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 u seful scheme that indicates the time at which thin shell formation beg ins for supernova remnants (SNRs) evolving in a range of interstellar environments, extending the previous analytical models to arbitrary po wer-law density media. The result depends on the gas cooling propertie s and the shock velocity and radius. This is then applied to the speci fic case of SNRs in low-density media. The procedure for defining the time for the onset of shell formation, t(sf), equates the value of the adiabat, kappa = p/rho(gamma), to zero using the known time dependenc e of the shock radius and velocity. For the case of a power-law densit y ambient medium of the form rho(r) = Br--omega, it is found that shel l formation can be prevented when the ambient density drops faster tha n a critical rate. For a cooling function of the form Lambda = Lambda( 0) T-beta, with beta = -0.5 (appropriate for line cooling), shell form ation never occurs for omega greater than or equal to 9/5. The shell f ormation time is then computed for spherical shocks in a power-law den sity medium. For omega = 0, the onset of shell formation is found to b e at t(sf) similar or equal to 2.87 x 10(4)E(51)(3/14)n(0)(-4/7) yr, w hich agrees well with previous estimates derived by other means. We co mpare 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.