W. Maciejewski et Dp. Cox, Supernova remnant in a stratified medium: Explicit, analytical approximations for adiabatic expansion and radiative cooling, ASTROPHYS J, 511(2), 1999, pp. 792-797
We propose simple, explicit, analytical approximations for the kinematics o
f an adiabatic blast wave propagating in an exponentially stratified ambien
t medium and for the onset of radiative cooling, which ends the adiabatic e
ra. Our method, based on the Kompaneets implicit solution and the Kahn appr
oximation for the radiative cooling coefficient, gives straightforward esti
mates for the size, expansion velocity, and progression of cooling times ov
er the surface when applied to supernova remnants (SNRs). The remnant shape
is remarkably close to spherical for moderate density gradients, but even
a small gradient in ambient density causes the cooling time to vary substan
tially over the remnant's surface, so that for a considerable period there
will be a cold dense expanding shell covering only a part of the remnant. O
ur approximation provides an effective tool for identifying the approximate
parameters when planning two-dimensional numerical models of SNRs, the exa
mple of W44 being given in a subsequent paper.