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We have computed numerical supernova remnant (SNR) models for which the emission spectrum is time integrated over the evolution of the remnant. The time integrated spectrum represents the total number of photons emitted by the remnant over its life in the range 0 to 10 keV at a spectral resolution of 10 eV. As such, the spectrum contains a wealth of information about the emission characteristics of an SNR during its multifaceted evolution. Of great utility, the time integrated spectrum can be used to construct the X-ray surface brightness of a galaxy containing a steady state population of SNRs. Comparison with X-ray observations then offers a means of determining an effective diffuse interstellar medium density in galaxies. Previous estimates of the surface brightness contribution from SNRs, limited by X-ray observations, marginally threaten or eliminate popular ideas concerning the diffuse interstellar medium density in galaxies. We have performed such an analysis for the Milky Way as well as for M101, NGC3184, NGC4395, NGC4736, and NGC5055 using three different effective diffuse medium densities as a prelude to a more advanced study. Estimates of the X-ray surface brightness in the halo of the Galaxy, and ROSAT observations of the other galaxies are compared to the expected X-ray surface brightness of remnants in each of the galaxies.
