Particle acceleration and relativistic shocks

Abstract

Abstract.Observations of both gamma-ray burst sources and certain classes of active galaxy indicate the presence of relativistic shock waves and require the production of high energy particles to explain their emission. In this paper we first review the basic theory of shock waves in relativistic hydrodynamics and magneto-hydrodynamics, emphasising the astrophysically interesting cases. This is followed by an overview of the theory of particle acceleration at such shocks. Whereas, for diffusive acceleration at non-relativistic shocks, it is the compression ratio which fixes the energetic particle spectrum uniquely, acceleration at relativistic shocks is more complicated. In the absence of scattering, particles are simply 'compressed' as they pass through the shock front. This mechanism -called shock-drift acceleration -enhances the energy density in accelerated particles, but does so without changing the spectral index of upstream particles. Scattering due to MHD waves leads to multiple encounters between the particles and the shock front, producing an energetic particle population which depends on the properties of the shock front and the level and nature of particle scattering. We describe the method of matching the angular distributions of the upstream and downstream distributions at the shock front which leads to predictions of the spectral index. Numerical simulation of particle transport provides an alternative means of calculating spectral indices, and has recently been extended to cover ultra relativistic shocks. We review these calculations and summarise the applications to the astrophysics of relativistic jets and fireball models of gamma-ray-bursts.

Particle acceleration in rotating and shearing jets from AGN

“…Moreover, as a general mechanism this process is able to provide high energy particles, which are required as seed particles for the (localised) first-order Fermi acceleration widely believed to occur in relativistic jets (e.g. Drury 1983;Kirk & Duffy 1999). Particularly, in the beginning the injection of seed particles could naturally occur at the base of the jet due to centrifugal acceleration (cf.…”

A Kinetic Approach to Relativistic Shocks in Astrophysics

“…Indeed, in even the seemingly simple case of a postulated scattering in pitch angle alone in the presence of a perpendicular ambient magnetic field, Kirk and Schneider [5] and Kirk and Duffy (1999) had to resort to left-handed and right-handed eigenfunctions to effect even an approximate solution and the final approximate analysis had then to be performed numerically. An investigation of this pitch angle scattering situation has been given in considerable generality by Vietri [6] and Blasi and Vietri [4] and represents the most advanced solution of the shock diffusion equation available to date under the pitch angle scattering assumption.…”

“…As noted in Part I Kirk and Duffy [1] have stated that the de Hoffman-Teller reference frame is likely not to be of much direct application to the problem of highly relativistic beams because the allowable angles for the upstream magnetic field, as viewed from the rest frame of the shock, are typically O(1/Γ) with respect to the shock front plane. Thus, the probability is that the remaining part of the angular regime ahead of the shock [O(π − 1/Γ)] is the most appropriate situation, for which the ambient magnetic field can always be arranged to be perpendicular to the shock front.…”

“…Because the structure of F 0 enters the behavior of G then the determination of the balanced shock conditions is a very complex problem. Indeed, even in the MHD approach as discussed in Kirk and Duffy [1] the formidable problem of obtaining a relevant shock crossing balance was only recently addressed in a significant manner by Blasi and Vietri [4]. There is no good reason to suppose that the full boundary problem, including electric field fluctuations should be any easier-although future numerical calculations may point the way to a good approximation scheme.…”

“…This question is of considerably more than just pure academic interest. The review by Kirk and Duffy [1] emphasizes the fact that, to date, the description of such relativistic shocks has been handled as an MHD problem with, therefore, a prescribed equation of state and with test particle diffusion only. Indeed, the corresponding diffusion coefficient is kinematically given and, so far, appears to involve only pitch angle scattering in a momentum independent manner.…”