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Daniel M. Siegel

Publications and source records attributed to Daniel M. Siegel.

At least 19 recordsLinked to original sources

Inferring the role of binary neutron star mergers in r-process nucleosynthesis with multi-messenger observations using Cosmic Explorer and Einstein Telescope

Identifying the cosmic origin of rapid neutron-capture (r-process) elements remains an open problem. Binary neutron-star (BNS) mergers and rare classes of core-collapse supernovae (CCSNe) represent the main contenders as major r-process production sites. Although BNS mergers could exclusively account for r-process nucleosynthesis, results from chemical evolution studies taking into account their delays with respect to star formation, observed BNS rates by gravitational-wave (GW) detectors, as well as issues with retention in low-mass halos suggest otherwise. Here, we propose a method to measure the contribution of BNS mergers to cosmic r-process nucleosynthesis with the third-generation GW detectors Cosmic Explorer and Einstein Telescope. It exploits the redshift-dependent correlation between the total number of BNS GW events and the average r-process abundances at redshifts $z \lesssim 1$. We apply this correlation technique to mock GW and abundance data, accounting for expected observational uncertainties in two limiting scenarios: GW events with electromagnetic counterpart (multi-messenger 'bright-sirens') and without ('dark-sirens'). Using Fisher forecasts, we demonstrate that the fractional cumulative contribution of BNS mergers to the total cosmic r-process $F_{\rm{BNS,z0}}$ can be estimated to the $\lesssim 5-6\%$ precision level for both scenarios at $1σ$ for fiducial astrophysical scenarios with $F_{\rm{BNS,z0}} \gtrsim 0.1-1$. Furthermore, the method also yields estimates of the BNS delay-time distribution parameters comparable to other approaches. Although cosmic r-process abundances may be reconstructed from local observations at low metallicity, this method also provides a science case to identify signatures of neutron-capture elements beyond the local Universe.

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Mergers Fall Short: Non-merger Channels Required for Galactic Heavy Element Production

Since the discovery of the binary neutron star merger GW170817 and its associated kilonova, neutron star mergers have been established as a key production channel for r-process elements in the Universe. However, various lines of evidence, including observations of r-process abundances inferred from stellar spectra of Milky Way disk stars, suggest that additional channels are needed to fully account for r-process element enrichment in the Milky Way. Neutron star-black hole mergers and fast-merging binary neutron star systems are among the leading alternative candidates. In this paper, we combine gravitational-wave observations from LIGO-Virgo-KAGRA with data from short gamma-ray bursts, Galactic pulsars, and Galactic Eu/Fe versus Fe/H abundance observations to assess the contribution of these mergers to r-process enrichment in the Galactic disk. Our analysis employs a unified, likelihood-based inference framework that consistently propagates uncertainties in merger rates, delay-time distributions, mass- and spin-dependent ejecta yields, and stellar abundance measurements. We find that neither neutron star-black hole mergers nor fast- merging binary neutron star populations can serve as the dominant additional channel without generating strong tension with existing observations and theoretical expectations. These results constrain the viable sources of Galactic r-process enrichment and underscore the necessity of non- merger production channels.

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Relativistic jets from millisecond proto-magnetars

Rapidly rotating, strongly magnetized neutron stars (``millisecond proto-magnetars'') formed in stellar core-collapse, neutron star mergers, and white dwarf accretion-induced collapse have long been proposed as central engines of gamma-ray bursts (GRB) and accompanying supernovae/kilonovae. However, during the first few seconds after birth, neutrino heating drives baryon-rich winds from the neutron star surface, potentially limiting the magnetization and achievable Lorentz factors of the outflow and casting doubt on whether proto-magnetars can launch ultra-relativistic jets at early times, as needed to power short-duration GRB. We present 3D general-relativistic magnetohydrodynamic simulations of neutrino-heated proto-magnetar winds that incorporate M0 neutrino transport. While the global wind properties broadly agree with previous analytic estimates calibrated to one-dimensional models, our simulations reveal essential multidimensional effects. For rapidly rotating models with spin periods P = 1 ms, centrifugal forces strongly enhance mass loss near the rotational equator, producing a dense, sub-relativistic outflow ( ~0.1c). This equatorial wind naturally confines and collimates less baryon-loaded outflows emerging from higher latitudes, leading to the formation of a structured bipolar jet with a peak magnetization up to ~ 30-100 along the pole, sufficient to reach bulk Lorentz factors ~ 100 on larger scales. The resulting angular stratification of the outflow energy into ultra-relativistic polar and sub-relativistic equatorial components is broadly consistent with the observed partition between beaming-corrected GRB energies and supernova/kilonova ejecta. Our results demonstrate that millisecond proto-magnetars can launch relativistic jets within seconds of formation and highlight their potential role in powering the diverse electromagnetic counterparts of compact-object explosions.

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Jet-driven explosion of an accretion-induced white-dwarf collapse via a magnetorotational dynamo

The accretion-induced collapse (AIC) of a rotating white dwarf (WD) offers a potential site of millisecond pulsars/magnetars, gamma-ray bursts, and r-process nucleosynthesis. We present three-dimensional general-relativistic magneto-hydrodynamical simulations including neutrinos of magnetorotational AIC, assuming the WD is rapidly spinning with a weak magnetic field confined below its surface (likely a prerequisite for rapid rotation). Within milliseconds after core bounce, the magnetic field is exponentially amplified near the surface of the proto-neutron star (PNS). We witness the emergence of a small-scale turbulent and mean-field, large-scale MRI-driven dynamo in the neutrino-cooled centrifugally supported disk formed around the PNS, which generates bundles of large-scale toroidal field with alternating polarity. The amplified field becomes buoyant and is advected above the PNS, generating a magnetic tower that drives a mildly relativistic striped jet. The jet breaks out of the WD, clearing the way for a powerful magnetized neutron-rich wind from the disk. Although our simulation cannot follow the long-term Kelvin-Helmholtz cooling phase of the PNS, the conditions are ripe for the formation of a GRB powered by magnetar spin-down. A similar dynamo may operate in magnetorotational core-collapse supernovae and neutron-star mergers.

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Inference of multi-channel r-process element enrichment in the Milky Way using binary neutron star merger observations

Observations of GW170817 strongly suggest that binary neutron star (BNS) mergers produce rapid neutron-capture nucleosynthesis (r-process) elements. However, it remains an open question whether these mergers can account for all the r-process element enrichment in the Milky Way's history. Here, we constrain the contributions of the BNS channel using astrophysical neutron star observations. The rate and mass distributions are constrained by LIGO/Virgo/Kagra through the latest catalog GWTC-3, the neutron star equation of state by gravitational-wave, radio, and X-ray observations, and the delay time distribution by short gamma-ray burst (GRB) host galaxy associations. We present a Bayesian framework to consistently combine these lines of observations with abundance data to quantify the contribution and uncertainties of single and multiple astrophysical enrichment sources. Whereas we obtain a distribution of per-event BNS r-process element yields consistent with geophysical and astrophysical abundance constraints, BNS-only enrichment scenarios are inconsistent with the observed r-process abundance trend of disk stars in the Galaxy. Using stellar abundance observations instead of the short GRB constraints, we infer a shorter delay time distribution with power-law index $α\leq -2.0$ and minimum delay time $t_{\rm min}\leq 40$ Myr at 90\% confidence. Such delay times are in tension with those predicted by standard BNS formation models. Alternatively, we confirm that a two-channel scenario, in which the second channel tracks the star formation history without significant delay, can account for both Galactic stellar and short GRB observations. We show that 45--90\% of the r-process abundance in the Milky Way today was produced by a star-formation-tracking channel, rather than BNS mergers with significant delay times.

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Accretion Regimes of Neutrino-Cooled Flows onto Black Holes

Neutrino-cooled accretion disks can form in the aftermath of neutron-star mergers as well as during the collapse of rapidly rotating massive stars (collapsars) and the accretion-induced collapse of rapidly rotating white dwarfs. Due to Pauli blocking as electrons become degenerate at sufficiently high accretion rates $\dot{M}$, the resulting 'self-neutronization' of the dissociated accreting plasma makes these astrophysical systems promising sources of rapid neutron capture nucleosynthesis (the r-process). We present a one-dimensional general-relativistic, viscous-hydrodynamic model of neutrino-cooled accretion disks around black holes. With collapsars, super-collapsars and very massive star collapse in mind, we chart the composition of the accretion flow and systematically explore different radiatively efficient and inefficient accretion regimes with increasing $\dot M$, across a vast parameter space of $\dot{M}\sim 10^{-6}-10^6 M_\odot \,\text{s}^{-1}$, black hole masses of $M_\bullet\sim 1 - 10^4 M_\odot$ and dimensionless spins of $χ_\bullet \in [0,1)$, as well as $α$-viscosity values of $α\sim 10^{-3}-1$. We show that these accretion regimes are separated by characteristic thresholds $\dot{M}_{\rm char}$ that follow power laws $\dot M_{\rm char}\propto M_{\bullet}^αα^β$ and that can be understood based on analytic approximations we derive. We find that outflows from such disks are promising sites of r-process nucleosynthesis up to $M_\bullet \lesssim 3000 M_\odot$. These give rise to lanthanide-bearing 'red' super-kilonovae transients mostly for $M_\bullet \lesssim 200-500 M_\odot$ and lanthanide suppressed 'blue' super-kilonovae for larger $M_\bullet$. Proton-rich outflows can develop specifically for large black hole masses ($M_\bullet \gtrsim 100 M_\odot$) in certain accretion regimes, which may give rise to proton-rich isotopes via the $ν$p-process.

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Magnetized Accretion onto Neutron Stars: from Photon-trapped to Neutrino-cooled Flows

When a neutron star (NS) intercepts gas from a non-degenerate star, e.g., in a tidal disruption event, a common-envelope phase, or the collapsing core of a massive star, photons become trapped in the hot flow around the NS. This gas forms a radiatively inefficient accretion flow (RIAF) until the density and temperature close to the NS surface grow large enough for binding energy to be converted to neutrinos. Here we present three-dimensional, general-relativistic, magnetohydrodynamic simulations of accretion onto a non-rotating, unmagnetized NS. These connect, for the first time, an extended accretion disk with a self-consistent hydrostatic atmosphere around the star. The impact of different seed magnetic fields and accretion rates is studied by approximating the radiation-pressure dominated flow as an ideal gas with an adiabatic index of $4/3$, coupled to a variable neutrino emissivity. At low accretion rates, the hydrostatic atmosphere shows slow rotation and weak magnetization, transitioning to an outer RIAF structure. A toroidal magnetic field mediates the inward flow of energy and angular momentum through the atmosphere, which reaches a steady state when neutrino emission balances the accretion power. We develop a one-dimensional analytical model connecting these results with more general initial conditions and describing the main features of the flow. Our results have implications for the spin and mass evolution of hypercritically accreting NSs.

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Ignition of weak interactions and r-process outflows in super-collapsar accretion disks

The collapse of rotating massive (~$10 M_\odot$) stars resulting in hyperaccreting black holes (BHs; "collapsars") is a leading model for the central engines of long-duration gamma-ray bursts (GRBs) and a promising source of rapid neutron capture ("r-process") elements. R-process nucleosynthesis in disk outflows requires the accretion flow to self-neutronize. This occurs because of Pauli-blocking at finite electron degeneracy, associated with a critical accretion rate $\dot M > \dot{M}_{\rm ign}$. We analytically examine the assumptions underlying this "ignition threshold" and its possible breakdown with increasing BH mass $M$. Employing three-dimensional general-relativistic magnetohydrodynamic simulations with weak interactions, we explore the physical conditions of collapsar accretion disks with $M$ ~ 80-3000 $M_\odot$ over more than a viscous timescale as they transition through the threshold. There is remarkable agreement between our simulations and the analytic result $\dot{M}_{\rm ign}\propto α^{5/3}M^{4/3}$ for $M$ ~ 3-3000 $M_\odot$. Simulations and analytic analyses consistently show that the largest BHs leading to r-process nucleosynthesis at $\dot{M}_{\rm ign}$ are $\approx 3000 M_\odot$, beyond which self-neutronization ceases, since the disk temperature $T\propto M^{-1/6}$ decreases below the neutron-proton mass difference (~MeV), suppressing the conversion of protons into neutrons. We show that stellar models of ~$250-10^5M_\odot$ can give rise to BHs of $M$ ~30-1000 $M_\odot$ accreting at $\dot M\gtrsim \dot{M}_{\rm ign}$, yielding ~$10-100 M_\odot$ of light and heavy r-process elements per event. These rare but prolific r-process sources in low-metallicity environments are associated with super-kilonovae and likely extremely energetic GRBs. Such signatures may be used to probe Population III stars.

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Jets from neutron-star merger remnants and massive blue kilonovae

We perform high-resolution three-dimensional general-relativistic magnetohydrodynamic simulations with neutrino transport of binary neutron star (BNS) mergers resulting in a long-lived remnant neutron star, with properties typical of galactic BNS and consistent with those inferred for the first observed BNS merger GW170817. We demonstrate self-consistently that within $\lesssim\!30$ ms post-merger magnetized ($σ\sim 5-10$) twin polar jets emerge with asymptotic Lorentz factor $Γ\sim 5-10$, which successfully break out from the merger debris within $\lesssim\!20$ ms. A fast ($v\lesssim 0.6c$), magnetized ($σ\sim 0.1$) wind surrounds the jet core and generates a UV/blue kilonova precursor on timescales of hours, similar to the precursor signal due to free neutron decay in fast dynamical ejecta. Post-merger ejecta are quickly dominated by MHD-driven outflows from an accretion disk. We demonstrate that within only 50 ms post-merger, $\gtrsim 2\times 10^{-2}M_\odot$ of lanthanide-free, quasi-spherical ejecta with velocity $\sim\!0.1c$ is launched, yielding a kilonova signal consistent with GW170817 on timescales of $\lesssim\!5$\,d.

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JWST Observations of the Extraordinary GRB 221009A Reveal an Ordinary Supernova Without Signs of $r$-Process Enrichment in a Low-Metallicity Galaxy

Identifying the astrophysical sites of the $r$-process, one of the primary mechanisms by which heavy elements are formed, is a key goal of modern astrophysics. The discovery of the brightest gamma-ray burst of all time, GRB 221009A, at a relatively nearby redshift, presented the first opportunity to spectroscopically test the idea that $r$-process elements are produced following the collapse of rapidly rotating massive stars. Here we present spectroscopic and photometric $\textit{James Webb Space Telescope}$ (JWST) observations of GRB 221009A obtained $+168$ and $+170$ rest-frame days after the initial gamma-ray trigger, and demonstrate they are well-described by a supernova (SN) and power-law afterglow, with no evidence for an additional component from $r$-process emission, and that the SN component strongly resembles the near-infrared spectra of previous SNe, including SN 1998bw. We further find that the SN associated with GRB 221009A is slightly fainter than the expected brightness of SN 1998bw at this phase, concluding that the SN is therefore not an unusual GRB-SN. We infer a nickel mass of $\approx0.09$ M$_{\odot}$, consistent with the lack of an obvious SN detection in the early-time data. We find that the host galaxy of GRB 221009A has a very low metallicity of $\approx0.12$ Z$_{\odot}$ and our resolved host spectrum shows that GRB 221009A occurred in a unique environment in its host characterized by strong H$_2$ emission lines consistent with recent star formation, which may hint at environmental factors being responsible for its extreme energetics.

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Three-Dimensional General-Relativistic Simulations of Neutrino-Driven Winds from Magnetized Proto-Neutron Stars

Formed in the aftermath of a core-collapse supernova or neutron star merger, a hot proto-neutron star (PNS) launches an outflow driven by neutrino heating lasting for up to tens of seconds. Though such winds are considered potential sites for the nucleosynthesis of heavy elements via the rapid neutron capture process ($r$-process), previous work has shown that unmagnetized PNS winds fail to achieve the necessary combination of high entropy and/or short dynamical timescale in the seed nucleus formation region. We present three-dimensional general-relativistic magnetohydrodynamical (GRMHD) simulations of PNS winds which include the effects of a dynamically strong ($B \gtrsim 10^{15}$ G) dipole magnetic field. After initializing the magnetic field, the wind quickly develops a helmet-streamer configuration, characterized by outflows along open polar magnetic field lines and a ``closed'' zone of trapped plasma at lower latitudes. Neutrino heating within the closed zone causes the thermal pressure of the trapped material to rise in time compared to the polar outflow regions, ultimately leading to the expulsion of this matter from the closed zone on a timescale of $\sim$60 ms, consistent with the predictions of \citet{Thompson03}. The high entropies of these transient ejecta are still growing at the end of our simulations and are sufficient to enable a successful 2nd-peak $r$-process in at least a modest $\gtrsim 1\%$ of the equatorial wind ejecta.

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GRMHD simulations of neutron-star mergers with weak interactions: r-process nucleosynthesis and electromagnetic signatures of dynamical ejecta

Fast material ejected dynamically over $<10$ ms during the merger of a binary neutron-star (BNS) system can give rise to distinctive electromagnetic counterparts to the system's gravitational-wave emission that can serve as a "smoking gun" to distinguish between a BNS and a NS-black-hole merger. We present novel ab-initio modeling of the associated kilonova precursor and kilonova afterglow based on three-dimensional general-relativistic magneto-hydrodynamic simulations of BNS mergers with tabulated, composition-dependent, finite-temperature equations of state (EOSs), weak interactions, and approximate neutrino transport. We analyze dynamical mass ejection from 1.35-1.35Msun binaries, typical of Galactic double-NS systems and consistent with properties of the first observed BNS merger GW170817, using three nuclear EOSs that span the range of allowed compactness. Nuclear reaction network calculations yield a robust 2nd-to-3rd-peak r-process. We find few 1e-6Msun of fast ($v>0.6$c) ejecta that give rise to broad-band synchrotron emission on ~yr timescales, consistent with recent tentative evidence for excess X-ray/radio emission following GW170817. We find 2e-5Msun of free neutrons that power a kilonova precursor on <h timescale. A boost in early UV/optical brightness by a factor of a few due to previously neglected relativistic effects, with appreciable enhancements up to 10h post-merger, provides promising prospects for future detection with UV/optical telescopes such as Swift or ULTRASAT out to 250Mpc. We find that a recently predicted opacity boost due to highly ionized lanthanides at ~70000K is unlikely to affect the early kilonova lightcurve based on the obtained ejecta structures. Azimuthal inhomogeneities in dynamical ejecta composition for soft EOSs found here ("lanthanide/actinide pockets") may have observable consequences for both early kilonova and late-time nebular emission.

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Three-Dimensional General-Relativistic Simulations of Neutrino-Driven Winds from Rotating Proto-Neutron Stars

We explore the effects of rapid rotation on the properties of neutrino-heated winds from proto-neutron stars (PNS) formed in core-collapse supernovae or neutron-star mergers by means of three-dimensional general-relativistic hydrodynamical simulations with M0 neutrino transport. We focus on conditions characteristic of a few seconds into the PNS cooling evolution when the neutrino luminosities obey $L_{ν_e} + L_{\barν_e} \approx 7\times 10^{51}$ erg s$^{-1}$, and over which most of the wind mass-loss will occur. After an initial transient phase, all of our models reach approximately steady-state outflow solutions with positive energies and sonic surfaces captured on the computational grid. Our non-rotating and slower-rotating models (angular velocity relative to Keplerian $Ω/Ω_{\rm K} \lesssim 0.4$; spin period $P \gtrsim 2$ ms) generate approximately spherically symmetric outflows with properties in good agreement with previous PNS wind studies. By contrast, our most rapidly spinning PNS solutions ($Ω/Ω_{\rm K} \gtrsim 0.75$; $P \approx 1$ ms) generate outflows focused in the rotational equatorial plane with much higher mass-loss rates (by over an order of magnitude), lower velocities, lower entropy, and lower asymptotic electron fractions, than otherwise similar non-rotating wind solutions. Although such rapidly spinning PNS are likely rare in nature, their atypical nucleosynthetic composition and outsized mass yields could render them important contributors of light neutron-rich nuclei compared to more common slowly rotating PNS birth. Our calculations pave the way to including the combined effects of rotation and a dynamically-important large-scale magnetic field on the wind properties within a 3D GRMHD framework.

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"Super-Kilonovae" from Massive Collapsars as Signatures of Black-Hole Birth in the Pair-instability Mass Gap

The core collapse of rapidly rotating massive ~10 Msun stars ("collapsars"), and resulting formation of hyper-accreting black holes, are a leading model for the central engines of long-duration gamma-ray bursts (GRB) and promising sources of r-process nucleosynthesis. Here, we explore the signatures of collapsars from progenitors with extremely massive helium cores >130 Msun above the pair-instability mass gap. While rapid collapse to a black hole likely precludes a prompt explosion in these systems, we demonstrate that disk outflows can generate a large quantity (up to >50 Msun) of ejecta, comprised of >5-10 Msun in r-process elements and ~0.1-1 Msun of $^{56}$Ni, expanding at velocities ~0.1c. Radioactive heating of the disk-wind ejecta powers an optical/infrared transient, with a characteristic luminosity $\sim 10^{42}$ erg s$^{-1}$ and spectral peak in the near-infrared (due to the high optical/UV opacities of lanthanide elements) similar to kilonovae from neutron star mergers, but with longer durations $\gtrsim$ 1 month. These "super-kilonovae" (superKNe) herald the birth of massive black holes >60 Msun, which, as a result of disk wind mass-loss, can populate the pair-instability mass gap 'from above' and could potentially create the binary components of GW190521. SuperKNe could be discovered via wide-field surveys such as those planned with the Roman Space Telescope or via late-time infrared follow-up observations of extremely energetic GRBs. Gravitational waves of frequency ~0.1-50 Hz from non-axisymmetric instabilities in self-gravitating massive collapsar disks are potentially detectable by proposed third-generation intermediate and high-frequency observatories at distances up to hundreds of Mpc; in contrast to the "chirp" from binary mergers, the collapsar gravitational-wave signal decreases in frequency as the disk radius grows ("sad trombone").

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Neutrino Fast Flavor Conversions in Neutron-star Post-Merger Accretion Disks

A compact accretion disk may be formed in the merger of two neutron stars or of a neutron star and a stellar-mass black hole. Outflows from such accretion disks have been identified as a major site of rapid neutron-capture (r-process) nucleosynthesis and as the source of 'red' kilonova emission following the first observed neutron-star merger GW170817. We present long-term general-relativistic radiation magnetohydrodynamic simulations of a typical post-merger accretion disk at initial accretion rates of $\dot{M}\sim 1\,M_\odot\,\text{s}^{-1}$ over 400ms post-merger. We include neutrino radiation transport that accounts for effects of neutrino fast flavor conversions dynamically. We find ubiquitous flavor oscillations that result in a significantly more neutron-rich outflow, providing lanthanide and 3rd-peak r-process abundances similar to solar abundances. This provides strong evidence that post-merger accretion disks are a major production site of heavy r-process elements. A similar flavor effect may allow for increased lanthanide production in collapsars. The formalism presented here may also be used in simulations of core-collapse supernovae to explore whether fast conversions strengthen or weaken the explosion.

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Collapsars as a major source of r-process elements

The production of elements by rapid neutron capture (r-process) in neutron-star mergers is expected theoretically and is supported by multimessenger observations of gravitational-wave event GW170817: this production route is in principle sufficient to account for most of the r-process elements in the Universe. Analysis of the kilonova that accompanied GW170817 identified delayed outflows from a remnant accretion disk formed around the newly born black hole as the dominant source of heavy r-process material from that event. 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 elements. Recent observations of stars rich in such elements in the dwarf galaxy Reticulum II, as well as the Galactic chemical enrichment of europium relative to iron over longer timescales, 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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Heavy elements form short and long gamma-ray bursts

The gravitational-wave detectors LIGO and Virgo together with their electromagnetic partner facilities have transformed the modus operandi in which we seek information about the Universe. The first ever-observed neutron-star merger---GW170817---confirmed the association of short gamma-ray bursts with neutron-star mergers and the production of heavy (r-process) elements. Based on recent theoretical and observational developments, I briefly present and discuss a conjecture, namely that compact accretion disks in both short and long gamma-ray bursts synthesize most of the heavy r-process elements in the Universe. The upcoming era of multi-messenger astronomy may allow us to verify or falsify this conjecture.

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Nuclear Burning in Collapsar Accretion Disks

The core collapse of massive, rapidly-rotating stars are thought to be the progenitors of long-duration gamma-ray bursts (GRB) and their associated hyper-energetic supernovae (SNe). At early times after the collapse, relatively low angular momentum material from the infalling stellar envelope will circularize into an accretion disk located just outside the black hole horizon, resulting in high accretion rates necessary to power a GRB jet. Temperatures in the disk midplane at these small radii are sufficiently high to dissociate nuclei, while outflows from the disk can be neutron-rich and may synthesize r-process nuclei. However, at later times, and for high progenitor angular momentum, the outer layers of the stellar envelope can circularize at larger radii $\gtrsim 10^{7}$ cm, where nuclear reaction can take place in the disk midplane ((e.g.~$^{4}$He + $^{16}$O $\rightarrow$ $^{20}$Ne + $γ$).. Here we explore the effects of nuclear burning on collapsar accretion disks and their outflows by means of hydrodynamical $α$-viscosity torus simulations coupled to a 19-isotope nuclear reaction network, which are designed to mimic the late infall epochs in collapsar evolution when the viscous time of the torus has become comparable to the envelope fall-back time. Our results address several key questions, such as the conditions for quiescent burning and accretion versus detonation and the generation of $^{56}$Ni in disk outflows, which we show could contribute significantly to powering GRB supernovae. Being located in the slowest, innermost layers of the ejecta, the latter could provide the radioactive heating source necessary to make the spectral signatures of r-process elements visible in late-time GRB-SNe spectra.

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