Interaction of a magnetized shell with an ambient medium: limits on impulsive magnetic acceleration

Abstract

The interaction of relativistic magnetized ejecta with an ambient medium is studied for a range of structures and magnetization of the unshocked ejecta. We particularly focus on the effect of the ambient medium on the dynamics of an impulsive, high-sigma shell. It is found that for sufficiently high values of the initial magnetization $\sigma_0$ the evolution of the system is significantly altered by the ambient medium well before the shell reaches its coasting phase. The maximum Lorentz factor of the shell is limited to values well below $\sigma_0$; for a shell of initial energy $E=10^{52}E_{52}$ ergs and size $r_0=10^{12}T_{30}$ cm expelled into a medium having a uniform density $n_i$ we obtain $\Gamma_{\rm max}\simeq180(E_{52}/T_{30}^3 n_i)^{1/8}$ in the high sigma limit. The reverse shock and any internal shocks that might form if the source is fluctuating are shown to be very weak. The restriction on the Lorentz factor is more severe for shells propagating in a stellar wind. Intermittent ejection of small sub-shells doesn't seem to help, as the shells merge while still highly magnetized. Lower sigma shells start decelerating after reaching the coasting phase and spreading away. The properties of the reverse shock then depend on the density profiles of the coasting shell and the ambient medium. For a self-similar cold shell the reverse shock becomes strong as it propagates inwards, and the system eventually approaches the self-similar solution derived recently by Nakamura \& Shigeyama.