Magnetic acceleration of ultra-relativistic jets in gamma-ray burst sources

Abstract

We present a relativistic-MHD numerical study of axisymmetric, magnetically driven jets with parameters applicable to gamma-ray burst (GRB) flows. We also present analytic expressions for the asymptotic jet shape and other flow parameters that agree very well with the numerical results. All current-carrying outflows exhibit self-collimation and consequent acceleration near the rotation axis, but unconfined outflows lose causal connectivity across the jet and therefore do not collimate or accelerate efficiently in their outer regions. Magnetically accelerated jets confined by an external pressure that varies with distance with a power-law index < 2 assume a paraboloidal shape and have an acceleration efficiency > 50%. They attain Lorentz factors > 30 on scales 10^9-3x10^10 cm, consistent with the possibility that short/hard GRB jets are accelerated on scales where they can be confined by moderately relativistic winds from accretion discs, and > 100 on scales 10^10-10^12 cm, consistent with the possibility that long/soft GRB jets are accelerated within the envelopes of collapsing massive stars. We also find that the Lorentz factor of a magnetically accelerated jet is approximately inversely proportional to the opening half-angle of the poloidal streamlines. This implies that the gamma-ray emitting components of GRB outflows are very narrow, with a half-angle < 1 degree in regions where the Lorentz factor exceeds 100, and that the afterglow light curves of these components would either exhibit a very early jet break or show no jet break at all.