THE MAXIMUM ENERGY OF ACCELERATED PARTICLES IN RELATIVISTIC COLLISIONLESS SHOCKS

Abstract

The afterglow emission from gamma-ray bursts (GRBs) is usually interpreted as\nsynchrotron radiation from electrons accelerated at the GRB external shock,\nthat propagates with relativistic velocities into the magnetized interstellar\nmedium. By means of multi-dimensional particle-in-cell simulations, we\ninvestigate the acceleration performance of weakly magnetized relativistic\nshocks, in the magnetization range 0<sigma<1e-1. The pre-shock magnetic field\nis orthogonal to the flow, as generically expected for relativistic shocks. We\nfind that relativistic perpendicular shocks propagating in electron-positron\nplasmas are efficient particle accelerators if the magnetization is sigma<1e-3.\nFor electron-ion plasmas, the transition to efficient acceleration occurs for\nsigma<3e-5. Here, the acceleration process proceeds similarly for the two\nspecies, since the electrons enter the shock nearly in equipartition with the\nions, as a result of strong pre-heating in the self-generated upstream\nturbulence. In both electron-positron and electron-ion shocks, we find that the\nmaximum energy of the accelerated particles scales in time as t^(1/2). This\nscaling is shallower than the so-called (and commonly assumed) Bohm limit, and\nit naturally results from the small-scale nature of the Weibel turbulence\ngenerated in the shock layer. In magnetized plasmas, the energy of the\naccelerated particles increases until it reaches a saturation value that scales\nwith the magnetization as sigma^(-1/4). Further energization is prevented by\nthe fact that the self-generated turbulence is confined within a finite region\nof thickness proportional to sigma^(-1/2) around the shock. Our results can\nprovide physically-grounded inputs for models of non-thermal emission from a\nvariety of astrophysical sources, with particular relevance to GRB afterglows.\n