On the sideways expansion of relativistic non-spherical shocks and GRB afterglows

TL;DR

This paper investigates the sideways expansion of relativistic non-spherical shocks in gamma-ray burst afterglows, finding that relativistic effects suppress lateral expansion unless the shock is extremely collimated or becomes mildly relativistic.

Contribution

It demonstrates that relativistic motion effectively halts lateral expansion in non-spherical shocks unless the shock is highly collimated or mildly relativistic.

Findings

Relativistic shocks with opening angles > 1/Γ² show minimal sideways expansion.

Lateral expansion becomes significant only when shocks are mildly relativistic.

Relativistic motion 'freezes' the lateral dynamics of the shock front.

Abstract

Expansion of non-spherical relativistic blast waves is considered in the Kompaneets (the thin shell) approximation. We find that the relativistic motion effectively "freezes out" the lateral dynamics of the shock front: only extremely strongly collimated shocks, with the opening angles $\Delta \theta \leq 1/\Gamma^2$, show appreciable modification of profiles due to sideways expansion. For less collimated profiles the propagation is nearly ballistic; the sideways expansion of relativistic shock becomes important only when they become mildly relativistic.