Which physical parameters can be inferred from the emission variability of relativistic jets?

¹ Max-Planck-Institut für Astrophysik, Postfach 1312, 85741 Garching, Germany e-mail: [pere;maa]@mpa-garching.mpg.de
² Departamento de Astronomía y Astrofísica, Universidad de Valencia, 46100 Burjassot, Spain
³ Max-Planck-Institut für extraterrestrische Physik, Postfach 1603, 85740 Garching, Germany

Received: 9 April 2005
Accepted: 22 June 2005

Abstract

We present results of a detailed numerical study and theoretical analysis of the dynamics of internal shocks in relativistic jets and the non-thermal flares associated with these shocks. In our model internal shocks result from collisions of density inhomogeneities (shells) in relativistic jet flows. We find that the merged shell resulting from the inelastic collision of shells has a complicated internal structure due to the non-linear dynamics of the interaction. Furthermore, the instantaneous efficiency for converting kinetic energy into thermal energy is found to be almost twice as high as theoretically expected during the period of significant emission. The Lorentz factors of the internal shocks are correlated with the initial inertial masses of the shells. 
Because of the complexity of the non-linear evolution the merged shell becomes very inhomogeneous and simple one-zone models are inadequate to extract physical parameters of the emitting region from the resulting light curves. In order to improve on these one-zone approximations, we propose a novel way of analyzing the space-time properties of the emission. Based on these properties we construct an analytic model of non-thermal flares which can be used to constrain some (unobservable) physical parameters of the internal shocks. These are the ratio of the Lorentz factors between the forward and the reverse shock (caused by the shell collision), and the shell crossing times of these shocks. The analytic model is validated by applying it to the synthetic light curves computed from our models. It can equally well be applied to observations.