Letter to the Editor

Dynamics and stability of relativistic gamma-ray-bursts blast waves

¹ Centre for Plasma Astrophysics, Celestijnenlaan 200B, 3001 Heverlee, K.U. Leuven, Belgium
² FOM-Institute for Plasma Physics Rijnhuizen, Nieuwegein, The Netherlands
³ Astronomical Institute, Utrecht University, The Netherlands e-mail: [zakaria.meliani;rony.keppens]@wis.kuleuven.be

Received: 18 July 2010
Accepted: 3 September 2010

Abstract

Aims. In gamma-ray-bursts (GRBs), ultra-relativistic blast waves are ejected into the circumburst medium. We analyse in unprecedented detail the deceleration of a self-similar Blandford-McKee blast wave from a Lorentz factor 25 to the nonrelativistic Sedov phase. Our goal is to determine the stability properties of its frontal shock.

Methods. We carried out a grid-adaptive relativistic 2D hydro-simulation at extreme resolving power, following the GRB jet during the entire afterglow phase. We investigate the effect of the finite initial jet opening angle on the deceleration of the blast wave, and identify the growth of various instabilities throughout the coasting shock front.

Results. We find that during the relativistic phase, the blast wave is subject to pressure-ram pressure instabilities that ripple and fragment the frontal shock. These instabilities manifest themselves in the ultra-relativistic phase alone, remain in full agreement with causality arguments, and decay slowly to finally disappear in the near-Newtonian phase as the shell Lorentz factor drops below 3. From then on, the compression rate decreases to levels predicted to be stable by a linear analysis of the Sedov phase. Our simulations confirm previous findings that the shell also spreads laterally because a rarefaction wave slowly propagates to the jet axis, inducing a clear shell deformation from its initial spherical shape. The blast front becomes meridionally stratified, with decreasing speed from axis to jet edge. In the wings of the jetted flow, Kelvin-Helmholtz instabilities occur, which are of negligible importance from the energetic viewpoint.

Conclusions. Relativistic blast waves are subject to hydrodynamical instabilities that can significantly affect their deceleration properties. Future work will quantify their effect on the afterglow light curves.