Supercriticality of the same kind as that in a nuclear pile can take place in high-energy astrophysical objects producing a number of impressive effects. For example, it could cause an explosive release of the energy of a cloud of ultrarelativistic protons into radiation. More certainly, supercriticality should be responsible for energy dissipation of very energetic relativistic fluids such as ultrarelativistic shocks in gamma-ray bursts and jets in active galactic nuclei (AGNs). In this case, the photon breeding process operates. It is a kind of the converter mechanism with the high-energy photons and e^+ e^- pairs converting into each other via pair production and inverse Compton scattering. Under certain conditions, which should be satisfied in powerful AGNs, the photon breeding mechanism becomes supercritical: the high-energy photons breed exponentially until their feedback on the fluid changes its velocity pattern. Then the system comes to a self-adjusting near-critical steady state. Monte-Carlo simulations with the detailed treatment of particle propagation and interactions demonstrate that a jet with the Lorentz factor Gamma ~ 20 can radiate away up to a half of its total energy and for Gamma=40 the radiation efficiency can be up to 80 per cent. Outer layers of the jet decelerate down to a moderate Lorentz factor 2-4, while the spine of the jet has the final Lorentz factor in the range 10-20 independently on the initial Gamma. Such sharp deceleration under the impact of radiation must cause a number of interesting phenomena such as formation of internal shocks and an early generation of turbulence.
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