Trans-relativistic blast waves in supernovae as gamma-ray burst progenitors

We investigate the acceleration of shock waves to relativistic velocities i n the outer layers of exploding stars. By concentrating the energy of the e xplosion in the outermost ejecta, such trans-relativistic blast waves can s erve as the progenitors of gamma-ray bursts (GRBs); in particular, the "bar yon-loading" problem that plagues many models of GRBs is circumvented. Post shock acceleration is effective in boosting the kinetic energy in relativis tic ejecta. We present physically motivated analytic expressions to describ e trans-relativistic blast waves in supernovae, and we validate these expre ssions against numerical simulations of test problems. Investigating the ef fect of stellar structure on mass ejection, we find that relativistic eject a are enhanced in more centrally condensed envelopes, e.g., for radiative e nvelopes, when the luminosity approaches the Eddington limit. Convenient fo rmulae 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, findin g significantly enhanced relativistic ejecta compared to previous studies. We propose that GRB 980425 is associated with SN 1998bw and may have result ed from an approximately spherical explosion producing similar to 10(-6) M- . of mildly relativistic ejecta with mean Lorentz factor (T) over bar simil ar to 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 asymmetr ic explosion is not required. An extreme model of "hypernova" explosion sin massive stars is able to account for the energetics and relativistic eject a velocities required by many of the observed cosmological GRBs. However, t he most energetic bursts require asymmetric expulsion of ejecta, perhaps ca used by rotationally flattened progenitors. We present simplified models an d simulations of explosions resulting from accretion-induced collapse of wh ite dwarfs and phase transitions of neutron stars. While we find increased energies in relativistic ejecta compared to previous studies, these explosi ons are unlikely to be observed at cosmological distances with current dete ctors, unless extreme explosion energies and asymmetries are invoked.