Impulsive Acceleration of Strongly Magnetized Relativistic Flows

Abstract

The strong variability of magnetic central engines of AGN and GRBs may result in highly intermittent strongly magnetized relativistic outflows. We find a new magnetic acceleration mechanism for such impulsive flows that can be much more effective than the acceleration of steady-state flows. This impulsive acceleration results in kinetic-energy-dominated flows at astrophysically relevant distances from the central source. For a spherical flow, a discrete shell ejected from the source over a time t_0 with Lorentz factor Gamma~1 and initial magnetization sigma_0 = B_0^2/(4 pi rho_0 c^2) >> 1 quickly reaches a typical Lorentz factor Gamma ~ sigma_0^{1/3} and magnetization sigma ~ sigma_0^{2/3} at the distance R_0 ~ ct_0. At this point the magnetized shell of width Delta ~ R_0 in the lab frame loses causal contact with the source and continues to accelerate by spreading significantly in its own rest frame. The expansion is driven by the magnetic pressure gradient and leads to relativistic relative velocities between the front and back of the shell. While the expansion is roughly symmetric in the center of momentum frame, in the lab frame most of the energy and momentum remain in a region (or shell) of width Delta ~ R_0 at the head of the flow. This acceleration proceeds as Gamma ~ (sigma_0 R/R_0)^{1/3} and sigma ~ sigma_0^{2/3} (R/R_0)^{-1/3} until reaching a coasting radius R_c ~ R_0 sigma_0^2 where the kinetic energy becomes dominant: Gamma ~ sigma_0 and sigma ~ 1 at R_c. Then the shell starts coasting and spreading (radially) causing its magnetization to drop as sigma ~ R_c/R at R>R_c. Given the typical variability time-scales of AGN and GRBs, the magnetic acceleration in these sources is a combination of the quasi-steady-state collimation acceleration close to the source and the impulsive acceleration further out. The interaction with the external medium is briefly discussed.