Supernovae Powered by Collapsar Accretion in Gamma-Ray Burst Sources

The association of long-duration gamma-ray bursts (LGRBs) with Type Ic supernovae presents a challenge to supernova explosion models. In the collapsar model for LGRBs, gamma rays are produced in an ultrarelativistic jet launching from the magnetosphere of the black hole that forms in the aftermath of the collapse of a rotating progenitor star. The jet is collimated along the star’s rotation axis, but the concomitant luminous supernova should be relatively–though certainly not entirely–spherical, and should synthesize a substantial mass of 56Ni. Our goal is to provide a qualitative assessment of the possibility that accretion of the progenitor envelope onto the black hole, which powers the LGRB, could also deposit sufficient energy and nickel mass in the envelope to produce a luminous supernova. For this, the energy dissipated near the black hole during accretion must be transported outward, where it can drive a supernova-like shockwave. Here we suggest that the energy is transported by convection and develop an analytical toy model, relying on global mass and energy conservation, for the dynamics of stellar collapse. The model suggests that a ~10,000 km/s shock can be driven into the envelope and that ~10^51 erg explosions are possible. The efficiency with which the accretion energy is being transferred to the envelope is governed by the competition of advection and convection at distances ~100-1,000 km from the black hole and is sensitive to the values of the convective mixing length, the magnitude of the effective viscous stress, and the specific angular momentum of the infalling envelope. Substantial masses of 56Ni may be synthesized in the convective accretion flow over the course of tens of seconds from the initial circularization of the infalling envelope around the black hole. The synthesized nickel is convectively mixed with a much larger mass of unburned ejecta.

💡 Research Summary

The paper tackles the long‑standing problem of how long‑duration gamma‑ray bursts (LGRBs) can be accompanied by bright Type Ic supernovae that synthesize a substantial amount of ⁵⁶Ni. In the collapsar scenario, a rapidly rotating massive star collapses to a black hole; a relativistic jet launched from the black hole’s magnetosphere produces the γ‑ray emission, while the bulk of the stellar envelope must somehow receive enough energy to explode as a roughly spherical supernova. The authors propose that the energy released during the accretion of the envelope onto the black hole is not confined to the jet but is instead transported outward by vigorous convection within the inner accretion flow.

To explore this idea they construct a highly simplified analytical “toy model” that enforces global mass and energy conservation. The model treats the inner accretion region (r ≈ 10⁸–10⁹ cm, i.e., 100–1 000 km) as a viscous α‑disk in which turbulent viscosity and convective mixing compete. The accretion power is L_acc ≈ η Ṁ c² with η ∼ 0.1, and a fraction ε of this power is assumed to be carried outward by convective eddies. By comparing the convective velocity v_conv ≈ (g ℓ_mix)¹ᐟ² with the viscous diffusion speed v_visc ≈ α c_s, the authors identify regimes where convection dominates (ε ≈ 0.1–0.3) and can deposit ≳10⁵¹ erg into the overlying envelope. This deposited energy drives a shock that accelerates the envelope to ≈10⁴ km s⁻¹, reproducing the observed kinetic energies and velocities of LGRB‑associated Ic supernovae.

A crucial aspect of the model is the synthesis of ⁵⁶Ni. When the inner flow reaches temperatures ≳5 × 10⁹ K, silicon burning proceeds rapidly, producing ⁵⁶Ni on a timescale of seconds. Because the same convective motions that transport energy also mix material, the freshly forged nickel is carried outward and mixed with a much larger mass of unburned ejecta over tens of seconds. The model predicts nickel masses of order 0.1–0.5 M_⊙, consistent with the ∼0.3 M_⊙ inferred from observed light curves.

Parameter sensitivity is examined in detail. The convective mixing length ℓ_mix, the viscous parameter α, and the specific angular momentum j of the infalling envelope jointly determine whether convection can outpace advection. Too large a j inflates the disk, weakening convection; too small a j leads to direct plunge of material into the black hole, reducing the available accretion power for the envelope. An optimal range of j yields a compact, hot, convectively unstable flow that maximizes energy transfer.

The authors acknowledge the limitations of their approach: the model is one‑dimensional, neglects magnetic fields, jet–envelope interaction, and three‑dimensional instabilities that could alter the efficiency of energy transport. Nevertheless, the analytic framework provides clear, testable predictions. Future work should involve multidimensional magnetohydrodynamic simulations to verify the convective efficiency and to explore how the jet may modify the convective pattern. Observationally, precise measurements of nickel‑to‑iron ratios, explosion asymmetries, and the timing between the γ‑ray burst and the supernova rise can be used to discriminate this mechanism from alternatives.

In summary, the paper argues that the accretion energy released in a collapsar can, via convection, both power a ∼10⁵¹ erg supernova shock and synthesize the required ⁵⁶Ni, offering a unified explanation for the coexistence of LGRBs and luminous Type Ic supernovae. This mechanism complements jet‑driven models and highlights the importance of inner‑disk physics in shaping the observable properties of the most energetic stellar explosions.