Viscid and inviscid self-similar blast waves: Spherical, isothermal flows and inferences for supernova remnants

Abstract

We investigate the spherically symmetric, self-similar flow behind a blast wave from a point explosion in a medium whose density varies with distance asr−ω with the assumption that the flow is isothermal and viscid. If 0<ω<ω c where\(\omega _c = \tfrac{1}{9}[13 - (160)^{1/2} ]\) Lerche and Vasyliunas have shown in the inviscid situation that there exist two critical points in the flow speed-radial distance plane, and that all solutions are degenerate in that they pass through the lower critical point with thesame slope. The present paper shows that as the viscosity tends to zero, the viscid flow does not tend towards the inviscid flow pattern. Now the validity of adiabatic blast wave models has elsewhere been shown to be questionable for supernova remnants, and the inviscid blast wave models have also been shown to be inappropriate for supernova remnants. Taken together with these previous results, the results of the present calculations strongly suggest that the assumption of isothermal blast wave behavior of supernova remnants, either viscid or inviscid is not valid. Since the adiabatic blast wave models have elsewhere been shown to be inappropriate descriptions of supernova remnants, it is doubtful whether the self-similar property can be invoked at all in the case of supernova remnants.