Limits on supernova rates and interstellar densities from X-ray observations of M101

Measurements of the X-ray surface brightness of a face-on disk galaxy M101 have previously been used to place upper limits on the power radiated by a hot corona. Such analysis constrains the effective density of the disk; either it must be so low that the remnants drive a fast hot wind (low radiated power), or so high that the remnant temperature at overlap is low (low X-ray power). These X-ray measurements are here used to constrain the properties of the population of supernova remnants evolving in the disk. This adds a further constraint since young remnants evolving in higher density radiate more of their energy in X-rays, whether or not they eventually overlap to generate a hot corona. The strength of this second limit depends strongly on the density history of the remnants (e.g., evaporative vs. nonevaporative evolution) and on the assumed supernova rate. For evaporative evolution the analysis rules out the McKee (1977) and Ostriker (1977) interstellar medium model in particular and evaporative evolution in general unless the supernova rate is at least several times lower than current expectations. For standard Sedov evolutions, the density limit marginally admits 0.2/cu cm, a popular alternative to the McKee and Ostriker model.