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 $\dot{M}_{\rm ign}\propto \alpha^{5/3}M^{4/3}$ 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.