Trans‐Relativistic Blast Waves in Supernovae as Gamma‐Ray Burst Progenitors

Abstract

We investigate the acceleration of shock waves to relativistic velocities in the outer layers of exploding stars. By concentrating the energy of the explosion in the outermost ejecta, such trans-relativistic blast waves can serve as the progenitors of gamma-ray bursts (GRBs); in particular, the "baryon-loading" problem that plagues many models of GRBs is circumvented. Postshock acceleration is effective in boosting the kinetic energy in relativistic ejecta. We present physically motivated analytic expressions to describe trans-relativistic blast waves in supernovae, and we validate these expressions against numerical simulations of test problems. Investigating the effect of stellar structure on mass ejection, we find that relativistic ejecta are enhanced in more centrally condensed envelopes, e.g., for radiative envelopes, when the luminosity approaches the Eddington limit. Convenient formulae are presented with which to estimate the production of relativistic ejecta from a given progenitor. We apply our analytic and numerical methods to a model of SN 1998bw, finding significantly enhanced relativistic ejecta compared to previous studies. We propose that GRB 980425 is associated with SN 1998bw and may have resulted from an approximately spherical explosion producing ~10 -6 M ☉ of mildly relativistic ejecta with mean Lorentz factor ~ 2, which then interacted with a dense circumstellar wind with a mass-loss rate of approximately a few times 10 -4 M ☉ yr -1 . A highly asymmetric explosion is not required. An extreme model of "hypernova" explosions in massive stars is able to account for the energetics and relativistic ejecta velocities required by many of the observed cosmological GRBs. However, the most energetic bursts require asymmetric expulsion of ejecta, perhaps caused by rotationally flattened progenitors. We present simplified models and simulations of explosions resulting from accretion-induced collapse of white dwarfs and phase transitions of neutron stars. While we find increased energies in relativistic ejecta compared to previous studies, these explosions are unlikely to be observed at cosmological distances with current detectors, unless extreme explosion energies and asymmetries are invoked.