# Collapsars as a major source of r-process elements

## Abstract

The production of elements by rapid neutron capture (r-process) in neutron-star mergers is expected theoretically and is supported by multimessenger observations1,2,3 of gravitational-wave event GW170817: this production route is in principle sufficient to account for most of the r-process elements in the Universe4. Analysis of the kilonova that accompanied GW170817 identified5,6 delayed outflows from a remnant accretion disk formed around the newly born black hole7,8,9,10 as the dominant source of heavy r-process material from that event9,11. Similar accretion disks are expected to form in collapsars (the supernova-triggering collapse of rapidly rotating massive stars), which have previously been speculated to produce r-process elements12,13. Recent observations of stars rich in such elements in the dwarf galaxy Reticulum II14, as well as the Galactic chemical enrichment of europium relative to iron over longer timescales15,16, are more consistent with rare supernovae acting at low stellar metallicities than with neutron-star mergers. Here we report simulations that show that collapsar accretion disks yield sufficient r-process elements to explain observed abundances in the Universe. Although these supernovae are rarer than neutron-star mergers, the larger amount of material ejected per event compensates for the lower rate of occurrence. We calculate that collapsars may supply more than 80 per cent of the r-process content of the Universe.

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## Data availability

No datasets were generated or analysed during the current study.

## Code availability

A public version of the GRMHD code used to conduct the simulations of collapsar accretion disks is available through the Einstein Toolkit at https://einsteintoolkit.org; the framework for the recovery of primitive variables used here is available at https://doi.org/10.5281/zenodo.1213306. The nuclear reaction network employed for the r-process nucleosynthesis calculations is available at https://bitbucket.org/jlippuner/skynet/src/master. The radiation transport code used to explore r-process signatures in GRB supernovae is not currently available as it is in the process of being readied and approved for public release.

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## Acknowledgements

Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. Support for this work was provided by NASA through Einstein postdoctoral fellowships (award numbers PF6-170159 and PF7-180162) issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. B.D.M. acknowledges support from NASA, through the Astrophysics Theory Program (NNX16AB30G).

### Reviewer information

Nature thanks Andrew MacFadyen and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

Authors

### Contributions

D.M.S. designed and performed the numerical simulations and led the interpretation of their results, developed the toy model of collapsar fallback accretion and Galactic chemical evolution, and drafted initial versions of most sections of Methods. J.B. performed the radiative transfer calculations of the light curves of collapsar supernovae with r-process enrichment and led their interpretation and incorporation into Methods. B.D.M. helped with designing the numerical calculations and with their interpretation, developed the analytic model for 56Ni production, and wrote the initial draft of the main text and some sections of Methods.

### Corresponding author

Correspondence to Daniel M. Siegel.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Extended data figures and tables

### Extended Data Fig. 1 MHD characteristics of simulations.

a, Simulation snapshot of the meridional plane for run 2, showing the rest-mass density (ρ; upper half; contours at 106, 107, 108, 109, 1010 g cm−3) and number of grid points per wavelength of the fastest-growing MRI mode (λMRIx; lower half) once the stationary state has been reached after 30 ms. Note that the MRI is well resolved. b, Space–time diagram of the y component of the magnetic field (By; colour scale at right) for run 2, radially averaged between 45 and 70 km from the rotation axis in the xz (meridional) plane, as a function of height z relative to the equatorial plane, and time, indicating a fully operational dynamo and a steady turbulent state of the disk after about 20−30 ms.

### Extended Data Fig. 2 Numerical characteristics of simulations.

a, Resolution study showing the maximum magnetic field strength in the disk midplane for run 2 and additional runs with varying resolution (but otherwise identical), indicating that magnetic field amplification has converged for the fiducial run with finest grid spacing, Δx (see key). b, Comparison of the accretion rate of run 2 (‘B’ in key) to a run with much lower initial magnetic field (but otherwise identical; ‘low B’ in key), showing that angular momentum transport and viscous heating are set by MHD turbulence.

### Extended Data Fig. 3 Black hole accretion rate.

Shown are the black hole accretion rates as a function of time for the three main runs (1, 2 and 3), which represent the state of a collapsar accretion flow at consecutively later times following the core collapse of the star (see Fig. 1).

### Extended Data Fig. 4 Effective MHD viscosity of the collapsar accretion disk.

Shown are radial profiles of the effective α-viscosity parameter for run 1 at different times (see key) spanning 100 ms of evolution.

### Extended Data Fig. 5 Nickel and helium production in the collapsar disk outflows.

Shown are estimated 56Ni (red) and 4He (blue) mass fractions based on equation (13) along with extracted mass fractions from run 3 (uncertainties in the accretion rate are defined as in Fig. 1), at accretion rates below the ignition threshold (equation (6)). The coloured bands correspond to estimates bracketing the distribution of expansion timescales between 5 and 30 ms.

### Extended Data Fig. 6 r-process enrichment through neutron-star mergers (left) and collapsars (right).

Although collapsars are somewhat less frequent than mergers over cosmic time, their higher r-process yields (by a factor of about 30, if calibrated using the energetics of long versus short GRB jets) make them an important and probably dominant r-process site (equation (26)). See Methods for nomenclature.

### Extended Data Fig. 7 Oxygen abundance and metallicity of Milky Way stars.

Oxygen abundances for high-signal-to-noise (>200) stars from the full APOGEE DR14 sample114 are plotted versus metallicity, with individual stars being colour-coded by their effective temperature (colour scale at right). Shown for comparison with dashed lines are the range of oxygen thresholds for GRB generation113, with the fraction fZ of stars below the threshold indicated. An order-unity fraction of stars in the Milky Way were formed at metallicities below the threshold needed for collapsar production.

### Extended Data Fig. 8 Radioactive heating rate from the r-process and the nickel burned in the GRB supernova.

The specific radioactive heating rate of the 56Ni/56Co chain from the associated supernova (blue) exceeds that of r-process nuclei (red) for $$1{\rm{d}}{\rm{a}}{\rm{y}}\lesssim t\lesssim 600{\rm{d}}{\rm{a}}{\rm{y}}{\rm{s}}$$. This makes it possible to conceal large quantities of r-process material from collapsars in the centre of long GRB supernovae until very late times, $$t\gtrsim 100{\rm{d}}{\rm{a}}{\rm{y}}{\rm{s}}$$. The difference between the released (dashed lines) and deposited (solid lines) energy reflects energy lost to neutrinos, to incomplete deposition of γ-ray energy from 56Ni/56Co decay144, and to inefficient thermalization of r-process decay products (as previously calculated102). Figure adapted from previous work115.

### Extended Data Fig. 9 Galactic chemical evolution.

Shown are comparisons of model predictions with observational data for magnesium and europium abundances in Milky Way stars from the SAGA database140 (http://sagadatabase.jp) and europium abundances of Galactic disk stars132. For definitions of error bars we refer to the SAGA database140. Model predictions are shown for different minimum delay times (see keys) of type Ia supernovae with respect to star formation. a, Comparison for magnesium as a representative α-element. b, Comparison for europium as an r-process tracer, assuming both neutron-star mergers and collapsars (NS+Coll.) contribute to Galactic r-process nucleosynthesis. Note that the decreasing trend of [Eu/Fe] at high metallicity can be obtained. c, As b but assuming that only neutron-star mergers (NS only) contribute to Galactic r-process nucleosynthesis, showing that merger-only models cannot explain the [Eu/Fe] trend of stars in the Galactic disk.

### Extended Data Fig. 10 Galactic chemical evolution with varying collapsar contribution to the r-process.

The figure shows a comparison of model predictions with observational data for europium abundances as in Extended Data Fig. 9 (light blue points with error bars refer to the SAGA dataset140 (http://sagadatabase.jp), that is, stars in the Milky Way disk plus halo, while cyan points refer to disk stars only132), assuming a minimum type Ia supernova delay time of 400 Myr and varying the contribution of neutron-star mergers. For definitions of error bars we refer to the SAGA database140. The curves are labelled (see key) by the fraction of overall r-process material contributed to the Galaxy by collapsars at the time of formation of the Solar System. The neutron-star merger contribution is altered by renormalizing the neutron-star merger rates, tuning fNSRNS(z = 0) (compare equation (37)) by a factor between 0.3 and 100. The fiducial model in Extended Data Fig. 9 corresponds to the red curve. A dominant contribution to the total Galactic r-process from collapsars improves the evolution of r-process enrichment at high metallicity relative to merger-only models.

## Supplementary information

### Supplementary Table

Table listing the amount of collapsar disk wind ejecta during different accretion stages, computed for various presupernova models.

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Siegel, D.M., Barnes, J. & Metzger, B.D. Collapsars as a major source of r-process elements. Nature 569, 241–244 (2019). https://doi.org/10.1038/s41586-019-1136-0

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