# SELF-SIMILAR ULTRARELATIVISTIC JETTED BLAST WAVE Academic Article

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### 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 $\sim1/2$ of its maximal, nose value; a geometrically self-similar, expanding envelope slightly narrower than a paraboloid; and an axial core in which the radial flow $U$ converges inward towards the axis. Most ($\sim 80\%$) of the energy lies well beyond the head. 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 $\sim 1/6$, $\sim1/4$, and $\sim3/4$ 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.

### publication date

• December 15, 2015