We propose a simple, analytical approximation for an adiabatic shock wave propagating in an exponentially stratified ambient medium. We aim to provide an effective tool for exploring the parameter space of 2-dimensional numerical models of supernova remnants (SNRs). We start from Kompaneets's (1960, Soviet Phys. Doklady, 5, 46) axisymmetric generalization of Sedov's spherically symmetric problem, to which he derived an implicit solution. We notice that the SNR shape in his solution can be closely approximated as an ellipsoid. In this case, an explicit solution for the size, eccentricity and expansion velocity of the remnant can be found. Our results are in excellent agreement with Kompaneets's solution, even when the ambient density varies across the remnant by factors as large as 1000. Beyond that, the blowout occurs, and Kompaneets's assumptions no longer hold. The remnant shapes are remarkably close to spherical for moderate density gradients. Using Kahn's cooling law (alpha T(-1/2) ) we derived a formula to estimate how long it takes for a cold shell to form. Even a small gradient in ambient density causes this time to vary substantially within a single remnant, so that for a period the H I shell will be only partially formed. To demonstrate how our approximation can be used, the parameter space for models of the supernova remnant W44 is explored.
American Astronomical Society Meeting Abstracts #188
- Pub Date:
- May 1996