Highly r-process enhanced stars in ultra-faint dwarf galaxies

In the runs LV1 and LV2, we model NSM events with a fiducial rate of one merger per $10^{5}{\,M_{\odot}}$ in stars, consistent with the average expected rate for such mergers (e.g. Tsujimoto et al., 2015). Assuming an empirical stellar IMF, one NSM is expected per 1000-2000 CCSNe, corresponding to a stellar mass of $\sim 10^{5}{\,M_{\odot}}$. This estimate is consistent with the rate inferred from the observed UFDs (Ji et al., 2016a), where it is suggested that a single NSM event might occur in the sample of ten UFDs. Such tens of UFDs would host $\sim$2000 SNe in total. We note, however, that the canonical NSM rate can be boosted by up to a factor of 10, due to uncertainties in the underlying population synthesis modeling (Dominik et al., 2012).

For the fiducial single galaxy run (fiducial), we adopt a rate of one NSM per $3.5\times 10^{3}{\,M_{\odot}}$, an order of magnitude larger than the canonical value, to ensure that at least one NSM event happens in the SFH of our simulated galaxies, in line with the stellar mass of Ret II of only $M_{\ast}\approx 5\times 10^{3}{\,M_{\odot}}$. To assess the impact of model uncertainty, we carry out comparison simulations:

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  fiducial: we adopt a rate of one NSM per $3.5\times 10^{3}{\,M_{\odot}}$ and the europium yield of $M_{\rm Eu}\approx 4.5\times 10^{-5}{\,M_{\odot}}$.

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  fiducial-2x: we decrease the NSM rate by a factor of 2, such that one NSM event takes place per $7\times 10^{3}{\,M_{\odot}}$.

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  fiducial-3x: we decrease the NSM rate by a factor of 3, such that one NSM event takes place per $1\times 10^{4}{\,M_{\odot}}$.

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  fiducial-2x-half: we decrease the NSM rate by a factor of 2 and reduce the Eu yield by half, $M_{\rm Eu}\approx 2\times 10^{-5}{\,M_{\odot}}$.

The parameter ranges for those simulations are summarized in Table 1. We assume that the final merger occurs about 5 Myr after the binary neutron star system forms. Such delay time of $\sim 5$ Myr adopted here corresponds to a fast-merging channel (e.g. Belczyński & Kalogera, 2001; De Donder & Vanbeveren, 2004; Dominik et al., 2012). In addition, we ignore natal kicks and the explosion energy of the NSM event, which means that the estimated r-process element abundances in this work should be considered as upper limits.

We choose a fiducial value for the europium yield of $M_{\rm Eu}\approx 4.5\times 10^{-5}{\,M_{\odot}}$ for each NS merger event, adopted by Naiman et al. (2018), as inferred by the chemical evolution of europium in MW-sized galaxies in the IllustrisTNG simulation. This value, however, is three times higher than the upper limit based on the NS-NS merger detected by LIGO/Virgo for the GW170817 event (Cowperthwaite et al., 2017; Côté et al., 2018). We use this high europium yield from Naiman et al. (2018) in order to assess whether the high europium abundance observed in Ret II can be reproduced through simulations. In addition, we have conducted another simulation (Fiducial-2x-half), where the Eu yield is reduced by half, more consistent with the value inferred from GW170817. We treat the ejection and transport of europium in the same way as other metal species from SN explosions. Once europium nuclei are ejected, they are initially distributed among the neighboring gas particles, followed by the subsequent diffusive transport according to our numerical scheme (see above for details).

As a first step, we consider whether any of the simulated UFDs in LV1, in which 8 UFD analogs ($M_{\rm vir}\approx 10^{7}-10^{8}{\,M_{\odot}}$) emerge, could host MP r-II stars by adopting the empirical NSM rate (Ji et al., 2016a), where one NSM event is expected per $M_{\ast}\approx 10^{5}{\,M_{\odot}}$. We further use the fiducial value for the europium yield, $M_{\rm Eu}\approx 4.5\times 10^{-5}{\,M_{\odot}}$. However, none of the simulated galaxies has stars with $\rm[Eu/Fe]>1$ and $[\rm Fe/H]<-1.5$, despite the occurrence of the NSM event in LV1. We find that the simulated galaxies in LV1 continue to form stars after the NSM event, but the NSM ejecta is too diluted due to the long time delay between the NSM event and the subsequent star formation, resulting in the lack of MP r-II stars.

Using the same empirical parameters used in LV1, on the other hand, out of a total of 32 UFD analogs in LV2, we identify a single galaxy (Halo 26), containing MP r-II stars. The corresponding halo has virial and stellar masses of $\rm M_{vir}\approx 4.6\times 10^{7}{\,M_{\odot}}$ and $M_{\ast}\approx 3.4\times 10^{3}{\,M_{\odot}}$, respectively, at $z=0$. For illustrative purposes, in Figure 2, we show the projected dark matter profile of the representative UFD analogs at $z=0$ in LV2. Pop II stellar components are denoted as filled circles, with color indicating the $\rm[Eu/Fe]$ ratio such that MP r-II stars are shown in red. For further analysis, we only focus on Halo 26, displayed in the bottom-middle panel of Figure 2, as it is the only simulated galaxy with abundances similar to Ret II.

In Figure 3, we present stellar abundances (C, Si, Mg, and Eu), calculated from stars hosted in Halo 26, by comparing with the observed values¹¹1The original references for the abundance ratios of the observed UFDs are as follows: Norris et al., 2010; Lai et al., 2011 (Bootes I); Ji et al., 2016b; Roederer et al., 2016 (Reticulum II); Norris et al., 2010; Frebel et al., 2014 (Segue I); Ji et al., 2016c; Chiti et al., 2018b; Chiti et al., 2018a (Tucana II); Frebel et al., 2010 (Ursa Minor II); Simon et al., 2010 (Leo IV); Frebel et al., 2010 (Coma Berenices). The first point to note here is that there are no CEMP stars ($\rm[C/Fe]\geq 0.7$, $\rm[Fe/H]\leq-1$) in this galaxy. We compute the $\rm[C/Fe]$ ratio based on the metals separately released by Pop III (pink circles in the top left panel of Fig. 3) and Pop II (blue color), respectively (e.g. Jeon et al., 2021). There are three CEMP stars in Ret II (Ji et al., 2016b), accounting for 40% of stars at $\rm[Fe/H]\lesssim-3$. In general, Pop III SNe are one of the favoured pathways of forming CEMPs (e.g. Iwamoto et al., 2005; Heger & Woosley, 2010; Ishigaki et al., 2014). Although we include Pop III stars, giving rise to a number of CEMP stars in the overall sample of UFD analogs in LV2, no CEMP stars are found in Halo 26. This deficiency can simply be understood as a stochastic effect (e.g. Jeon et al., 2021). Meanwhile, as shown in the upper-right panel of Figure 3, $\alpha$-element abundances of stars in Halo 26 are in good agreement with those of Ret II.

The estimated europium abundances, $\rm[Eu/Fe]$ and $\rm[Eu/H]$, of the Pop II clusters are presented in the bottom panels of Figure 3. Out of 7 Pop II clusters, 6 (red inverse triangles) show extremely high europium abundances ($\rm[Eu/Fe]\gtrsim 2.5,[Eu/H]>-0.6$), comparable to MP r-II stars in Ret II. Despite the same assumptions for the NSM model in both LV1 and LV2, Ret II-like systems are produced only in LV2. To better understand the formation of MP r-II stars in the context of overall galaxy assembly, in Figure 4, we illustrate star formation rates (top panel) and cumulative SFH (bottom panel) for Pop III (black solid lines) and Pop II (red solid lines) stars in Halo26, as a function of cosmic time. We find that in Halo26 Pop III star formation begins at $z\approx 10.3$, and the transition from Pop III to Pop II star formation mode occurs after $\sim$30 Myr. The heavier the halo, the earlier the star formation occurs, and the onset of star formation in the all simulated galaxies ranges from $z\approx 13$ to $z\approx 8$. Halo26 experiences self-quenching even before reionization, implying that the gas evaporated by SN feedback could not recollapse onto the halo prior to reionization (Jeon et al., 2014). Note that the SFH of Halo 26 is not unusual, as about $25\%$ of the simulated galaxies tend to exhibit the self-quenching feature.

At $z\approx 9.7$, a binary neutron star system forms, and after a time delay of 5 Myr we assume that the final merger takes place, ejecting r-process elements into the surrounding medium, out of which r-process enhanced Pop II stars are formed. We will further discuss such a fast-merging channel below (see Section 3.3). It takes $\Delta t=17$ Myr to form MP r-II stars with $\rm[Eu/Fe]\approx 2.6$ ($\rm[Eu/H]\approx-0.2$) since the release of r-process elements. Subsequently, a second burst of star formation occurs at $\Delta t=85$ Myr, creating MP r-II stars with $\rm[Eu/Fe]\approx 2.7$ ($\rm[Eu/H]\approx-0.6$). To examine the gas conditions, when the MP r-II stars are formed, we show the hydrogen number density (top) and europium abundance (bottom) in Figure 5, as a function of distance from the NSM site at $\Delta t=17$ Myr (left) and $\Delta t=85$ Myr (right), corresponding to the first and second burst of star formation.

The NSM occurs at $z=9.7$ towards the center of Halo26, when the virial mass and radius of the progenitor are $M_{\rm vir}=4.3\times 10^{6}{\,M_{\odot}}$ and $R_{\rm vir}=480$ pc, respectively. During the first period of suppressing star formation, lasting $\Delta t=17$ Myr, a gas mass of $M_{\rm gas}\approx 4.3\times 10^{5}{\,M_{\odot}}$ within the halo is polluted by europium up to $\rm[Eu/H]=-0.2$. Out of the Eu-enriched density peak, located at $\sim 44$ pc from the NSM site, as illustrated in the left-top panel of Figure 5, MP r-II stars are formed. The gas density inside the halo decreases mainly due to SN feedback, and the europium is diluted beyond the virial radius. However, we find that the density peak at $\sim$550 pc still maintains a high europium abundances of $\rm[Eu/H]\approx-0.6$, resulting in the formation of another MP r-II stars at $\Delta t=85$ Myr.

To assess how quickly the r-process elements are diluted, we calculate the diffusion coefficient, $D$, assuming a Gaussian distribution function for the transport of metals, with a standard deviation of $\sigma_{\rm D}$ (e.g. Tarumi et al., 2020). By fitting the relation, $2Dt=\sigma_{\rm D}^{2}$, the derived diffusion coefficient within Halo 26 is $D=2.3\times 10^{-3}\,\rm kpc^{2}\,Myr^{-1}$ at $\Delta t=17$ Myr. This value agrees within a factor of $\sim 2$ with the estimates in Tarumi et al. (2020), where $D=1\times 10^{-3}\rm\,kpc^{2}\,Myr^{-1}$ is suggested inside a $M_{\rm vir}\approx 10^{8}{\,M_{\odot}}$ halo at $z=8$. The impact of turbulent mixing on the r-process elements is also stressed in the work by Dvorkin et al. (2020), where they reveal that metal mixing is essential to account for the large scatter in the [Eu/Fe] ratio, especially for low $\rm[Fe/H]<-3$, observed in the MW stars. Recently, Beniamini & Hotokezaka (2020) propose a new constraint on the diffusion coefficient, $D>10^{-4}\rm\,kpc^{2}\,Myr^{-1}$, assuming an r-process rate of $4\times 10^{-5}\,\rm yr^{-1}$, based on MW stars using a Monte Carlo simulation and analytic approach.

As a second approach, we perform several comparison simulations of a single UFD, varying key NSM model parameters. To increase the frequency of NSMs, we allow one NSM event to take place per $M_{\ast}\approx 3.5\times 10^{3}{\,M_{\odot}}$. Although this frequency is higher than the empirical estimate by an order of magnitude, it assures the simulated UFD to experience at least one NSM event during its SFH. We carry out additional simulations by extending the period (or decreasing the frequency) of NSM events by a factor of $\sim$2 and $\sim$3, compared to the fiducial value, such that a single NSM occurs per $7\times 10^{3}{\,M_{\odot}}$ or $1\times 10^{4}{\,M_{\odot}}$ in stars, respectively. We also study the effect of reducing the europium yield by half, $M_{\rm Eu}\approx 2\times 10^{-5}{\,M_{\odot}}$, to achieve a value similar to the one inferred from GW170817.

We note that, for the purpose of the r-process study, in "Single galaxy" runs we terminate the simulations immediately after reionization due to computational cost. Any derived r-process abundances presented here may thus not reflect the final sample for a given UFD analog at $z=0$. In Figure 6, we compare the resulting europium abundances for the simulated UFDs with the values observed in Ret II. Although we set up the four simulations so that all should experience a NSM event, only two runs (fiducial-2x and fiducial-2x-half) contain stars with highly enhanced europium abundances. In the runs where we double the NSM period, or additionally reduce the Eu yield by half, the resulting [Eu/H] and [Eu/Fe] values at [Fe/H]$\simeq-3.5{\rm\ to}-2$ are lower than what is observed for the stars in Ret II. The high values in fiducal-2x-half for [Eu/Fe] at [Fe/H]$\lesssim-3.5$, where no counterparts are observed, are mainly due to the small amount of Fe, resulting in high [Eu/Fe].

To investigate how far the r-process elements, ejected from the NSM, could reach and pollute the surrounding gas, we display in Figure 7 the europium abundances (encoded in color) of the simulated stars as a function of the time elapsed after the NSM event (for the same runs as in Fig. 6). We distinguish these histories for different distances between the NSM site and the location of the newly formed stars. The open circles indicate the stars showing a lack of europium abundance because they are far away from the NSM site. It is evident that stars with relatively high europium values, [Eu/H]$\,\gtrsim-2$ or [Eu/Fe]$\,\gtrsim 2$, formed close to the NSM site, within $\sim$300 pc. Both panels demonstrate that the Eu abundances decrease with increasing distance from the NSM site. However, the gas close to the NSM site can maintain such high europium values for a long period of time, $80-100$ Myr, giving rise to r-process enhanced stars. Considering that the Eu-enhanced stars still emerge in the run with the yield reduced by half (right panels), it appears that the most important determining factor in forming such highly Eu-enhanced stars is how quickly new stars can form around the merger site, rather than the Eu yield. Put differently, the key here is how quickly the gas, altered by stellar feedback, could recombine and recollapse, reaching the high density required to form subsequent stars.

To further study this, in Figure 8 we show the hydrogen number density (top panels) and europium abundance (bottom panels) of the gas as a function of distance from the NSM site about 10 (left), 50 (middle), and 100 (right) Myr after the NSM event for the fiducial-2x-half run (same as the right panels of Fig. 6). As can be seen, about 10 Myr after the NSM (left panels), the surrounding gas begins to be contaminated by the ejected europium. Even though the gas density in the inner region, $r\lesssim$50 pc, is lowered by stellar feedback, the density peaks at $r<$300 pc are high enough to form stars with [Eu/H]$\approx-2$. Until 100 Myr after the onset of the NSM event, the evacuated gas continues to fall back to the central region, so that next generation stars can form out of this highly enriched dense gas cloud. The [Eu/H] ratios of those high density peaks decline from [Eu/H]$\approx 0$ at $\Delta t\approx 10$ Myr to [Eu/H]$\approx-1$ ($r\approx$10 pc) and [Eu/H]$\approx-2$ ($r\approx$ 40 pc) at $\Delta t\approx 100$ Myr. As illustrated in Figure 8, multiple gas density peaks could exist in close proximity to the NSM site, such that a number of r-process enhanced stars could form within those high-density clouds.

One of the main obstacles for producing r-process enhanced stars in the UFD analogs is the short duration of their star formation histories. We find that all the simulated UFDs stop forming stars at the epoch of reionization. Consequently, if a NSM takes place just before the onset of reionization, with insufficient time for the enriched gas to reach high density, no r-process enhanced stars will form. When we double the interval between NSM events, such that one NSM event occurs per $7\times 10^{3}{\,M_{\odot}}$, stars with high europium abundance can still form. However, in the run with three times longer intervals (fiducial-3x), no high europium stars are found, because the NSM happens right before reionization. As explained previously, the amount of europium produced does not seem to be the main factor, because Eu-enhanced stars can still form, even if the europium yield decreases by a half. Therefore, the decisive factor in forming r-process enhanced stars is whether or not the stars can form in the close spatial and temporal vicinity of the NSM event.