Weibel Instability in Hot Plasma Flows with the Production of Gamma-Rays and Electron–Positron Pairs

Abstract

We present the results of the theoretical analysis and numerical simulations of the Weibel instability in two counterstreaming hot relativistic plasma flows, for instance the flows of electron–proton plasmas with rest-mass densities , Lorentz factors , and proper temperatures . The instability growth rate and the filament size at the linear stage are found analytically and are in qualitative agreement with the results of three-dimensional particle-in-cell simulations. In the simulations, incoherent synchrotron emission and pair photoproduction in electromagnetic fields are taken into account. If the plasma flows are dense, fast, and hot enough, the overall energy of the synchrotron photons can be much higher than the energy of the generated electromagnetic fields. Furthermore, a sizable number of positrons can be produced due to the pair photoproduction in the generated magnetic field. We propose a rough criterion to judge copious pair production and considerable synchrotron losses. By means of this criterion, we conclude that the incoherent synchrotron emission and the pair production during the Weibel instability can have implications for the collapsar model of gamma-ray bursts.