On the existence of a reverse shock in magnetized gamma-ray burst ejecta

The role of magnetic fields in gamma-ray burst (GRB) flows remains controversial. The study of the early afterglow phases and, in particular, of the reverse shock dynamics and associated emission offers a promising probe of the magnetization of the ejecta. In this paper, we derive the conditions for the existence of a reverse shock in arbitrarily magnetized ejecta that decelerate and interact with the circumburst medium. Both constant and wind-like density profiles are considered. We show, in contrast to previous estimates, that ejecta with magnetization $\sigma_0\gtrsim$ 1 are not crossed by a reverse shock for a large fraction of the parameter space relevant to GRB flows. Allowing for shell spreading, there is always a relativistic or mildly relativistic reverse shock forming in $\sigma_0\lesssim$ 0.3 ejecta. From this, we conclude that the paucity of optical flashes, believed to be a distinctive signature of a reverse shock, may be explained by the existence of dynamically important magnetic fields in the ejecta