Self-similar ultrarelativistic jetted blast wave

Following a suggestion that a directed relativistic explosion may have a universal intermediate asymptotic, we derive a self-similar solution for an ultrarelativistic jetted blast wave. The solution involves three distinct regions: an approximately paraboloid head where the Lorentz factor γ exceeds ∼ 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 converges inward toward the axis. Most (∼80%) of the energy lies well beyond the leading, head region. Here, a radial cross section shows a maximal γ (separating the core and the envelope), a sign reversal in u, and a minimal γ, at respectively ∼1/6, ∼1/4, and ∼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 γ-ray burst.