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We report results from the analysis and modeling of data for the supernova remnant (SNR) W44. Spectral analysis of archival data from the Einstein Solid State Spectrometer, the ROSAT Position Sensitive Proportional Counter, and the Large Area Counters on {\it Ginga}, covering an energy range from 0.3 to 8~keV, indicates that the SNR can be described well using a nonequilibrium ionization model with temperature $\sim$0.8 keV, ionization timescale $\sim$9000 cm$^{-3}$ years, and elemental abundances close to the solar ratios. The column density toward the SNR is high: greater than 10$^{22}$ atoms cm$^{-2}$.
As has been known for some time, W44 presents a centrally peaked surface brightness distribution in the soft X-ray band while at radio wavelengths it shows a limb-brightened shell morphology, in contradiction to predictions of standard models (e.g., Sedov) for SNR evolution. We have investigated two different evolutionary scenarios which can explain the centered X-ray morphology of the remnant: (1) the White and Long (1991) model involving the slow thermal evaporation of clouds engulfed by the supernova blast wave as it propagates though a clumpy interstellar medium (ISM), and (2) a hydrodynamical simulation of a blast wave propagating through a homogeneous ISM, including the effects of radiative cooling. Both models can have their respective parameters tuned to reproduce approximately the morphology of the SNR. We find that, for the case of the radiative-phase shock model, the best agreement is obtained for an initial explosion energy in the range $(0.5 - 0.6) \times 10^{51}$~ergs and an ambient ISM density of between 1.5 and 2 cm$^{-3}$.
