _et al._
(2018); Schmidt and Jurado (2018), have to be known for r-process simulations.
As discussed above, the fission yields determine the abundance of r-process
elements in the second r-process peak and above and can play an important role
for abundance distribution of rare-earth elements Bengtsson and Howard (1975);
Steinberg and Wilkins (1978); Panov  _et al._ (2008); Goriely  _et al._
(2013); Eichler  _et al._ (2015); Vassh  _et al._ (2018).

It should be emphasized that during the last phase of the r-process alpha
decays compete with fission. This competition determines the final abundances
of Pb, U and Th and of long-lived actinides. Consequently, an improved
description of transuranic nuclides is necessary for the determination of the
r-process abundances produced in the dynamic ejecta from neutron star mergers,
with important consequences for the kilonova lightcurves (Hotokezaka  _et al._
, 2016; Barnes  _et al._ , 2016; Rosswog  _et al._ , 2017; Zhu  _et al._ ,
2018; Wanajo, 2018; Wu  _et al._ , 2018).

###  V.5 Nuclear Equation of State

Most environments expected to be sites of a strong r process involve objects
at highest densities, whether related to core-collapse, compact binary
mergers, or the inner areas of black hole accretion disks. The nuclear and
supra-nuclear equation of state is of highest importance for modelling these
sites, providing the pressure response during dynamic phases, the nuclear and
particle composition, the existence of electron/positron pairs and their
degeneracy, and last but not least determining maximum neutron star masses,
which are important e.g. for answering the question whether in compact binary
mergers a hypermassive neutron star lives for period or remains as a final
outcome. The recent discovery of massive $\sim 2$ M⊙ neutron stars (Demorest
_et al._ , 2010; Antoniadis  _et al._ , 2013) had a major impact. Thus,
simulations of neutron-star mergers and core-collapse supernovae are quite
sensitive to the adopted Equation of State (EoS), particularly its stiffness,
mainly related to the symmetry energy (for some recent literature see e.g.,
Lattimer, 2012; Hebeler  _et al._ , 2013; Steiner  _et al._ , 2013; Lattimer,
2014; Fischer  _et al._ , 2014; Baldo and Burgio, 2016; Steiner  _et al._ ,
2016; Özel and Freire, 2016; Lattimer and Prakash, 2016). Oertel  _et al._
(2017) give an excellent overview about the various EoS implementations
available, as well as the experimental nuclear and astronomical constraints.

##  VI Astrophysical Sites and their ejecta composition

In section I we have whetted the appetite already by mentioning possible
sources/sites for the origin of the heavy r-process elements. Section III has
discussed the optimal conditions that any astrophysical site should attain in
order to produce r-process nuclei. They reduce to particular combinations of
entropy, expansion time scale, and $Y_{e}$ in the ejecta. As a minimum
requirement the ejecta should be characterized by a high neutron-to-seed
nuclei ratio. This is certainly the case for neutron-rich matter, pointing
naturally to neutron stars as an important reservoir of neutrons. However,
ejecting material from the deep gravitational field of a neutron star requires
a cataclysmic event. Thus could be either associated to the birth of a neutron
star in a supernova explosion or to ejecta from a compact binary merger
involving a neutron star. This leads logically to the most promising sites for
a strong r process: (i) The innermost ejecta of regular core-collapse
supernovae. But opposite to initial expectations (e.g. Hillebrandt  _et al._ ,
1976), the ejecta of a neutrino-driven core-collapse supernova are not very
neutron-rich. However, for high entropies high neutron-to-seed ratios could be
obtained, permitting a strong r process (Woosley  _et al._ , 1994; Takahashi
_et al._ , 1994; Hoffman  _et al._ , 1997; Qian and Wasserburg, 2007; Farouqi
_et al._ , 2010; Roberts  _et al._ , 2012; Martínez-Pinedo  _et al._ , 2012;
Arcones and Thielemann, 2013; Martínez-Pinedo  _et al._ , 2014; Mirizzi  _et
al._ , 2015; Fischer  _et al._ , 2018b). (ii) A special class of core collapse
supernovae (magneto-rotational MHD-jet supernovae or collapsars), with fast
rotation and high magnetic fields responsible for their explosion mechanism,
can come with neutron-rich jet ejecta along the poles or from accretion disk
outflows (Fujimoto  _et al._ , 2006, 2007, 2008; Ono  _et al._ , 2012;
Winteler  _et al._ , 2012; Mösta  _et al._ , 2014; Nishimura  _et al._ ,
2015a; Mösta  _et al._ , 2015; Shibagaki  _et al._ , 2016; Nishimura  _et al._
, 2017; Mösta  _et al._ , 2018; Halevi and Mösta, 2018; Siegel  _et al._ ,
2018). (iii) Ejecta from binary neutron star mergers are naturally neutron-
rich (Lattimer and Schramm, 1974, 1976; Eichler  _et al._ , 1989; Freiburghaus
_et al._ , 1999b; Nishimura  _et al._ , 2006; Korobkin  _et al._ , 2012;
Bauswein  _et al._ , 2013; Wanajo  _et al._ , 2014; Just  _et al._ , 2015a;
Eichler  _et al._ , 2015; Goriely, 2015; Ramirez-Ruiz  _et al._ , 2015;
Mendoza-Temis  _et al._ , 2015; Shibagaki  _et al._ , 2016; Just  _et al._ ,
2016; Radice  _et al._ , 2016; Wu  _et al._ , 2016; Rosswog  _et al._ , 2017;
Lippuner  _et al._ , 2017; Siegel and Metzger, 2017; Bovard  _et al._ , 2017;
Baiotti and Rezzolla, 2017; Thielemann  _et al._ , 2017b), all predicted
before the observation of GW170817.

A common feature of these scenarios is that matter reaches such high
temperatures that neutrinos become the main cooling mechanism. Those neutrinos
and in particular electron flavor neutrinos can interact with the ejecta and
reset the composition that is commonly determined by a balance between the
following reactions:

$\displaystyle\nu_{e}+n$ $\displaystyle\rightleftarrows$ $\displaystyle
p+e^{-}$ (8) $\displaystyle\bar{\nu}_{e}+p$ $\displaystyle\rightleftarrows$
$\displaystyle n+e^{+}.$ (9)

In the case of neutrino-driven winds and potentially also for neutron star
mergers ejecta, the material is subject long enough to the processes above to
reach an equilibrium between neutrino and antineutrino captures (Qian and
Woosley, 1996; Martínez-Pinedo  _et al._ , 2016), resulting in

$Y_{e}=Y_{e,\text{eq}}=\left[1+\frac{L_{\bar{\nu}_{e}}W_{\bar{\nu}_{e}}}{L_{\nu_{e}}W_{\nu_{e}}}\frac{\varepsilon_{\bar{\nu}_{e}}-2\Delta+\Delta^{2}/\langle
E_{\bar{\nu}_{e}}\rangle}{\varepsilon_{\nu_{e}}+2\Delta+\Delta^{2}/\langle
E_{\nu_{e}}\rangle}\right]^{-1}.$ (10)

with $L_{\nu_{e}}$ and $L_{\bar{\nu}_{e}}$ being the neutrino and antineutrino
luminosities, $\varepsilon_{\nu}=\langle E_{\nu}^{2}\rangle/\langle
E_{\nu}\rangle$ the ratio between the second moment of the neutrino spectrum
and the average neutrino energy (similarly for antineutrinos), $\Delta=1.2933$
MeV the neutron-proton mass difference, and $W_{\nu}\approx 1+1.01\langle
E_{\nu}\rangle/(m_{n}c^{2})$, $W_{\bar{\nu}}\approx 1-7.22\langle
E_{\bar{\nu}}\rangle/(m_{n}c^{2})$ the weak-magnetism correction to the cross
sections for neutrino and antineutrino absorption (Horowitz, 2002) with
$m_{n}$ the nucleon mass.

These reactions turn matter neutron-rich provided the following condition is
fulfilled:

$\varepsilon_{\bar{\nu}_{e}}-\varepsilon_{\nu_{e}}>4\Delta-\left[\frac{L_{\bar{\nu}_{e}}W_{\bar{\nu}_{e}}}{L_{\nu_{e}}W_{\nu_{e}}}-1\right](\varepsilon_{\bar{\nu}_{e}}-2\Delta).$
(11)

Figure 27: (left panel) Evolution of the luminosities and average energies of
neutrinos emitted during the protoneutron star cooling phase following a core-
collapse supernova explosion (adapted from Martínez-Pinedo  _et al._ , 2014).
(right panel) Luminosities and average energies of neutrinos emitted after a
NS-NS merger that forms and hypermassive neutron star surrounded by an
accretion disk. (based on the simulations from Perego  _et al._ , 2017b,
courtesy of Albino Perego).

One should keep in mind an important difference between neutrino emission from
protoneutron stars formed in core-collapse supernovae and the emission from a
neutron-star merger remnant (see Fig. 27). In the supernova case, we deal with
the deleptonization of a hot neutron star and consequently we expect slightly
higher fluxes for $\nu_{e}$’s than $\bar{\nu}_{e}$’s. However, due to the fact
that the $\bar{\nu}_{e}$ spectrum is slightly hotter than the $\nu_{e}$
spectrum, the luminosities of both flavors are rather similar. According to
Eq. (11) this implies that the average energies between $\bar{\nu}_{e}$ and
$\nu_{e}$ should differ by at least $4\Delta\approx 5.2$ MeV. Such large
differences are not reached in any modern neutrino-wind simulation Hüdepohl
_et al._ (2010); Fischer  _et al._ (2010); Martínez-Pinedo  _et al._ (2012);
Roberts  _et al._ (2012); Martínez-Pinedo  _et al._ (2014); Mirizzi  _et al._
(2015). In the case of a neutron star merger the initial configuration
corresponds to a cold very neutron-rich neutron star. Due to the merger
dynamics the final merger remnant and accretion disk is heated to large
temperatures. The large temperatures favor the production of electron-positron
pairs and the material tends to protonize towards the new equilibrium $Y_{e}$
on timescales of hundreds of ms as determined by the weak interaction
timescale in matter affected by neutrino interactions (Beloborodov, 2003;
Arcones  _et al._ , 2010). During this phase the luminosities and average
energies of $\bar{\nu}_{e}$ are much larger than those of $\nu_{e}$ (see right
panels of Fig. 27), reducing the required energy difference of Eq. (11).
Hence, even if the impact of neutrino process in mergers is expected to be
substantial Wanajo  _et al._ (2014); Perego  _et al._ (2014); Sekiguchi  _et
al._ (2015); Martin  _et al._ (2015); Sekiguchi  _et al._ (2016); Foucart  _et
al._ (2016); Martin  _et al._ (2018) the (late) ejecta affected by neutrino
interactions are expected to be still neutron-rich enough to produce a (weak)
r process, while early dynamic ejecta, emerging from spiral arms after the
collision, stay in any case very neutron-rich and lead to a strong r process.

There is also an important difference between the nucleosynthesis operated in
neutrino heated ejecta for supernova and mergers. In the supernova case, due
to the high entropies and moderate electron fractions the material suffers an
$\alpha$-rich freeze-out (see Fig. 20). Under this conditions, if the material
is subject to strong neutrino fluxes during the phase of alpha formation, the
so-called $\alpha$-effect Meyer  _et al._ (1998) will drive the composition to
$Y_{e}\approx 0.5$, hindering the occurrence of an r process. In the case of
merger ejecta due to the more moderate entropies no alpha formation takes
place for $Y_{e}\lesssim 0.45$ (see Fig. 17) and hence the $\alpha$-effect
plays no role.

The discussion above neglects neutrino flavor transformations and their impact
on the $Y_{e}$ of the ejected material. In the supernova case, the very
similar spectra for all neutrino flavors hinders the impact of neutrino
active-active flavor transformations (see e.g. Wu  _et al._ , 2015). Active-
sterile transformations, involving sterile neutrinos on the eV mass scale, as
suggested by the reactor Mention  _et al._ (2011) and Gallium Giunti  _et al._
(2012) anomalies, tend to drive the composition more neutron-rich (Nunokawa
_et al._ , 1997; McLaughlin  _et al._ , 1999; Wu  _et al._ , 2014; Pllumbi
_et al._ , 2015). As discussed above in the case of mergers the
$\bar{\nu}_{e}$ fluxes dominate over those of $\nu_{e}$. Hence, the neutrino
self-interaction potential has a different sign than the neutrino matter
potential in the Hamiltonian that describes flavor transformations. This
induces conversions via matter-neutrino resonances Malkus  _et al._ (2012);
Foucart  _et al._ (2015); Malkus  _et al._ (2016); Zhu  _et al._ (2016);
Frensel  _et al._ (2017) and fast pairwise conversions Wu and Tamborra (2017);
Wu  _et al._ (2017b). The existing investigations clearly point to a potential
impact on $Y_{e}$ and thus on the resulting nucleosynthesis.

After this general outline, disussing in detail how weak interactions are
setting the stage for the resulting $Y_{e}$ (and entropy), being the dominant
criteria for the operation of an r process, we want to go through
environments/sites suggested so far in a more detailed way than in the
introduction. However, we want to leave out the r process in He-layers,
initiated by ${}^{13}\text{C}(\alpha,n){}^{16}$O reactions but ruled out since
realistic stellar models are in existence (Woosley  _et al._ , 2002), and
straight forward assumptions of neutron-rich ejecta from the collapsed core of
a massive star (e.g. Hillebrandt  _et al._ , 1976), ruled out since the
neutrino-powered explosion mechnism has been established (Bethe, 1990). Here
we will pass through suggested sites related either to massive stars or
compact objects in binary systems.

###  VI.1 Possible r-process sites related to massive stars

####  VI.1.1 Neutrino winds from core-collapse supernovae

Supernovae have been thought to be the origin of the strong r process for many
years, with the intrinsic expectation that the innermost ejecta, coming from
regions close to the neutron star, should be neutron-rich (see e.g. the
reviews by Cowan  _et al._ , 1991; Sumiyoshi  _et al._ , 2001; Arnould  _et
al._ , 2007). While the prompt explosion mechanism has been shown to fail
(Bethe, 1990), the development of multidimensional neutrino radiation
transport simulations has shown that the neutrino delayed explosion mechanism
remains the most promising scenario to explain the observations (see Kotake
_et al._ , 2012; Burrows, 2013; Foglizzo  _et al._ , 2015; Janka  _et al._ ,
2016; Müller, 2016; Hix  _et al._ , 2016; Janka, 2017; Burrows  _et al._ ,
2018; Cabezón  _et al._ , 2018, for reviews). These simulations predict that
after the onset of the supernova explosion the hot proto-neutron star enters
the so-called Kelvin-Helmholtz cooling phase. During this phase that lasts
around 10 s, the proto-neutron star deleptonizes, emitting neutrinos of all
flavors. Those neutrinos are responsible of producing an outflow of matter
known as neutrino-driven wind (Duncan  _et al._ , 1986) that is expected to
operate in each supernova explosion that produces a neutron star. The basic
properties of the wind are well understood, based on semianalitical models
(Duncan  _et al._ , 1986; Qian and Woosley, 1996; Hoffman  _et al._ , 1997;
Thompson  _et al._ , 2001; Otsuki  _et al._ , 2000; Arcones and Thielemann,
2013). These models relate the nucleosynthesis relevant conditions (see sect.
III.3) to fundamental properties including neutrino luminosities, average
energy, and mass and radius of the proto-neutron star. Early simulations and
parametric models Woosley and Hoffman (1992); Meyer  _et al._ (1992); Woosley
_et al._ (1994); Witti  _et al._ (1994); Takahashi  _et al._ (1994);
Freiburghaus  _et al._ (1999a); Farouqi  _et al._ (2010); Arcones and
Martínez-Pinedo (2011); Kratz  _et al._ (2014) led to impressive results.
However, large uncertainties remained, particularly in the determination of
entropy and $Y_{e}$. Fig. 28, taken from Kratz  _et al._ (2014), shows a close
to excellent fit to solar r-process abundances, especially when utilizing
modern input from nuclear mass models, but also requiring a superposition of
entropies of up to 280 $k_{B}$ per baryon (and a $Y_{e}<0.5$).

Figure 28: Results from an r-process calculation, assuming an initial $Y_{e}$
of 0.45, the adiabatic expansion of matter in a so-called neutrino wind with a
given expansion speed $v_{exp}$ of ejected mass shells, and that a
superposition of entropies $S$ between 120 and 280 $k_{B}$/baryon can be
attained. The abundance plot assumes that similar amounts of matter are
ejected per entropy interval and indicates the changes which occur due to
utilizing an improved nuclear mass model (Möller  _et al._ , 2012a, 2016).
Figure 29: Isotopic abundances relative to solar abundances of nuclei produced
in neutrino driven winds (adapted from Martínez-Pinedo  _et al._ , 2014).

The development of hydrodynamics simulations (Arcones  _et al._ , 2007;
Arcones and Janka, 2011) showed that such high entropies were out of reach.
Nevertheless, they still allowed for the occurrence of a weak r process
(Roberts  _et al._ , 2010; Arcones and Montes, 2011). Further progress,
including the development of neutrino radiation hydrodynamics simulations that
follow the whole cooling phase (Hüdepohl  _et al._ , 2010; Fischer  _et al._ ,
2010; Roberts, 2012), improvements in the treatment of neutrino opacities in
the decoupling region Martínez-Pinedo  _et al._ (2012); Roberts  _et al._
(2012); Horowitz  _et al._ (2012); Rrapaj  _et al._ (2015); Janka (2016);
Roberts and Reddy (2017); Martínez-Pinedo  _et al._ (2014); Bollig  _et al._
(2017); Fischer  _et al._ (2018b), and the treatment of convection in the
proto-neutron star Roberts  _et al._ (2012); Mirizzi  _et al._ (2016) have
shown that most or all of the ejecta are proton-rich. Under these conditions
the nucleosynthesis proceeds via the $\nu p$ process Fröhlich  _et al._
(2006); Pruet  _et al._ (2006); Wanajo (2006), producing neutron deficient
isotopes, including light p-process nuclei like 92Mo, as illustrated in Fig.
29 (see Martínez-Pinedo  _et al._ , 2014; Pllumbi  _et al._ , 2015; Wanajo
_et al._ , 2018; Eichler  _et al._ , 2018a).

The above result can be understood by considering that in neutrino driven
winds matter is ejected by neutrino energy deposition and is subject to
neutrino reactions for sufficient amounts, permitting $Y_{e}$ to attain the
equilibrium value given in Eq. (10). For the very similar spectra of $\nu_{e}$
and $\bar{\nu}_{e}$ (see Fig. 27) predicted by modern simulations, this
results in proton-rich ejecta. These results are robust against the inclusion
of neutrino flavor transformations between active flavors Wu  _et al._ (2015);
Pllumbi  _et al._ (2015) but may be affected by the active-sterile flavor
transformations Wu  _et al._ (2014); Pllumbi  _et al._ (2015).

####  VI.1.2 Electron-capture supernovae

A way out of the problem that neutrino irradition is turning matter proton-
rich is by considering matter that is ejected promptly with little exposure to
neutrinos. This occurs in the so-called electron-capture supernovae in the
stellar mass range 8-10 M⊙ (Jones  _et al._ , 2014), which could lead to a
weak r process (Kitaura  _et al._ , 2006; Janka  _et al._ , 2008; Wanajo  _et
al._ , 2009, 2011), possibly producing nuclei up to Eu, but not up to and
beyond the third r-process peak (for more details see Mirizzi  _et al._ ,
2016). However, there are strong indications based on multidimensional
hydrodynamic simulations of the oxygen deflagration Jones  _et al._ (2016b)
and nuclear physics data on the electron capture rate on 20Ne (Kirsebom  _et
al._ , 2019) that intermediate mass stars may end their lives as a
thermonuclear supernova triggered by electron captures on 20Ne (see Nomoto and
Leung, 2017a, for a recent review).

####  VI.1.3 Neutrino-induced r process in the He-shell

One of the major requirements for an r process to take place is to attain a
sufficiently high neutron-to-seed ratio. As already discussed above for the
high entropy wind, this can also be achieved via a (very) low seed abundance.
Banerjee  _et al._ (2011) and Banerjee  _et al._ (2016), following on an idea
by Epstein  _et al._ (1988), could show that for core-collapse supernovae with
metallicities as low as $\text{[Fe/H]}\leq 3$, i.e. indicating a very low seed
abundance, the neutrons released in the He-shell by
4He$(\bar{\nu}_{e},e^{+}n)^{3}$H can be captured to produce nuclei with mass
numbers up to $A=200$ in the stellar mass range of 11–15 M⊙. The caveat of
this environment is, that while a sufficiently high neutron-to-seed ratio
permits the production of heavy nuclei via neutron captures, the relatively
low neutron density $n_{n}$ leads to a larger $S_{n}$ for the maximum in each
isotopic chain (with ${Y(Z,A+1)/Y(Z,A)}\approx 1$, see Eq. III.2) and thus a
process path closer to stability than for a regular r process (see the
discussion in III.2). Such a path, in between an r-process and an s-process
path leads to abundance peaks shifted to higher masses numbers than found for
the solar r-abundances. Thus, such a process cannot be an explanation for
solar as well as the r-process abundance patterns observed in low-metallicity
stars.

####  VI.1.4 Quark deconfinement supernovae

This suggested scenario considers objects which undergo core collapse at the
end of their evolution and form a central compact proto-neutron star, but the
neutrino emission from the hot proto-neutron star and accreted matter is not
sufficient to prevent a further collapse with ongoing mass accretion. The
question is whether this second collapse leads directly to black hole
formation or can come to a halt (Fischer  _et al._ , 2018a). A specific
equation of state effect was initially introduced by Sagert  _et al._ (2009);
Fischer  _et al._ (2011), with a quark-hadron phase transition taking place
just at the appropriate density/temperature conditions. When adjusting the
equation of state properties to presently observed maximum neutron star
masses, Fischer  _et al._ (2018) could show that in such supernovae
explosions, expected for a certain stellar mass range, an r process can take
place. When examining their results, they show that abundance up to the third
r-process peak can be obtained, however, the abundances beyond the second
r-process peak show a subsolar behavior. Thus, while there remains hope that
core-collapse supernovae can produce r-process elements, they probably do not
support a solar-type r process up to the third r-process peak.

####  VI.1.5 Magneto-rotational supernovae with jets

Core-collapse with fast rotation and strong magnetic fields is considered to
lead to neutron stars with extremely high magnetic fields of the order
$10^{15}$G (magnetars, see e.g. Duncan and Thompson, 1992; Kramer, 2009; Kaspi
and Beloborodov, 2017) and connected to a special class of supernovae (Kasen
and Bildsten, 2010; Greiner  _et al._ , 2015; Nicholl  _et al._ , 2017b). Such
supernovae, induced by strong magnetic fields and/or fast rotation of the
stellar core, i.e., magneto-hydrodynamic supernovae (MHD-SNe), are considered
to provide an alternative and robust astronomical source for the r process
(Symbalisty  _et al._ , 1985). Nucleosynthetic studies were carried out by
Nishimura  _et al._ (2006), based on adiabatic MHD simulations which exhibited
a successful r process in jet-like explosions. One important question is
whether these earlier results, assuming axis symmetry, also hold in full
three-dimensional (3D) simulations, i.e., lead to the ejection of jets along
the polar axis. 3D MHD simulations with an improved treatment of neutrino
physics were performed by Winteler  _et al._ (2012) for a 15 M⊙ progenitor,
utilizing an initial dipole magnetic field of $5\times 10^{12}$ G and a ratio
of magnetic to gravitational binding energy, $E_{mag}/W=2.63\times 10^{-8}$.
These calculations supported and confirmed the ejection of polar jets in 3D,
attaining magnetic fields of the order $5\times 10^{15}$ G and
$E_{mag}/W=3.02\times 10^{-4}$ at core-bounce, with a successful r process up
to and beyond the third r-process peak at $A=195$ (see e.g. Winteler  _et al._
, 2012, and Fig. 30).

Figure 30: In an MHD-jet supernova the winding up of magnetic field lines
causes the ”squeezing-out” of polar jets, along the rotation axis (Winteler
_et al._ , 2012). This environment leads to quite low entropies, much lower
than those discussed in Fig. 20. But opposite to the $Y_{e}$-values utilized
for Fig. 20, the collapse to high densities resulted in large amounts of
electron captures and $Y_{e}$-values close to 0.1-0.15 (see top part of this
figure and the right part of Fig. 21 as well as Fig. 22). Such low $Y_{e}$’s,
similar to neutron star merger conditions (where even values as low as
0.03-0.05 can be attained, see next subsection) lead also to a strong r
process - even at low entropies - and the abundance predictions displayed here
in the bottom part result (shown for two fission fragment distributions
utilized Kelic  _et al._ , 2008; Panov  _et al._ , 2008). As $Y_{e}$ is
moderately low, the effect of late neutron-capture by fission neutrons is also
moderate, avoiding a final shift of the third r-process peak as indicated in
Fig. 19.

More recent general relativistic simulations in 3D-MHD (Mösta  _et al._ ,
2014), involving a 25 M⊙ progenitor with an initial magnetic field of
$10^{12}$ G, led in the early phase to jet formation, but experienced
afterwards a kink instability which deformed the jet-like feature. Possibly
the difference between the two latter investigations in 3D hydrodynamics marks
a transition due to passing critical limits in stellar mass, the initial
rotation, and magnetic fields between a clear jet-like explosion and a
deformed explosion. When we see the time evolution of jet-like explosions with
the hydrodynamic instability (see results in Mösta  _et al._ , 2014, 2015),
the region with the highest magnetic pressure contains essentially the matter
corresponding to the initially forming jets before the deformation. Further
investigations by Mösta  _et al._ (2018); Obergaulinger  _et al._ (2018)
underlined, that very high magnetic fields are required to avoid such kink
instabilities (and ensure a strong r process). Further studies by Halevi and
Mösta (2018) also analyze the dependence on the alignment between rotation
axis and magnetic fields, where the most aligned cases result in the strongest
r process.

A number of 2D axissymmetric simulations tested nucleosythesis features (e.g.
Nishimura  _et al._ , 2015a; Shibagaki  _et al._ , 2016), the most recent ones
also resolving the magnetorotational (Nishimura  _et al._ , 2017). The latter
simulations analyzed a whole variety of conditions in terms of rotation rates,
initial magnetic fields, and ratios of neutrino luminosities vs. magnetic
field strengths, under the assumption that the fields are high enough in order
to avoid kink instabilities. Their study included a series of long-term
explosion simulations, based on special relativistic MHD (Takiwaki  _et al._ ,
2009; Takiwaki and Kotake, 2011), following the amplification of magnetic
fields due to differential rotation (winding of magnetic fields) and the
launch of jet-like explosions. One finds possible outcomes from prompt-
magnetic-jet over delayed-magnetic-jet explosions up to dominantly neutrino-
powered explosions, determined by the ratio of magnetic field strengths in
comparison to neutrino heating. This causes also a variation of r-process
nucleosynthesis results, from full-blown strong r process environments (see
Fig. 31), over a weak r process, not producing nuclei of the third r-process
peak, down to no r process at all.

A fully self-consistent treatment requires high resolution simulations which
can resolve magneto-rotational instabilities (MRI) and predict reliably the
possible amplificaton of magnetic fields during the explosion. While the
latter is actually possible by now (Nishimura  _et al._ , 2017), present
calculations still depend on the uncertain and therefore assumed initial
conditions, that either cause strong jet ejection or can develop kink
instabilities of the jets. Based on initial conditions, somewhat parametrized
in terms of the impact, either neutrino heating or magnetic pressure is
causing the supernova explosion. The production for heavy neutron capture
elements varies strongly, being either Fe and Zn dominated like in regular
core-collapse SNe or Eu dominated, indicating a strong r process. This is
shown in Fig. 32.

Figure 31: Abundances from nucleosynthesis calculations with varying ratios of
magnetic field strength with respect to the neutrino heating mechanims of
regular core-collaspe SNe, increasing for the models h, i-, i, i+, and m (for
details see Nishimura  _et al._ , 2017). For comparison also (a) solar
r-process abundances are shown (black dots Arlandini  _et al._ , 1999), (b)
abundances from metal-poor stars with a weak r process, i.e. HD122563 (black
dots Honda  _et al._ , 2006), and solar-type r-process observations from
CS22892-052 (blue dots Sneden  _et al._ , 1996). Abundances are normalized for
Z = 40 of HD122563. Observations of low metallicity stars with strong
r-process contributions vary for abundances below Z=50 (Sneden  _et al._ ,
2008).

In terms of applications to galactic chemical evolution it should be noticed
that the MHD-jet supernovae discussed here are expected to occur as a fraction
of 0.1-1 percent of all core-collapse supernovae, probably being somewhat
metallicity dependent. Higher metallicities lead to stronger stellar wind loss
which will be accompanied by a loss of angular momentum, thus reducing the
fast rotation necessary for this type of SN explosions. Another feature is
that these events can lead to only small amounts of Fe-group ejecta for the
cases of strong r processing (Nishimura  _et al._ , 2015b, 2017). As indicated
in Fig. 32, with respect to the relative influence of neutrino heating vs.
magnetic field effects, one can see that the Ni/Eu-ratio (and similarly the
Fe/Eu-ratio) varies strongly. Thus, if these types of supernovae would
contribute already at low metallicities, they alone would be able to provide a
large spread in Eu/Fe and might even explain the variations in actinides vs.
Eu, seen in a number of cases at low metallicities (see e.g. Wehmeyer  _et
al._ , 2015; Thielemann  _et al._ , 2017a).

Figure 32: Nucleosymthesic features of rotating core-collapse SN models (h,
i-, i, i+, m) with varying ratios of neutrino luminosity and magnetic field
strengths as in Fig. 31. Model m represents a strong MHD-jet supernova. One
can see the transition from a regular core-collapse SN pattern, dominated by
56Ni, total Fe (after decay), and Zn, to a strong r-process pattern with a
high Eu abundance (for details see Nishimura  _et al._ , 2017).

####  VI.1.6 Collapsars, Hypernovae, long-duration Gamma-Ray Bursts

One of the most interesting developments in the study of supernovae (SNe) is
the discovery of some very energetic supernovae (see e.g. Nomoto  _et al._ ,
2006), dubbed hypernovae, whose kinetic energy (in spherically symmetric
analysis, see also Piran, 2004) exceeds $10^{52}$ erg, about 10 times the
value of normal core-collapse SNe ($10^{51}$ erg). The most luminous and
powerful of these objects, the Type Ic supernova (SN Ic) 1998bw, was probably
linked to the gamma-ray burst GRB 980425, thus establishing for the first time
a connection between (long-duration) gamma-ray bursts (lGRBs) and the well-
studied phenomenon of core-collapse SNe. However, SN 1998bw was exceptional,
indicating that it synthesized $\sim 0.5$ M⊙ of 56Ni with an estimated
explosion energy of $E\sim 3\times 10^{52}$ erg.

The question is where these events should be placed in the stellar mass range
and which other features should be related. We know that for non-rotating
cases only the (regular) supernova “branch” (with neutron stars as final
outcome) can be attained, probably followed towards increasing stellar mass by
a faint or failed supernova branch (leading eventually to black holes, but not
to gamma-ray bursts and high ejecta masses). Thus, massive stars, which fail
to explode as supernovae via neutrino-powered explosions, will eventually
experience the formation of a central black hole (BH) (see e.g. Pan  _et al._
, 2018a; Kuroda  _et al._ , 2018). However, rotating BHs and the formation of
accretion disks with accretion rates of about $\approx 0.1$ M⊙ s-1 can lead -
for certain conditions (strong magnetic fields) - to long duration gamma-ray
bursts (lGRBs) or hypernovae, also dubbed collapsars as they result from a
core-collapse to the formation of a black hole. Many authors have contributed
to the discovery and shaping of first ideas (for theoretical explanations see
e.g. the review by Piran, 2004). The collapsar model was proposed by Woosley,
MacFadyen and others (see also MacFadyen and Woosley, 1999; MacFadyen  _et
al._ , 2001; Nagataki  _et al._ , 2007; Sekiguchi and Shibata, 2011; Nagataki,
2011), based on neutrino heating from the accretion disk and/or the winding of
strong magnetic fields and MHD jets (e.g. Ono  _et al._ , 2012; McKinney  _et
al._ , 2013; Janiuk  _et al._ , 2018). Early hydrodynamic simulations
(injecting explosion energies artificially) were performed either by
introducing high explosion energies (up to $10^{52}$ erg) in a sperically
symmetric way or aspherically in order to understand jet-like explosions
(Nakamura  _et al._ , 2001; Nomoto  _et al._ , 2006, 2013; Nomoto, 2017).

The basic (consensus) picture has been the following: explosion energies can
be found up to $5\times 10^{52}$ erg, 56Ni ejecta up to 0.5 M⊙, and there
exist relativistic jets responsible for lGRBs. Many attempts have been
undertaken to model such events. There exists uncertainty in predicting
$Y_{e}$, due to weak interactions and especially neutrino transport in disks
and jets. The observational constraint of high 56Ni ejecta argues for a
dominant $Y_{e}$ in matter of the order of 0.5. High explosion energies also
lead to high entropies and a strong $\alpha$-rich freeze-out, including
interesting amounts of 45Sc, large amounts of 64Zn (from 64Ge-decay), and also
other Fe-group elements. Nakamura  _et al._ (2001) and Nomoto (2017) concluded
that larger abundance ratios for (Zn, Co, V, Ti)/Fe and smaller (Mn, Cr)/Fe
ratios are expected than for normal SNe, a feature which seems to be
consistent with observations in extremely metal-poor (EMP) stars, as will be
discussed later.

Self-consistent modeling of the complete event, from collapse, black hole
formation, accretion disk modeling, jet ejection, and GRB occurrence are only
forthcoming slowly. There have been investigations with respect to the role of
weak interactions and resulting nucleosynthesis in the accreation disk and
corresponding outflows (for specific nucleosynthesis results see e.g. Pruet
_et al._ , 2003; Beloborodov, 2003; Pruet  _et al._ , 2004; Surman  _et al._ ,
2006; Janiuk, 2014; Siegel and Metzger, 2017; Janiuk, 2017; Siegel  _et al._ ,
2018).

Beloborodov (2003) found conditions for the minimum accretion rate required,
leading to neutron-rich environments with low $Y_{e}$’s at a given radius:

$\dot{M_{n}}=0.0152\times\left(\frac{r}{3r_{g}}\right)^{1/2}\left(\frac{\alpha}{0.1}\right)\left(\frac{M_{\text{BH}}}{M_{\odot}}\right)^{2}\
\text{M}_{\odot}\ \text{s}^{-1}$ (12)

Here $r_{g}$ is the gravitational Schwarzschild radius, $\alpha$ the disk
viscosity, $M_{BH}$ the mass of the central black hole. I.e. for typical
accretions rates of 0.1 M⊙ s-1, this can lead to a low $Y_{e}$ at small radii
in the disk. Larger accretion rates are in favor of reducing $Y_{e}$, so are
larger BH masses (as the Schwarzschild $r_{g}$ radius is linear in $M_{BH}$,
an overall power of 3/4 on the BH mass results).

Fig. 33 shows the $Y_{e}$ distribution obtained by Janiuk (2014) as a function
of the radius. While the central parts of the disk experience a low $Y_{e}$,
its value reaches $Y_{e}\approx 0.5$ in the outermost regions and even exceeds
beyond 0.5 in intermediate regions. If the disk outflow occurs from the outer
regions, this is consistent with the large 56Ni ejecta (observed and) found
e.g. by Pruet  _et al._ (2004); Surman  _et al._ (2006); Janiuk (2014, 2017).
However, Pruet  _et al._ (2004) also speculated that in case of strong
magnetic fields low $Y_{e}$ matter can be flung out from more central regions
of the disk along magnetic field lines, possibly causing r-process production.
Additionally, MHD-driven collapsar models, involving black hole accretion disk
systems (Nagataki  _et al._ , 2007; Fujimoto  _et al._ , 2008; Harikae  _et
al._ , 2009), have argued that the jets produced by the central engine of long
duration gamma-ray-bursts can produce heavy r-process nuclei (Fujimoto  _et
al._ , 2007, 2008; Ono  _et al._ , 2012; Nakamura  _et al._ , 2015). However,
it should be mentioned that early studies assumed a quite simplified treatment
of the black hole and the required microphysics. Siegel and Metzger (2017);
Siegel  _et al._ (2018); Janiuk (2018), having performed multi-D MHD
simulations for accretion disk outflows, argue that large amounts, up to
($\approx 1$M⊙) of r-process material can be ejected. If this scenario
materializes, it would be sufficient to have about one such event per 10 000
core-collapse supernovae to explain the solar r-process abundances.

Figure 33: Radial distribution of $Y_{e}$ in the disk for different accretion
rates. $r_{g}$, the gravitational radius, stands for the Schwarzschild radius
of the black hole. $Y_{e}$ indicates very neutron-rich conditions deep inside
the disk but developes aymptotically to values of 0.5 in the outer layers
above 100 rg from where the nucleosynthesis outflow will occur (from Janiuk,
2014))

The open question is whether both, large amounts of 56Ni expected for
hypernovae as well as r-process ejecta can be produced in the same event?
Siegel  _et al._ (2018) argue that the 56Ni would have to come from a
preceding supernova explosion phase, leaving an intermittent neutron star
before further accretion causes black hole formation and a black hole
accretion disk. This brings up the following questions: (a) At which stellar
progenitor masses do we have a transition from the formation of neutron stars
to the formation of black holes after collapse? (b) In which transition region
are initially neutron stars formed, causing a regular supernova explosion, but
ongoing accretions leads to a black hole? (c) For which progenitor masses are
black holes formed directly during collapse and how can this be observed? (d)
What is the role of rotation and magnetic fields to cause lGRBs and can we
give reliable nucleosynthesis yields for such events? (e) Is there a
separation in different types of events, depending on the parameters in (d),
leading either to hypernovae and strong 56Ni ejecta or systems with a large
outflow of r-process elements? (f) Are jets and lGRBs occurring in both types
of events?

The scenario suggested by Siegel  _et al._ (2018) would relate to case (b),
but it is not clear whether for such a case a strong supernova explosion with
lots of Ni production takes place before the accretion disk outflows eject
r-process material. It could, however, also be possible that such an event
does not cause a hypernova and only creates r-process outflows. Further
observations will have to constrain such events.

###  VI.2 Neutron-star and neutron-star / black hole mergers

Figure 34: Ejection channels in compact binary mergers including estimates
based on simulations of the ejecta mass, $Y_{e}$ and velocity during the
different ejection phases. The NS-NS merger system is shown in the upper part
including the two possible outcomes: a log lived massive neutron star and a
hypermassive neutron star that collapses to a black hole on a timescale
shorter than the disk lifetime. The BH-NS merger is shown in the lower part.
(Adapted from Rosswog  _et al._ , 2017)

Neutron stars, postulated by Landau (1932) even before the discovery of the
neutron (Yakovlev  _et al._ , 2013), were predicted as the final fate of
massive stars, ending in supernova events (Baade and Zwicky, 1934). Their
existence was proven in the 1960’s after the first observations of pulsars
(Hewish and Okoye, 1965). We have by now an extensive knowledge of the
distribution of neutron star masses and the underlying equation of state,
(e.g. Lattimer and Prakash, 2016; Özel and Freire, 2016; Oertel  _et al._ ,
2017), with the most precise determinations existing for binary systems.
Shortly after the discovery of the binary pulsar by Hulse and Taylor (1975),
with an energy loss in agreement with the emission of gravitational waves
predicted by General Relativity, it was found that this system would merge in
$\sim 10^{8}$ years (Weisberg and Huang, 2016). In parallel came the
prediction that neutron star or neutron star - black hole mergers would eject
r-process nuclei Lattimer and Schramm (1974, 1976); Symbalisty and Schramm
(1982), followed up by a first detailed analysis of possible abundance
distributions Meyer and Schramm (1988). Later predictions included that such
mergers would be accompanied by neutrino bursts and gamma-ray bursts Eichler
_et al._ (1989). The very first and later more precise estimates of the mass
ejection from neutron star mergers in Newtonian approximation followed Davies
_et al._ (1994); Ruffert  _et al._ (1996); Rosswog  _et al._ (1999, 2000),
together with the very first detailed nucleosynthesis predictions Freiburghaus
_et al._ (1999b).

More recently, extensive investigations have been undertaken with respect to
nucleosynthesis predictions (Panov and Thielemann, 2004; Panov  _et al._ ,
2008; Goriely  _et al._ , 2011; Korobkin  _et al._ , 2012; Panov  _et al._ ,
2013; Bauswein  _et al._ , 2013; Goriely  _et al._ , 2013; Hotokezaka  _et
al._ , 2013; Rosswog  _et al._ , 2014; Wanajo  _et al._ , 2014; Just  _et al._
, 2015a; Goriely  _et al._ , 2015; Perego  _et al._ , 2014; Eichler  _et al._
, 2015; Martin  _et al._ , 2015; Mendoza-Temis  _et al._ , 2015; Ramirez-Ruiz
_et al._ , 2015; Hotokezaka  _et al._ , 2015; Shibagaki  _et al._ , 2016; Just
_et al._ , 2016; Wu  _et al._ , 2016; Radice  _et al._ , 2016; Roberts  _et
al._ , 2017; Martin  _et al._ , 2018; Wojczuk and Janiuk, 2018; Papenfort  _et
al._ , 2018). Initial Newtonian approaches have been replaced with conformally
flat and fully relativistic treatments (e.g. Ruffert  _et al._ , 1996; Shibata
and Uryū, 2000; Ruffert and Janka, 2001; Oechslin  _et al._ , 2002, 2004;
Shibata and Uryū, 2006; Oechslin  _et al._ , 2007; Shibata and Taniguchi,
2011; Bauswein and Janka, 2012; Bauswein  _et al._ , 2013; Hotokezaka  _et
al._ , 2013; Wanajo  _et al._ , 2014; Sekiguchi  _et al._ , 2015, 2016; Radice
_et al._ , 2016; Baiotti and Rezzolla, 2017; Bovard  _et al._ , 2017;
Papenfort  _et al._ , 2018), and further followed by the inclusion of magnetic
fields Price and Rosswog (2006); Anderson  _et al._ (2008); Liu  _et al._
(2008); Giacomazzo  _et al._ (2009); Obergaulinger  _et al._ (2010); Zrake and
MacFadyen (2013); Kiuchi  _et al._ (2015); Giacomazzo  _et al._ (2015) as well
as their interplay with neutrinos (Palenzuela  _et al._ , 2015; Guilet  _et
al._ , 2017)

In parallel to neutron star (NS-NS) mergers also neutron star - black hole
(NS-BH) mergers have been investigated (e.g. Rosswog, 2005; Shibata and Uryū,
2006; Chawla  _et al._ , 2010; Shibata and Taniguchi, 2011; Korobkin  _et al._
, 2012; Wanajo and Janka, 2012a; Kyutoku  _et al._ , 2013; Foucart  _et al._ ,
2014a; Mennekens and Vanbeveren, 2014; Rosswog  _et al._ , 2017; Brege  _et
al._ , 2018). Both NS-NS and NS-BH mergers are accompanied by the formation of
a massive accretion disk surrounding the central compact object (Ruffert  _et
al._ , 1997).

From the point of view of r-process nucleosynthesis, simulations should
predict the amount of ejecta, their properties (particularly $Y_{e}$), spatial
distribution and temporal evolution. In the following, we discuss the major
phases of ejection and the general dependencies with the merging system. The
discussion is mostly based on a presentation of Shibata (2018). Fig. 34
summarizes the main ejection channels in compact binary mergers and provides
summarizes the estimates of ejecta mass, $Y_{e}$ and velocity discussed below.

Due to the emission of gravitational waves, that reduces the eccentricity of
the orbit, at times close to coalescence NS-NS systems are expected to have
almost circular orbits and spins much smaller than the orbital frequency
(Rosswog, 2015). During the coalescence phase matter is ejected dynamically
due to angular momentum conservation on timescales of milliseconds with mildly
relativistic speed $v\sim 0.2\text{--}0.4$ c (Rosswog  _et al._ , 1999, 2000;
Bauswein  _et al._ , 2013; Hotokezaka  _et al._ , 2013b; Palenzuela  _et al._
, 2015; Sekiguchi  _et al._ , 2015, 2016; Radice  _et al._ , 2016; Foucart
_et al._ , 2016).

The amount of dynamic ejecta and their properties depend on the compactness of
the neutron stars and their mass ratio Bauswein  _et al._ (2013); Hotokezaka
_et al._ (2013b); Radice  _et al._ (2018b). Two components can be distinguish:
cold tidal ejecta in the equatorial plane and shock heated ejecta originating
from the contact interface with a more isotropic distribution. Systems with
small mass ratios tend to eject larger amounts of material mainly in the
equatorial region, while for similar mass ratios the shock heated component
dominates (Bauswein  _et al._ , 2013; Hotokezaka  _et al._ , 2013b; Palenzuela
_et al._ , 2015; Lehner  _et al._ , 2016). While the cold tidal ejecta
maintain the original low $Y_{e}$ of the neutron star crust from which they
are ejected, the shock component is heated to very large temperatures. This
drives electron and positron captures that contribute to increase $Y_{e}$ from
a very low initial value. As the material moves away, it is further increased
by $\nu_{e}$ and $\bar{\nu}_{e}$ absorption (Wanajo  _et al._ , 2014; Goriely
_et al._ , 2015; Martin  _et al._ , 2015; Sekiguchi  _et al._ , 2016; Radice
_et al._ , 2016; Martin  _et al._ , 2018). The impact of neutrino absorptions
is sensitive to the evolution of the central remnant (Sekiguchi  _et al._ ,
2015) as will be discussed below. The total amount of dynamic ejecta are in
the range $10^{-4}$–$10^{-2}$ M⊙ Bauswein  _et al._ (2013); Hotokezaka  _et
al._ (2013b); Sekiguchi  _et al._ (2015, 2016); Lehner  _et al._ (2016);
Radice  _et al._ (2018b) with an angular mass distribution well approximated
by $F(\theta)=\sin^{2}\theta$ (Perego  _et al._ , 2017a) and a $Y_{e}$
distribution that can reach up to $Y_{e}\sim 0.5$ in the polar region (Shibata
_et al._ , 2017; Radice  _et al._ , 2018b). Magnetohydrodynamic instabilities,
operating during the merger, can produce a third component denoted as
“viscous-dynamical” ejecta by (Radice  _et al._ , 2018a) with asymptotic
velocities extending up to $\sim 0.8\ c$. Population synthesis studies
(Belczynski  _et al._ , 2008), formation studies (Tauris  _et al._ , 2017),
pulsar observations (Özel and Freire, 2016), and the gravitational wave signal
from GW170817 (Abbott  _et al._ , 2017; De  _et al._ , 2018; Abbott  _et al._
, 2018) favour binary NS systems with nearly equal-mass stars $\sim 1.35$ M⊙.
For such systems the ejecta are mainly sensitive to the compactness of the
neutron stars. The analysis of the tidal deformability from the Gravitational
Wave observations of GW170817 (Most  _et al._ , 2018; De  _et al._ , 2018;
Abbott  _et al._ , 2018), the observation of an electromagnetic transient
which disfavors a prompt collapse to a black hole (Margalit and Metzger, 2017;
Bauswein  _et al._ , 2017; Shibata  _et al._ , 2017; Coughlin  _et al._ ,
2018), together with nuclear physics constraints (Fattoyev  _et al._ , 2018;
Annala  _et al._ , 2018; Tews  _et al._ , 2018) favors moderately compact
neutron stars with a radius in the range 8.9–13.2 km. In this case, the major
source of ejecta is the contact interface between the neutron stars (Bauswein
_et al._ , 2013; Sekiguchi  _et al._ , 2015; Radice  _et al._ , 2018b). The
maximum mass of a neutron star has been constrained to $M_{\text{max}}\lesssim
2.17$ M⊙ (Margalit and Metzger, 2017; Shibata  _et al._ , 2017; Rezzolla  _et
al._ , 2018; Ruiz  _et al._ , 2018) following the observation of GW170817.

In the case of NS-BH systems, in order to eject material it is necessary that
the NS is disrupted before entering the innermost stable circular orbit of the
BH. Tidal disruption means that the BH tidal force is larger than the self-
gravity of the NS and requires a large NS radius, a small BH mass or small
BH/NS mass ratio, or a high spin for the BH. Population synthesis studies
favor a BH/NS mass ratio $\sim 7$ (Belczynski  _et al._ , 2010). This,
together with the NS radius constraints mentioned above, suggests that mass
ejection will only take place for BH with spin parameter
$\chi=cJ/(GM^{2})\gtrsim 0.5$ (Foucart  _et al._ , 2013, 2014b; Kyutoku  _et
al._ , 2015; Brege  _et al._ , 2018; Kyutoku  _et al._ , 2018). The tidal
dynamic ejecta are much more anisotropic than those of NS-NS mergers. They are
mainly concentrated around the orbital plane and often sweeps out only half of
the plane. The ejected mass can reach $\sim 0.1$ M⊙ with asymptotic velocities
of 0.2–0.3 $c$. The material is very neutron-rich $Y_{e}\lesssim 0.1$ and not
affected by neutrino irradiation (Foucart  _et al._ , 2014b; Kyutoku  _et al._
, 2018).

An equally common outcome of compact binary mergers is the production of a
rotating torus surrounding the newly-formed central object with a typical mass
of 0.1 M⊙ (Radice  _et al._ , 2018b). In the case of BH-NS mergers the central
remnant is a BH and we deal with a neutrino cooled disk that evolves on
viscous timescales of seconds. Such systems have been studied based on
$\alpha$-viscosity prescriptions Fernandez and Metzger (2013); Fernández  _et
al._ (2015); Just  _et al._ (2015a) and more recently by three-dimensional
General-Relativistic Magnetohydrodynamic simulations Siegel and Metzger (2017,
2018); Fernández  _et al._ (2019). These works find that up to 40% of the disk
mass, depending on the BH spin, is unbound in a quasi-spherical fashion. The
electron fraction in the outflow is in the range $Y_{e}\sim 0.1$–0.4 with
velocities $v\approx 0.1$ c (Siegel and Metzger, 2018; Fernández  _et al._ ,
2019). For the case of NS-NS mergers, the possibilities for the central object
are a stable NS, a long-lived massive neutron star (MNS, i.e. a NS with a mass
above the maximum mass for a non-spinning NS and below the one for a uniformly
rotating NS), a hypermassive neutron star (HMNS, i.e. a NS with a mass above
the maximum mass for a uniformly rotating NS, Baumgarte  _et al._ , 2000) or a
black hole (BH) depending primarily on the total mass of the binary, $M_{t}$
(Hotokezaka  _et al._ , 2013a; Shibata, 2018). If $M_{t}$ exceeds a critical
value $M_{c}$, the central object produced by the merger collapses promptly to
a BH on the dynamical time scale of a few ms (Sekiguchi  _et al._ , 2011). On
the other hand, if $M_{t}<M_{c}$ the resulting HMNS is at least temporarily
supported against gravitational collapse by differential rotation and thermal
pressure (Hotokezaka  _et al._ , 2013a; Kaplan  _et al._ , 2014). The value of
$M_{c}$ depends on the uncertain EoS of nuclear matter, particularly its
stiffness, mainly related to the symmetry energy (Baldo and Burgio, 2016;
Oertel  _et al._ , 2017). The discovery of massive $\sim 2$ M⊙ neutron stars
(Demorest  _et al._ , 2010; Antoniadis  _et al._ , 2013), places a lower limit
to $M_{c}\gtrsim 2.6-2.8$ M⊙ (Hotokezaka  _et al._ , 2013a). Hydrodynamical
simulations of neutron star mergers for a large sample of temperature-
dependent equations of state, show that the ratio between critical mass and
the maximum mass of a non-rotating NS are tightly correlated with the
compactness of the non-rotating NS (Bauswein  _et al._ , 2013). This allows to
derive semi-analytical expressions for the critical mass (Bauswein and
Stergioulas, 2017; Bauswein  _et al._ , 2016) that combined with the GW170817
constraints on the maximum mass and radius of NS give $M_{c}\approx 2.8$ M⊙.
It thus appears likely that the canonical 1.35 + 1.35 M⊙, including GW170817,
binary merger goes through a HMNS phase. The duration of this phase depends on
the EoS: for a soft EoS that results in rather compact initial neutron stars
before the merger, the HMNS collapses to a black hole on timescales of several
10s of milliseconds, while for a stiff EoS the HMNS is long-lived with a
lifetime longer than the timescales relevant for matter ejection. The NS
radius constraints mentioned above favor the first case. For the case of
prompt collapse to a BH, the BH-torus system evolves similarly to the BH-NS
merger case considered before. However, systems with large $M_{t}$ are
expected to eject little mass dynamically and produce a low mass accretion
disk. In these cases, the total amount of ejecta, dynamical plus accretion
disk, is $\sim 10^{-3}$ M⊙ of neutron-rich material, $Y_{e}\lesssim 0.1$
(Shibata, 2018).

The HMNS-torus is characterized by a more important role of neutrino heating
that increases the amount of ejecta and raises their $Y_{e}$ to values that
depend on the lifetime of HMNS remnant (Metzger and Fernández, 2014; Perego
_et al._ , 2014; Kaplan  _et al._ , 2014; Martin  _et al._ , 2015; Lippuner
_et al._ , 2017; Fujibayashi  _et al._ , 2018). The ejecta consist of two-
components being either neutrino-driven or viscous-driven (also known as
secular). The neutrino-driven component is ejected mainly on the polar
direction with velocities $v\lesssim 0.08$ c and $Y_{e}\gtrsim 0.25$ and
containing around 5% of the disk mass (Martin  _et al._ , 2015; Perego  _et
al._ , 2017a). The viscous-driven component occurs mainly in the equatorial
direction with a velocity $v\sim 0.05$ c and contains around 40% of the disk
mass Metzger and Fernández (2014); Lippuner  _et al._ (2017); Fujibayashi  _et
al._ (2018). The $Y_{e}$ distribution depends on the lifetime of the HMNS
(Fujibayashi  _et al._ , 2018). If the HMNS survives at least for the
timescale of neutrino cooling of the disk ($\sim 10$ s), neutrino heating
drives $Y_{e}$ to values above 0.25. If the HMNS collapses to a black hole on
a timescale shorter than the disk lifetime, the $Y_{e}$ distribution is in the
range 0.1–0.4, similar to the BH-torus case.

There exists extensive literature relating these events to short duration
Gamma-Ray Bursts (sGRBs) and/or macronovae/kilonovae as electromagnetic
counterparts (for literature before GW170817 see e.g., Li and Paczyński, 1998;
Nakar, 2007; Metzger and Berger, 2012; Tanvir  _et al._ , 2013; Piran  _et
al._ , 2013; Tanaka and Hotokezaka, 2013; Kasen  _et al._ , 2013; Grossman
_et al._ , 2014; Rosswog  _et al._ , 2014; Metzger and Fernández, 2014;
Wanderman and Piran, 2015; Rosswog, 2015; Fryer  _et al._ , 2015; Hotokezaka
_et al._ , 2016; Barnes  _et al._ , 2016; Fernández and Metzger, 2016; Rosswog
_et al._ , 2017; Metzger, 2017a). Although these objects are also of major
importance as strong sources for gravitational wave emission (Shibata and
Taniguchi, 2011; Baiotti and Rezzolla, 2017), especially after GW170817
(Abbott  _et al._ , 2017a), underpinning the importance of multi-messenger
observations, we will essentially focus here on the ejected nucleosynthesis
composition. In the following subsections we will concentrate on (i) the
dynamic ejecta, (ii) the post-merger neutrino wind ejecta, and (iii) the late
time viscous or secular outflow from the accretion disk.

####  VI.2.1 Dynamic ejecta

Figure 35: Top: Resulting r-process abundances for dynamic tidal ejecta (in
comparison to solar values - black dots) from neutron star merger simulations
(Eichler  _et al._ , 2015), making use of $\beta$-decay half-lives from Möller
_et al._ (2003) together with a relatively old (Kodama and Takahashi, 1975)
and a modern set (Kelic  _et al._ , 2008) of fragment distributions from
fissioning nuclei. However, in both cases a shift of the third r-process peak
seems to occur in the final phases, driven by neutron capture of the released
fission neutrons. Bottom: Same as above, but utilizing recent $\beta$-decay
half-life predictions (Marketin  _et al._ , 2016a, dashed black line) in
comparison to an older set (red line, identical to the green line from top
figure). Faster $\beta$-decays for heavy nuclei cause a speed-up of the r
process and deliver (also in the final phases) nuclei which are prone to
fission at an earlier time. This way, the late release of fission neutrons
occurs earlier, to a large extent before the freeze-out from
$(n,\gamma)\rightleftarrows(\gamma,n)$ equilibrium. Therefore, final neutron
captures after freeze-out, which can distort this distribution, are strongly
reduced. This can be seen when comparing the top and bottom figure.

As discussed above the dynamic ejecta consist of two components: a cold
component consisting of very neutron-rich matter originating from the neutron
star crust that is “thrown out” via tidal interaction in the equatorial plane,
and a hotter component originating from the contact interface. The first
component is the only one present in NS-BH mergers and the second represents
most of the unbound material in NS-NS mergers. The tidal component was
originally found in Newtonian simulations (see for first investigations Davies
_et al._ 1994; Rosswog  _et al._ 1999 and more detailed discussions Korobkin
_et al._ 2012), while the contact interface component was found in
relativistic simulations, first within the conformal flatness approximation
(Oechslin  _et al._ , 2007; Goriely  _et al._ , 2011; Bauswein  _et al._ ,
2013) and then in fully relativistic simulations (Hotokezaka  _et al._ ,
2013b). Those simulations neglected the impact of weak processes in the ejecta
and hence the ejected material kept the very neutron-rich conditions
corresponding to $\beta$-equilibrium in the cold neutron star crust,
$Y_{e}\lesssim 0.01$.

The nucleosynthesis in low $Y_{e}$ ejecta, as found in BH-NS mergers and the
tidal component of NS-NS mergers, has been extensively studied Freiburghaus
_et al._ (1999b); Korobkin  _et al._ (2012); Bauswein  _et al._ (2013);
Rosswog  _et al._ (2014); Mendoza-Temis  _et al._ (2015); Eichler  _et al._
(2015); Martin  _et al._ (2016); Mumpower  _et al._ (2016); Bovard  _et al._
(2017) and found to be independent of the astrophysical conditions (Korobkin
_et al._ , 2012) but rather sensitive to the nuclear physics input (Panov and
Thielemann, 2004; Panov  _et al._ , 2008; Bauswein  _et al._ , 2013; Eichler
_et al._ , 2015; Mendoza-Temis  _et al._ , 2015; Goriely, 2015; Goriely and
Martínez-Pinedo, 2015; Martin  _et al._ , 2016; Mumpower  _et al._ , 2016;
Shibagaki  _et al._ , 2016; Thielemann  _et al._ , 2017b). For very neutron-
rich ejecta, we deal with rather large neutron-to-seed ratios that can even
reach several 1000, hence the nucleosynthesis becomes insensitive to the
initial composition and the material loses memory of the exact thermodynamic
conditions at ejection. The temperature evolution is characterized by having a
high temperature plateau, $T_{\text{max}}$, (see Fig. 16) whose value is
determined by a competition between the r-process energy generation rate,
$\dot{Q}$, and the expansion dynamical timescale (Mendoza-Temis  _et al._ ,
2015):

$T_{\text{max}}\approx 0.8\ \text{GK}\left[\biggl{(}\frac{\rho}{10^{5}\
\text{g cm}^{-3}}\biggr{)}\biggl{(}\frac{\dot{Q}}{4\ \text{MeV
s}^{-1}}\biggr{)}\biggl{(}\frac{\tau_{\text{dyn}}}{10\
\text{ms}}\biggr{)}\right]^{1/4},$ (13)

Hence, independent of the initial conditions, during the phase of neutron
captures one can have a hot ($T\gtrsim 0.7$ GK) or cold ($T\lesssim 0.3$ GK) r
process, see section III and Fig. 16 where dark gray and brown lines
correspond to cold r process conditions and light gray lines to hot r process
conditions. Typically the expansion of the material is “slow” enough to allow
for all neutrons to be captured. This leads to the occurrence of several
fission cycles with large amounts of very heavy nuclei prone to fission,
mainly around $A\sim 280$, remaining at freeze-out, see Figs. 14 and 19.
During the final freeze-out phase the fission yields of the heaviest nuclei
determine the final abundances of nuclei with $A\lesssim 140$ (Goriely and
Martínez-Pinedo, 2015). Fission also produces large amounts of neutrons that
tend to be captured on the third r-process peak material. Depending on the
amount of neutrons produced and the speed at which they are released the third
r-process peak can be shifted to higher mass numbers when compared with solar
abundances (see Fig. 35 from Eichler  _et al._ , 2015, and for more details on
the effects of fission subsection V.4). The final impact depends on the mass
model considered, see Fig. 25, and $\beta$-decay half-lives (Marketin  _et
al._ , 2016a; Panov  _et al._ , 2016). Shorter $\beta$-decay half-lives for
very heavy nuclei result in smaller abundances in the fissioning region and
hence less and faster release of neutrons during the freeze-out (Eichler  _et
al._ , 2015).

Fission rates and yields for neutron-rich superheavy nuclei are then
fundamental for the determination of the r-process abundances Goriely (2015).
This requires not only the determination of the region of the nuclear chart
where fission occurs (Thielemann  _et al._ , 1983; Petermann  _et al._ , 2012;
Giuliani  _et al._ , 2018, 2019) but also the modeling of all relevant fission
channels including neutron-induced fission, $\beta$-delayed fission, and
spontaneous fission (Thielemann  _et al._ , 1983; Panov  _et al._ , 2005;
Panov and Thielemann, 2004; Goriely  _et al._ , 2009; Panov  _et al._ , 2010;
Mumpower  _et al._ , 2018; Vassh  _et al._ , 2018) and corresponding yields
(Kelic  _et al._ , 2009; Goriely  _et al._ , 2013; Schmidt  _et al._ , 2016;
Schmitt  _et al._ , 2018; Schmidt and Jurado, 2018). Low $Y_{e}$ ejecta
produce a final abundance distribution that closely follows the solar
r-process abundance distribution for $A>140$ independently of the fission
yields used (Goriely and Martínez-Pinedo, 2015). The production of lighter
nuclei is rather sensitive to the fission rates and yields used and typically
no nuclei below $A\sim 110$ are produced in substantial amounts (Panov  _et
al._ , 2008; Goriely  _et al._ , 2013; Mendoza-Temis  _et al._ , 2015; Eichler
_et al._ , 2015; Vassh  _et al._ , 2018). Fission is also important for the
production of actinides with important consequences for late time kilonova
light curves (Barnes  _et al._ , 2016; Rosswog  _et al._ , 2017; Wanajo, 2018;
Wu  _et al._ , 2018; Holmbeck  _et al._ , 2018b; Zhu  _et al._ , 2018) and
U/Th cosmochronometry (see section VIII.4).

Figure 36: R-process abundances at a time of 1 Gyr for all trajectories shown
in Fig. 16. The grey (brown) curves correspond to the abundances of the
trajectories of the slow (fast) ejecta. The mass-averaged abundances for all
trajectories (red curves), the slow ejecta (green curves), and the fast ejecta
(blue curves) are also shown. The abundances for the slow and fast
trajectories and their averages have been scaled by the value of their
fractional contribution to the total ejecta. (Figure adapted from Mendoza-
Temis  _et al._ , 2015).

Several studies Goriely  _et al._ (2014); Metzger  _et al._ (2015); Mendoza-
Temis  _et al._ (2015); Radice  _et al._ (2018a); Fernández  _et al._ (2019);
Ishii  _et al._ (2018) have shown that part of the material, up to 10% in
mass, is ejected very fast and reaches such low densities that the timescale
for neutron captures becomes much longer than the expansion timescale Mendoza-
Temis  _et al._ (2015) (see brown lines on Fig. 16). Under such conditions
most of the neutrons are not captured, despite of having a large neutron-to-
seed ratio. The final abundances of this “frustrated” r process does not
correspond to solar abundances (see Fig. 36) and hence it cannot constitute a
major component of the total ejected mass, assuming mergers are a major
r-process site. However, it can drive an early (timescales of hours)
electromagnetic emission that is powered by the radioactive decay of the free
neutrons left after completion of the r process (Metzger  _et al._ , 2015).

Wanajo  _et al._ (2014) showed that weak processes operating on the shock
heated ejecta of NS-NS mergers can increase the $Y_{e}$. They are particular
efficient in the polar region, where the large neutrino fluxes from the HMNS
increase substantially the $Y_{e}$ of the ejecta, provided the HMNS does not
collapse promptly to a BH. Depending on the neutrino luminosities, $Y_{e}$
could be increased to values between 0.25 and 0.4. While it is currently
accepted that weak processes increase the $Y_{e}$ of the ejecta, an aspect
confirmed by the kilonova observations discussed in section VII, there is
still a relatively large spread between the predictions of different groups
(Shibata  _et al._ , 2017; Sekiguchi  _et al._ , 2016, 2015; Radice  _et al._
, 2016, 2018b; Foucart  _et al._ , 2016; Bovard  _et al._ , 2017; Foucart  _et
al._ , 2018) related to the different approximations in the treatment of
neutrino radiation transport. Dynamic ejecta from NS-NS mergers are expected
to contribute to the synthesis of a broad range of r-process nuclei, including
both light and heavy, once weak processes are considered (Wanajo  _et al._ ,
2014; Goriely  _et al._ , 2015; Martin  _et al._ , 2018). However, it should
be kept in mind that the predicted amount of high $Y_{e}$ matter is typically
much smaller that the one found in accretion disk outflows.

####  VI.2.2 Neutrino Winds and the Effect of Neutrinos

In addition to the dynamic ejecta, related directly to the merging/collision,
post merger ejecta will emerge as well. One component is a “neutrino-wind” as
found in core-collapse supernovae. For the typical merging system, the hot
central NS remnant, supported by high temperatures and differential rotation,
will not collapse to a black hole immediately, and will be surrounded by a hot
and dense torus. Hence, the structure of the wind is quite different from the
isolated NSs usually found in core-collapse supernova. The wind outflow occurs
mainly in the polar direction (Rosswog  _et al._ , 2014; Perego  _et al._ ,
2014; Metzger and Fernández, 2014; Martin  _et al._ , 2015). Matter is exposed
to neutrinos long enough for the material to reach an equilibrium between
electron neutrino and antineutrino absorption, changing $Y_{e}$, see Eq. (10),
from the initial (neutron-rich) conditions towards higher values that can even
be above $Y_{e}=0.5$. Due to the much larger $\bar{\nu}_{e}$ luminosities and
energy differences between $\bar{\nu}_{e}$ and $\nu_{e}$, found during the
post-merger evolution when compared with core-collapse supernova (see Fig.
27), the peak of the $Y_{e}$ distribution is expected to be neutron-rich with
$Y_{e}\gtrsim 0.25$ (Martin  _et al._ , 2015; Lippuner  _et al._ , 2017;
Fujibayashi  _et al._ , 2017, 2018). This leads to a weak r process and
produces mainly matter below the second r-process peak, i.e. no lanthanides
are produced.

Figure 37: Neutrino wind contribution to neutron star merger ejecta, dependent
on the delay time between the merger and BH formation Martin  _et al._ (2015).
In comparison also the dynamic, tidal ejecta of Korobkin  _et al._ (2012) are
shown. The neutrino wind, ejected dominantly in polar regions, contributes
nuclei with $A<130$, due to the effect of the neutrinos on $Y_{e}$.

Fig. 37 displays the results of Martin  _et al._ (2015) for the neutrino wind
component as a function of the delay time until black hole formation sets in.
It can be seen that predominantly nuclei below $A=130$ are produced,
complementing nicely the abundance features originating from prompt/dynamic
low $Y_{e}$ ejecta, also displayed. The latter, resulting here from the
Newtonian simulations (Korobkin  _et al._ , 2012).

Similarly to the situation in core-collapse supernova, the properties of
neutrino-wind ejecta, and particularly $Y_{e}$, are expected to be sensitive
to the spectral differences between $\nu_{e}$ and $\bar{\nu}_{e}$. This
requires an accurate prediction of neutrino luminosities and spectra.
Supernova neutrino-wind transport simulations are nowadays based on exact
numerical solutions of the Boltzmann transport equation (e.g. Hüdepohl  _et
al._ , 2010; Fischer  _et al._ , 2010; Roberts, 2012) exploiting the
spherically symmetric nature of the problem. In the case of mergers, due to
the multidimensional nature of the problem, simulations so far are based on
neutrino leakage schemes (Perego  _et al._ , 2014; Metzger and Fernández,
2014; Radice  _et al._ , 2016; Ardevol-Pulpillo  _et al._ , 2018) and $M1$
schemes (Just  _et al._ , 2015a, b; Foucart  _et al._ , 2015; Fujibayashi  _et
al._ , 2017, 2018). There are indications that they may not properly capture
the energy densities and fluxes of neutrinos in the polar regions (Just  _et
al._ , 2015a), hence, affecting the $Y_{e}$ estimates in the polar region
(Foucart  _et al._ , 2016, 2018). Additional opacity reactions so far not
considered, like neutrino-pair annihilation, may also play an important role
in determining the properties of the ejecta (Just  _et al._ , 2016;
Fujibayashi  _et al._ , 2017; Perego  _et al._ , 2017b; Fujibayashi  _et al._
, 2018; Foucart  _et al._ , 2018).

$Y_{e}$ can also be affected by modifications of neutrino and antineutrino
spectra due to neutrino flavor conversion. There have been a number of tests
to verify such neutrino conversions via matter-neutrino resonances Malkus  _et
al._ (2012); Foucart  _et al._ (2015); Malkus  _et al._ (2016); Zhu  _et al._
(2016); Frensel  _et al._ (2017) and fast pairwise flavor conversions (Wu and
Tamborra, 2017; Wu  _et al._ , 2017b). Due to the more complicated geometry of
a disk environment in comparison to core-collapse supernovae, most of the
calculations are based on single-angle approximations. Spherically symmetric
test calculations show that the matter-neutrino resonance still occurs in
multiangle models (Vlasenko and McLaughlin, 2018) but with reduced efficiency.
Nevertheless, the existing investigations clearly point to the potential
effect on $Y_{e}$, and thus the resulting nucleosynthesis can be affected.

####  VI.2.3 Accretion Disks outflows

Figure 38: Resulting r-process abundances (in comparison to solar values -
black dots) from black hole accretion disk simulations (Wu  _et al._ , 2016),
making use of a black hole mass of 3 M⊙, a disk mass of 0.03 M⊙, an initial
$Y_{e}$ of 0.1, entropy per baryon of 8$k_{b}$, an alpha parameter of the
viscous disk of 0.03, and a vanishing black hole spin. The figure illustrate
the impact of two different mass models, FRDM and DZ31, in the final
abundances

The long-term evolution, $t\sim 1$–10 s, of the accretion disc produces
outflows of material powered by viscous heating and nuclear recombination (Lee
and Ramirez-Ruiz, 2007; Beloborodov, 2008; Metzger  _et al._ , 2009; Fernandez
and Metzger, 2013). Those outflows can contain up to 40% of the disk mass. The
amount of ejected mass increases with the lifetime of the MNS formed in the
merger, but most importantly for nucleosynthesis the $Y_{e}$ distribution is
dramatically affected by the lifetime of the MNS Metzger and Fernández (2014).
For a long lived MNS, $t\gtrsim 1$ s, neutrino irradiation from the MNS
results in ejecta with $Y_{e}>0.3$ (Metzger and Fernández, 2014; Lippuner  _et
al._ , 2017; Fujibayashi  _et al._ , 2018). The nucleosynthesis in these
ejecta is simular to the neutrino-wind ejecta discussed in the previous
subsubsection.

For a short-lived MNS, $t\lesssim 1$ s, the impact of neutrino-irradiation is
small and from the point of view of nucleosynthesis outflows from accretion
disks formed in NS-NS and BH-NS mergers gives similar results. Early
nucleosynthesis studies where mainly parametric and considered mainly the
“neutrino-driven” wind outflow from the surface of the disk (Pruet  _et al._ ,
2003; Fujimoto  _et al._ , 2003, 2004; Pruet  _et al._ , 2004; McLaughlin and
Surman, 2005; Surman  _et al._ , 2006; Metzger  _et al._ , 2008; Surman  _et
al._ , 2008; Dessart  _et al._ , 2009; Kizivat  _et al._ , 2010; Wanajo and
Janka, 2012b; Surman  _et al._ , 2014). Detailed simulations have been
performed in recent years based on $\alpha$-viscosity prescriptions (Fernandez
and Metzger, 2013; Metzger and Fernández, 2014; Just  _et al._ , 2015a;
Fernández and Metzger, 2016; Just  _et al._ , 2016; Wu  _et al._ , 2016;
Wojczuk and Janiuk, 2018; Fujibayashi  _et al._ , 2018) and more recently on
three-dimensional General-Relativistic Magnetohydrodynamic simulations Siegel
and Metzger (2017, 2018); Fernández  _et al._ (2019). These simulations show
that neutrino winds from the accretion disk eject little mass and that most of
the material is ejected by viscous heating (Just  _et al._ , 2015a). The
results for disk outflows by Wu  _et al._ (2016) are displayed in Fig. 38,
which shows the integrated abundance pattern of all tracer particles. This
underlines that, in principle, disk outflows alone can produce the whole range
of r-process nuclei, with a significant production of $A\lesssim 130$ nuclei.
Disk outflows also reach the third peak at $A=195$ in most of the simulations.
The detailed results depend on the disk viscosity, the initial mass or entropy
of the torus, the black hole spin, and (of course) the nuclear physics input.
The latter is illustrated in Fig. 38 that compares the nucleosynthesis results
for two different mass models, FRDM Möller  _et al._ (1995) and Duflo-Zuker
(Duflo and Zuker, 1995). The production of heavy ($A\gtrsim 195$) nuclei is
also affected by uncertainties of the disk properties discussed above (Just
_et al._ , 2015a; Wu  _et al._ , 2016). However, such a possible deficit can
be counterbalanced by the dynamic ejecta, as the total nucleosynthesis of the
merger includes the components of the dynamic ejecta, the neutrino wind, and
the accretion disk.

Nucleosynthesis studies in mergers are commonly based on simulation data that
follow the evolution of the ejecta for timescales shorter, $\sim$ ms, than the
r-process nucleosynthesis timescale, $\sim$ s. This makes it necessary to
extrapolate the time evolution of thermodynamic properties like temperature
and density in order to follow the nucleosynthesis to completion. It is
commonly assumed that the expansion is homologous, $\rho\sim t^{-3}$, with the
temperature evolution determined by the nuclear energy production of the r
process. The nuclear energy production during the r process, originating
mainly from $\beta$ decays, is in the range $\dot{Q}\approx 1-4$ MeV s-1 nuc-1
(see lower panel of Fig. 16). Rosswog  _et al._ (2014) have performed long-
term simulations and found that the r-process energy release does not
qualitatively alter the properties of dynamic ejecta. Wu  _et al._ (2016)
found that r-process heating can increase the amount of ejecta up to a factor
2 in viscous outflows from accretion disks and remove an anomalously high
abundance of $A=132$ nuclei (see Fig. 38 and Lippuner  _et al._ , 2017; Siegel
and Metzger, 2018). R-process heating can increase the amount of ejecta and
critically shape the dynamics of marginally bound ejecta responsible for fall-
back accretion on timescales of the second to minutes (Metzger  _et al._ ,
2010a; Desai  _et al._ , 2018). Late-time fall-back accretion has been
suggested as possible mechanism to explain the extended X-ray emission
observed in some short GRBs (Rosswog, 2007). R-process heating on timescales
of days to weeks after the merger has been found responsible for powering the
“kilonova” electromagnetic emission (Li and Paczyński, 1998; Metzger  _et al._
, 2010b) as will be discussed in the next section.

##  VII Electromagnetic signatures of r-process nucleosynthesis

Figure 39: (left panel) Specific energy generation rate, $\dot{Q}$, in
r-process ejecta (black line). For comparison the energy production from the
decay chain
${}^{56}\text{Ni}\rightarrow{}^{56}\text{Co}\rightarrow{}^{56}\text{Fe}$ (red)
and the analytical estimate $\dot{Q}\sim t^{-1.3}$ are also shown (adapted
from Metzger  _et al._ , 2010b). (right panel) top: the fraction of total
radioactive energy produced by $\beta$-decays, $\alpha$-decays, and fission
for a representative trajectory corresponding to low $Y_{e}$ NS-NS merger
dynamical ejecta for four nuclear mass models While $\beta$-decay dominates,
fission ($\alpha$-decay) can be important at early (late) times. Agreement
between the four mass models shown is within an order of magnitude. Bottom:
energy released in $\alpha$-decays and fission, for the FRDM mass model, for a
range of initial $Y_{e,0}$ conditions. Lower electron fractions favor the
assembly of the heavy elements that later decay by fission and
$\alpha$-emission. As $Y_{e,0}$ increases, these processes become less
important, and are negligible for $Y_{e,0}>0.2$ (from Barnes  _et al._ ,
2016).

As discussed above the r process produces very neutron rich unstable nuclei on
timescales of a few seconds. Once produced they decay to stability by a
combination of beta, alpha and fission decays. These decays produce large
amounts of energy and can potentially lead to an observable electromagnetic
emission. The first suggestion of such a electromagnetic emission was due to
Burbidge  _et al._ (1956) who attributed type Ia supernova light curves to the
decay of 254Cf produced by the r process. Nowadays, we know that both type Ia
and type II supernova light curves are due mainly to the decay of 56Ni
(Bersten and Mazzali, 2017; Zampieri, 2017). The study of light curves and
spectra does not only constraint the nucleosynthesis yields (Diehl and Timmes,
1998; Seitenzahl  _et al._ , 2014) but also provide information about the
physical parameters of the progenitor system and the explosion itself (Bersten
and Mazzali, 2017; Zampieri, 2017). This illustrates the physics potential of
an electromagnetic transient observation associated with r-process ejecta. It
identifies one the sites where the r process occurs (Metzger  _et al._ ,
2010b) and serves as a promising electromagnetic counterpart to the
gravitational wave detection following a neutron star merger Metzger and
Berger (2012). All these aspects were confirmed by the electromagnetic
transient AT 2017gfo observed following the gravitational wave event GW170817
(Abbott  _et al._ , 2017a).

Figure 40: Bolometric light curve of the optical/infrared counterpart, AT
2017gfo, of GW170817 (red circles) from multi-band photometry (Cowperthwaite
_et al._ , 2017) compared with the fiducial model of Metzger  _et al._
(2010b). For comparison a line with the approximate power-law decay
$\dot{Q}\sim t^{-1.3}$ for r-process heating (see Fig. 39).

Li and Paczyński (1998) were the first to propose that radioactive ejecta from
a NS-NS merger could power a supernova-like transient. However, they did not
posses a physical model to describe the origin of the radioactive heating,
$\dot{Q}$, and considered two possible limiting cases: an exponential-law
decay and a power-law $\dot{Q}\sim t^{-1}$. In both cases the normalization
was left an a free parameter. Hence, even if the model predicted the right
timescale for the peak luminosity, it could not determine the absolute
luminosity, spectral peak frequency and time-evolution of the luminosity.
Indeed, their fiducial model reached extremely high values of the luminosity
$\sim 10^{44}$ erg s-1 with a spectral peak in the ultra-violet. Kulkarni
(2005) considered two possible origins for the heating: neutron and 56Ni
decay; and named such events “macronova”. Metzger  _et al._ (2010b) were the
first to relate the late time radioactive heating to the decay of freshly
produced r-process nuclei. Based on heating rates derived self-consistently
from a nuclear reaction network, they showed that the heating rate follows a
power law at time scales of a day with a steeper dependence than the one
assumed by (Li and Paczyński, 1998), $\dot{Q}\sim t^{-1.3}$. As shown in Fig.
39, the heating evolves very differently for r-process material than for
supernova-like ejecta dominated by 56Ni. A power law dependence is expected
whenever the heating is dominated by a broad distribution of nuclei all of
them decaying exponentially. It can be understood from basic physics of
$\beta$-decay and the properties of neutron-rich nuclei (Metzger  _et al._ ,
2010b; Hotokezaka  _et al._ , 2017). A similar dependence is found for the
decay rate of terrestrial radioactive waste (Way and Wigner, 1948).

The work of Metzger  _et al._ (2010b) predicted peak luminosities $\sim
3\times 10^{41}$ erg s-1 for 0.01 M⊙ of ejecta expanding at $v\sim 0.1\ c$ and
spectral peak at visual magnitude. As such value corresponds to 1000 times the
luminosity of classical novae they named these events “kilonova”. Fig. 40
compares their prediction with the recent observation of AT 2017gfo
(Cowperthwaite  _et al._ , 2017). Similar results were also found by Roberts
_et al._ (2011) and Goriely  _et al._ (2011).

The physical processes determining the kilonova light curve are (see Fernández
and Metzger, 2016; Metzger, 2017a; Tanaka, 2016, for reviews):

##### Radioactive heating.

The radioactive heating of r-process products is expected to follow a power
law whenever a large statistical ensemble of nuclei is produced. This is the
case for ejecta with $Y_{e}\lesssim 0.2$. For higher $Y_{e}$ ejecta, the
heating rate has ‘bumps’ as a function of time caused by being dominated by a
few nuclei (Grossman  _et al._ , 2014; Martin  _et al._ , 2015; Lippuner and
Roberts, 2015; Rosswog  _et al._ , 2018; Wanajo, 2018). However, when averaged
over $Y_{e}$ distributions as predicted by simulations the heating rate at
timescales of days to a week (of greatest relevance to determine the peak
luminosity) lies within a factor of a few for $Y_{e}\lesssim 0.4$ (Lippuner
and Roberts, 2015; Wu  _et al._ , 2018). At early times of a few hours the
heating may be dominated by neutron decay, assuming the presence of free
neutrons in the outermost layers of the ejecta, producing a Ultraviolet/Blue
precursor to the kilonova emission (Metzger  _et al._ , 2015; Metzger, 2017a).
At times between 10 and 100 days, the heating is dominated by a few decays,
(see Wu  _et al._ , 2018, for a complete listing), due to the scarcity of
nuclei with the appropriate half-life. R-process nuclei decay in a variety of
channels including $\beta$-decay, $\alpha$-decay and fission. The energy
production in each individual channel is important as the absorption of the
energy depends on the decay products being electrons, photons, alphas and
fission products. For high $Y_{e}$ ejecta, heating is dominated by
$\beta$-decay and only electrons and photons are relevant with neutrinos being
just an energy loss. For low $Y_{e}$ ejecta, actinides are produced and alpha
decay and fission become important (see Fig. 39). The right panel of Fig. 39
shows that the contribution alphas and fission to the energy production can be
substantial and sensitive to the underlying mass model (Barnes  _et al._ ,
2016; Rosswog  _et al._ , 2017; Wu  _et al._ , 2018).

##### Thermalization efficiency.

At early times the ejected material very dense and the energy produced by
radioactive decay, except neutrinos, is completely reabsorbed. However, as the
density decreases an increased fraction of the energy is lost and cannot be
used to drive a thermal electromagnetic emission. Hence, one normally
introduces a time dependent thermalization efficiency that corrects the energy
produced by radioactive processes (Barnes  _et al._ , 2016). The efficiency
depends on bulk properties of the ejecta like mass and velocity as they
determine the evolution of the density. It also depends on the presence of
magnetic field and its geometry. Furthermore, it varies with the decay product
and time evolution of the heating at each particular decay channel (Kasen and
Barnes, 2018), i.e. whether we have a statistical distribution of decaying
nuclei or a heating dominated by a few isotopes which is probably more
appropiate for late times. Earlier works considered the thermalization of
$\gamma$-rays (Hotokezaka  _et al._ , 2016) and were later extended to
consider charged particles (Barnes  _et al._ , 2016). This work has been
recently extended to the case of a few decays dominating the heating (Kasen
and Barnes, 2018; Wu  _et al._ , 2018). Qualitatively one finds that the
thermalization efficiency for $\gamma$-rays decreases very rapidly and becomes
negligible on timescales of a few 10’s of days. The thermalization efficiency
for changed particles and particularly alphas and fission products remains
substantial at late times. This makes kilonova light curves rather sensitive
the heating contribution of alpha decays and fission (Barnes  _et al._ , 2016;
Rosswog  _et al._ , 2017; Wu  _et al._ , 2018; Zhu  _et al._ , 2018; Vassh
_et al._ , 2018).

##### Atomic opacities.

A significant electromagnetic luminosity is only possible once the density
decreases sufficiently that photons can escape the ejecta on the expansion
time-scale (Arnett, 1980, 1982). Assuming an homogeneous spherical
distribution of ejecta with mass $M$, expanding homologously with velocity $v$
and radius $R=vt$, the diffusion time scale of the ejecta can be approximated
as $t_{\text{diff}}\approx\rho\kappa R^{2}/(3c)$, with $\rho=3M/(4\pi R^{3})$