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We present the results of theoretical analysis and numerical simulations ofthe Weibel instability in two counter-streaming hot relativistic plasma flows,e.g. flows of electron-proton plasma having rest-mass density $\rho \sim10^{-4}\; \text{g}\, \text{cm}^{-3}$, Lorentz factors $\Gamma \sim 10$ andproper temperature $T \sim 10^{13}\; \text{K}$. The instability growth rate andthe filament size at the linear stage are found analytically, and are inqualitative agreement with results of three-dimensional particle-in-cellsimulations. In the simulations, incoherent synchrotron emission and pairphotoproduction in electromagnetic fields are taken into account. If the plasmaflows are dense, fast and/or hot enough, the overall energy of synchrotronphotons can be much larger than the energy of generated electromagnetic fields.Furthermore, a sizable number of positrons can be produced due to the pairphotoproduction in the generated magnetic field. We propose a rough criterionfor judging copious pair production and synchrotron losses. By means of thiscriterion we conclude that incoherent synchrotron emission and pair productionduring the Weibel instability can have implications for the collapsar model ofgamma-ray bursts.

Weibel instability in hot plasma flows with production of gamma-rays and electron-positron pairs