ON THE r-PROCESS ENRICHMENT OF DWARF SPHEROIDAL GALAXIES

The Dark Energy Survey has discovered a new dwarf spheroidal galaxy, named Reticulum II, which lies at a distance of only ∼30 kpc from Earth (Bechtol et al. 2015; Koposov et al. 2015). The proximity of Reticulum II benefits indirect searches for dark matter (DM) annihilation. In fact, an analysis of data from the Fermi Large Area Telescope found a tentative (2.4–3.2σ local significance) excess in GeV γ-rays emanating from the position of the Reticulum II dwarf (Drlica-Wagner et al. 2015; Geringer-Sameth et al. 2015; Hooper & Linden 2015). Spectroscopic measurements of Reticulum II stars identify Reticulum II as an ultra-faint dwarf spheroidal galaxy (UFD), with a total stellar luminosity of only 2360 ± 200 L_⊙ and a mass to light ratio of 470 ± 210 (Simon et al. 2015), making it an excellent target for DM indirect detection studies (Bonnivard et al. 2015; Simon et al. 2015).

Recent measurements of stellar spectra indicate that Reticulum II is unique among known UFDs. The majority of stars in Reticulum II are overabundant in elements heavier than Zinc, a signature of rapid neutron capture (aka r-process) enrichment (Ji et al. 2016a; Roederer et al. 2016a). This is intriguing, because nine similar UFDs, namely Segue 1, Hercules, Leo IV, Segue II, Canes Venatici II, Bootes I, Bootes II, Ursa Major II, and Coma Berenices, show only trace r-process enrichment (Ji et al. 2016b), which may be consistent with r-process materials accreted through interactions of these systems with the Galactic disk. Moreover, the s-process metallicity of Reticulum II, [Fe/H] = $-{2.65}_{-0.07}^{+0.07}$ (Simon et al. 2015) is consistent with, and even lower than, other UFDs (Kirby et al. 2008; Frebel et al. 2014; Koch & Rich 2014; Ji et al. 2016b). Two of the nine stars observed by Ji et al. (2016a) show no r-process enrichment, a possible indication of multiple star formation epochs.

The excess of neutron-rich elements in Reticulum II has implications for the production of heavy r-process elements, which occurs at astrophysical sites harboring copious free neutrons. Within recent decades, core-collapse supernovae have been considered as a source of r-process materials (Duncan et al. 1986; Meyer et al. 1992). However, r-process elements in Milky Way (MW) stars show characteristic peak abundances at atomic masses A = 80, 130, 195 (Burbidge et al. 1957) and the entropy provided by core-collapse supernovae appears too low to reproduce the third peak (Qian & Woosley 1996; Thompson et al. 2001; Fischer et al. 2010). Alternatively, decompressing neutron fluid ejected from, e.g., the merger of a neutron star (NS) with another NS or a black hole (BH), reproduces the A = 195 peak (Lattimer & Schramm 1976; Lattimer et al. 1977; Eichler et al. 1989; Davies et al. 1994; Freiburghaus et al. 1999), and could be the source of most r-process elements (Symbalisty & Schramm 1982; Arnould et al. 2007; Surman et al. 2008; Shen et al. 2015; Matteucci et al. 2014; Cescutti et al. 2015; van de Voort et al. 2015). More recent proposals for r-process production include the accretion-induced collapse of white dwarfs (Woosley & Baron 1992) and rapidly rotating magnetars (Metzger et al. 2008).

Another method to distinguish between r-process models is to utilize the stochasticity of r-process enrichment in small, isolated, metal-poor systems (e.g., UFDs). For example, lest they overproduce r-process elements, frequent iron core-collapse supernovae must each produce a small r-process abundance (≲10⁻⁷ M_⊙), and also in this case the r-process abundance should scale with stellar metallicity. On the other hand, double NS mergers are expected to be rare and so they can produce copious r-process materials (≳10⁻⁴ M_⊙). Thus, the observation of significant r-process enrichment in Reticulum II (alongside its typical metallicity for a UFD) and the lack of r-process enrichment in any other UFD point toward a rare event, like a double NS merger, for the r-process enrichment of Reticulum II (Ji et al. 2016a). However, as we will show, NS mergers in UFDs appear too rare to account for the enrichment of Reticulum II.

In this article we examine the viability of many r-process production models in light of the r-process abundances now observed in both UFDs and the MW. We also propose a new r-process production site: the neutron-rich fluid ejected from DM-induced implosions of NSs. We find that DM-induced NS implosions could account for both the r-process abundance observed in Reticulum II and the MW. In Section 2 we study the rate of NS mergers in UFDs and find this scenario for r-process production to be disfavored at >3σ. Section 3 examines alternative proposals for r-process production. DM-imploded NSs are introduced as an r-process production site in Section 4 and DM r-process enrichment of UFDs and the MW is compared to other proposals in Section 5. Section 6 notes that a comparison between the r-process enrichment of UFDs and that of globular clusters can provide a diagnostic test specific to DM dominated r-process production. In Section 7, we conclude with additional applications of r-process observations to studies of DM, primordial BHs, and by extension the primordial power spectrum.

Due to the low-star formation rate in UFDs, it is reasonable to ask whether any NS–NS or BH–NS mergers are expected in the population of observed UFDs. Observations indicate that the total star formation history of all ten UFDs studied by Ji et al. (2016a) amounts to only 1.0 × 10⁵ M_⊙ (McConnachie 2012; Bechtol et al. 2015). While mass loss and tidal disruption may distort these measurements, we note that these observations lie on the mass–metallicity relationship, indicating that the mass lost from these systems has not drastically affected their stellar populations since the onset of their first supernovae (Kirby et al. 2008). In order to calculate the total number of NS–NS and NS–BH binary progenitors in UFDs, we employ a Kroupa (Kroupa & Weidner 2003) initial mass function with a minimum stellar mass of 0.08 M_⊙ and a high-mass index of α = 2.7, and conservatively assume a binary fraction of unity, with a flat secondary mass distribution (Kobulnicky et al. 2006). Using these values we find that the UFD population could form ∼800 initial binary systems with an initial primary mass exceeding 5 M_⊙.

To calculate the number of NS–NS mergers produced by this ensemble of systems, we utilize the results of Dominik et al. (2012), noting that the modeled results are produced at a higher metallicity of [Fe/H] = −1.0 and that this choice is conservative given that NS–NS mergers are similarly efficient at both metallicities (Dominik et al. 2013). We have confirmed this result using a simulation of 2.0 × 10⁶ binaries at a metallicity [Fe/H] = −2.30 finding the results to be identical to within the level of Poisson noise.³ In what follows we quote the statistical results for simulations at higher metallicity, as the larger number of test systems decreased the Poisson noise for these rare events. We remain agnostic as to the best models of binary stellar evolution and marginalize our results over all 16 models presented in Dominik et al. (2012). Conservatively (realistically) assuming that the NS–NS or NS–BH merger must occur within 1 Gyr (100 Myr) from system formation to produce r-process materials before the formation of the remaining UFD stellar population, we find that 2.1 (1.5) NS–NS and NS–BH mergers would be expected among the UFD population, in line with expectations.

However, the progenitor compact objects in NS–NS and NS–BH mergers must undergo significant natal kicks to move the system into a tightly bound, eccentric orbit (Willems & Kalogera 2004). At the time of reionization, the progenitors of observed UFDs are expected to have masses of ∼10⁷ M_⊙ (Salvadori & Ferrara 2009; Bland-Hawthorn et al. 2015; Webster et al. 2015) and escape velocities given by (Bovill & Ricotti 2011):

$$\begin{eqnarray}&&{v}_{\mathrm{esc}}\,=\,10.9{\left(\displaystyle \frac{M}{{10}^{7}{M}_{\odot }}\right)}^{1/3}{\left[\displaystyle \frac{1+z}{9.5}\right]}^{1/2}\mathrm{km}\,{{\rm{s}}}^{-1}\end{eqnarray} \tag{ 1 }$$

Examining the models of Dominik et al. (2012) and removing binaries that received a center of mass kick (during either compact object formation event) larger than 10 km s⁻¹ (20 km s⁻¹), we find that the total UFD population would be expected to produce <0.0001 (0.0008) mergers within 100 Myr after binary formation, and 0.0016 (0.0125) mergers within 1 Gyr after binary formation. In Table 1 we summarize these results, including several additional models for both the maximum merger age and escape velocity for the UFD population. We note that Reticulum II may have a unique star formation history, DM halo formation history, or escape velocity compared to other UFDs. In case Reticulum II has special properties compared to other UFDs, we recalculated the number of expected NS mergers based on the 2.6 × 10³ M_⊙ of star formation observed in Reticulum II. With this smaller stellar population, we find that r-process events in Reticulum II from an NS merger become less likely.

In the prior section we have considered the merger of binaries, occurring through the joint stellar evolution of two, initially bound stars. However, alternative scenarios are possible. For example, in globular clusters, the majority of stellar encounters are believed to occur through n-body dynamics, due to the high stellar density in globular cluster centers. However, UFDs, are expected to be underdense (compared to globular clusters) by nearly six orders of magnitude, making stellar encounters negligible. A more important consideration is whether NS–NS and NS–BH mergers in UFDs could be enhanced due to Kozai oscillations in triple systems (Thompson 2011; Sharpee & Thompson 2013). Notably, the eccentricities induced in the binary orbit through the Kozai mechanism can vastly decrease the merger time between widely separated binary companions. If we remove our cuts on the binary merger time in the previous section (assuming that the Kozai mechanism produces a binary merger within the required 100 Myr timeframe regardless of the initial binary configuration) then we would produce 1.7 (2.0) NS–NS and NS–BH binaries with maximum kick velocities of 10 km s⁻¹ (20 km s⁻¹). However, the fraction of triples in UFDs is unlikely to be unity, and it may also be difficult to keep these widely separated, low-mass, triple systems bound due to the mass loss and natal kicks of each supernova. A full investigation of this effect is warranted but lies beyond the scope of this paper.

A second possibility includes r-process enrichment from only a small subset of supernova events, such as those that produce a rapidly spinning, high-magnetic field, magnetar (Metzger et al. 2008; Nishimura et al. 2015; Tsujimoto & Nishimura 2015). While none have been observed, they are expected to be short lived, and so may have escaped detection thus far. Since the rate of rapidly rotating magnetars can be adjusted freely, it is difficult to utilize stochasticity arguments to determine whether this mechanism could produce a single r-process event throughout the population of UFDs.

Some authors have argued for r-process enrichment connected to the accretion-induced collapse of a white dwarf into an NS (Woosley & Baron 1992). While this method is connected to binary dynamics, its rate, dynamical equation of state, and r-process yield are unknown (Fryer et al. 1999; Thompson et al. 2001; Piro & Thompson 2014). However, similar to core-collapse supernovae, individual accretion-induced collapse events imply that r-process abundance scales linearly with star formation rate, and thus metallicity, while Reticulum II and other observed UFDs are metal-poor.

It should also be considered whether r-process enrichment of Reticulum II might result from direct, accretion-induced collapse of an NS, an event that should be significantly rarer than the accretion-induced collapse (AIC) of white dwarfs. AIC of an NS would result after either a high-mass or low-mass X-ray binary phase with mass transfer rates near the Eddington limit, which is ∼10⁻⁸ M_⊙ yr⁻¹ for an NS. Assuming a maximum NS mass of 2 M_⊙ and an initial NS mass of 1.4 M_⊙, this corresponds to persistent Eddington limited accretion over the course of 60 Myr. While some NS systems (e.g., the recently discovered M82 X-2 (Bachetti et al. 2014) may produce X-ray luminosities that significantly exceed the Eddington limit, these systems are thought to be transient, with the majority of observed NS X-ray binaries having maximum luminosities no more than a factor of two above the Eddington limit (Grimm et al. 2003). In the case of high-mass X-ray binaries, model runs performed at low metallicity (Z = 0.02 Z_⊙) predict only 0.03 NS X-ray binaries which produce consistent emission approaching the Eddington luminosity for a starburst of the size expected in all observed UFDs—10⁵ M_⊙ (Linden et al. 2010). Systems with significantly brighter emission, such as M82-X2, have stable mass transfer periods limited to ∼10⁵ years (Fragos et al. 2015). In the case of low-mass X-ray binaries, Roche lobe overflow systems may persist on much longer timescales. Constraining ourselves to systems which transfer 0.6 M_⊙ within 500 Myr, we consider any persistent system with an X-ray luminosity above 0.1 L_edd, or approximately 1 × 10³⁷ erg s⁻¹. Studies by (Fragos et al. 2008) indicate that approximately 1.7 × 10⁻⁴ persistent low-mass X-ray binaries (LMXBs), with luminosities exceeding 10³⁷ erg s⁻¹, would be produced in a 10⁵ M_⊙ system. While this model assumes higher metallicity and continuous star formation, this is conservative for our calculation as LMXBs are extremely long-lived and many form after the 500 Myr simulation time necessary to produce r-process enrichment in our model. Additionally, observations of globular clusters indicate that low-mass X-ray binary formation is stronger in higher metallicity systems than at low metallicities (Kim et al. 2013). Altogether, it seems r-process enrichment of Reticulum II via direct collapse of an NS is disfavored.

A final possibility is that an NS merger occurred in Reticulum II, but that the NS binary was sourced by another star-forming region, such as the ancient stars of the MW bulge. Assuming a total star formation of 10¹⁰ M_⊙ within the first Gyr after bulge formation (Wyse et al. 2009), we calculate an expected population of ∼4 × 10⁵ double NS mergers, the majority of which happen far from the MW bulge due to the natal kicks given to the NS population. Using the kick velocities, and binary merger times calculated in Dominik et al. (2012), we find only a probability of only 0.008% that a binary merger could occur within 100 pc of Reticulum II, assuming an average separation between the MW center and Reticulum II of 20 kpc during that epoch. However, this number may dramatically increase if the Reticulum II dwarf resided close to the MW bulge during early periods of intense star formation.

The r-process abundance in Reticulum II and the MW could result from DM instigating lone NS implosions that eject neutron-rich fluid. Extensive radio searches by the Green Banks Telescope and Arecibo array of the inner parsecs of the MW, have not revealed the expected population of Galactic Center (GC) pulsars (Macquart et al. 2010; Wharton et al. 2012; Chennamangalam & Lorimer 2014). In Bramante & Linden (2014) we found that DM could implode NSs in the GC and thus account for the missing pulsars. DM, more dense in the central parsec of the MW, can accumulate at the center of NSs and form a star-consuming BH within t_c ∼ 10⁵–10⁸ years, depending on the mass, local DM density (ρ_DM), and nucleon scattering cross-section (σ_nX) of the DM particle.

Outside the center of the MW, measurements of the characteristic age of pulsars, corroborated by the ages of binary partner white dwarfs, indicate that disk pulsars reach ages of at least ∼Gyr (Bramante & Elahi 2015). This puts an upper bound on σ_nX for a number of DM models (Goldman & Nussinov 1989; Starkman et al. 1990; Bertone & Fairbairn 2008; Kouvaris 2008; de Lavallaz & Fairbairn 2010; Kouvaris & Tinyakov 2011a, 2011b; Kouvaris 2012; McDermott et al. 2012; Bell et al. 2013; Bertoni et al. 2013; Bramante et al. 2013, 2014; Güver et al. 2014; Ángeles Pérez-García & Silk 2015; Brito et al. 2015; Zheng et al. 2015; Kurita & Nakano 2016).

Although NSs in the MW disk may be as old as 10¹⁰ years, NSs can still quickly implode in the GC. The DM capture rate in NSs scales linearly with ρ_DM and σ_nX. Therefore, because the DM density at the center of the MW is up to 10⁴ times denser than in the disk, pulsars in the central parsecs can collapse after ≲10⁶ years and are potentially sensitive to 10⁴ times larger σ_nX (de Lavallaz & Fairbairn 2010; Bramante & Linden 2014). During NS collapse, the reconfiguration of the NS's magnetosphere radiates ∼10⁴² erg in a millisecond; hence DM-induced NS implosions could also be the source of fast radio bursts (FRBs) (Fuller & Ott 2015).

For concreteness, in the following calculation of the r-process yield from a DM-induced NS implosion, we assume a non-annihilating, negligibly self-interacting DM candidate with a mass m_X = 10 PeV, that can either be bosonic or fermionic, and with a DM-nucleon scattering cross-section σ_nX ≳ 10⁻⁴⁵ cm². There are additional DM models, e.g., shift-symmetric bosons (Bramante & Linden 2014) and Higgs portal fermions (Bramante & Elahi 2015), which would induce GC pulsar collapse for DM masses m_X = keV−PeV. We consider PeV mass DM because its predicted cross-section complements imminent direct detection searches and it may be responsible for type Ia supernova ignition (Bramante 2015; Graham et al. 2015). We assume NSs with radius R_NS ∼ 10 km , mass M_NS ∼ 1.5 M_⊙, temperature T_NS ∼ 10⁴ K, and central density ${\rho }_{{\rm{NS}}}\sim {10}^{15}\,{\rm{g}}\,{\mathrm{cm}}^{-3}$. With these parameters, any σ_nX in excess of 10⁻⁴⁵ cm² saturates the geometric cross-section for DM capture in an NS. Therefore, ∼PeV mass DM-induced NS collapse models are robust against variations in σ_nX. For details, see (Bramante 2015).

Hereafter we demonstrate that during the growth of a small BH inside an NS, ∼10⁻⁵–10⁻¹ M_⊙ neutron-rich fluid could be ejected as a result of tidal squeezing. To precisely determine the mass ejected, it would be necessary to perform a detailed hydrodynamic simulation of tidal forces during the (likely turbulent) process of an NS's rapid inward accumulation onto a growing BH. We leave hydrodynamic simulations to future work. In the remainder of this section, we (1) find the maximum mass of r-process elements ejected, (2) show that the physical conditions prompting neutron fluid ejection in an NS–BH merger are also present when an NS implodes into a BH, and (3) find that substantial mass ejection by neutrino emission must occur outside a steady-state regime.

To set an upper limit on the mass that escapes from an imploding NS, we specify the binding energy of the implosion, ${E}_{{\rm{i}}}\approx 3{{GM}}_{{\rm{NS}}}^{2}({R}_{\mathrm{Sch}.}^{-1}-{R}_{{NS}}^{-1})/5=3\times {10}^{57}({M}_{{\rm{NS}}}/1.5{M}_{\odot })\,{\rm{GeV}}$, where ${R}_{\mathrm{Sch}.}$ is the star's Schwarzschild radius. We compare this binding energy to the energy required to accelerate a nucleon to escape velocity (v_ej ∼ 0.7 c) at the surface of the NS, ${E}_{{\rm{a}}}=\gamma ({v}_{{\rm{ej}}}){m}_{{\rm{n}}}$, where m_n is the nucleon mass. The maximum mass of ejected material is

$$\begin{eqnarray}&&{M}_{\mathrm{ej}}\leqslant {m}_{{\rm{n}}}\displaystyle \frac{{E}_{{\rm{i}}}}{{E}_{{\rm{a}}}}\lesssim 0.2\,\left(\displaystyle \frac{{M}_{{\rm{NS}}}}{1.5{M}_{\odot }}\right)\left(\displaystyle \frac{1.4}{\gamma ({v}_{{\rm{ej}}})}\right)\,{M}_{\odot }.\end{eqnarray} \tag{ 2 }$$

r-process production accompanies an NS–BH (or NS–NS) merger when ejected neutron-rich fluids decompress, providing enough free neutrons to synthesize heavy elements (Lattimer et al. 1977; Bauswein et al. 2014; Tanaka et al. 2014). The mechanism for neutron fluid expulsion from an NS as it approaches a BH, first described in Wheeler (1971) as the "tube of toothpaste" effect, was developed in Fishbone (1973), Mashhoon (1975), and Lattimer & Schramm (1976). As neutron fluid crosses the Roche limit of a BH (or other compact body), the tidal squeeze from the BH will eventually exceed the self-gravity of the neutron fluid. The resulting severe compression propels streams of neutron fluid away from the BH.

Here we verify that during DM-induced NS implosions, the entire NS crosses the Roche limit as it flows into the BH formed at its center. Initially, the Roche limit for the neutron fluid surrounding a newly formed BH is

$$\begin{eqnarray}&&{R}_{{\rm{Roche}}}\simeq 20{\left(\displaystyle \frac{{M}_{{\rm{BH}}}}{{10}^{-10}{M}_{\odot }}\right)}^{1/3}{\left(\displaystyle \frac{{10}^{14}{\rm{g}}{\mathrm{cm}}^{-3}}{{\rho }_{{\rm{NS}}}}\right)}^{1/3}\,{\rm{m}},\end{eqnarray} \tag{ 3 }$$

where ∼10⁻¹⁰ M_⊙ is the maximum DM mass an NS collects in 10 Gyr for ${\rho }_{{\rm{DM}}}\sim {10}^{4}\,\mathrm{GeV}\,{\mathrm{cm}}^{-3}$, see (Bramante et al. 2013). As the BH grows, the Roche limit expands, passing through the entire NS by the time M_BH ∼ 0.02 M_⊙.

To approximate the time for a natal BH to grow to M_BH ∼ 0.02 M_⊙, at which point it squeezes and consumes the bulk of the NS, we employ the Bondi accretion rate as in (Markovic 1995; Kouvaris & Tinyakov 2014). The Bondi accretion rate of neutron fluid onto the BH is ${\rm{d}}{M}_{{\rm{BH}}}/{\rm{d}}t=4\pi {\lambda }_{{\rm{s}}}{G}^{2}$ ${M}_{{\rm{BH}}}^{2}{\rho }_{{\rm{n}}}/{v}_{{\rm{s}}}^{3},$ where, in what follows, we take typical values for the neutron fluid's sound speed v_s ∼ 0.3 c, density ${\rho }_{{\rm{n}}}\sim {10}^{15}{\rm{g}}\,{\mathrm{cm}}^{-3}$, and accretion constant, λ = 0.25, (Shapiro & Teukolsky 1983). Because the BH growth rate accelerates with added mass, the time for the BH to consume the remainder of the NS is set by its initial mass. For m_X = 10 PeV mass DM, a BH forms once ∼10⁻¹⁴ M_⊙ DM has collected at the center of the NS (Colpi et al. 1986; Bramante 2015). This BH grows until the Roche limit encompasses the NS after

$$\begin{eqnarray}&&{t}_{{\rm{imp}}}\sim \displaystyle \frac{{v}_{{\rm{s}}}^{3}}{4\pi {\lambda }_{{\rm{s}}}{G}^{2}{M}_{{\rm{BH}}}{\rho }_{{\rm{n}}}}\simeq 50\left(\displaystyle \frac{{10}^{-14}\,{M}_{\odot }}{{M}_{{\rm{BH}}}}\right)\,{\rm{years}}.\end{eqnarray} \tag{ 4 }$$

This also implies that in a span of $\sim 1\,{\rm{ms}}$, the remaining 1.4 M_⊙ of neutron fluid crosses the Roche limit.

Finally, we note that because the bulk of the NS is accumulated within ∼1 ms, this disfavors the canonical r-process production mechanism proposed for core-collapse supernovae (Woosley et al. 1994), wherein an outpouring of neutrinos heat nuclear material expelled from the surface of a proto-NS (Duncan et al. 1986). In the standard scenario, which assumes steady-state neutrino-driven mass ejection from a collapse-heated NS, the neutrinos and NS crust must be in thermal equilibrium. This is established after ∼1 s, which is too long compared to a ∼1 ms timescale for the DM-induced NS implosion.

This section examines the DM r-process enrichment of the MW and UFDs. Results in the previous section indicate that each DM-induced NS implosion results in 1.5 M_⊙ of NS material crossing the Roche limit of a BH. Recent simulations of NS–BH mergers find that ∼10⁻⁴–10⁻¹ M_⊙ of ejecta is expelled at ∼0.1–0.3 c as NSs cross the Roche limit of 3–10 M_⊙ mass BHs, with lower mass and higher spin BHs tending to yield higher mass ejecta (see, e.g., Shibata & Taniguchi 2011; Deaton et al. 2013; Foucart et al. 2013; Bauswein et al. 2014; Kyutoku et al. 2015). Hereafter, we show that MW and UFD r-process enrichment from DM-induced implosions favors an ejecta mass M_ej ∼ 10⁻⁵–10⁻³ M_⊙.

Studies of the production and hydrodynamic redistribution of r-process elements in the MW (Argast et al. 2004) have recently been significantly improved to account for the time-evolved migration of r-process elemental abundances, including the effects of galactic subsystem mergers, mixing in the interstellar medium, and (outflows from) star formation during the dynamical evolution of the MW (Shen et al. 2015; van de Voort et al. 2015; Wehmeyer et al. 2015). Particularly, it has been shown that, as long as r-process production events occur at sites where NSs have formed within the inner kpc of the MW, models will match the observed r-process abundance and scatter in [Fe/H] versus [Eu/Fe] to currently available precision. The work of (van de Voort et al. 2015) demonstrated that r-process chemical evolution is consistent with observations as long as two criteria were met by an underlying NS-sourced r-process production model: (1) the time for r-process production to occur after NS formation should fall within t_min ∼ 3 × 10⁶ − 3 × 10⁸ years and (2) the amount of r-process elements produced should be ∼10⁴ solar masses, implying a rate between 10⁻⁵ and 10⁻⁶ r-process events per solar mass of stars in the MW. Building on these results, we consider the scenario of NS-implosion-induced r-process production in the MW to be viable, as long as it matches the per stellar mass rate (${10}^{-5}\mbox{--}{10}^{-6}\,{{M}_{\odot }}^{-1}$), total r-process abundance (∼10⁴ M_⊙ total r-process materials in the MW), and the minimum time for r-process enrichment to begin (${t}_{\min }\lt {10}^{8}\,{\rm{years}}$) found in (van de Voort et al. 2015).

In order to obtain the number of NSs which formed close enough to the center of the galaxy that they could have already imploded (compared to longer-lived NSs outside the GC), we model the stellar density of the inner ∼30 kpc of the MW using velocity-curve-fitted density parameters provided in Sofue (2013), namely ${\rho }_{{\rm{* }}}(r)={\sum }_{i=1}^{3}{\rho }_{i}{e}^{-r/{a}_{i}}$, where (${\rho }_{1}=4\times {10}^{4},\,{\rho }_{2}=2\,\times {10}^{2},\,{\rho }_{3}=0.1\,{M}_{\odot }\,{\mathrm{pc}}^{-3}$) and (${a}_{1}=0.0038,\,{a}_{2}=0.12,\,{a}_{3}\,=3\,\mathrm{kpc}$). One small difference between the NS-implosion scenario and the NS merger scenario is that, for parameters that match the total observed r-process abundance, NS implosions will occur mostly within the central kpc, where the DM density is ≳100 greater and NS implosions can occur. However, NS mergers are also expected to occur mostly within the central few kpc, so we do not expect the subsequent chemical and hydrodynamical evolution of r-process enrichment in the NS-implosion scenario to differ substantially from the NS merger scenario. This conclusion is supported by simulations showing that after r-process elements are produced, they are mixed through the outer ∼30 kpc of the MW on ≲Gyr timescales (Shen et al. 2015; van de Voort et al. 2015).

As previously explained, the observed abundance and scatter of r-process elements observed in the MW require ∼10⁴ M_⊙ of r-process production over ∼10¹⁰ years, with a substantial fraction produced within ∼10⁷ years of the initial star formation epoch. The second requirement is fulfilled naturally by GC NS implosions, which often occur within ∼10⁷ yr in the inner kiloparsec, for DM parameters that solve the missing pulsar problem (the parameter space shown within the green band in Figure 1). In Figure 1 we show DM–NS-implosion parameters for which a per-NS-implosion ejecta mass M_ej would provide 10⁴ M_⊙ of r-process elements over the lifetime of the MW, also fulfilling the requirement that the first implosions occur within 10⁷ years. The thick lines in Figure 1 show the parameter space where the fraction of NSs formed in the inner kpc that collapse within 10¹⁰ years provide for the MW's total r-process abundance. These thick lines have been made by using the aforementioned Sofue stellar distribution profile, along with a Navarro—Frenk—White (NFW) DM halo profile, ${\rho }_{{\rm{DM}}}^{{\rm{NFW}}}{(r)={\rho }_{0}/((r/{r}_{{\rm{s}}})(1+r/{r}_{{\rm{s}}})}^{2})$, where we take ${\rho }_{0}=0.24\,\mathrm{GeV}\,{\mathrm{cm}}^{-3}$ and ${r}_{{\rm{s}}}=20\,{\rm{kpc}}$. To find the number of NSs contained within radius r, we use the Kroupa & Weidner (2003) initial mass function as in Section 2 and a minimum zero-age main sequence mass of 8 M_⊙, normalizing with the assumption that ∼0.5% of ≳8 M_⊙ stars formed in the central 10 kpc will evolve to form NSs. Assuming a constant 200 km s⁻¹MW DM velocity dispersion, we calculate the number of NSs formed close enough to the GC that they will implode within the lifetime of the MW.

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To demonstrate that these results are robust against variations in the assumed DM halo density profile, we also employ a Burkert DM halo profile (Burkert 1996), ${\rho }_{{\rm{DM}}}^{{\rm{Burk}}}(r)={\rho }_{0}^{B}/((1+r/{r}_{{\rm{s,B}}})(1+{r}^{2}/{r}_{{\rm{s,B}}}^{2}))$, where we take ${\rho }_{0}^{B}=50\,\mathrm{GeV}\,{\mathrm{cm}}^{-3}$ and ${r}_{{\rm{s,B}}}=1\,{\rm{kpc}}$. The Burkert profile is flat or "cored" at its center and, with the aforesaid parameters, DM will have a constant $50\,\mathrm{GeV}\,{\mathrm{cm}}^{-3}$ density inside the central kpc of the MW. Figure 1 shows that in preferred NS-implosion parameter space, this does not substantially change the result.

In Figure 2 we display the expected rate of NS implosions in UFDs analyzed in Ji et al. (2016a). The star formation histories of UFDs are an area of active research; in accord with the results of Brown et al. (2014) and Bland-Hawthorn et al. (2015), we show the number of r-process events after 500 Myr, assuming half the UFD stars formed in a burst at z ∼ 5. We take a Plummer stellar density in UFDs, ${\rho }_{{\rm{p}}}{(r)=(3{M}_{{\rm{UFD}}}/4\pi {b}^{3})(1+{r}^{2}/{b}^{2})}^{-5/2}$, where b ∼ 42 pc. We assume the same 0.5% NS formation fraction as in the MW and using the double exponential NS kick model from Faucher-Giguere & Kaspi (2006), we find that 2% of NSs formed inside a UFD will experience a natal kick <5 km s⁻¹, and so remain bound inside the central parsecs. Note that a single event which produces ∼10⁻³–10⁻⁴ M_⊙ r-process materials within 500 Myr in the ten surveyed UFDs (along with Reticulum II) is consistent with the observed r-process abundance in these systems (Ji et al. 2016a; Roederer et al. 2016b).

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We then find the radius within which NSs implode within 500 Myr in the UFD. The UFD DM density is assumed to follow an NFW profile as defined above, with ${\rho }_{0}={10}^{-2}\,\mathrm{GeV}\,{\mathrm{cm}}^{-3}$ and scale factor r_s = 1.5 kpc, in accord with a 10⁷ M_⊙ DM halo at redshift z ∼ 5 (Klypin et al. 2011). For fixed DM density, DM capture by NSs in the central 50 parsecs of UFDs will be ∼200 times greater than in the MW, because DM capture in NSs scales inversely with halo velocity dispersion, which is about 1 km s⁻¹ in the central 50 parsecs of the UFD at z ∼ 5. Figure 2 shows that for UFDs with the afore mentioned stellar and DM density profiles, the DM-induced NS-implosion model predicts ${ \mathcal O }(1)$ event within 500 Myr, which is in line with observations of high r-process abundance in Reticulum II given the stochasticity of r-process enrichment in the UFD population. We also calculated the expected rate for a Burkert DM profile, with ${\rho }_{0,{\rm{B}}}\,={10}^{-2}\,\mathrm{GeV}\,{\mathrm{cm}}^{-3}$ and scale factor ${r}_{{\rm{s,B}}}=50\,{\rm{pc}}$. As with the r-process enrichment of the MW, this changed the result by less than a factor of two.

One potential diagnostic that can differentiate baryonic and DM mechanisms of r-process production is r-process enrichment in globular cluster populations compared to that in UFDs. Both environments exhibit simple star formation histories, dominated by a single massive star formation event, and contain stars with extremely low and uniform metallicities. The systems differ in two important aspects: (1) the DM density in the center of UFDs is extremely high and (2) the stellar density of globular clusters is orders of magnitude higher than UFDs, significantly enhancing the binary (and ternary) stellar processes which lie behind the majority of proposed baryonic r-process mechanisms.

Intriguingly, Roederer (2011) studied 11 globular clusters and found no stars with an r-process enrichment [Eu/Fe] > 1.2, a result that agrees with earlier studies of NGC 6397, NGC 6752, and 47 Tuc, which found average [Eu/Fe] ratios below 0.47 (James et al. 2004). On the other hand, six of the nine stars observed in Reticulum II contain [Eu/Fe] ratios exceeding 1.68 (Ji et al. 2016a; Roederer et al. 2016a). The preference for significant r-process enrichment in Reticulum II (compared to any globular cluster) is difficult to explain in terms of any binary (or ternary) stellar mechanism, since the rate of such encounters is expected to be orders of magnitude higher in the globular cluster population. If upcoming observations discover more UFDs with r-process enrichment, and more extensive surveys of globular clusters find no such enrichment, this would further support a DM origin for the r-process in UFDs.

We have shown that NS mergers are unlikely to produce the r-process overabundance observed in the Reticulum II dwarf, since the total production rate of NS mergers is low and supernova natal kicks efficiently remove binary stellar systems from the shallow gravitational well of UFDs. Additionally, we have examined several alternative explanations, finding that Kozai oscillations in a ternary system or r-process production in quickly rotating magnetars could potentially explain the observed signal, while the remaining models for r-process production appear in tension with the data.

We have found that DM-induced NS implosions could be the source of r-process enrichment in UFDs and the MW. This establishes a connection between the high DM density in UFDs and the r-process enrichment observed in Reticulum II. In addition, the DM-induced r-process scenario predicts that ejecta from DM-induced NS collapse will power an FRB kilonova afterglow, akin to the signal expected from NS–NS merger kilonovae (Li & Paczynski 1998; Metzger et al. 2010; Goriely et al. 2011; Kasen et al. 2013). Our findings also imply an r-process signature for primordial BH capture on NSs (Abramowicz et al. 2009; Capela et al. 2013; Defillon et al. 2014; Pani & Loeb 2014; Graham et al. 2015) and, in turn, small scale primordial perturbations (Carr et al. 1994). Of course, as with other proposed r-process sites (i.e., core-collapse supernovae, swiftly rotating magnetars, and NS mergers), DM-induced NS implosions may also provide a fraction of the total r-process elements in the MW.

It is worth noting that Reticulum II is now unique among UFDs in two independent ways: (1) it is the only UFD providing a possible γ-ray signal and (2) it is the only UFD showing signs of r-process enrichment. In the case that r-process production is caused through the DM-induced collapse of single NSs, these two observations are both consistent with enhanced DM density in the central region of the Reticulum II dwarf. Further observations will be necessary to rule out, or confirm, the contribution of DM to both the γ-ray signal and the r-process enrichment of Reticulum II. The results of these studies have the potential to provide new insights into the nature of DM.

We thank John Beacom, Keith Bechtol, Chris Belczynski, Michal Dominik, Alex Drlica-Wagner, Jennifer Johnson, Vicky Kalogera, Paul Lasky, Adam Martin, Grant Mathews, Annika Peter, Kris Sigurdson, Rebecca Surman, Todd Thompson, and MacKenzie Warren for helpful discussions, and the ABHM Workshop for their hospitality while this work was completed. J.B. thanks the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1066293. T.L. is supported by the National Aeronautics and Space Administration through Einstein Postdoctoral Fellowship Award No. PF3-140110.