NEUTRON STAR MERGERS AS THE ORIGIN OF r-PROCESS ELEMENTS IN THE GALACTIC HALO BASED ON THE SUB-HALO CLUSTERING SCENARIO

The astrophysical origin of rapid neutron-capture (r-process) elements is still unknown. Recent spectroscopic studies of Galactic halo stars have revealed the presence of Eu (an almost pure r-process element in the solar system) in the atmospheres of extremely metal-poor (EMP) stars down to [Fe/H]⁴ $\sim -3$ with large star-to-star scatter in [Eu/Fe] (more than two orders of magnitude, e.g., Honda et al. 2004; François et al. 2007; Sneden et al. 2008). These observational features are reasonably reproduced by models of inhomogeneous Galactic chemical evolution (GCE) where a limited mass range (e.g., $8-10\;{{M}_{\odot }}$) of core-collapse supernovae (CCSNe) is assumed to be the dominant source of r-process elements (Ishimaru & Wanajo 1999; Tsujimoto et al. 2000; Argast et al. 2004; Ishimaru et al. 2004). Previous homogeneous GCE models that assume a well-mixed, one-zone Galactic halo also suggest the low-mass end of CCSNe as the major r-process site (Mathews et al. 1992; Travaglio et al. 1999) but are not capable of accounting for the star-to-star scatter in [Eu/Fe].

To date, however, no study of CCSN nucleosynthesis has satisfactorily accounted for the production of heavy r-process elements (see, e.g., Wanajo et al. 2011; Wanajo 2013). As an alternative scenario, it has long been suggested that the binary mergers of double neutron stars (NSMs) as well as those of neutron-star–black-hole pairs are the r-process sites (Lattimer & Schramm 1974, 1976; Lattimer et al. 1977; Symbalisty & Schramm 1982; Eichler et al. 1989; Meyer 1989). In fact, a number of recent nucleosynthesis studies based on hydrodynamical simulations support NSMs as promising sources of r-process elements in the Galaxy (Freiburghaus et al. 1999; Goriely et al. 2011; Korobkin et al. 2012; Bauswein et al. 2013; Rosswog et al. 2014; Wanajo et al. 2014).

Recent GCE models appear to disfavor the NSM scenario, except for those cases invoking very short lifetimes of neutron star binaries (1–10 Myr, Argast et al. 2004; De Donder & Vanbeveren 2004; Komiya et al. 2014; Matteucci et al. 2014; Mennekens & Vanbeveren 2014; Tsujimoto & Shigeyama 2014; Cescutti et al. 2015; van de Voort et al. 2015; Wehmeyer et al. 2015).⁵ Estimates of binary lifetimes, ${{t}_{{\rm NSM}}}\sim 0.1$–1 Gyr (e.g., Dominik et al. 2012), are in conflict with the presence of r-process-enhanced stars below [Fe/H] $\sim -2.5$ in those models. Even if a short-lived channel with ${{t}_{{\rm NSM}}}\sim 1$ Myr exists (Belczynski & Kalogera 2001; De Donder & Vanbeveren 2004), the low Galactic rate of such events (0.4–77.4 Myr⁻¹, Dominik et al. 2012) leads to a too large star-to-star scatter in [Eu/Fe] at [Fe/H] $\gtrsim -2.5$ (Qian 2000; Argast et al. 2004). It should be noted, however, that the inhomogeneous GCE model of Argast et al. (2004) also appears to be in conflict with the observed small scatter of α elements relative to iron (Argast et al. 2002). This problem would be resolved if the inhomogeneity of the inter-stellar medium (ISM) were modest because of effective matter mixing (or if more massive CCSNe had greater iron yields, Wehmeyer et al. 2015).

It should be noted that the aforementioned GCE models assume a single halo system (except for Komiya et al. 2014; van de Voort et al. 2015), which is incompatible with the currently dominant paradigm of the hierarchical merging scenario of galaxy formation. Prantzos (2006, 2008) has shown that the overall shape of the Galactic halo's metallicity distribution (MD) can be well reproduced by a merging sub-halo model with smaller sub-halos having suffered larger outflows (see also Komiya 2011). More importantly for the issue of the r-process, Prantzos (2006) showed that if the sub-halos evolved at different rates, then there would be no more unique relation between time and metallicity; in that case, he argued that the observed "early" (in terms of metallicity) appearance of r-elements and their large dispersion can be explained even if the main source of those elements is long-lived (∼100 Myr) NSMs. A recent study using a high resolution, cosmological simulation, supports that idea (Shen et al. 2015).

In this Letter, we study the role of NSMs in the early Galaxy with a GCE model based on the framework of such a hierarchical merging scenario and on recent estimates of the progenitor binary lifetimes.

Each sub-halo is modeled as a one-zone, well-mixed single system that is losing gas due to outflow (because of stellar winds, SN explosions and tidal interactions). The GCE model used in this work is the same as that for the ISM evolution of the Galactic halo in Ishimaru & Wanajo (1999), Ishimaru et al. (2004), and Wanajo & Ishimaru (2006) but it differs in what follows. Each sub-halo is composed of stars with a final total stellar mass M_* evolving homogeneously (i.e., with its ISM well mixed at every time). We consider sub-halos with ${{M}_{*}}/{{M}_{\odot }}={{10}^{4}},{{10}^{5}},{{10}^{6}},{{10}^{7}},{{10}^{8}}$, and $2\times {{10}^{8}}$. The heaviest mass is set to be about half the estimated stellar mass of the Galactic halo, $\sim 4\times {{10}^{8}}\;{{M}_{\odot }}$ (Bell et al. 2008). The lowest mass corresponds to those of recently discovered ultrafaint dwarf galaxies (Kirby et al. 2008).

Although we have no direct observational clues as to the property of each sub-halo, recent observations of MDs of dwarf galaxies in the Local Group can provide some hints (Helmi et al. 2006). We know that [Fe/H] at the peak of an MD, [Fe/H]_peak, corresponds to the effective yield y_eff, i.e., the iron productivity of a galaxy system which depends on the adopted stellar yields and IMF (Helmi et al. 2006; Prantzos 2008). If a dwarf galaxy loses a significant amount of iron through outflow with the rate (OFR) proportional to the star formation rate (SFR), then y_eff is approximately proportional to ${{\eta }^{-1}}$, where ${\rm OFR}\equiv \eta {\rm SFR}$ (Prantzos 2008). In practice, limited data are available for MDs, and thus the observed median metallicities ([Fe/H]₀) of dwarf galaxies are used instead of [Fe/H]_peak. The observed mass–metallicity relation for dwarf galaxies suggests that [Fe/H]₀ approximately scales as $M_{*}^{0.3}$ (Kirby et al. 2013). We thus assume $y_{{\rm eff}}^{-1}\propto \eta =5.0\;{{({{M}_{*}}/{{10}^{8}}{{M}_{\odot }})}^{-0.3}}$ as in Prantzos (2008).⁶ This can be naturally interpreted as a result of smaller SFR and/or greater OFR because of the shallower gravitational well for a less-massive sub-halo (see also Section 4). SFR is assumed to be proportional to the mass of the ISM, (${{M}_{{\rm ISM}}}$): ${\rm SFR}={{k}_{{\rm SF}}}{{M}_{{\rm ISM}}}$, where the constant ${{k}_{{\rm SF}}}$ corresponds to the star formation efficiency, and ${\rm OFR}={{k}_{{\rm OF}}}{{M}_{{\rm ISM}}}$, where ${{k}_{{\rm OF}}}=\eta {{k}_{{\rm SF}}}$. However, we cannot constrain either ${{k}_{{\rm SF}}}$ or ${{k}_{{\rm OF}}}$ based on observations. Thus, we assume two extremes: Cases 1 and 2 for the fixed ratios of η, respectively (Table 1). The sub-halo of ${{M}_{*}}={{10}^{8}}\;{{M}_{\odot }}$ is (arbitrary) set to have the same values of ${{k}_{{\rm SF}}}$ and ${{k}_{{\rm OF}}}$ for both Cases 1 and 2.

Table 1.  Models of Sub-halos for Cases 1 and 2

		${{k}_{{\rm OF}}}$ (Gyr−1)		${{k}_{{\rm SF}}}$ (Gyr−1)
M* (${{M}_{\odot }}$)	η	Case 1	Case 2	Case 1	Case 2
104	79	1.0	16	0.013	0.20
105	40	1.0	7.9	0.025	0.20
106	20	1.0	4.0	0.050	0.20
107	10	1.0	2.0	0.10	0.20
108	5.0	1.0	1.0	0.20	0.20
$2\times {{10}^{8}}$	4.1	1.0	0.81	0.25	0.20

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The CCSN abundances of Mg and Fe (which we assume to be representative of CCSN products and metallicity, respectively) are taken from Nomoto et al. (2006). We ignore the Fe contribution from Type Ia SNe because they appear to have played a negligible role during the Milky Way halo evolution (the observed α/Fe ratio of halo stars is ∼constant). The evolution of each sub-halo is computed up to 2 Gyr, which is considered to be a reasonable estimate of the timescale of the Milky Way halo formation suggested from the observed ages of globular clusters (Roediger et al. 2014). The value of ${{k}_{{\rm SF}}}$ for the sub-halo with ${{M}_{*}}={{10}^{8}}\;{{M}_{\odot }}$ is set to account for the most metal-rich stars in the Galactic halo.

Binary population synthesis models indicate an average binary lifetime of $\langle {{t}_{{\rm NSM}}}\rangle \sim 1$ Gyr (e.g., Dominik et al. 2012), which is comparable with the lifetimes of sub-halos. A significant fraction of NSMs are, however, expected to have ${{t}_{{\rm NSM}}}\lesssim 100$ Myr ($\sim 40\%$, Belczynski et al. 2008). In addition, a short-lived channel of ${{t}_{{\rm NSM}}}\lesssim 1$ Myr is also predicted (Belczynski & Kalogera 2001; Belczynski et al. 2002; De Donder & Vanbeveren 2004). Dominik et al. (2012) estimate the fraction of such a putative short-lived channel to be up to $\sim 7\%$ (for the solar metallicity case). For illustrative purposes, here we assume a bimodal distribution of ${{t}_{{\rm NSM}}}=1$ and 100 Myr with corresponding fractions of 5% and 95%, respectively (Table 2). For the total average frequency of NSMs (f_NSM) relative to that of CCSNe, we assume $\langle {{f}_{{\rm NSM}}}\rangle =2\times {{10}^{-3}}\langle {{f}_{{\rm CCSN}}}\rangle$ adopting the estimates of recent population synthesis calculations (Dominik et al. 2012). The mass of the ejected Eu, representative of r-process elements in the Galactic halo, is taken from the latest nucleosynthesis result of Wanajo et al. (2014), ${{M}_{{\rm Eu},{\rm NSM}}}=2\times {{10}^{-5}}\;{{M}_{\odot }}$ (see also Goriely et al. 2011; Korobkin et al. 2012). The mass of the ejected Ba, which is also predominantly produced by the r-process in the early Galaxy, is set to be ${{M}_{{\rm Ba},{\rm NSM}}}=9\;{{M}_{{\rm Eu},{\rm NSM}}}$ according to the solar r-process ratio of these elements (Burris et al. 2000).

Table 2.  Parameters Adopted for NSMs

Type	tNSM (Myr)	${{f}_{{\rm NSM}}}/{{f}_{{\rm CCSN}}}$	${{M}_{{\rm Eu},{\rm NSM}}}$ (${{M}_{\odot }}$)
Short-lived	1.00	$1.0\times {{10}^{-4}}$	$2\times {{10}^{-5}}$
Long-lived	100	$1.9\times {{10}^{-3}}$	$2\times {{10}^{-5}}$

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Our results for Case 1 (with constant ${{k}_{{\rm OF}}}$) are shown in Figure 1. Those results for less (more) massive sub-halos are indicated by the thinner (thicker) curves. The cumulative number of CCSNe in each sub-halo monotonically increases with time (Figure 1(a)). For NSMs, the cumulative number steeply rises when the long-lived binaries start contributing at 100 Myr. [Fe/H] monotonically increases with time for all of the sub-halos; at a given time, [Fe/H] is greater for more massive sub-halos because of their higher ${{k}_{{\rm SF}}}$. MDs for all of the sub-halos are also shown in Figure 1(c). The metallicity at the peak of each MD, [Fe/H]$_{{\rm peak}}$ (Table 3), is in agreement with the observed mass–metallicity relation (Kirby et al. 2013) scaled downward by −0.4 dex to exclude the SNe Ia contribution. The dark halo mass of each sub-halo, M_D (Table 3), estimated from the initial baryonic mass and the initial baryon to dark mass ratio (which is assumed to be equal to the cosmic value ${{{\Omega }}_{B}}/{{{\Omega }}_{D}}=0.046/0.24\sim 0.19$), implies ${{M}_{D}}\propto {{M}_{*}}^{0.7}$. Since the reasonable mass function of M_D can be regarded as $dN/d{{M}_{D}}\propto M_{D}^{-2}$ (e.g., Prantzos 2008 and references therein), we obtain the sub-halo mass function as $\propto M_{*}^{-1.7}$. We find that the total MD (thick black curve) weighted with the sub-halo mass function is in reasonable agreement with the observed one (gray hatched region, An et al. 2013). We also find that the evolution of Mg (Figure 1(d), representative of CCSN products) is in reasonable agreement with the observed stellar abundances of Galactic halo stars. In contrast to r-process elements, the observed scatter in [α/Fe] is known to be as small as the measurement errors (e.g., Cayrel et al. 2004). This result is consistent with such small scatters in [Mg/Fe] because each evolutionary trend is almost independent of M_*.

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Table 3.  Results Related to MDs of Sub-halos

	MD (${{M}_{\odot }}$)		[Fe/H]$_{{\rm peak}}$
M* (${{M}_{\odot }}$)	Case 1	Case 2	Case 1	Case 2
104	$7.6\times {{10}^{6}}$	$6.6\times {{10}^{6}}$	−2.63	−2.56
105	$3.8\times {{10}^{7}}$	$3.3\times {{10}^{7}}$	−2.33	−2.30
106	$1.9\times {{10}^{8}}$	$1.7\times {{10}^{8}}$	−2.03	−2.02
107	$1.0\times {{10}^{9}}$	$9.0\times {{10}^{8}}$	−1.74	−1.74
108	$5.3\times {{10}^{9}}$	$5.3\times {{10}^{9}}$	−1.46	−1.46
$2\times {{10}^{8}}$	$8.8\times {{10}^{9}}$	$9.3\times {{10}^{9}}$	−1.38	−1.39

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The resulting evolution of Eu (representative of r-process elements) is presented in Figure 1(e) and compared to observed stellar values. We note a transition from slow to rapid evolution of [Eu/Fe] for each sub-halo at ∼100 Myr as a result of the contribution from long-lived binaries beginning. The corresponding [Fe/H] (see Figure 1(b)) differs from one sub-halo to another, being lower than [Fe/H] $\sim -3$ for ${{M}_{*}}\leqslant {{10}^{6}}\;{{M}_{\odot }}.$ This indicates that the presence of stars at [Fe/H] $\sim -3$ with star-to-star scatter in [Eu/Fe] ($\lesssim 0.5$) can be interpreted as a result of NSM activity in sub-halos with various ${{k}_{{\rm SF}}}$. Our model cannot, however, explain the presence of r-process-enhanced stars with [Eu/Fe] $\gt 1$. In addition, our result predicts the presence of stars with [Eu/Fe] $\sim -1$ for [Fe/H] $\lesssim -3$. This is due to the contribution of the short-lived NSM at early times $(\lt 100\;{\rm Myr}).$ Measurements of Eu in such stars would be challenging because of the weak spectral lines. Such a signature has been seen in the Ba abundances of EMP stars, [Ba/Fe] $\sim -2$ to −1 at [Fe/H] $\lesssim -3$ (Figure 1(f)), which could also be explained as being due to the contribution of short-lived binaries. Note that the [Ba/Fe] values for [Fe/H] $\gtrsim -2.5$ are underpredicted compared to the observed ones; in this metallicity, the contribution from the s-process becomes important (Burris et al. 2000).

Figure 2 shows the results for Case 2, where a constant ${{k}_{{\rm SF}}}$ is assumed. We find that the cumulative numbers of NSMs and CCSNe are similar to those in Case 1 (Figure 1(a)). However, the evolutions stop earlier for less-massive sub-halos. This is due to the termination of star formation because of gas removal by their significant outflows with greater values of ${{k}_{{\rm OF}}}$. In contrast to Case 1, the [Fe/H] evolution (Figure 2(b)) is identical among sub-halos because of the same ${{k}_{{\rm SF}}}$, although the termination points differ depending on their ${{k}_{{\rm OF}}}$. The resulting MDs (Figure 2(c)) as well as the evolutions of Mg (Figure 2(d)) are similar between Cases 1 and 2. In Figure 2(e), we find that the r-process abundances increase to values greater than [Eu/Fe] ∼ 1 for the sub-halos with ${{M}_{*}}\leqslant {{10}^{5}}\;{{M}_{\odot }}$. This is a consequence of the fact that the higher ${{k}_{{\rm OF}}}$ lead to smaller amounts of Fe, and thus higher Eu/Fe ratios. It is interesting to note that even without invoking the inhomogeneity of the ISM, the enhancement of Eu can be explained in part by our sub-halo models. However, our result here cannot account for the r-process enrichment at [Fe/H] $\sim -3$ because the [Eu/Fe]s start rising at [Fe/H] $\sim -2.4$ for all of the sub-halos.

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Our results imply that the reality may be between these two extremes, Cases 1 and 2; reasonable combinations of ${{k}_{{\rm SF}}}$ and ${{k}_{{\rm OF}}}$ might account for the presence of r-process-enhanced stars at [Fe/H] $\sim -3$. It is also important to note that the cumulative numbers for the least-massive sub-halos (${{M}_{*}}={{10}^{4}}\;{{M}_{\odot }}$) are ∼0.1 around the end of their evolutions. This could be another source of large enhancements of [Eu/Fe] ($\gtrsim 1$). The [Eu/Fe] values would be substantially higher than the averaged curves of our models, provided that only a fraction of sub-halos experienced NSMs.

We studied the role of NSMs for the chemical evolution of r-process elements in the framework of Galactic halo formation from merging sub-halos. It has been found that the appearance of Eu at [Fe/H] $\sim -3$ with star-to-star scatter in [Eu/Fe] ($\lesssim 0.5$) at [Fe/H] $\sim -3$ can be interpreted as a result of lower star formation efficiency ${{k}_{{\rm SF}}}$ for less-massive sub-halos. On the other hand, the presence of highly r-process-enhanced EMP stars ([Eu/Fe] $\gtrsim \;0.5$) can be explained if values of ${{k}_{{\rm OF}}}$ (the multiplicative factor for the outflow rate) are higher for less massive sub-halos. These may be reasonable assumptions because less massive sub-halo systems have weaker gravitational potential (as indicated by M_D in Table 3), and thus are expected to form stars less efficiently and/or expel the ISM more easily. The ratio of OFR–SFR, η, is assumed to be proportional to ${{M}_{*}}^{-0.3}$. Recent observations of relatively massive galaxies (${{10}^{7}}-{{10}^{11}}\;{{M}_{\odot }}$) also suggest a similar anti-correlation between M_* and η (Chisholm et al. 2014). Under this assumption, the metallicity at the peak of each sub-halo's MD (Table 3) appears to be consistent with the observed mass–metallicity relation. In addition, the total MD weighted with the sub-halo mass function shows reasonable agreement with that observed for the Galactic halo.

The low-level Ba abundances ([Ba/Fe] $\sim -1.5$) observed in the EMP stars of [Fe/H] $\lesssim -3$ may be due to contribution from the short-lived binaries (with ${{t}_{{\rm NSM}}}=1$ Myr in this study). Thus, the main features of the r-process abundances observed in EMP stars, their appearance at [Fe/H] $\sim -3$ with large star-to-star scatter and their sub-solar amounts for [Fe/H] $\lesssim -3$, can potentially be explained solely by the contribution of NSMs.

The highly Eu enhanced stars at [Fe/H] $\sim -3$ may be accounted for by reasonable combinations of ${{k}_{{\rm SF}}}$ and ${{k}_{{\rm OF}}}$. The small cumulative numbers of NSMs ($\lt 1$) for  the least-massive sub-halos could be another reason for the observed large scatter in [Eu/Fe] because NSMs may occur only in some, while no NSMs occur in others. Once NSMs occur in such less-massive systems, their ISM must be highly enriched by r-process elements.

In conclusion, our results imply that the current observational evidence of r-process signatures in EMP stars can be interpreted as a consequence of Galactic halo formation from merging sub-halos. If the model is a reasonable simplification for such chemo-dynamical evolutions of sub-halos, NSMs can be the main r-process contributors throughout the Galactic history. Contributions from CCSNe are not necessarily needed as invoked in previous GCE studies. Note that our assumption of a well-mixed ISM might not necessarily be an oversimplification, at least for less-massive sub-halos, in which a small number of explosive events would easily homogenize their smaller amount of ISM before the next episode of star formation. The observed small scatters of abundance ratios of other elements such as iron-peak elements or α-elements in EMP stars should be examined using a consistent assumption. Possible effects of ISM inhomogeneity as well as of stochastic nature of NSM events (i.e., ${{N}_{{\rm NSM}}}\lt 1$) will be discussed in a forthcoming paper.

This work was supported by the RIKEN iTHES Project and the JSPS Grants-in-Aid for Scientific Research (26400232, 26400237).