Self-similar ultra-relativistic jetted blast wave

Abstract

Following a suggestion that a directed relativistic explosion may have a universal intermediate asymptotic, we derive a self-similar solution for an ultra-relativistic jetted blast wave. The solution involves three distinct regions: an approximately paraboloid head where the Lorentz factor $\gamma$ exceeds $\sim 1/2$ of its maximal, nose value; a geometrically self-similar, expanding envelope slightly narrower than a paraboloid; and an axial core in which the (cylindrically, henceforth) radial flow $u$ converges inward towards the axis. Most ($\sim 80\%$) of the energy lies well beyond the leading, head region. Here, a radial cross section shows a maximal $\gamma$ (separating the core and the envelope), a sign reversal in $u$, and a minimal $\gamma$, at respectively $\sim 1/6$, $\sim 1/4$, and $\sim 3/4$ of the shock radius. The solution is apparently unique, and approximately agrees with previous simulations, of different initial conditions, that resolved the head. This suggests that unlike a spherical relativistic blast wave, our solution is an attractor, and may thus describe directed blast waves such as in the external shock phase of a $\gamma$-ray burst.

Revised version (discussion added) accepted by ApJ

References in corpus (2)

• The Dynamics and Afterglow Radiation of Gamma-Ray Bursts. I. Constant Density Medium
• AMRVAC and Relativistic Hydrodynamic simulations for GRB afterglow phases

Cited by in corpus (3)

• Off-Axis Emission of Short GRB Jets from Double Neutron Star Mergers and GRB 170817A
• Gamma-ray burst afterglow blast waves
• On the Deceleration and Spreading of Relativistic Jets I: Jet Dynamics