On the sideways expansion of relativistic non-spherical shocks and gamma-ray burst afterglows

Authors

  • Maxim Lyutikov

    Corresponding author
    1. Department of Physics, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907-2036, USA
      E-mail: lyutikov@purdue.edu
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E-mail: lyutikov@purdue.edu

ABSTRACT

Expansion of non-spherical relativistic blast waves is considered in the Kompaneets (the thin-shell) approximation. We find that relativistic motion effectively ‘freezes out’ the lateral dynamics of the shock front: only extremely strongly collimated shocks, with opening angles Δθ≤ 1/Γ2, show appreciable modification of profiles due to sideways expansion. For less collimated profiles, the propagation is nearly ballistic; the sideways expansion of relativistic shocks becomes important only when they become mildly relativistic. Even though the post-shock pressure is equilibrated downstream on the sound crossing time-scale, this does not mean that the shape of the shock changes on the post-shock sound crossing time-scale.

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