A Self-Similar Solution for the Propagation of a Relativistic Shock in an Exponential Atmosphere

Details A Self-Similar Solution for the Propagation of a Relativistic Shock in an Exponential Atmosphere A Self-Similar Solution for the Propagation of a Relativistic Shock in an Exponential Atmosphere

2002-03-13

arxiv.org/abs/astro-ph/0203208v1

Astronomy and Astrophysics

Astrophysics

ApJL in press

Scientific paper

10.1086/340667

We derive a fully relativistic, self-similar solution to describe the propagation of a shock along an exponentially decreasing atmosphere, in the limit of very large Lorentz factor. We solve the problem in planar symmetry and compute the acceleration of the shock in terms of the density gradient crossed during its evolution. We apply our solution to the acceleration of shocks within the atmosphere of a HyperNova, and show that velocities consistent with the requirements of GRB models can be achieved with exponential atmospheres spanning a wide density range.

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