Modeling W44 as a Supernova Remnant in a Density Gradient, with a Partially Formed Dense Shell and Thermal Conduction in the Hot Interior

Abstract

(shortened version) We show that many observations of W44, a supernova remnant in the galactic plane at a distance of about 2500 pc, are remarkably consistent with the simplest realistic model. The model remnant is evolving in a smooth ambient medium of fairly high density, about 6 cm^-3 on average, with a substantial density gradient. At the observed time it has an age of about 20,000 years, consistent with the age of the associated pulsar, and a radius of 11 to 13 pc. Over most of the outer surface, radiative cooling has become important in the post shock gas; on the denser end there has been sufficient compression of the cooled gas to develop a very thin dense half shell of about 450 M_sun, supported against further compression by nonthermal pressure. The half shell has an expansion velocity of about 150 km s^-1, and is bounded on the outer surface by a radiative shock with that speed. We provide several analytic tools for the assembly of models of this type. We review the early evolution and shell formation analyses and their generalizations to evolution in a density gradient. We also calculate the density and temperature that should be present in the hot interior of a remnant with thermal conduction. We supply the van der Laan mechanism in a particularly useful form for the calculation of radio continuum from radiative remnants. Finally, we demonstrate a simple technique for estimating the optical emission expected. These tools are employed to choose parameters of models which we then explore with our 1d and 2d hydrocodes, providing, respectively, the detailed x-ray spectra and dynamical characteristics.