Shock dynamics in relativistic jets
Abstract
We present a formalism of the dynamics of internal shocks in relativistic jets where the source has a timedependent injection velocity and massloss rate. The variation of the injection velocity produces a twoshock wave structure, the working surface, that moves along the jet. This new formalism takes into account the fact that momentum conservation is not valid for relativistic flows where the relativistic mass lost by radiation must be taken into account, in contrast to the classic regime. We find analytic solutions for the working surface velocity and radiated energy for the particular case of a step function variability of the injection parameters. We model two cases: a pulse of fast material and a pulse of slow material (with respect to the mean flow). Applying these models to gammaray burst light curves, one can determine the ratio of the Lorentz factors γ_{2}/γ_{1} and the ratio of the massloss rates dot{m}_2/dot{m}_1 of the upstream and downstream flows. As an example, we apply this model to the sources GRB 080413B and GRB 070318 and find the values of these ratios. Assuming a Lorentz factor γ_{1} = 100, we further estimate jet massloss rates between dot{m}_1 ∼ 10^{5} {and } 1 M_{odot } yr^{1}. We also calculate the fraction of the injected mass lost by radiation. For GRB 070318 this fraction is ∼7 per cent. In contrast, for GRB 080413B this fraction is larger than 50 per cent; in this case radiation losses clearly affect the dynamics of the internal shocks.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 April 2013
 DOI:
 10.1093/mnras/stt072
 arXiv:
 arXiv:1301.6204
 Bibcode:
 2013MNRAS.430.2703C
 Keywords:

 hydrodynamics;
 relativistic processes;
 shock waves;
 galaxies: jets;
 gammarays: general;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 13 pages, 9 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journal