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

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 an 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-j(thr), for successfully launching a jet. This threshold depends on the structure of the progenitor and, thus, it is sensitive to its mass and to its metallicity. For a prototype host of cosmological long GRBs, a low-metallicity star of 35 M-circle dot, it is L-j(thr) similar or equal to 1.35 x 10(49) erg s(-1). The observed equivalent isotropic gamma-ray luminosity, L-gamma,L- iso,L- BO similar or equal to 4 epsilon gamma L-j theta(-2)(BO), crucially depends on the jet opening angle after breakout, theta(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 an 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 X-ray flashes than to GRBs.