Thin shell formation in radiative shocks. 1: Supernova remnants in low-density media

This paper explores the onset of thin-shell formation in interstellar shocks associated with supernova explosions. We outline a simple but useful scheme that indicates the time at which thin shell formation begins for supernova remnants (SNRs) evolving in a range of interstellar environments, extending the previous analytical models to arbitrary power-law density media. The result depends on the gas cooling properties and the shock velocity and radius. This is then applied to the specific case of SNRs in low-density media. The procedure for defining the time for the onset of shell formation, tsf, equates the value of the adiabat, kappa = p/rhogamma, to zero using the known time dependence of the shock radius and velocity. For the case of a power-law density ambient medium of the form rho(r) = Br-omega, it is found that shell formation can be prevented when the ambient density drops faster than a critical rate. For a cooling function of the form Lambda = Lambda0 taubeta, with beta = -0.5 (appropriate for line cooling), shell formation never occurs for omega greater than or equal to 9/5. The shell formation time is then computed for spherical shocks in a power-law density medium. For omega = 0, the onset of shell formation is found to be at tsf approx. equal to 2.87 x 104 E513/14 n0 exp -4.7 yr, which agrees well with previous estimates derived by other means. We compare the analytical shell formation time with the results of detailed numerical models for omega = 0 and three different ambient densities and find good agreement. The extension of the criterion for the onset of thin shell formation using the ratio of cooling to swept-up column density is also described. This method provides a useful approximation for cases when the exact solution is not known.