Neutron Star Mergers Might not be the Only Source of r-Process Elements in the Milky Way

Probing the origin of r-process elements in the universe represents a multi-disciplinary challenge. We review the observational evidence that probe the properties of r-process sites, and address them using galactic chemical evolution simulations, binary population synthesis models, and nucleosynthesis calculations. Our motivation is to define which astrophysical sites have significantly contributed to the total mass of r-process elements present in our Galaxy. We found discrepancies with the neutron star (NS-NS) merger scenario. Assuming they are the only site, the decreasing trend of [Eu/Fe] at [Fe/H]\,$>-1$ in the disk of the Milky Way cannot be reproduced while accounting for the delay-time distribution (DTD) of coalescence times ($\propto~t^{-1}$) derived from short gamma-ray bursts and population synthesis models. Steeper DTD functions ($\propto~t^{-1.5}$) or power laws combined with a strong burst of mergers before the onset of Type~Ia supernovae can reproduce the [Eu/Fe] trend, but this scenario is inconsistent with the similar fraction of short gamma-ray bursts and Type~Ia supernovae occurring in early-type galaxies, and reduces the probability of detecting GW170817 in an early-type galaxy. One solution is to assume an extra production site of Eu that would be active in the early universe, but would fade away with increasing metallicity. If this is correct, this extra site could be responsible for roughly 50% of the Eu production in the early universe, before the onset of Type~Ia supernovae. Rare classes of supernovae could be this additional r-process source, but hydrodynamic simulations still need to ensure the conditions for a robust r-process pattern.


INTRODUCTION
Understanding the origin of rapid neutron-capture process (r-process) elements in the universe requires a multi-scale framework including nuclear astrophysics, stellar spectroscopy, gravitational waves, short gammaray bursts (GRBs), and galaxy formation theories (e.g., Arnould et al. 2007;Berger 2014;Frebel & Norris 2015;Fernández & Metzger 2016;Abbott et al. 2017b;Thielemann et al. 2017;Frebel 2018;Horowitz et al. 2018;Cowan et al. 2019). To best interpret stellar abundances of r-process elements 1 derived from spectroscopy, nucleosynthesis calculations must be convolved with galaxy evolution simulations. To include r-process sites in such simulations, the general properties of those sites must be known, which in the case of neutron star (NS-NS) mergers can be constrained by gravitational wave and short GRBs detections.
The goal of our study is to build a coherent interdisciplinary picture to identify which astrophysical site(s) have significantly contributed to the amount of r-process elements present in the Milky Way. We review the different observational evidence that probe the properties of r-process sites, and investigate them from the perspective of galactic chemical evolution (GCE) simulations, binary population synthesis models, and theoretical nucleosynthesis. In particular, we focus on the tensions that emerge when NS-NS mergers are assumed to be the only r-process site (see Table 1). We refer to Duggan et al. (2018) and Skúladóttir et al. (in preparation) for a discussion of r-process sites in dwarf galaxies.
Many studies addressed the challenge of explaining with NS-NS mergers the presence of Eu, a lanthanide element, in the atmosphere of the most metal-poor stars ([Fe/H] −2) of the Galactic halo (e.g., Argast et al. 2004;Matteucci et al. 2014;Cescutti et al. 2015;Ishimaru et al. 2015;Shen et al. 2015;Wehmeyer et al. 2015;Safarzadeh et al. 2018;Haynes & Kobayashi 2019, see also Section 5.5). In this paper, we instead focus on the decreasing trend of [Eu/Fe] 2 at [Fe/H] > −1 in the Galactic disk. Currently, this trend cannot be well reproduced by invoking a proper delay-time distribution (DTD) for NS-NS mergers (Côté et al. 2017a;Hotokezaka et al. 2018;Simonetti et al. 2019). This distri-1 By r-process elements we mean neutron-capture elements that are, to the best of our knowledge, mostly produced by the rprocess.
2 [A/B] ≡ log 10 (n A /n B )− log 10 (n A /n B ) , where n A and n B represent the number density in the stellar atmosphere of elements A and B, respectively. The second term on the right-hand side represents the solar composition. bution can be seen as the probability of a merger event to occur at a given delay time following the formation of the binary system.
In this paper, we explore different DTD functions for NS-NS mergers in order to recover the evolution of [Eu/Fe] in the Galactic disk using chemical evolution models. We then discuss whether those new DTD functions are consistent with other constraints outside the world of chemical evolution, such as the host galaxies of short GRBs, gravitational wave detections, and binary population synthesis predictions. We also present a list of alternative r-process enrichment scenarios in the Milky Way with multiple r-process sites involving rare classes of supernova, and discuss their implications with respect to a diverse range of observational and theoretical constraints. Overall, this work aims to isolate and highlight the current inter-disciplinary tensions that need to be addressed in future studies in order to identify the dominant r-process site(s) in the Milky Way.
The outline of this paper is as follows. We review the observational evidence related to the production of rprocess elements in Section 2. In Sections 3, 3.4, 4, we address the properties of r-process sites from the point of view of galactic chemical evolution simulations, binary population synthesis models, and theoretical nucleosynthesis calculations, respectively. In Section 5, we highlight the inter-disciplinary tensions associated with existing r-process enrichment scenarios involving compact binary mergers and magneto-rotational supernovae, and propose alternative scenarios to be confirmed or disproved by future work. Our discussion and conclusions are in Sections 6 and 7, respectively.

OBSERVATIONAL EVIDENCE
Here we review the observational evidence that probe the properties of the r-process sites. We interpret these observables with numerical simulations in Sections 3 and 4, and attempt to build a consistent multi-disciplinary picture in Section 5.

Neutron-Capture Elements in Metal-Poor Stars
Metal-poor stars in the Galactic halo and in dwarf galaxies can be unique tracers of r-process nucleosynthesis in the early universe (e.g., Sneden et al. 2008;Frebel 2018;Horowitz et al. 2018). Throughout this paper, we will refer to the three peaks in the r-process abundance distribution, the first peak at Se-Kr, the second peak at Te-Xe, and the third peak at Os-Pt-Au. Heavier than the third peak are the actinide elements such as Th and U. We note that the solar r-process residual pattern is obtained by subtracting the contribution of the slow neutron-capture process (s-process) from the total solar abundances (e.g., Kappeler et al. 1989;Arlandini et al. 1999;Burris et al. 2000;Simmerer et al. 2004;Sneden et al. 2008;Bisterzo et al. 2014).

r-Process Enhanced Stars
For stars with strong enhancements in neutroncapture elements, abundances of more than 35 elements between Sr and U can be derived (Roederer et al. 2012b;Roederer & Lawler 2012;Siqueira Mello et al. 2013;Mashonkina et al. 2014;Ji & Frebel 2018), typically with accuracies better than ± 0.2 dex, owing to large telescopes, high resolution spectrographs, and improved knowledge of stellar parameters and atomic physics (e.g., Sneden et al. 2003;Hansen et al. 2015a;Ezzeddine et al. 2017). Some metal-poor stars are moderately or strongly enhanced in r-process elements and are classified based on their [Eu/Fe] and [Ba/Eu] ratios: r-I stars when [Eu/Fe] > 0.3 and [Ba/Eu] < 0, r-II stars when [Eu/Fe] > 1.0 and [Ba/Eu] < 0. We note that Ba is actually past the second r-process peak. Eu is located between the second and third r-process peak. Sneden et al. (2003) first showed that the abundances of CS 22892-052, an r-II star, was similar within 0.2 − 0.3 dex to the solar r-process pattern between the second and third peak. Since then, many studies found additional r-process enhanced stars that also show this pattern with similar precisions (Roederer et al. 2009a;Cowan et al. 2011;Roederer et al. 2012b;Mashonkina et al. 2014;Ji et al. 2016b;Placco et al. 2017;Holmbeck et al. 2018;Sakari et al. 2018). This pattern has also been found in dwarf galaxy stars, such as in Reticulum II (Ji et al. 2016b;Ji & Frebel 2018). This universal abundance pattern, between the second and third r-process peak, is referred to as the main r-process. Deriving abundances for elements in the second r-process peak requires space telescopes with spectrographs operating in the ultraviolet. This has been done for a handful of stars only, and their abundances are consistent with the main portion of the scaled solar r-process pattern (Roederer & Lawler 2012;Roederer et al. 2012a).
While the main r-process observationally appears very robust, r-process enhanced stars do show large variations up to ∼ 1 dex among first-peak neutron-capture elements such as Sr, Y, and Zr (e.g., Hansen et al. 2014;Roederer et al. 2014a;Ji et al. 2016b;Hansen et al. 2018b;Ji & Frebel 2018;Spite et al. 2018). Although the origin of those variations is still unclear, it suggests there is more than one astrophysical site that can produce the first-peak elements (e.g., Hansen et al. 2014;Cescutti et al. 2015;Spite et al. 2018). At low metallicity, these elements could be made by different nucleosynthesis processes (see, e.g., Montes et al. 2007;Roederer et al. 2010) such as neutrino-driven winds and the νpprocess in CC SNe (Fröhlich et al. 2006;Farouqi et al. 2009;Roberts et al. 2010;Arcones & Montes 2011;Arcones & Thielemann 2013), the s-process in fast-rotating massive stars (Pignatari et al. 2008;Frischknecht et al. 2016), or the intermediate neutron-capture process (iprocess, Roederer et al. 2016a).
Besides variations in the first peak, there is also a range of abundances found in the actinide elements with atomic number Z ≥ 80 (e.g., Hill et al. 2002;Roederer et al. 2009b). Stars with an high Th/Eu ratio relative to the solar r-process pattern have been termed actinideboost stars. Ji & Frebel (2018) recently reported the discovery of an actinide-deficient star in Reticulum II. This has broadened the range of Th abundances relative to the solar pattern to ∼ 0.6 dex (see also Schatz et al. 2002;Roederer et al. 2009a;Mashonkina et al. 2014;Hansen et al. 2018a;Holmbeck et al. 2018). We note that U abundances scale with Th values, but only very few U measurements are available. It is currently difficult to determine whether the variations in actinide abundances is a result of different r-process sites, or the trace of different ejecta with different physical conditions within the same site (see discussion in Section 6.4).

Limited r-Process Stars
In contrast to the r-process enhanced stars, the majority of very metal-poor stars with [Fe/H] < −2.0 do not show any significant enhancements in neutron-capture elements. Although their abundances or upper limits among halo stars are often extremely low, they still show large star-to-star scatter. Some of these stars display no super-solar enhancement in neutron-capture elements but nevertheless display a systematic depletion of Ba and heavier elements relative to the abundances of lighter neutron-capture elements such as Sr. Stars with this signature has recently been termed limited r-process stars (Frebel 2018). The metal-poor star HD 122563 (Honda et al. 2006) is a famous example. However, as for the large scatter in the abundances of first-peak elements in r-process enhanced metal-poor stars (see Section 2.1.1), the nucleosynthetic origin(s) of limited rprocess stars is still unclear.

Scatter of [Eu/Fe] in Galactic Halo Stars
The large scatter seen in the [Eu/Fe] ratio of r-process enhanced metal-poor stars in the Milky Way halo (blue crosses in Figure 1), compared to the smaller scatter seen in [α/Fe] 3 , indicates that the production of Eu  (Asplund et al. 2009).
in the early universe must have been rare and prolific compared to the production of α elements by standard CC SNe (e.g., Cescutti et al. 2015;Hirai et al. 2015;Wehmeyer et al. 2015;Naiman et al. 2018). The recent analysis of Macias & Ramirez-Ruiz (2018) suggests a minimum ejection of ∼ 10 −3 M of r-process material per event to explain the most Eu-enhanced stars. The rarity of r-process events is also necessary to explain the low frequency of r-process enhanced ultra-faint dwarf galaxies such as Reticulum II (Ji et al. 2016a;Roederer et al. 2016c). A comparison between the abundance of 244 Pu in the Earth's ocean crust and the value derived for the early solar system also supports the idea that the r-process elements should be produced in rare events that eject a large amount of mass (Wallner et al. 2015;Hotokezaka et al. 2015;Lugaro et al. 2018).

Evolution of [Eu/Fe] in the Galactic Disk
At higher metallicity ([Fe/H] > −1.5) in the Galactic disk, there is no star with a clean r-process signature because of the production of neutron-capture elements by the s-process (e.g., Gallino et al. 1998). To probe the evolution of r-process elements in disk stars, we use Eu. According to the solar r-process pattern, defined by subtracting the s-process pattern from the total solar abundance pattern, Eu was produced at ∼ 97 % by the r-process (e.g., Burris et al. 2000), at the time the solar system formed 4.6 Gyr ago (Connelly et al. 2017). We note, however, that there are uncertainties in s-process yields (e.g., Bisterzo et al. 2014;Cristallo et al. 2015), and that the i-process could potentially alter the exact composition of the r-process residuals by contributing to the production of neutron-capture elements (see e.g., Dardelet et al. 2014;Hampel et al. 2016;Roederer et al. 2016b;Côté et al. 2018a;Denissenkov et al. 2018). We discuss the possible production of Eu by the i-process in Section 6.5. Throughout this paper, we assume that Eu is a reliable r-process tracer.
An important feature of the chemical evolution of Eu in the Milky Way is the decreasing trend of [Eu/Fe] in the disk, as recorded in stars with [Fe/H] > −1 (cyan dots in Figure 1). This data behaves similar to the chemical evolution of [α/Fe] (see e.g., Bensby et al. 2014;Buder et al. 2018;Spina et al. 2018). Because α elements are mostly produced in massive stars (e.g., Woosley et al. 2002;Nomoto et al. 2013), we can assume that the overall production rate of r-process elements should also follow the lifetime of massive stars. In particular, because this decreasing trend originates from the extra production of Fe by Type Ia supernovae (SNe Ia) that mixes with the material ejected by CC SNe (e.g., Matteucci & Greggio 1986;Matteucci et al. 2009;Few et al. 2014), the production of r-process elements should occur on timescales shorter than SNe Ia, as for α elements (see Section 3 for more details). We note that the AMBRE Project recently measured abundances for Gd and Dy, two other tracer elements of the r-process, in the Galactic disk (Guiglion et al. 2018

Short Gamma Ray Bursts and Type Ia Supernovae
While long-duration GRBs are associated with the explosion of massive stars, the progenitors of shortduration GRBs are believed to be NS-NS or black holeneutron star (BH-NS) mergers (see Berger 2014 for a review). The detection of the short GRB that followed the NS-NS merger event GW170817 measured by LIGO/Virgo (Abbott et al. 2017b) reinforced even more this idea. We discuss the broad implication of GW170817 in Section 2.4. For now, we focus on the properties of short GRBs to probe the coalescence timescales of compact binary systems. We also compare results from short GRB observations with those of SNe Ia observations in order to investigate whether those two types of events occur on similar timescales. This is relevant for GCE simulations (see Section 3).

Host Galaxies
In the review of Berger (2014), ∼ 30 % of the 26 short GRBs with classified host galaxies are found in earlytype galaxies (see also Fong et al. 2013;D'Avanzo 2015). A similar fraction of ∼ 1/3 has been derived by Fong et al. (2017) with the 36 short GRBs detected between 2004 and 2017. Early-type (giant elliptical and S0) galaxies typically show a lack or low level of recent star formation compared to late-type (spiral) galaxies (e.g., González Delgado et al. 2016) and are dominated by old stellar populations (e.g., van de Sande et al. 2018). This implies that a certain fraction of NS-NS mergers, if they are the source of short GRBs, must have long coalescence timescales. Otherwise, they would be exclusively found in star-forming late-type galaxies, as for core-collapse supernovae (CC SNe) (e.g., Li et al. 2011) and long GRBs (e.g., Berger 2014).
A fraction of SNe Ia is also observed in early-type galaxies (e.g., Mannucci et al. 2005;Li et al. 2011). Using the ∼ 370 classified SNe Ia found in the Lick Observatory Supernova Search (LOSS), between 15 % and 35 % of SNe Ia occur in early-type galaxies ( Figure 5 in Leaman et al. 2011, see also Graur et al. 2017a,b), depending on whether we exclude or include S0-type galaxies in the early-type category. Similar percentages of 10 % and 32 % are obtained using the 103 SNe Ia with classified host galaxies from the Carnegie Supernova Project (Krisciunas et al. 2017). Using ∼ 450 classified SNe Ia found in the Sloan Digital Sky Survey-II (SDSS-II) Supernova Survey 4 (Sako et al. 2014), between 12 % and 40 % of SNe Ia are found in galaxies with stellar masses above 0.5 − 1.0 × 10 11 M (see also Uddin et al. 2017), which is roughly the mass range above which early-type galaxies become the dominant type in galaxy populations (e.g., Kelvin et al. 2014;Moffett et al. 2016;Thanjavur et al. 2016). Using the same sample, we find that ∼ 25 % of SNe Ia occur in passive galaxies that do not form stars anymore.
Compared to the ∼ 30 % derived for short GRBs with classified host galaxies, this suggests that short GRBs and SNe Ia occur on average on similar timescales.

Delay-Time Distributions
The DTD function of an astronomical event represents the probability of that event to occur at a given time t following the formation of its progenitor objects. Different approaches for deriving observationally the DTD 4 https://data.sdss.org/sas/dr10/boss/papers/supernova/ function of SNe Ia are described in Maoz et al. (2014). Regardless of the different methodologies, most studies point toward a DTD in the form of t −1 (Totani et al. 2008;Maoz et al. 2010Maoz et al. , 2012Graur et al. 2011Graur et al. , 2014Perrett et al. 2012), which is consistent with the predictions of population synthesis models (e.g., Ruiter et al. 2009).
Similar techniques can be applied to short GRBs. According to Fong et al. (2017), and references therein, the DTD function of short GRBs could also be in the form of t −1 . This is also in agreement with population synthesis studies (e.g., Dominik et al. 2012;Chruslinska et al. 2018). As mentioned in Section 2.3.1, the statistics of short GRB detections is still low and the derived DTD function could change in the near future (see also discussion in Fong et al. 2017). We note that D'Avanzo (2015) argued for a steeper DTD function in the form of t −1.5 for short GRBs. However, this provides tension with respect to the similar fraction of short GRBs and SNe Ia occurring in different types of galaxies (see Section 2.3.1), unless the DTD function of SNe Ia turns out to also be in the form of t −1.5 , as suggested by the recent analysis of Heringer et al. (2017).
According to the 13 confirmed NS-NS binary systems observed in the Milky Way compiled by Tauris et al. (2017), six of them have an estimated coalescence time. This excludes systems that will merge in more than 50 Gyr. The additional NS-NS binary PSR J1946+2052 discovered by Stovall et al. (2018) has an estimated coalescence time of 46 Myr. When put in an increasing order, these seven NS-NS binaries should merge in 46, 86, 217, 301, 480, 1660, and 2730 Myr. Although a larger sample is needed to derive a reliable DTD function, the fact that two of the seven systems have coalescence timescales larger than 1 Gyr is consistent with the idea that the number of NS-NS mergers, if they are responsible for short GRBs, should be distributed following a long-lasting DTD function.

The Gravitational Wave GW170817
The detection of GW170817 by LIGO/Virgo (Abbott et al. 2017b) and its associated electromagnetic emissions is to date the best direct evidence that NS-NS mergers can synthesize r-process elements. In the next subsections, we review the implication of this event on the contribution of NS-NS mergers on the origin of rprocess elements in the Milky Way.

The Host Galaxy NGC 4993
This first NS-NS merger detection occurred in NGC 4993, an early-type galaxy (Abbott et al. 2017d;Coulter et al. 2017). Analysis of the properties of this galaxy revealed a current stellar mass of about 0.3 − 1.4 × 10 11 M and a star formation rate (if any) below ∼ 10 −2 M yr −1 Im et al. 2017;Levan et al. 2017;Pan et al. 2017), which is significantly lower compared to what is observed in late-type galaxies having similar stellar masses (see Figure 4 in González Delgado et al. 2016). According to Levan et al. (2017), an upper limit of only ∼ 1 % of the stellar mass could originate from young stars. Given the properties of the host galaxy of GW170817, Pan et al. (2017) argued that the delay between the formation of the progenitor binary system and the NS-NS merger event have likely been greater than ∼ 3 Gyr. By convolving the star formation history of NGC 4993 with a DTD function in the form of t −1 , Blanchard et al. (2017) calculated the probability of the merger timescale to be between 6.8 and 13.6 Gyr, with 90 % confidence.
According to population synthesis models, the DTD function of NS-NS mergers does extend up to ∼ 10 Gyr, but most of the merger events are likely to occur within the first Gyr following the formation of the progenitor stars (e.g., Chruslinska et al. 2018). Therefore, according to Belczynski et al. (2017b), detecting the first NS-NS merger event in an early-type galaxy was unlikely, although not impossible. The low probability of this event is also discussed in Levan et al. (2017). With only one NS-NS gravitational wave detection, conclusions are limited, but the host galaxy of GW170817 does inform us that it is at least possible for NS-NS mergers to have Gyr-long coalescence timescales. We refer to Palmese et al. (2017) for a discussion on a possible formation mechanism for the binary neutron star system that led to GW170817 in NGC 4993.

The Kilonova AT 2017gfo (SSS17a)
The ultraviolet, optical, and infrared emission from GW170817 suggest a significant production of r-process elements (e.g, Chornock et al. 2017;Cowperthwaite et al. 2017;Drout et al. 2017;Pian et al. 2017;Tanaka et al. 2017;Villar et al. 2017). In particular, its late-time infrared emission suggests the production of lanthanide elements (e.g., Barnes & Kasen 2013;Fernández & Metzger 2016;Tanvir et al. 2017;Wollaeger et al. 2018, but see Rosswog et al. 2018;Wanajo 2018;Wu et al. 2018). Multi-dimensional simulations are based on twocomponent models (e.g., Tanvir et al. 2017). The first component is the neutron-rich dynamical ejecta that produces heavy r-process elements up to the third peak, at the time the compact objects collide. The second one is a wind component primarily composed of firstpeak r-process elements, which is launched at later time once the compact objects have merged. We refer to Ap-pendix C.1 for more details on those two components and on their nucleosynthesis.
All models, however, used approximate opacities since detailed databases of opacities for all heavy elements are not yet available. State-of-the-art studies used a few opacities as surrogates for the entire rare-Earth lanthanide element distribution (Barnes & Kasen 2013;Wollaeger et al. 2018), but many others used constant opacities as a function of temperature, density, and wavelength. In some calculations, the inferred ejected mass of heavy r-process elements is less than 10 −5 M (Arcavi et al. 2017). But most models predicted ∼ 0.001 − 0.01 M of dynamical ejecta, and ∼ 0.01 − 0.03 M of wind ejecta (see Table 1 in Côté et al. 2018b).
The ejected mass of the dynamical and wind components both depend on the total mass and the mass ratio of the merging neutron stars. Typically, systems with extreme mass ratios eject more dynamical mass (Korobkin et al. 2012;Bovard et al. 2017, and references therein) and produce larger disk masses (Giacomazzo et al. 2013). If the wind ejecta represent a constant fraction of the disk mass, we would expect the wind ejecta to also increase with more extreme mass ratios, although the exact amount of ejected mass depends on the simulation (see , and references therein). The current constraint on the neutron star mass ratio for GW170817 ranges from 0.4 to 1.0 (Abbott et al. 2017c).
Although the wind ejecta are thought to mostly be composed of first-peak r-process elements, they may also include some heavier elements. This could alter the ratio of the abundances between the second and third rprocess peaks, an undesired effect given the robustness of the r-process between the second and third peaks, as observed in r-process enhanced metal-poor stars (see Section 2.1.1).

The Merger Rate Density
The local NS-NS merger rate density of 1540 +3200

−1220
Gpc −3 yr −1 provided by LIGO/Virgo (Abbott et al. 2017c) represents a significant step forward in constraining the role of NS-NS mergers on the production of r-process elements in the universe. Several analytical calculations, based on estimates for the total mass of r-process elements currently present in the Milky Way, showed that the rate could be high enough to explain all the r-process mass with NS-NS mergers only (Abbott et al. 2017a;Chornock et al. 2017;Cowperthwaite et al. 2017;Gompertz et al. 2017;Kasen et al. 2017;Rosswog et al. 2017b;Tanaka et al. 2017;Wang et al. 2017;Hotokezaka et al. 2018, see also Rosswog et al. 1999). A similar conclusion was derived using a compilation of galactic chemical evolution simulations (Côté et al. 2018b).
Unfortunately, the uncertainties in the merger rate and in the total mass ejected per NS-NS merger (see Section 2.4.2) remain very large and it is not possible at the moment to come to a firm conclusion regarding the actual contribution of NS-NS mergers (see Figure 3 in Côté et al. 2018b). Therefore, although NS-NS mergers are likely to be an important site of r-process nucleosynthesis, their existence does not rule out possible contributions by other r-process sites, such as rare classes of CC SNe and BH-NS mergers.

CHEMICAL EVOLUTION SIMULATIONS
GCE simulations can bridge nuclear astrophysics efforts and stellar abundances derived from spectroscopy. In addition to the yields and properties of different enrichment sites, GCE simulations also take into account galaxy evolution processes such as star formation and interactions between galaxies and their surrounding medium (e.g., Gibson et al. 2003;Prantzos 2008;Nomoto et al. 2013;Matteucci 2014;Somerville & Davé 2015). In this section, we describe how GCE simulations can be used to test the impact of NS-NS mergers on the evolution of r-process elements in the Milky Way. The goal is not to use GCE simulations to define what is the dominant r-process site. The goal is rather to use those simulations to provide a constraint that must be combined with other constraints coming from the other fields of research covered in this paper.
There are two approaches commonly used to include NS-NS mergers in GCE simulations. The first one is to assume that all NS-NS mergers occur after a constant delay time following the formation of the NS-NS binaries (e.g., Argast et al. 2004;Matteucci et al. 2014). The second approach is to assume that NS-NS mergers in a given stellar population are distributed in time according to a long-lasting DTD function typically in the form of t −1 (e.g., Shen et al. 2015;van de Voort et al. 2015). In the later approach, NS-NS mergers can have a wide range of coalescence times, from a few tens of Myr to several Gyr (e.g., Rosswog 2015). We explore alternative forms of DTD functions in Section 5.3.

Reproducing the Decreasing Trend of [Eu/Fe]
The bottom panel of Figure 2 shows the predicted evolution of [Eu/Fe] as a function of galactic age assuming a constant delay time (black solid line) and a long-lasting DTD function (∝ t −1 , black dashed line) for NS-NS mergers, assuming they are the only source of Eu. These predictions come from a simplified version of the one-zone chemical evolution code OMEGA (Côté et al. 2017b). We adopted a constant star formation rate as a function of time and a closed-box environment, implying no gas exchange between the galaxy and its surrounding environment. This simplification, although not realistic, was adopted to facilitate the understanding of the decreasing trend of [Eu/Fe] in a GCE context. The top panel of Figure 2 shows the production rate of Fe by CC SNe (blue solid line) and SNe Ia (red solid line), and the production rate of Eu by NS-NS mergers (black solid and dashed lines), following the two approaches described above. The interpretation of the residual pink dashed line is discussed in Section 5.5. In this simplified framework, because massive stars only live for a few tens of Myr, the Fe production reaches an equilibrium after ∼ 40 Myr. The production of Fe by SNe Ia does not show this equilibrium, since SNe Ia have a wide range of delay times spanning from ∼ 100 Myr to more than ∼ 10 Gyr (e.g., Ruiter et al. 2009). This means that the first stellar population formed at the beginning of the simulation will still produce SNe Ia after ∼ 10 Gyr, which is roughly the lifetime of the simulated galaxy.
When assuming that NS-NS mergers follow the lifetime of massive stars, the production rate of Eu also reaches an equilibrium before the onset of SNe Ia (black solid line in top panel of Figure 2). Under this assumption, when SNe Ia start to appear at ∼ 100 Myr, the [Eu/Fe] ratio will bend and start to decrease as a function of time (black solid line in bottom panel of Figure 2). Indeed, while the production rate of Eu is in equilibrium, the production rate of Fe is increasing, thus progressively reducing the [Eu/Fe] ratio.
On the other hand, when using a long-lasting DTD function in the form of t −1 , the production rate of Eu no longer reaches an equilibrium (black dashed line in top panel of Figure 2). In fact, because the adopted DTD function of SNe Ia is also in the form of t −1 (see Section 2.3), the production rates of Eu and Fe evolve in a similar way once SNe Ia start to contribute. This results in a nearly constant value for [Eu/Fe] beyond ∼ 100 Myr (black dashed line in bottom panel of Figure 2). This flat trend, however, is not consistent with the decreasing trend observed in the Galactic disk (see Figure 1).

Common Message Sent by Different Studies
The inability of reproducing the decreasing trend of [Eu/Fe] in the Galactic disk using NS-NS mergers with a DTD function in the form of t −1 is independent of the complexity of the GCE simulations. Indeed, when assuming constant delay times for NS-NS mergers, all Milky Way simulations reproduce the decreasing trend of [Eu/Fe] (Argast et al. 2004;Matteucci et al. 2014;Cescutti et al. 2015;Wehmeyer et al. 2015;Côté et al. 2017a). On the other hand, when assuming a DTD function in the form of t −1 , all GCE simulations fail to match the decreasing trend of [Eu/Fe] for −1 < [Fe/H] < 0 (Shen et al. 2015;van de Voort et al. 2015;Komiya & Shigeyama 2016;Côté et al. 2017a;Hotokezaka et al. 2018;Naiman et al. 2018). The latter studies represent a wide variety of GCE approaches including simple one-zone models, semi-analytic models of galaxy formation, and cosmological hydrodynamic zoom-in simulations. Matteucci et al. (2014), Cescutti et al. (2015), and Côté et al. (2017a) suggested that GCE predictions at [Fe/H] > −1 are unaffected by the choice of the minimum delay time for NS-NS mergers 5 (see Appendix A). In order to recover the decreasing trend of [Eu/Fe], it seems not sufficient to make NS-NS mergers appear before SNe Ia, they also need to reach an equilibrium in the production of Eu. Since [Eu/Fe] and [α/Fe] both start to decrease at [Fe/H] ∼ −1, this equilibrium must be reached within the first few hundreds of Myr. Although in this section we assumed NS-NS mergers to be the only r-process site, the equilibrium requirement would be the same for any other site. It can also be applied in the context of multiple r-process sites (see Section 5.5). We refer to Hotokezaka et al. (2018) for a discussion on the impact of the minimum delay time of SNe Ia, as it could help generating a decreasing trend if that minimum delay time is set to 400 Myr or 1 Gyr.

Confirmation From Our Study
To support the conclusion made in Section 3.2, we tested the t −1 DTD function using the benchmark Milky Way model of Matteucci et al. (2014), which is based on the two-infall model originally described in Chiappini et al. (1997). We refer to Simonetti et al. (2019) for more details on this new implementation. In this multi-zone framework, which relaxes the instantaneous recycling approximation, the halo and thick disk form on a relatively short timescale (1-2 Gyr) by accretion of primordial gas. This represents the first infall event, while the thin disk forms on a much longer timescale by means of a second independent episode of gas accretion. The thin disk is assumed to form inside out with a timescale of 7 Gyr for the solar neighborhood. In this work, we only focus on the thin disk.
The model predicts at all times the gas fraction and its chemical composition. It takes into account the enrichment from stars of all masses ending their lives as white dwarfs and SNe of all types (II, Ia, Ib, Ic), in addition to the nucleosynthesis occurring in novae and compact binary mergers. The adopted yields are taken from Karakas (2010) and Doherty et al. (2014a,b) for asymptotic giant branch (AGB) and super-AGB stars, from Nomoto et al. (2013) for massive stars, from Iwamoto et al. (1999) for SNe Ia, from José & Hernanz (1998) for novae, and from Korobkin et al. (2012) for NS-NS mergers. The SN Ia rate is computed following the formalism of Greggio (2005). The rate of NS-NS mergers is calculated by convolving its DTD function with the star formation history of the Milky Way, which is generated following a Kennicutt-Schmidt law with a threshold in the gas surface density (Kennicutt 1998). The fraction of NS-NS binaries that eventually merge has been tuned to reproduce the current rate derived in Abbott et al. (2017b). The bottom panel of Figure 3 shows the predictions of this model when using a constant delay time (black solid line) and a t −1 DTD function (black dashed line) to calculate the rate of NS-NS mergers. As in previous studies (see Section 3.2), the long-lasting DTD function generates a flat trend for [Eu/Fe] and does not reproduce the decreasing trend of the Galactic disk (cyan dots). The little loop at [Fe/H] ∼ −0.5 is caused by the second in-fall episode that introduces primordial gas in the galaxy that momentarily dilutes the Fe concentration relative to H. The top panel Figure 3 shows the evolution of [O/Fe] as a comparison baseline for the decreasing trend of [Eu/Fe].
Throughout this study, we also use the GCE code OMEGA (Côté et al. 2017b) in order to explore different DTD functions for NS-NS mergers (see Section 5.3), and to compare with the results of the GCE code of Matteucci et al. (2014) (see orange lines in Figure 3). It consists of a classical one-zone model that adopts homogeneous mixing but relaxes the instantaneous recycling approximation. SNe Ia are distributed in time following a DTD function in the form of t −1 that is multiplied by the fraction of white dwarfs (see Côté et al. 2016 andRitter et al. 2018a for more details.) Yields for low-and intermediate-mass stars, massive stars, SNe Ia, and NS-NS mergers are taken from Ritter et al. (2018b), Nomoto et al. (2013), Iwamoto et al. (1999), and Arnould et al. (2007), respectively. In this paper, every OMEGA simulations have the same physical setup, only the delay time assumptions of NS-NS mergers are changed. By the end of all OMEGA simulations, the mass of gas within our Milky Way model is 9.5×10 9 M , the star formation efficiency is 2.9×10 −10 yr −1 , and the star formation rate is 2 M yr −1 .

Population Synthesis Models
Population synthesis models aim to follow the evolution of binary systems involving stars and compact remnants (white dwarfs, neutron stars, and black holes). The predictions of such models are typically for individual stellar populations where all stars are assumed to form at the same time with the same initial metallicity. In the context of this paper, these models are important because they predict the DTD functions of NS-NS and BH-NS mergers, which are crucial inputs for GCE simulations.
For this study, we use the already-calculated models M10, M13, M20, M23, M25, and M26 (see Belczynski et al. 2017a) obtained with the upgraded population synthesis code StarTrack (Belczynski et al. 2002(Belczynski et al. , 2008. These six models aim to provide a range of solutions for the predicted DTD functions that reflects uncertainties in the evolution of binary systems. A short description of the StarTrack code and the models is included in Appendix B. An important physical ingredient driving the slope of the DTD function of NS-NS mergers is the distribution of orbital separations (a) of massive stars in binary systems (e.g., Tauris et al. 2017). According to Belczynski et al. (2018a), an orbital separation distribution in the form of a −1 tends to generate NS-NS merger DTD functions in the form of t −1 , while a distribution in the form of a −3 tends to generate steeper NS-NS merger DTD functions in the form of t −1.5 (see also Figure 2 in Belczynski et al. 2018b). Figure 5 shows the predictions for BH-NS mergers for the three models that generated the highest number of BH-NS mergers. Relative to NS-NS mergers, BH-NS mergers can appear earlier during the lifetime of a stellar population. But, as described in Section 3.2, this fact alone is unlikely to help generating a decreasing trend for [Eu/Fe] in chemical evolution simulations. The shape of their DTD functions is less in agreement with a power law in the form of t −1 , as there is typically a bump in between 0.1 and 1 Gyr. Compared to a t −1 power law, this implies a flatter power law before 1 Gyr followed by a steeper power law after 1 Gyr, at least for the M20 and M26 models.

R-PROCESS NUCLEOSYNTHESIS CALCULATIONS
Here we discuss the connections of the GCE results above to theoretical r-process calculations. We give a more detailed review of the nucleosynthesis of rprocess elements in different types of environments in Appendix C. R-process nucleosynthesis calculations are usually based on hydrodynamic simulations of scenarios that can provide very neutron-rich conditions. Among those, the most promising are currently compact binary mergers and magneto-rotational (MR) supernovae, a rare class of CC SNe. Other possible scenarios include magnetized winds from proto-neutron stars (Thompson 2003;Metzger et al. 2007Metzger et al. , 2008Vlasov et al. 2014;Thompson & ud-Doula 2018), pressure-driven outflows (Fryer et al. 2006), accretion disk winds from collapsars , and the jets generated by a neutron star that accretes matter from its giant companion star (Papish et al. 2015;Soker & Gilkis 2017;Grichener & Soker 2018).
The evolution of the mass ejected depends on the evolution of density and temperature as a function of time, 10 7 10 8 10 9 10 10 Stellar population age [yr] M20 10 7 10 8 10 9 10 10 M26 Figure 5. Same as in Figure 4, but for BH-NS mergers. Predictions showing vertical drops and discontinuities did not have sufficient BH-NS mergers to generate a statistically meaningful DTD function. Only the M10, M20, and M26 models are shown, as the others did not predict enough BH-NS mergers to generate conclusive DTD functions.
and on the initial electron fraction (Y e ). The latter serves as a measurement of the neutron fraction in the environment as it is defined as the proton-to-baryon ration, Y e = Y p /(Y p + Y n ). If the Y e is low (Y e 0.25), the neutron fraction (Y n ) will be high, and more neutrons will be available to be captured by seed nuclei, i.e. the neutron-to-seed ration (Y n /Y seed ) is high. Typically, the Y e value is taken when the temperature drops below ∼ 10 GK. The evolution of density and temperature is often categorized by the entropy and the expansion timescale of the ejecta, which are used as nucleosynthesis parameters.

Robustness of the Main r-Process
An individual simulation of an environment can provide very different conditions for the ejecta. When several simulations are considered, the variations are even larger. For example, with NS-NS mergers, one can study different possibilities by varying the masses of both neutron stars, the equation of state, and other input physics. We say that the r-process nucleosynthesis is robust when the relative abundance pattern is insensitive to such variations and is always similar between the second and third r-process peak. If the initial neutron-to-seed ratio is high enough (Y n /Y seed > 150), the r-process path runs into isotopes that are prone to fission, producing two (or more) fission fragments that can in turn continue to capture neutrons. This so-called "fission cycling" guarantees that the final yields produce a robust and reproducible abundance pattern, independently of the exact hydrodynamical conditions (Beun et al. 2006;Goriely et al. 2011;Roberts et al. 2011;Korobkin et al. 2012;Rosswog et al. 2013;Eichler et al. 2015;Mendoza-Temis et al. 2015).

Neutron Star Mergers vs Supernovae
Since the uncertainties in nuclear properties and reaction rates involved in the r-process are still very large, model compositions for ejecta of different r-process sites should be considered qualitative predictions rather than precise results. Nevertheless, some key differences can be expected in the final abundance patterns of NS-NS mergers and MR SNe, if the conditions in the ejecta are reasonably different.
Hydrodynamic simulations suggest that the dynamical ejecta of NS-NS mergers are generally more neutronrich than those of MR SNe, even if the entropy range is similar. This directly translates to higher initial neutron-to-seed ratios and, as a consequence, to a larger fraction of the ejecta where the third peak and the actinides region can be reached. While a large fraction of NS-NS mergers ejecta co-produce the second and third r-process peaks, MR SN ejecta contain regions where the neutron-to-seed ratio is not large enough to produce third-peak elements, leading to the build-up of a distinct second r-process peak. As a result, the abundance ratio between the third and second peak for the total ejecta should be larger in dynamical ejecta of NS-NS mergers than in MR SNe. Varying contributions from disk and neutrino-driven wind ejecta in NS-NS mergers could unfortunately wash out this distinction.
Another observable could be the shape of the second peak itself. As described above, in MR SN ejecta, the predominant contribution in the build-up of the second peak comes from regions with moderate Y e where the r-process flow is stopped at the shell closure at N = 82. In that case, the final shape of the second peak is mostly determined by β-decays and β-delayed neutron emissions. On the other hand, the neutron-rich NS-NS merger ejecta can produce a considerable amount of actinides which fission (and α-decay) on timescales . Predicted abundances of the second r-process peak for a neutron star (NS-NS) merger calculation (blue) and a magneto-rotational supernova (MR SN) scenario (red), assuming either a continuous fission fragment production ("regular fission") or a setup where fission fragment production is disabled after the r-process freeze-out ("no late fission"). The shaded regions represent the fission contribution to the final abundances of the second peak.
that are similar to or longer than the r-process duration. Most nuclear mass models predict the majority of fissioning nuclei in the mass range 240 < A < 280, which leads to fission fragments at or around the second peak. The production of fission fragments after the end of the r-process implies that the second peak in this case is shaped by the fission fragment distribution and their subsequent β-decays on top of the abundances already present at the time of r-process freeze-out 6 .
To illustrate this, we have performed r-process calculations based on the NS-NS merger simulation of Rosswog et al. (2013) involving two neutron stars of 1.4 M each, and based on the MR SN model of Winteler et al. (2012) (see Figure 6). Both sets of calculations were performed with fully enabled fission reactions (blue and red solid lines), as well as with a modified setup disabling fission from the moment when Y n /Y seed ≤ 1 onwards. The dashed lines in Figure 6 represent the β-decayed second peak material already present at the r-process freeze-out without any later fission contribution. The differences in the two approaches therefore arise solely from fission fragments after the r-process freeze-out.
We should point out, however, that the distributions of fission fragments hold at least the same uncertainties as the nuclear reaction rates in the r-process. Our calculations shown in Figure 6 have been performed using the ABLA07 fission fragment distribution model (Kelic et al. 2009). Other fission models predict different distributions (Eichler et al. 2015;Goriely 2015). Nevertheless, the different mechanisms forming the second r-process peak should result in different peak shapes, as long as fission produces fragments in the second peak. Following this argumentation, metal-poor stars with larger actinide abundances should also exhibit second peak abundances reflecting the fission fragment production more closely than stars with a lower actinide content.

R-PROCESS SITES AND THEIR CHALLENGES
This section highlights the agreements and inconsistencies that emerge when assuming that current models of NS-NS mergers or MR SNe are the only source of r-process elements in galaxies. The results of this investigation are summarized in Table 1. In particular, we find that NS-NS mergers alone cannot be consistent with all the observational constraints listed in Section 2. In Section 5.5, we discuss the possibility of multiple sites for the heavy r-process element production.

Neutron Star Mergers with no Delay-Time Distribution
As described in Section 3, delaying the occurrence of NS-NS mergers by a constant coalescence timescale following the lifetime of massive stars (i.e., not taking into account a DTD function) allows GCE simulations to reproduce the decreasing trend of [Eu/Fe] in the Galactic disk. If NS-NS mergers are the dominant r-process site, it guarantees a robust r-process pattern for elements between the second and third r-process peaks (see Sections 2.1.1 and Appendix C.1). In addition, they eject a sufficiently large amount of material per merger event to explain the large scatter of [Eu/Fe] ratios in the metalpoor stars in the Galactic halo (see Section 2.1.3).
However, because this scenario does not use a DTD function for the coalescence times of NS-NS mergers, but rather adopts a maximum coalescence time of 100 Myr, it is incompatible with several observations. In particular, it cannot explain the detection of short GRBs in early-type galaxies (see Section 2.3.1) and the long-lasting DTD functions predicted by population synthesis models (see Section 3.4) and expected theoretically from the wide variety of orbital parameters in binary systems (Rosswog 2015). Furthermore, a constant coalescence time of 100 Myr is incompatible with the seven known NS-NS binaries with estimated coalescence times ranging from 46 to 2730 Myr (see Tauris et al. 2017 and Section 2.3.2). Finally, this scenario does not allow the gravitational wave event GW170817 to be detected in an early-type galaxy.

Neutron Star Mergers with a Delay-Time Distribution in the Form of t −1
A DTD function in the form of t −1 for NS-NS mergers is consistent with the detection of short GRBs (see Section 2.3.2) and the predictions of population synthesis models (see Section 3.4). It is also consistent with the fact that SNe Ia and short GRBs are both detected in similar proportions in early-type galaxies (see Section 2.3), given that most studies agree that SNe Ia do follow a DTD function in the form of t −1 as well (but see Heringer et al. 2017). Many GCE simulations have explored the role of NS-NS mergers on the chemical evolution of Eu in the Milky Way using this canonical DTD function. However, as described in Section 3, this scenario does not allow to reproduce the decreasing trend of [Eu/Fe] in the Galactic disk between [Fe/H] = −1 and 0, assuming that NS-NS mergers are the only source of heavy r-process elements.
A potential solution to this discrepancy is to claim that short GRB observations suffer from a lack of statistics, and that more detections should increase the fraction of short GRBs in late-type star-forming galaxies. This would imply a steeper DTD function for NS-NS mergers (see Section 5.3). Another solution is to assume a flatter DTD function for SNe Ia. But this goes in the opposite direction of recent observations suggesting that, if the DTD function of SNe Ia is different than t −1 , it should be steeper (Heringer et al. 2017).

Neutron Star Mergers with Our Exploratory Delay-Time Distributions
As discussed in the last section, using a DTD function in the form of t −1 for NS-NS mergers in chemical evolution simulations does not allow to reproduce the decreasing trend of [Eu/Fe] in the Galactic disk. In this section, we test alternative and exploratory DTD functions, which are shown in the top panel of Figure 7 (see also Simonetti et al. 2019). The idea is to recover the decreasing trend of [Eu/Fe] by concentrating the bulk of NS-NS mergers at early times, before the onset of SNe Ia, while still allowing NS-NS mergers to have a wide range of coalescence timescales (up to ∼ 10 Gyr). As shown in the bottom panel of Figure 7, it is possible to recover a decreasing trend for [Eu/Fe] using a steep power law in the form of t −1.5 (black solid line, see also Côté et al. 2017a andHotokezaka et al. 2018). This could be in agreement with the t −1.5 DTD function derived by D'Avanzo (2015) for short GRBs, although the recent analysis of Fong et al. (2017) rather points toward a function in the form of t −1 . We note that some of our population synthesis models do predict DTD functions steeper than t −1 (see thick blue line in Figure 4), although the majority are consistent with a t −1 distribution. We note that the presence of a third object interacting with a NS-NS binary could potentially help to concentrate NS-NS mergers at shorter coalescence timescales (Bonetti et al. 2018).
Alternatively, if one assumes a strong burst of mergers before the onset of SNe Ia, followed by a power law in the form of t −1 , the decreasing trend of [Eu/Fe] can also be recovered (see orange lines in Figure 7). This type of DTD function for NS-NS mergers has been seen in the population synthesis predictions of Dominik et al. 2012, as shown in the lower-left panel of their Figure 8. When using the DTD functions predicted by Dominik et al. 2012, the decreasing trend of [Eu/Fe] has been recovered with the GCE code OMEGA (Côté et al. 2017b), as shown with the black solid line in Figure 5 of Mishenina et al. (2017). Figure 8 shows the difference between the observed chemical evolution trend of [Eu/Fe] and the trends predicted using the different DTD functions explored in Figure 7. The steep power law (t −1.5 ) and the DTD with the strongest burst (f b = 100) provide the best fit and generate trends that are consistent within 25 % with the median trend observed at [Fe/H] > −0.75. Overall, the more the bulk of Eu is released at early time, the better will be the fit (see middle panel of Figure 7).
With the DTD functions explored in this section, more than half of all NS-NS mergers produced by a stellar population will have occurred by ∼ 100 Myr (see middle panel of Figure 7). This is because in order to generate a decreasing trend with chemical evolution models, the bulk of Eu must be released before the onset of the Fe production by SNe Ia. However, this significant difference between NS-NS mergers and SNe Ia is currently inconsistent with their similar fraction of occurrence in early-type galaxies (see Section 2.3.1). Furthermore, assuming the DTD functions explored in this section are representative of the real ones, detecting the first gravitational wave signal of a NS-NS merger in an early-type galaxy becomes even more improbable, although not impossible (see Section 2.4.1).

Rare Classes of Core-Collapse Supernovae
Rare classes of CC SNe, such as MR SNe, would naturally explain how Eu can be present in the atmosphere of the most metal-poor stars (Argast et al. 2004;Matteucci et al. 2014;Cescutti et al. 2015;Wehmeyer et al. 2015;Thielemann et al. 2017;Haynes & Kobayashi 2019). In addition, because the lifetime of massive stars is short relative to the production timescale of Fe in SNe Ia, using CC SNe in GCE simulations allows to reproduce the decreasing trend of [Eu/Fe] in the Milky Way between [Fe/H] = −1 and 0 (see Section 3).
But hydrodynamic simulations cannot guarantee that MR SNe will systematically produce the conditions for a robust r-process pattern between the second and third peak (see Appendix C.2). While some parts of the ejecta in SNe simulations can synthesize the second and third r-process peaks, there are several other parts (other trajectories) that will mostly produce the first and second peaks only. When summed together, it is therefore not guaranteed that the ratio between the second and the third r-process peaks will always be similar from one SN to another. If we assume that rare CC SNe are the only source of r-process elements, there is then a potential tension with the robust main r-process abundance pattern observed in r-process enhanced metal-poor stars (see Section 2.1.1). But on the other hand, those SNe could explain the diversity of abundances for the firstpeak elements (see Section 2.1 and Roederer et al. 2010).
This scenario could also be in tension with the high NS-NS merger rate established by LIGO/Virgo (see Section 2.4). Once the rate and ejecta of NS-NS mergers will be better constrained, we will be in a better situation to quantify how much room there is for additional r-process sites besides NS-NS mergers.

Multiple r-Process Sites Scenario
To summarize the previous sections, neither NS-NS mergers or MR SNe can reproduce on their own all the observational constraints simultaneously. One solution to this tension is to assume that some of the observational evidence are biased in some way, and that future observations will modify our interpretation of these constraints. But if the current observations are representative, then there are challenges to be solved. Assuming that future gravitational wave and kilonova detections will prove that NS-NS merger do play an important role in the r-process inventory of the Milky Way, something must be added in chemical evolution simulations in order to recover the decreasing trend of [Eu/Fe] in the Galactic disk.
A description of how to reproduce such a decreasing trend was presented in Section 3.1. According to this analysis, the production rate of Eu needs to reach an equilibrium before the onset of SNe Ia. But the production rate of Eu from NS-NS mergers do not reach such an equilibrium, given the long-lasting nature of their DTD function (see black dashed line in top panel of Figure 2). The black solid line in the top panel of that same figure represents the production rate that is required to generate a decreasing trend, as shown in the bottom panel. But this rate does not have to come from only one site. Indeed, by subtracting the production rate of NS-NS mergers (black dashed line) from the required rate (black solid line), one ends up with a residual production rate, highlighted as a pink dashed line in Figure 2. This residual line represents the production rate that needs to be added to the production rate of NS-NS mergers to recover the decreasing trend of [Eu/Fe].
Assuming that NS-NS mergers do contribute to the chemical evolution of Eu in the Milky Way, this suggests that there should be an additional production site of Eu active in the early universe, at low metallicity (see also Skúladóttir et al. in preparation). To be consistent with chemical evolution studies, this hypothetical extra site should fade away at later times, at higher metallicity. According to Figure 2, NS-NS mergers should become the dominant r-process site roughly when SNe Ia start to bend the [Eu/Fe] trend, which roughly corresponds to [Fe/H] ∼ −1 (e.g., Battistini & Bensby 2016;Buder et al. 2018).
By integrating the residual and NS-NS merger lines (dashed lines in Figure 2), about 10 % of the current Eu production budget could come from this extra site. With this simple approach, we estimate that this site could have produced 60 % and 40 % of the Eu during the first 100 Myr and 1 Gyr of Galactic evolution, respectively. These estimates are based on the assumptions that NS-NS mergers have a DTD function in the form of t −1 , and that the overall production rate needed to fit the evolution of [Eu/Fe] is similar to the rate of SNe from massive stars. Furthermore, our estimates depend on the minimum delay time of SNe Ia and are based on the predictions made by a simple toy model that assumes a constant star formation history. To summarize, our estimates are first order approximations and should serve as a motivation for further studies, rather than be taken for solid predictions.
MR SNe could provide this extra site of Eu production. They require a strong magnetic field to synthesize heavy r-process elements (see also, e.g., Thompson & ud-Doula 2018), and that magnetic field can be amplified by stellar rotation (see Appendix C.2). Because stars are expected to rotate faster at low metallicity (e.g., Maeder et al. 1999;Maeder & Meynet 2001;Martayan et al. 2007), it is possible that MR SNe would preferentially produce the heavy r-process elements in the early universe, while they would mostly produce lighter r-process elements (lighter than Eu) at higher metallicity. In addition, because the nucleosynthesis in MR SNe is not expected to always reach the second and third r-process peak, they could explain the patterns of limited r-process metal-poor stars (see Section 2.1.2 and Hansen et al. 2014;Spite et al. 2018), a pattern that is unlikely to occur when summing all ejecta components of a NS-NS merger.
BH-NS mergers could also be this extra site, as long as their contribution peaks at low metallicity. However, as shown in Figure 5, the DTD function of BH-NS mergers might not be steep enough to generate a significant boost of Eu before the onset of SNe Ia. More investigation is needed to validate this scenario. BH-NS mergers will hopefully be discovered in the next observing run of LIGO/Virgo. We stress that any other site that, for some reason, has a peak of Eu production in the early universe is a viable candidate.
We note that previous chemical evolution studies also suggested that SNe alongside with NS-NS mergers should contribute to the chemical evolution of Eu (Argast et al. 2004;Matteucci et al. 2014; Cescutti et al. Table 1. List of agreements and inconsistencies when assuming that current models of NS-NS mergers and MR SNe are the only r-process site for elements in between the second and third peaks. Three assumptions are made for the delay-time distribution (DTD) function of NS-NS mergers: 1 -follow the lifetime of massive stars with short constant delay times (without a DTD function), 2 -DTD function in the form of t −1 , 3 -modified DTD functions, either a steeper t −1.5 power law or a t −1 power law combined with a prompt burst of mergers before the onset of SNe Ia. For each observational constraint, a Yes or a No highlights whether or not the selected r-process site is consistent with the constraint. A Maybe means that the situation is unclear. We refer to Section 5.5 for a discussion on the possible contribution of multiple sites on the total budget of r-process elements in the Milky Way. This table reflects our current state of understanding. Further observations and/or improved models could change the interpretation shown in this Although complementary to our work, this was motivated by the difficulty to inject r-process elements early enough to explain the Eu abundances in metal-poor stars (see also Safarzadeh et al. 2018). Here we suggest the possible contribution of an extra site to solve the problem of reproducing the decreasing trend of [Eu/Fe] in the Galactic disk, a cleaner feature that is the result of ∼ 12 Gyr of chemical evolution in a less stochastic environment. In addition, our scenario strictly requires that the contribution of this extra r-process site fades away as a function of time and metallicity (pink line in Figure 1). This scenario has also been worked out in parallel by , who suggested that a metallicity-dependent second r-process site (the collapsars), combined with NS-NS mergers, can help to recover the decreasing trend of [Eu/Fe]. As described in Section 3.4, tighter orbital separations in binary systems can lead to steeper DTD functions for NS-NS mergers. If one assumes that the orbital separation distribution of massive stars was steeper at low metallicity, one could theoretically predict a burst of NS-NS mergers in the early universe, while still recovering a DTD function in the form of t −1 at current time (at low redshift). This idea is explored in Simonetti et al. (2019) and could provide a potential solution for the inconsis-tencies highlighted in Table 1, even with NS-NS mergers only. Furthermore, Schönrich & Weinberg (2019) suggested that the decreasing trend problem for [Eu/Fe] could potentially be solved by accounting for a multiphase interstellar medium where NS-NS would preferentially deposit their ejecta in a cold gas component, instead of a hot gas component in which core-collapse supernovae deposit their ejecta. This represents a motivation for future studies to better understand the mixing process of r-process elements in the early universe.

FUTURE STUDIES
In this section, we discuss the current state of the hydrodynamic simulations used to calculate r-process nucleosynthesis in compact binary mergers and CC SNe, and provide guidance for future work to address the tensions highlighted in this paper.

Simulations of Compact Binary Mergers
Most hydrodynamic simulations of compact binary mergers agree on the amount of dynamical mass ejected and on the impact of the mass asymmetry between the two merging objects (see, e.g., Table 1 in Horowitz et al. 2018). However, there are disagreements regarding the properties of the ejecta.
Neutrino interactions can change the electron fraction of the ejecta, and therefore the r-process nucleosynthesis (e.g., Wanajo et al. 2014). Detailed neutrino Boltzmann transport is currently not possible for compact binary merger simulations, and approximations must be made (e.g., Fujibayashi et al. 2017;Kyutoku et al. 2018). Furthermore, the neutrino luminosities and energies depend on the uncertain equation of state (e.g., Sekiguchi et al. 2015;Bovard et al. 2017). Improvements in all those aspects is necessary in order to reliably constrain the range of electron fractions in all ejecta components of compact binary mergers. In addition, magneto-hydrodynamical effects can influence the behaviour of the dynamical and disk ejecta, but only a few codes currently include them (Palenzuela et al. 2015;Ciolfi et al. 2017;. A further challenge is the need for high spatial resolution simulations, as all relevant features of the merger need to be resolved (e.g., Kelvin-Helmholtz instabilities at the contact interface). Simulations also need a high temporal resolution, as the ejecta leave the computational domain after a few milliseconds only. In the rare cases where the ejecta were followed for a longer time, the ejecta distribution at the end of the initial simulation was mapped to a different code Roberts et al. 2017;Martin et al. 2018), in order to study the impact of different heating sources on the dynamical ejecta.
Consistent long-term simulations, going up to about one second or longer, with an accretion disk and the emergence of a hypermassive neutron star that eventually collapses into a black hole would considerably improve the predictive power of compact binary merger simulations. Further investigations of the impact of nuclear heating on the dynamical ejecta ) as well as further increasing the parameter space of NS-NS and NS-BH merger simulations (masses, spins, etc.) are also promising paths to follow in the future.

Simulations of Core Collapse Supernovae
The initial conditions of MR SN simulations come from previously calculated stellar evolution models and these include several uncertainties and simplifications. Due to resulting uncertain magnetic field strengths, the magnetic field is artificial enhanced or decreased in MR SN simulations. In addition, there are small scale turbulences and instabilities such as the magneto-rotational instability (e.g., Obergaulinger et al. 2009) that can amplify the magnetic field. But to resolve such small scale effects, high-resolution and thus computationally-expensive simulations are needed (Mösta et al. 2017;Nishimura et al. 2017). Studies that follow explosions for one or two seconds with 3D simulations including detailed neutrino transports and general relativity will help to understand the dynamic of MR SNe in greater details.

Impact of Natal Kicks
Something we have not included in our study is the natal kicks imparted onto neutron stars after the explosion of their progenitor stars (see Tauris et al. 2017 for a review). Depending on the coalescence timescales of NS-NS mergers and on the velocity of those kicks, it is possible for NS-NS binaries to merge outside galaxies (e.g., Bloom et al. 1999;Fryer et al. 1999;Belczynski et al. 2006;Zemp et al. 2009;Kelley et al. 2010;Behroozi et al. 2014;Safarzadeh & Côté 2017). The simulations of Safarzadeh & Scannapieco (2017) showed that the spatial location of NS-NS mergers can play an important role on the amount of r-process material recycled into stars.
If the NS-NS mergers that occur outside galaxies are the ones that have the longest coalescence times, NS-NS mergers with short coalescence times would then be the ones that actively participate to the enrichment of Eu inside galaxies. From the point of view of galactic chemical evolution modeling, this would be similar to using a DTD function truncated at some given timescale. If that timescale is similar to or below the delay time needed for SNe Ia to appear in the lifetime of stellar populations, this would be sufficient to reproduce the decreasing trend of [Eu/Fe] in the Galactic disk. In that case, however, the total number of NS-NS mergers would need to be increased in order to account for the ones that inject Eu outside the star-forming regions. This scenario is to be confirmed or disproved by future studies.

Actinides
Actinide abundances in metal-poor stars could hold the key to disentangle the hydrodynamical environment(s) of the r-process. The existence of stars with super-and sub-solar actinide yields (Schatz et al. 2002;Roederer et al. 2009a;Holmbeck et al. 2018;Ji & Frebel 2018) possibly indicate varying r-process conditions. The fact that all currently known actinide-boost stars are very metal-poor ([Fe/H] −2.0) is another interesting finding. The fraction of actinide-boost stars and the Th/Eu ratios in metal-poor stars could potentially be used as an additional diagnostic tool to probe the contribution of different r-process sites. Astrophysical models of dynamical and disk ejecta in neutron star mergers predict suitable environments for actinide production, and also several MR SN models can provide the required conditions. Progress is needed before being able to quantify the typical mass of actinides ejected by NS-NS mergers and MR SNe (see sections 6.1 and 6.2).
There might also be a possibility to infer actinide yields from direct kilonova observations. Barnes et al. (2016) and Rosswog et al. (2017a) showed that actinides undergoing α-decay could represent an important contribution to the total nuclear heating powering the kilonova from a few days after the merger onwards. Furthermore, Zhu et al. (2018) showed that, given its half-life of ∼ 60 days, the fission of 254 Cf could be detectable several days after a NS-NS merger event, and could potentially be seen in the middle infrared band of future kilonova lightcurves.

Possible Production of Europium by the i-Process
The r-process solar residual pattern does not take into account the potential contribution of the i-process (Cowan & Rose 1977). The i-process can be activated at all metallicities in massive stars (even down to metal-free stars, e.g., Banerjee et al. 2018;Clarkson et al. 2018), in rapidly accreting white dwarfs (Denissenkov et al. 2017), and in AGB and post-AGB stars of different types (e.g., Herwig et al. 2011;Jones et al. 2016). Observations of possible i-process abundance signatures have been detected in metal-poor stars (e.g., Dardelet et al. 2014;Lugaro et al. 2015;Abate et al. 2016;Hampel et al. 2016;Roederer et al. 2016b,a) and in young open stellar clusters (Mishenina et al. 2015), for different elements including Eu all the way up to Pb.
In the simulations of Bertolli et al. (2013) and Dardelet et al. (2014), considering an i-process activation between ∼ 1 hour and ∼ 1 day, the 151 Eu/ 153 Eu isotopic ratio varies between 0.7 and 1.5, which is close to the solar value of 0.92. In spite of this interesting result, it does not necessarily mean that the i-process significantly contributed to the total amount of Eu found in the Milky Way. Because of the complex hydrodynamic simulations required to constrain the stellar conditions where the i-process takes place (e.g., Herwig et al. 2014;Woodward et al. 2015), and because of the large uncertainties in nuclear physics Denissenkov et al. 2018), it is currently difficult to quantify the i-process contribution to the solar composition. In addition, large uncertainties in r-process nucleosynthesis calculations (e.g., Mumpower et al. 2016;Thielemann et al. 2017;Horowitz et al. 2018) do not allow at the moment to derive strong constraints on the i-process component.
The conclusions presented in this paper are drawn under the assumption that the i-process does not contribute to the current inventory of Eu in our Galaxy. More investigations are needed to validate or invalidate this assumption.

CONCLUSIONS
In this work, we compiled and analyzed a series of observational evidence that probe the properties of rprocess sites, and addressed them using nucleosynthesis calculations, population synthesis models, and galactic chemical evolution simulations. At the moment, we cannot build a consistent picture when assuming that there is only one r-process site for elements between the second and third r-process peak. The list of agreements and inconsistencies are shown in Table 1.
It is not possible to reproduce the decreasing trend of [Eu/Fe] in the Galactic disk with NS-NS mergers only using a DTD function in the form of t −1 for the distribution of their coalescence timescales (see Sections 3.2 and 5.2). This, however, is the form currently predicted by population synthesis models (see Section 3.4) and inferred from short GRB detections (see Section 2.3.2). We can reproduce the decreasing trend by steepening the slope of the DTD function (see also Côté et al. 2017a andHotokezaka et al. 2018), or by adding a burst of NS-NS mergers before the onset of SNe Ia on top of a t −1 distribution (see Section 5.3). But this is not consistent with the similar distribution of short GRBs and SNe Ia in early-type galaxies (see Section 2.3.1). Assuming a constant short delay time for NS-NS mergers is inconsistent with several observations (see Section 5.1), including the detection of GW170817 in an early-type galaxy.
Because nucleosynthesis calculations show that NS-NS mergers are able to produce a robust r-process pattern (see Appendix C.1), and because the merger rate established by LIGO/Virgo is significantly high (see Section 2.4.3), NS-NS mergers are likely to play an important role in the evolution of r-process elements. If that is the case, and if we assume current observational constraints are all reliable, then one solution is to involve a second r-process site in the early universe capable of producing Eu (see Section 5.5). This extra site should fade away at later times, at higher metallicity (see pink dashed line in Figure 2), and would roughly account for ∼ 50 % of the Eu produced in the early universe, and ∼ 10 % of all Eu currently present in the Milky Way. This is a plausible solution, but it does not mean it is the correct solution.
MR SNe could be this extra site of Eu. To reach the third r-process peak and produce Eu along the way, these SNe need very strong magnetic fields (see Appendix C.2). Because massive stars are likely to rotate faster at low metallicity, the magnetic field present during a MR SN could also be higher at low metallicity, which would explain why this second site fades away at higher metallicity (see Section 5.5). This conclusion is based on the chemical evolution of the Galactic disk, which encodes most of the evolution history of the Milky Way. We note that any other production site of Eu that respect this metallicity dependency is a possible candidate.
Although we presented a possible solution to the current inter-disciplinary tensions, the information shown in Table 1 should be taken as the starting point for future work. Other possible solutions exist (e.g., Sections 6.3 and 6.5), and further observations might change our interpretation of the observational evidence listed in Section 2. In particular, more detections of NS-NS mergers by LIGO/Virgo and improvements in the interpretation of kilonova lightcurves will better define how much room there is for other r-process sites.
We are thankful to Erika Holmbeck, and Ian Roederer for discussions on the abundances of metal-poor stars, to Gabriele Cescutti for discussions on modeling neutron-capture elements in a chemical evolution framework, and to Mohammadtaher Safarzadeh for discussions on the impact of natal kicks. This research is supported by the ERC Consolidator Grant (Hungary) funding scheme (project RADIOSTAR, G.A. n. 724560) and by the National Science Foundation (USA) under grant No. PHY-1430152 (JINA Center for the Evolution of the Elements). This paper included work from the ChETEC (Chemical Elements as Tracers of the Evolution of the Cosmos) COST Action (CA16117), supported by COST (European Cooperation in Science and Technology), and has benefited from discussions at the 2018 Frontiers in Nuclear Astrophysics Conference supported by the JINA Center for the Evolution of the Elements. AA, ME, and MR were supported by the ERC starting grant EUROPIUM (Grant No. 677912)  In this section, we test this statement when adopting a DTD function in the form of t −1 , using t min = 1, 10, and 100 Myr, where t min refers to the minimum delay time between the formation of the progenitor stars and the merger event. We note that according to the population synthesis predictions presented in Figure 4, t min is typically below 100 Myr. As shown in Figure 9, using the GCE code OMEGA, the predicted trends at [Fe/H] > −1 are similar when using a constant delay time (blue band, see also Matteucci et al. 2014;Cescutti et al. 2015;Côté et al. 2017a), but are significantly different when using a DTD function (black band). Nevertheless, varying t min can still not provide a good agreement with the measured [Eu/Fe] trend when using a DTD function in the form of t −1 . This parameter therefore do not affect the general conclusions of this work, although it could affect the estimated contribution of the hypothetical extra r-process site (see Section 5.5).
As a complement, we also explored the impact of the star formation history (see also Hotokezaka et al. 2018). Figure 10 shows the predictions made by the OMEGA code when using a decreasing star formation history (solid lines) and a constant star formation history (dashed lines). Overall, we find that the effect of the star formation history is minor in comparison to the effect of using different delay time assumptions for NS-NS mergers. As in Figure 7 of Hotokezaka et al. (2018), the maximum [Fe/H] reached by our predictions is shifted to lower [Fe/H] values when using a constant star formation history (dashed lines), likely because of the larger amount of infalling gas compared to the decreasing star formation history, which has a current star formation rate three times lower than in the constant case. Overall, as for the minimum delay time for NS-NS mergers, the adopted star formation history should not affect the general conclusions of this work. Here we discuss the properties of the population synthesis models adopted for our study in more detail (see section 3.4). We use the upgraded population synthesis code StarTrack (Belczynski et al. 2002(Belczynski et al. , 2008. Improvements relevant for massive stars include a better treatment of the common envelope evolution (Dominik et al. 2012) and a remnant mass prescription ) that reproduces the first gap found in between the observed mass distributions of neutron stars and black holes in the Milky Way ). Effects of pair-instability pulsation SNe and pair-instability SNe are taken into account, as they are believed to create the second mass gap in the observed mass distribution of compact objects (Belczynski et al. 2016).
We account for the formation of neutron stars via electron-capture SNe (e.g., Miyaji et al. 1980;Podsiadlowski et al. 2004;Chruslinska et al. 2018) and through accretion-induced collapse of white dwarfs (e.g., Nomoto & Kondo 1991;Ruiter et al. 2018). The maximum mass of neutron stars is set to 2.5 M , which is consistent with the heaviest known neutron stars of 2.3 M (Linares et al. 2018). The initial conditions of the binary systems are constrained by observations (de Mink & Belczynski 2015). The differences between the models can also be seen in Figures 4 & 5 in the main body of this article. Model M10 represents the standard input physics in StarTrack. In particular, the natal kick velocities initially imparted on black holes are small, and in some cases non-existent. For neutron stars, the natal kicks are defined by a Maxwellian distribution with σ = 265 km s −1 . However, the exact values of the natal kicks can be altered by the amount of material falling back onto the compact objects after the SN explosions (see Belczynski et al. 2017a for details). The magnitude of natal kicks is an important quantity, as it can significantly modify the coalescence timescales of NS-NS and BH-NS systems (e.g., Belczyński & Bulik 1999).
The M13 model is similar to the M10 model, but the Maxwellian natal kick distribution with σ = 265 km s −1 is adopted for both black holes and neutron stars. In addition, the amount of fallback does not regulate the kick velocities. We note that neutron stars formed by electron-capture SNe and by the accretion-induced collapse of white dwarfs still have natal kicks set to zero, as it is the case for all models presented in this section.
In model M20, the natal kick prescription for black holes and neutron stars is the same as in the M10 model, but the input physics describing the evolution of binary systems during the common envelope phase is modified. This includes for example 80 % non-conservative Roche Lobe overflow and 5 % Bondi-Hoyle rate accretion, as opposed to 50 % and 10 %, respectively, in the M10 model (see Belczynski et al. 2017a for details).
The M23, M25, and M26 models have the same modified input physics as in the M20 model, but adopt a Maxwellian natal kick velocity distribution for both neutron stars and black holes, as in Model M13. The dispersion velocity σ for models M23, M25, and M26 is 265, 130, and 70 km s −1 , respectively.

C.1. Neutron Star Mergers
In NS-NS mergers, there are various ways of ejecting matter and those lead to different conditions and nucleosynthesis. The total amount of ejecta depend on the configuration of the binary system (e.g., neutron star masses, eccentricity of the orbit). For the dynamical ejecta, between about 10 −3 and 10 −2 M of very neutron-rich (low Y e ) material can be ejected by means of tidal effects or shocks in the interaction zone between the two neutron stars. These numbers are in agreement with estimates of the ejected mass for GW170817 (see Section 2.4.2), and are large enough to recover the scatter seen in the [Eu/Fe] abundances of metal-poor stars (see Section 2.1.3).
The dynamical ejecta robustly produce the heavy r-process nuclei from the second peak up to the actinide region with mass numbers A above 200. The extreme neutron-richness of the dynamical ejecta leads to fission cycling and an r-process path close to the neutron drip line (further favoured by rapid expansion/cooling). As a consequence, such environment only produces nuclei from the typical fission fragment mass numbers A ≈ 120 and larger. The do not produce the lighter first-peak r-process nuclei. NS-NS mergers are thus consistent with the robust main r-process patterns seen in metal-poor stars (Sneden et al. 2008, see also Section 2.1).
However, other hydrodynamical codes lead to broader ranges in electron fraction and entropy (Bauswein et al. 2013;Sekiguchi et al. 2015;Foucart et al. 2016;Radice et al. 2016;Bovard et al. 2017). Simulations incorporating general relativity effects exhibit a more energetic collision, since the neutron star radii are smaller. This leads to strong shocks that increases the Y e and the entropy in the ejecta. But even these simulations produce robust abundances between the second and third r-process peak, since the ejecta consist of two major components: those that stop at or before the second peak, and those that produce the full mass range of r-process nuclei up to the actinides in a robust way. Some recent works have found conditions with low Y e and large entropies (related to shocked ejecta with very fast expansion velocities) which result in an unusual abundance pattern (reported, e.g., in Metzger et al. 2015;Barnes et al. 2016;Bovard et al. 2017). However, these conditions contribute to only a very small fraction of the total ejecta, and therefore have no real effect on the integrated abundances.
In addition to the dynamical ejecta, there are other mass loss channels operating on longer timescales that are related to the formation of a post-merger disk around the central remnant object (Beloborodov 2008;Dessart et al. 2009;Foucart 2012;Fernández & Metzger 2013;Perego et al. 2014;Fernández et al. 2015;Just et al. 2015;Martin et al. 2015;Siegel & Metzger 2017). Again, the formation of the disk and its mass depend on the binary system configuration. If the central object does not promptly collapse to a black hole, it emits neutrinos that, together with the neutrinos emitted from the disk, can generate a mass outflow similar to neutrino-driven winds in CC SNe (Perego et al. 2014;Martin et al. 2015;Just et al. 2015). Simulations also show that disk material can become gravitationally unbound by means of viscous effects and nuclear recombination (Fernández & Metzger 2013;Just et al. 2015;Fernández et al. 2015). Due to the longer timescales of these ejecta, they are exposed to neutrinos for a longer time compared to the dynamical ejecta. And because neutrinos transform neutrons into protons, these longer-timescale ejecta are typically less neutron-rich.
While the viscous ejecta can still produce the heaviest r-process nuclei , the neutrino-driven ejecta have been found to produce first-peak elements only (Perego et al. 2014;Martin et al. 2015). The viscous and the neutrino-driven ejecta represent about 5-20 % (Fernández & Metzger 2013;Just et al. 2015;Fernández et al. 2015) and 5 % (Martin et al. 2015) of the initial disk mass, respectively. These numbers depend on the fate of the central remnant. For example, a quicker collapse into a black hole leads to a smaller ejected mass via these two mass loss channels. Finally, magnetic fields can also contribute to the acceleration and ejection of mass (Siegel & Metzger 2017). However, only preliminary results are available and it is still early to make conclusive statements about the importance of magnetic fields.

C.2. Core-Collapse Supernovae
At the surface of a proto-neutron star, electron capture can deleptonize the material. If this material is ejected, it can produce r-process elements. But in standard CC SNe, the matter is mainly ejected by neutrinos, which reduce the number of neutrons by converting them into protons. In such conditions, current simulations indicate that standard CC SNe could at most produce trans-iron elements like Sr, Y, Zr, Mo, and Ru (first-peak elements), and perhaps in some cases elements up to Ag (e.g., Roberts et al. 2010;Arcones & Montes 2011;Eichler et al. 2018;Bliss et al. 2018 and references therein). In order to produce heavier elements such as Eu, another ejection mechanism is necessary. Magnetic fields and rotation have been identified as a possibility by Cameron (2003) and Nishimura et al. (2006). Simulations of magneto-rotational (MR) SNe have become possible at least with simplifications in the neutrino transport. We refer to the introduction of Section 4 for a list of other possible r-process sites.
Based on three-dimensional simulations with a simple leakage treatment for the neutrinos, Winteler et al. (2012) found that the heavy r-process can be synthesized in MR SNe. The two-dimensional simulations of Nishimura et al. (2015Nishimura et al. ( , 2017 with parametric neutrino treatment found that when the magnetic field is strong, and neutrino emission is reduced, a jet-like explosion develops and neutron-rich material is ejected. Again with a strong magnetic field, Mösta et al. (2017) have shown, however, that in 3D simulations it becomes harder to reach the neutron-richness required for a robust r-process. They also confirm the results of Nishimura et al. (2015), demonstrating that when the neutrino emission is artificially increased, one can go from producing a robust r-process to producing a weak r-process up to the second peak only.
This behavior could potentially explain the abundance patterns of metal-poor stars, such as HD 122563 (Honda et al. 2006), enhanced in Sr and other elements at the neutron shell closure N = 50 relative to Ba. Furthermore, because MR SNe might synthesize a variety of r-process abundance patterns depending on the conditions, from a week to a robust r-process including the second and third peaks, such SNe could explain the variety of metal-poor stars having abundance patterns in between stars like HD 122563 and stars showing the full r-process pattern (see Roederer et al. 2010). Improved neutrino transport is mandatory before making any definite conclusions, since neutrinos can lead to a broad variability in the conditions of the matter ejected (Obergaulinger & Aloy 2017;Reichert et al. in preparation).
Regarding the total amount of r-process material ejected, MR SNe may contribute very differently depending on the strength of the magnetic field. In general, the ejected mass containing r-process elements will be larger than with neutrino-driven winds in regular CC SNe, but will be smaller than with NS-NS mergers. This kind of explosions is expected to occur in a few percent of all SNe at most, preferentially at low metallicities where the magnetic field could be amplified by faster stellar rotation velocities. Because of this possible dependence on metallicity, MR SNe represent an interesting candidate for our multiple r-process sites scenario presented in Section 5.5.