Giuseppe Palma
Hyper-relativistic Blast Waves from Gamma-Ray Bursts

There is strong evidence that (long) GRBs involve flows of dense
shells thrown by a dying compact star at Lorentz factors > 10^2 -
10^3. When the ejecta impact on the relic stellar wind, a shock is
formed and begins to propagate into a decreasing atmosphere. This
circumstance leads, for sufficiently steep density profiles, to the
shock acceleration. Here, I will first present the self-similar
solution for a planar relativistic shock wave accelerating into an
exponential atmosphere, in both its unperturbed and linearly wrinkled
regimes. Second, I will show numerical solutions to the shock
non-linear evolution for two classes of perturbing upstream
atmospheres. Finally, I will discuss the departure of the shock speed
in an arbitrary atmosphere from the quasi-self-similar prediction, and
I will derive analytically a statistical description of the
geometrical effects on the discontinuity surface produced by a
turbulent ambient density.