A self-similar solution for a supernova explosion with allowance for accelerated relativistic particles

A self-similar solution to Sedov’s problem of a strong explosion in a homogeneous medium is generalized to the case of relativistic-particle generation in a supernova remnant; the particles are accelerated by Fermi’s mechanism at the shock front and in the perturbed post-shock region. Self-similarity takes place if the thickness of the prefront is small compared to its radius and if the pressure ratio of the relativistic and nonrelativistic components at the shock front is kept constant. In the presence of relativistic particles, the time dependence of the shock-front radius remains the same as that in their absence, but the plasma parameters in the inner perturbed region change appreciably. The shell of the matter raked up by the explosion is denser and thinner than that in the nonrelativistic case, the relativistic-particle pressure in the central region remains finite, and the nonrelativistic-gas pressure at the explosion center approaches zero. The influence of relativistic particles on the transition to the radiative phase of expansion of the supernova remnant and on its dynamics is studied. It is shown that relativistic particles can decrease several-fold the remnant radius at which the transition to the radiative phase occurs.