On the Efficiency of Producing Gamma-Ray Bursts from Isolated Population III Stars

TL;DR

This work probes whether isolated Population III stars can produce gamma-ray bursts by combining 1D MESA stellar evolution with semi-analytic core-collapse, accretion-disc formation, and jet breakout modeling. By surveying a grid of $M_{ m ZAMS}=20-100\,M_\odot$, rapid rotation with $0.6\leq \hat{\Omega}_0\leq0.9$, and wind efficiencies $0.2\leq \eta_{ m wind}\leq1$, the authors derive pre-collapse structures, BH birth properties, disc masses, jet powers, and breakout criteria, identifying a GRB phase space governed by CHE and angular-momentum retention. They find GRB production efficiencies in the range $\eta_{\rm GRB} \sim 10^{-5}-3\times10^{-4}\,M_\odot^{-1}$ (top-heavy IMF) and predict all-sky Swift-Yr$^{-1}$ rates of $\sim2-40$ for plausible wind efficiencies, with $75\%$ of events at $z\lesssim8$. A higher wind efficiency would suppress Pop III GRBs, favoring binary scenarios, while the results emphasize the critical role of line-driven winds and rotation in shaping the high-redshift GRB landscape and constraining the Pop III IMF.

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 ($M_{\rm ZAMS}\gtrsim20M_\odot$) 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 $20\leq M_{\rm ZAMS}/M_\odot \leq 100$, which are initially rotating with surface angular velocities $0.6\leq Ω_0/Ω_{\rm crit}\leq 0.9$, where centrifugally-driven mass loss ensues for $Ω>Ω_{\rm crit}$. 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 $η_{\rm wind}=0.45-0.35$, the Pop III GRB production efficiency is $η_{\rm GRB}\sim10^{-5}-3\times10^{-4}\,M_\odot^{-1}$, respectively, for a top-heavy IMF. This yields an observable all-sky equivalent rate of $\sim2-40\,{\rm yr}^{-1}$ by \textit{Swift}, with 75\% of the GRBs located at $z\lesssim8$. If the actual observed rate is much lower, then this would imply $η_{\rm wind}>0.45$, which leads to significant loss of mass and angular momentum that renders isolated Pop III stars incapable of producing GRBs and favors a binary scenario instead.

Figures (17)

• Figure 1: Evolutionary tracks in the HR diagram for stellar models with initial masses ranging from 20 to 100 $M_{\odot}$, assuming an initial rotation fraction of $\hat{\Omega}_0\equiv\Omega_0/\Omega_{\rm crit} = 0.9$ (left) and $\hat{\Omega}_0 = 0.6$ (right). Each track shows luminosity evolution as a function of the effective temperature from the ZAMS to advanced core nuclear burning stages before core-collapse. These different nuclear burning stages are highlighted with different symbols. (Top) Stellar evolution with Dutch wind scaling factor of $\eta_{\rm wind} = 1.0$, with evolutionary tracks shown up to a central temperature of $\log T_{\rm core} < 9.6$. (Bottom) The panel presents the scenario for $\eta_{\rm wind} = 0.2$, where tracks are presented up to $\log T_{\rm core} < 9.4$. These temperature thresholds are imposed to prevent numerical instabilities that arise in the late evolutionary stages.
• Figure 2: (Left) Evolution of the core temperature as a function of core density for stellar models with masses ranging from $20M_{\odot}$ to $100M_{\odot}$ for $\eta_{\rm wind} = 0.2$ and for an initial rotation of $\hat{\Omega}_0=0.6$ (top) and $\hat{\Omega}_0=0.9$ (bottom). The tracks illustrate the progression through different nuclear burning stages (C, Ne, O, Si) as the core evolves. The red shaded area indicates the $\Gamma < 4/3$ instability criterion, valid particularly for non-rotating stars, where the stellar core becomes dynamically unstable due to the creation of electron-positron pairs that reduce the adiabatic index below the critical threshold, while the blue region corresponds to the criteria for a degenerate electron gas. (Right) Evolution of the pre-core-collapse mass as a function of the initial mass ($M_{\rm{ZAMS}}$), for different values of $\eta_{\rm wind}$ and initial rotation of $\hat{\Omega}_0 = 0.9$ (solid) and $\hat{\Omega}_0 = 0.6$ (dashed). Slower rotating massive stars ($M_{\rm ZAMS}>70M_\odot$) enter the (pulsational) pair-instability region and their evolution was not followed all the way to core-collapse. Hence, the non-monotonic behavior in the pre-core-collapse mass.
• Figure 3: Temporal evolution of the stellar surface rotation for $20\,M_\odot$ (left) and $100\,M_\odot$ (right) stars. (Top) Normalized surface angular velocity $\hat{\Omega} \equiv \Omega / \Omega_{\rm crit}$, as a function of stellar age, for different wind scaling factors: $\eta_{\rm wind} = 1.0$ (dotted lines), $\eta_{\rm wind} = 0.5$ (dashed lines), $\eta_{\rm wind} = 0.2$ (solid lines), and for different initial rotation rates: $\hat{\Omega}_0 = 0.6$ (blue), $\hat{\Omega}_0 = 0.7$ (red), $\hat{\Omega}_0 = 0.8$ (green), and $\hat{\Omega}_0 = 0.9$ (purple). (Bottom) Corresponding evolution of the surface angular velocity.
• Figure 4: Mass loss rates as a function of stellar age for the entire mass grid with wind efficiency factor of $\eta_{\rm wind} = 0.2$, shown for two different initial rotation rates: $\hat{\Omega}_0=0.9$ (left), and $\hat{\Omega}_0=0.6$ (right). Higher $\eta_{\rm wind}$ yields similar mass loss rates. Models with higher initial $\hat{\Omega}_0$ reach critical rotation earlier (see Fig. \ref{['fig:Omega_Age_eta_variation']}) and therefore show a sudden increase in mass loss caused by centrifugal effects.
• Figure 5: Pre-core-collapse density profiles as a function of radius for stellar models with initial masses ranging from $20M_{\odot}$ to $100M_{\odot}$, shown for initial $\hat{\Omega}_0 = 0.9$ (left) and $\hat{\Omega}_0 = 0.6$ (right) and wind scaling factor of $\eta_{\rm wind} = 1.0$ (top) and $\eta_{\rm wind} = 0.2$ (bottom).