On the existence of a luminosity threshold of GRB jets in massive stars

TL;DR

This study investigates the minimum jet luminosity needed for successful gamma-ray burst (GRB) jet emergence in massive stars, considering progenitor structure, and explores how supernova shocks influence this threshold through simulations.

Contribution

It introduces an analytic and simulation-based estimate of the luminosity threshold for GRB jets, accounting for progenitor properties and supernova shock effects.

Findings

Threshold luminosity depends on progenitor mass and metallicity.

Supernova shock waves can lower the jet luminosity threshold.

Jets near the threshold may produce low-luminosity transients like llGRBs or XRFs.

Abstract

Motivated by the many associations of $\gamma$-ray bursts (GRBs) with energetic supernova (SN) explosions, we study the propagation of relativistic jets within the progenitor star in which a SN shock wave may be launched briefly before the jets start to propagate. Based on analytic considerations and verified with an extensive set of 2D axisymmetric relativistic hydrodynamic simulations, we have estimated a threshold intrinsic jet luminosity, $L_{\rm j}^{\rm thr}$, for successfully launching a jet. This threshold depends on the structure of the progenitor and, thus, it is sensible to its mass and to its metallicity. For a prototype host of cosmological long GRBs, a low-metallicity star of 35$\,M_{\odot}$, it is $L_{\rm j}^{\rm thr} \simeq 1.35\times 10^{49}\,$erg$\,$s$^{-1}$. The observed equivalent isotropic $\gamma$-ray luminosity, $L_{\rm \gamma,iso,BO} \simeq 4 \epsilon_\gamma L_{\rm j} \theta_{\rm BO}^{-2}$, crucially depends on the jet opening angle after breakout, $\theta_{\rm BO}$, and on the efficiency for converting the intrinsic jet luminosity into $\gamma$-radiation, $\epsilon_\gamma$. Highly energetic jets can produce low-luminosity events if either their opening angle after the breakout is large, which is found in our models, or if the conversion efficiency of kinetic and internal energy into radiation is low enough. Beyond this theoretical analysis, we show how the presence of a SN shock wave may reduce this luminosity threshold by means of numerical simulations. We foresee that the high-energy transients released by jets produced near the luminosity threshold will be more similar to llGRBs or XRFs than to GRBs.