Gamma-ray burst afterglows from transrelativistic blast wave simulations

Abstract

We present a study of the intermediate regime between ultrarelativistic and non-relativistic flow for gamma-ray burst afterglows. The hydrodynamics of spherically symmetric blast waves is numerically calculated using the AMRVAC adaptive mesh refinement code. Spectra and light curves are calculated using a separate radiation code that, for the first time, links a parametrization of the microphysics of shock acceleration, synchrotron self-absorption and electron cooling to a high-performance hydrodynamic simulation. For the dynamics, we find that the transition to the non-relativistic regime generally occurs later than expected, the Sedov–Taylor solution overpredicts the late-time blast wave radius and the analytical formula for the blast wave velocity from Huang, Dai & Lu overpredicts the late-time velocity by a factor of 4/3. Also, we find that the lab frame density directly behind the shock front divided by the fluid Lorentz factor squared remains very close to four times the unshocked density, while the effective adiabatic index of the shock changes from relativistic to non-relativistic. For the radiation, we find that the flux may differ up to an order of magnitude depending on the equation of state that is used for the fluid and that the counterjet leads to a clear rebrightening at late times for hard-edged jets. Simulating GRB 030329 using predictions for its physical parameters from the literature leads to spectra and light curves that may differ significantly from the actual data, emphasizing the need for very accurate modelling. Predicted light curves at low radio frequencies for a hard-edged jet model of GRB 030329 with opening angle 22◦ show typically two distinct peaks, due to the combined effect of jet break, non-relativistic break and counterjet. Spatially resolved afterglow images show a ring-like structure.