DYNAMICS OF ADIABATIC BLAST WAVES IN MEDIA OF FINITE MASS

A simple and general formulation is developed to describe the integrated properties of nonrelativistic adiabatic blast waves in media with a finite total mass, such as media with an exponentially decreasing density. Both impulsive and continuous energy injection are considered. Blast waves in such media eventually accelerate, and the shock separates from the swept up mass. As a result, these blast waves are not self-similar. Exact equations are derived which describe the mean radius and velocity of the swept up mass; approximate analytic solutions of these equations are generally accurate to within 10%, which is adequate for most astrophysical applications. We then present a modification of the Kompaneets approximation for the motion of the shock which incorporates the asymptotic behavior of the shock and is generally more accurate than the original Kompaneets approximation. Our discussion focuses on the case of spherically symmetric blast waves in order to facilitate comparison with accurate numerical results, but the generalization to axisymmetric blast waves is given also. Approximate analytic results are provided for a variety of density distributions, including exponential, Gaussian, and asymptotic power law. It is shown that if the density falls off more rapidly than r-7,3, then the shock reaches infinite distance in a finite time (neglecting relativistic effects). The shell of swept up gas is likely to be disrupted by Rayleigh-Taylor instability when energy is continuously supplied to the blast wave, as in the case of wind-blown bubbles.