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We model the size distribution of supernova remnants to infer the surroundingISM density. Using simple, yet standard SNR evolution models, we find that thedistribution of ambient densities is remarkably narrow; either the standardassumptions about SNR evolution are wrong, or observable SNRs are biased to anarrow range of ambient densities. We show that the size distributions areconsistent with log-normal, which severely limits the number of modelparameters in any SNR population synthesis model. Simple Monte Carlosimulations demonstrate that the size distribution is indistinguishable fromlog-normal when the SNR sample size is less than 600. This implies that theseSNR distributions provide only information on the mean and variance, yieldingadditional information only when the sample size grows larger than $\sim{600}$SNRs. To infer the parameters of the ambient density, we use Bayesianstatistical inference under the assumption that SNR evolution is dominated bythe Sedov phase. In particular, we use the SNR sizes and explosion energies toestimate the mean and variance of the ambient medium surrounding SNRprogenitors. We find that the mean ISM particle density around our sample ofSNRs is $\mu_{\log{n}} = -1.33$, in $\log_{10}$ of particles per cubiccentimeter, with variance $\sigma^2_{\log{n}} = 0.49$. If interpreted at facevalue, this implies that most SNRs result from supernovae propagating in thewarm, ionized medium. However, it is also likely that either SNR evolution isnot dominated by the simple Sedov evolution or SNR samples are biased to thewarm, ionized medium (WIM).

Inferring Properties of the ISM from Supernova Remnant Size Distributions