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**Session 44 - The Local Diffuse ISM.**

*Display session, Tuesday, June 11*

*Great Hall, *

## [44.10] Adiabatic Expansion of Supernova Remnants - An Explicit, Analytical Approximation in Two Dimensions

*W. Maciejewski, R. L. Shelton, D. P. Cox (U. Wisconsin, Madison)*
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.

**Program
listing for Tuesday**