Early Solar System $r$-process Abundances Limit Collapsar Origin

TL;DR

This study uses simulations and Solar System abundance data to show that collapsars are unlikely the main source of $r$-process elements, favoring neutron star mergers instead.

Contribution

It provides quantitative constraints on the contribution of collapsars to $r$-process element production in the early Solar System.

Findings

Collapsars contribute less than 20% to Solar $r$-process abundances.

$r$-process ejecta from collapsars is limited to less than 10% of neutron star merger ejecta.

Neutron star mergers are the dominant source of $r$-process elements in the Solar System.

Abstract

Heavy elements produced exclusively through rapid neutron capture (the '$r$-process') originate from violent cosmic explosions. While neutron star mergers are the primary candidates, another plausible production site are 'collapsars'---collapsing massive stars that form a black hole with an accretion disk. Here we show that collapsars are too rare to be the prime origin of $r$-process elements in the Solar System. By comparing numerical simulations with the early Solar System abundances of actinides produced exclusively through the $r$-process, we exclude higher than 20% contribution from collapsars with 90% confidence. We additionally limit $r$-process ejecta masses from collapsars to less than 10% of the ejecta mass from neutron star mergers, about $10^{-2}$M$_\odot$.

Equations

$$D\approx 0.1\text{mbox}{kpc}^2\text{mbox}{Gyr}^{-1}\left(\frac{\alpha }{0.1}\right)\left(\frac{v_{\mathrm{t}}}{7\text{mbox}{kms}^{-1}}\right)\left(\frac{H}{0.2\text{mbox}kpc}\right)$$

$$m_{\mathrm{ej},\mathrm{c}}\approx m_{\mathrm{ej},\mathrm{ns}}\frac{0.6f_{\mathrm{c}}}{1-f_{\mathrm{c}}}.$$

Full text

††thanks: imrebartos@ufl.edu

1 Introduction

The cosmic creation of heavy $r$-process elements is still not well understood. Core-collapse supernovae, which were historically considered to be the main source (Burbidge et al., 1957; Woosley et al., 1994), are too frequent to explain the measured isotopic abundances in the early Solar System, in deep-sea sediments and in metal-poor stars (Bartos & Marka, 2019; Wallner et al., 2015; Hotokezaka et al., 2015; Macias & Ramirez-Ruiz, 2018).

Neutron star mergers are natural candidates as a major production site. They eject high-density, neutron-rich matter in sufficient quantities to be the main source of Galactic $r$-process elements (Goriely et al., 2011; Shen et al., 2015; van de Voort et al., 2015). This possibility is further corroborated by recent multi-messenger observations of a neutron star merger accompanied by a kilonova (Abbott et al., 2017; Coulter et al., 2017; Abbott et al., 2017). The rate of neutron star mergers in the Milky Way is $10-100$ Myr*-1* (Pol et al., 2019), about a 1000 times less than the rate of supernovae (Tammann et al., 1994), which is consistent with expectations from isotopic abundances in the early Solar System and deep-sea sediments (Wallner et al., 2015; Hotokezaka et al., 2015; Bartos & Marka, 2019).

Rare source types other than neutron star mergers may also contribute to $r$-process enrichment. Collapsars are stellar core-collapse events that have sufficiently massive cores to form black holes, and sufficient angular momentum at the time of collapse to form an accretion disk (MacFadyen & Woosley, 1999). The resulting accreting black holes could produce $r$-process elements through disk winds similarly to neutron star mergers (Pruet et al., 2004; Kohri et al., 2005; Siegel et al., 2019).

Collapsars are only expected in stars with low metallicities, while neutron star mergers are delayed compared to star formation. Therefore, a collapsar origin could help explain the presence of $r$-process elements in extremely metal poor stars, which is more difficult with neutron star mergers (Ji et al., 2016; Côté et al., 2017; Safarzadeh et al., 2019). On the other hand, the observed $r$-process enrichment of some metal-poor stars disfavors sources like collapsars that are significant metal producers (Macias & Ramirez-Ruiz, 2019). Additional challenges to the neutron star mergers as the main $r$-process production site include the strong enhancements in heavy $r$-process elements of some stars in ultra faint dwarf galaxies (Ji et al., 2016; Hansen et al., 2017), as the low escape velocities and short star-formation epochs in such galaxies would require unusually small natal kick velocities and fast merger time (Siegel, 2019). Further, Galactic $r$-process enrichment at high metallicities appears to be slower than expected from neutron star mergers, although this is dependent on the uncertain event rate and time delay compared to star formation (Côté et al., 2017; Hotokezaka et al., 2018).

We examined the origin of $r$-process elements in the early Solar System by considering fractional contributions from both neutron star mergers and collapsars. We used the abundances of short-lived radioactive isotopes that encode information on their production and deposition history. Even though these elements are by now extinct in the Solar System, meteorites that condensed during the early Solar System still carry their imprint (Nittler & Dauphas, 2006). The early Solar System abundance of a short-lived radioactive isotope ($N_{\rm SLR}$) can be estimated by comparing the abundance of its decay product with that of a chemically identical isotope ($N_{\rm stable}$). The measured abundance ratio $N_{\rm SLR}/N_{\rm stable}$ relative to the elements’ production ratio $P_{\rm SLR}/P_{\rm stable}$ tells us the time interval between the astrophysical event that synthesized the elements and the formation of the Solar System.

2 Methods

2.1 Abundances

The ratios of the abundances of different elements produced in the ejecta are taken to be their production ratios. Here, we adopted estimates of production ratios found in Tissot et al. (2016) (see also Bartos & Marka 2019). For 247Cm and 244Pu we used another actinide, 232Th, as our reference isotope. 232Th is long-lived with $t_{1/2}=1.4\times 10^{10}$yr, therefore it is still detectable in remnants from the Early Solar System. Our reference isotope for 129I is another $r$-process product, 127I, which is stable. For 129I for which Tissot et al. (2016) obtained the ratios by averaging the results of multiple previous studies, we adopted the mean difference between the average value and the values of these studies.

We adopted early Solar System abundance ratios for 247Cm and 244Pu from Tissot et al. (2016), and for 129I from Lugaro et al. (2018).

2.2 Collapsar rate in the Milky Way

Long GRBs occur in low-metallicity, highly star-forming environments (Woosley & Heger, 2006). Ongoing star formation is important since massive stars that produce collapsars only live for a few million years, while low-metallicity limits stellar winds that would otherwise reduce the star’s mass before collapse. These requirements make collapsars rare in the Milky Way (Fruchter et al., 2006; Langer & Norman, 2006).

To estimate the Galactic rate of collapsars as a function of time, we consider its dependence on metallicity and star formation rate in the Milky Way. For fixed metallicity, we assume that the collapsar rate is proportional to the core-collapse supernova rate. Based on the fraction of stars in the Milky Way that have low metallicities similar to long-GRB host galaxies, the Galactic collapsar rate at present is expected to be about 5% of the collapsar rate in the local universe implied by star formation only (Piran & Jimenez, 2014). We extend this 95% metallicity-suppression by assuming that the collapsar rate is suppressed by $0.95Z(t)/Z(t_{0})$, where $Z(t)$ is the Galactic metallicity at time $t$, with $t_{0}$ being the present day. The precise shape of this suppression does not meaningfully affect our results. We adopt the metallicity evolution of the Milky Way from Hayden et al. (2015) (see their Fig. 9. We chose their result at 4 kpc as that region has the highest star formation; the difference is not large at different radii).

We assume that all collapsars produce a long gamma-ray burst. We take a local long gamma-ray burst rate of 1.3 Gpc*-3yr-1* (Wanderman & Piran, 2010). Using a characteristic long gamma-ray burst beaming factor of $5\times 10^{-3}$ defined as the fraction of the sky in which a gamma-ray burst can be observed from cosmological distances (Goldstein et al., 2016), the corresponding local collapsar rate is $\sim 260$  Gpc*-3yr-1*. The local star formation rate density is $\sim 10^{7}$ M⊙Gpc*-3yr-1* (Cucciati et al., 2012), while the present star formation rate in the Milky Way is $\sim 1$ M*⊙yr-1* (Prantzos & Silk, 1998).

Combining these, we arrive at a present Galactic collapsar rate of $\sim 1$ Myr*-1*. Beyond taking into account the metallicity-suppression above, we computed past collapsar rate by additionally taking into account the evolution of the core-collapse supernova rate in the Milky Way. We adopted the Galactic core collapse supernova rate as a function of time based on the high resolution, zoom-in cosmological simulation of a Milky Way Galaxy analog, called Eris (Guedes et al., 2011), computed by Shen et al. (2015).

2.3 Neutron star merger rate in the Milky Way

We adopted the Galactic rate of neutron star mergers as a function of time based on the Eris simulation (Guedes et al., 2011), computed by Shen et al. (2015). This rate varies within about $5-10$ Myr*-1* over the history of the Milky Way, consistent with population synthesis estimates (Artale et al., 2019; Shen et al., 2015).

2.4 Monte Carlo simulations

In one Monte Carlo realization of the Milky Way, neutron star mergers and collapsars were randomly placed in space and time using the above rates throughout the lifetime of the Galaxy. The spatial probability distribution of neutron star merger followed the Galactic stellar mass distribution (McMillan, 2011). Collapsars were placed randomly following a probability density radially proportional to the Galactic star formation rate, with no azumithal dependence, and with a scale height of 80 pc (Robitaille & Whitney, 2010).

We simulated the chemical mixing of $r$-process elements following Hotokezaka et al. (2015), accounting for radioactive decay and turbulent diffusion within the Milky Way with diffusion coefficient

[TABLE]

where $\alpha$ is the mixing length parameter, $v_{\rm t}$ is the typical turbulence velocity in the interstellar medium, and $H$ is the interstellar-medium scale height. We adopt $D=0.1$ kpc2Gyr*-1* below following Hotokezaka et al. (2015) (see also Yang & Krumholz 2012). We used identical ejecta mass and composition for all mergers and, independently, all collapsars. Abundance ratios in the early Solar System were taken to be proportional to abundance ratios in the interstellar medium near the pre-Solar nebula at the time of the formation of the Solar System. We assumed that the time between deposition into the pre-Solar nebula and the condensation of meteorites that preserved the imprint of short-lived isotopes in the early Solar System is negligible (Tang et al., 2017; Dauphas & Chaussidon, 2011).

We obtained the probability distribution of actinide abundance ratios in the early Solar System by varying the time when the Solar System was formed between $8-9$ Gyr within a Monte Carlo realization of the Milky Way, and by computing $10^{3}$ realizations.

3 Results

3.1 Comparison of expected abundance ratios

We carried out Monte Carlo simulations of neutron star mergers and collapsars in the Milky Way to calculate the expected $r$-process abundances in the early Solar System (Hotokezaka et al., 2015; Bartos & Marka, 2019). We computed the abundances of Curium-247 (247Cm; half-life $t_{1/2}=15.6$ Myr), Iodine-129 (129I; $t_{1/2}=15.7$ Myr) and Plutonium-244 (244Pu; $t_{1/2}=80.8$ Myr) separately, normalized by the abundances of long-lived $r$-process elements such that the obtained abundance ratios could be compared to measured early Solar System values. The results, shown in Fig. 1, are instructive. We see that the abundance ratio probability densities for neutron star mergers are distributed around the early Solar System values. As collapsars are more rare and, their expected contribution to the short-lived abundances is diminished, resulting in a probability distribution that is mostly much below the measured value. In addition, the collapsar rate of the Milky Way was significantly higher in its early period much before the formation of the Solar System. This injected long-lived elements into the Milky Way, further reducing the abundance ratios at the time of the Solar System’s formation.

3.2 Limit on the fractional collapsar contribution

We computed the probability density of the fraction $f_{\rm c}$ of $r$-process elements from collapsars in the Solar System. We randomly selected simulated early Solar System abundances from both the collapsar and the neutron star merger simulations, and combined them such that collapsars contribute $f_{\rm c}$ fraction of the total stable $r$-process elements. We then checked whether this combination reproduces the measured early Solar System abundance ratios to within $\pm 30\%$. The probability density of a given $f_{\rm c}$ was taken to be proportional to the fraction of simulated abundances that satisfy this criterion.

The resulting cumulative probability densities are shown in Fig. 2. We show these densities both by requiring that the abundance ratios of either a single or all elements match the measured values. From the distributions for individual mass ratios, we see that collapsar contribution is particularly constrained by 244Pu.

To explain this, we used our simulations to compute the average fraction of different isotopes in the early Solar System that came from collapsars, as a function of $f_{\rm c}$. The obtained fractions are shown in Fig. 3. We see that the fraction of long-lived isotopes is similar to $f_{\rm c}$, while we find a limited collapsar contribution to 244Pu, and essentially no contribution to 247Cm and 129I.

By requiring all simulated abundance ratios to simultaneously match the measured early Solar System values, we see in Fig. 2 that a collapsar contribution $\gtrsim 20\%$ to $r$-process elements is excluded at 90% confidence level.

3.3 Limits on the collapsar ejecta mass

Using our simulations we can convert the fractional collapsar contribution $f_{\rm c}$ to the early Solar System to an estimate on the collapsar $r$-process ejecta mass. For this, we measured from our simulation the $r$-process density near the early Solar System from collapsars and neutron star mergers, in both cases normalized by their respective ejecta mass. By fixing the required collapsar fraction, we can use these abundances to find the relative ejecta masses for the two source types. We find that For $m_{\rm ej,c}$ and $m_{\rm ej,ns}$ $r$-process ejecta masses, for collapsars and neutron star mergers, respectively, we find

[TABLE]

Taking our exclusion limit of $f_{\rm c}]\lesssim 0.2$, this means that $m_{\rm ej,c}\lesssim 0.15m_{\rm ej,ns}$. Assuming $m_{\rm ej,ns}<0.1$ M⊙ (Siegel, 2019), we obtain $m_{\rm ej,c}\approx 0.01$ M⊙.

4 Conclusion

We found that the measured early Solar System abundances of short-lived $r$-process elements (244Cm, 129I and 244Pu) are typical for a neutron star merger population, while they are unlikely from a collapsar population.

Considering contributions from both neutron star mergers and collapsars, we find that a more than 20% collapsar contribution is excluded at 90% confidence level for our model. This limit is due to the lower rate of collapsars compared to mergers, and their higher relative rate in the early Milky Way compared to the time of the formation of the Solar System.

Using the above limit on the fractional $r$-process contribution from collapsars and the computed deposition rate in our simulations, we exclude $r$-process ejecta masses from collapsars greater than $10^{-2}$ M⊙.

The observational limits on the $r$-process ejecta mass from collapsars suggests that outflows from collapsar disks may produce less $r$-process matter than previously thought (Siegel et al., 2019). It is also possible that collapsar outflows are less neutron rich and therefore only produce lighter $r$-process elements, but not actinides. Alternatively, a currently unknown sub-population of collapsars that do not produce gamma-ray bursts would mean a higher collapsar rate than considered here that would allow a higher overall fractional collapsar contribution. The results presented here will help convert future observations of kilonovae from neutron star mergers to probe the rate of collapsars, their connection to gamma-ray bursts, and the properties of accretion disks.

The authors thank Enrico Ramirez-Ruiz and Mohammad Safarzadeh for their useful feedback. The authors are grateful for the generous support of the University of Florida and Columbia University in the City of New York.