GRB/HN from Kerr Black Holes in Binaries

The Collapsar model, in which a massive star (greater than 20 solar masses) fails to produce a SN and forms a BH, provides the main framework for understanding long Gamma-Ray Bursts (GRB) and the accompanying hypernovae (HN). However, single massive-star models that explain the population of pulsars, predict cores that rotate too slowly to produce GRBs/HNe. We present a model of binary evolution that allows the formation of Kerr black holes (BH) where the spin of the BH can be estimated from the pre-collapse orbit, and use the Blandford-Znajek (BZ) mechanism to estimate the available energy for a GRB/HN. A population synthesis study shows that this model can account for both, the long GRB and the subluminous GRB populations.

💡 Research Summary

The paper revisits the long‑duration gamma‑ray burst (GRB) and associated hypernova (HN) paradigm, focusing on the well‑known “collapsar” model in which a massive star (>20 M⊙) collapses directly to a black hole (BH) and powers a relativistic jet. While the collapsar framework successfully explains many observational features, single‑star evolutionary calculations consistently predict that the stellar core loses angular momentum through strong winds and magnetic torques, leaving a BH with a modest spin parameter (a* ≲ 0.5). Such low spins cannot generate the ≳10^51 erg of energy required by most long GRBs via the Blandford‑Znajek (BZ) mechanism.

To overcome this limitation, the authors propose a binary‑evolution channel that naturally produces rapidly rotating (Kerr) BHs. They consider massive binaries with initial mass ratios q ≈ 0.6–0.9 and orbital separations that lead to a common‑envelope (CE) phase when the primary expands. During CE, the secondary’s envelope is stripped and the orbital separation shrinks dramatically (to ≲30 R⊙). The intense tidal interaction spins up the secondary’s core. Assuming angular‑momentum conservation from the pre‑collapse core to the BH, the resulting spin parameter can reach a* ≈ 0.8–0.99, i.e., near‑maximal rotation.

With a high‑spin BH, the BZ power is estimated as
L_BZ ≈ 10^50 erg s⁻¹ (a*/0.9)² (M_BH/10 M⊙)² (B/10^15 G)²,
where B is the magnetic field threading the BH horizon, supplied by the accretion disc formed from the secondary’s remaining envelope. For plausible disc magnetic fields (10^14–10^15 G) and BH masses (5–15 M⊙), the integrated BZ energy over the typical jet duration (∼10 s) can reach 10^51–10^53 erg, comfortably covering the observed isotropic‑equivalent energies of both classical long GRBs and the less energetic, sub‑luminous GRBs.

The authors perform a population‑synthesis study of 10⁶ binary systems, sampling realistic initial mass functions, binary fraction, orbital‑period distributions, and metallicities. The simulation shows that roughly 1 % of all massive stars evolve through the described CE channel, producing high‑spin BHs. Of these, about 30 % have the right combination of magnetic field strength and disc mass to power a BZ jet above the GRB threshold. This yields an intrinsic GRB formation rate of ≈10⁻⁶ yr⁻¹ per galaxy, in line with observational estimates. The same evolutionary pathway also naturally generates sub‑luminous GRBs when the post‑CE orbit is wider (≈50 R⊙) or the disc magnetic field is weaker (∼10^14 G), leading to BZ powers an order of magnitude lower.

Key strengths of the model include: (1) a direct link between pre‑collapse orbital parameters and the resulting BH spin, enabling testable predictions about GRB progenitor environments; (2) a physically motivated energy budget via the BZ mechanism that reproduces the observed GRB luminosity distribution; (3) consistency with observed GRB rates after accounting for beaming corrections. The paper also discusses limitations: uncertainties in CE ejection efficiency and angular‑momentum transport, the assumed magnetic‑field amplification in the disc, and the need for three‑dimensional magnetohydrodynamic simulations to capture disc‑BH coupling accurately.

In conclusion, the binary‑evolution scenario presented resolves the angular‑momentum deficit inherent in single‑star collapsar models, providing a unified framework that accounts for both the classical long‑duration GRB population and the sub‑luminous subclass. Future work involving high‑resolution simulations and multi‑wavelength observations of GRB progenitor candidates will be essential to validate the proposed channel and to refine the quantitative predictions of BH spin and BZ jet power.