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

Abstract

The collapse of rotating massive (~$10M_{\odot }$) 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 $\dot{M}>{\dot{M}}_{\mathrm{ign}}$. 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 ${\dot{M}}_{\mathrm{ign}}\propto \hat{I}{\pm }^{5/3}{M}^{4/3}$ for $M$ ~ 3-3000 $M_{\odot }$. Simulations and analytic analyses consistently show that the largest BHs leading to r-process nucleosynthesis at ${\dot{M}}_{\mathrm{ign}}$ are $\approx 3000M_{\odot }$, 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 ~$250-10^5{M}_{\odot }$ can give rise to BHs of $M$ ~30-1000 $M_{\odot }$ accreting at $\dot{M}\gtrsim {\dot{M}}_{\mathrm{ign}}$, yielding ~$10-100M_{\odot }$ 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.

25 pages, 16 figures