On the efficiency of producing gamma-ray bursts from isolated Population III stars

ABSTRACT The rate of long-duration gamma-ray bursts (GRBs) from isolated Pop III stars is not well known, as it depends on our poor understanding of their initial mass function (IMF), rotation rates, stellar evolution, and mass loss. Some massive ($M_{\rm ZAMS}\gtrsim 20\,\mathrm{ M}_\odot$) Pop III stars are expected to suffer core-collapse and launch a relativistic jet that would power a GRB. In the collapsar scenario, a key requirement is that the pre-supernova star imparts sufficient angular momentum to the remnant black hole to form an accretion disc and launch a relativistic jet, which demands rapid initial rotation of the progenitor star and suppression of line-driven mass-loss during its chemically homogeneous evolution. Here, we explore a grid of stellar evolution models of Pop III stars with masses $20\le M_{\rm ZAMS}/M_\odot \le 100$, which are initially rotating with surface angular velocities $0.6\le \Omega _0/\Omega _{\rm crit}\le 0.9$, where centrifugally driven mass-loss ensues for $\Omega >\Omega _{\rm crit}$. Realistic accretion and jet propagation models are used to derive the initial black hole masses and spins, and jet breakout times for these stars. The GRB production efficiency is obtained over a phase space comprising progenitor initial mass, rotation, and wind efficiency. For modest wind efficiency of $\eta _{\rm wind}=0.45\!-\!0.35$, the Pop III GRB production efficiency is $\eta _{\rm GRB}\sim 10^{-5}-3\times 10^{-4}\, \mathrm{ M}_\odot ^{-1}$, respectively, for a top-heavy IMF. This yields an observable all-sky equivalent rate of $\sim 2\!-\!40\, {\rm yr}^{-1}$ by Swift, with 75 per cent of the GRBs located at $z\lesssim 8$. If the actual observed rate is much lower, then this would imply $\eta _{\rm wind}>0.45$, which leads to significant loss of mass and angular momentum that renders isolated Pop III stars incapable of producing GRBs and favours a binary scenario instead.