Title: Inferring Properties of the ISM from Supernova Remnant Size Distributions,
Abstract: We model the size distribution of supernova remnants to infer the surrounding
ISM density. Using simple, yet standard SNR evolution models, we find that the
distribution of ambient densities is remarkably narrow; either the standard
assumptions about SNR evolution are wrong, or observable SNRs are biased to a
narrow range of ambient densities. We show that the size distributions are
consistent with log-normal, which severely limits the number of model
parameters in any SNR population synthesis model. Simple Monte Carlo
simulations demonstrate that the size distribution is indistinguishable from
log-normal when the SNR sample size is less than 600. This implies that these
SNR distributions provide only information on the mean and variance, yielding
additional information only when the sample size grows larger than $\sim{600}$
SNRs. To infer the parameters of the ambient density, we use Bayesian
statistical inference under the assumption that SNR evolution is dominated by
the Sedov phase. In particular, we use the SNR sizes and explosion energies to
estimate the mean and variance of the ambient medium surrounding SNR
progenitors. We find that the mean ISM particle density around our sample of
SNRs is $\mu_{\log{n}} = -1.33$, in $\log_{10}$ of particles per cubic
centimeter, with variance $\sigma^2_{\log{n}} = 0.49$. If interpreted at face
value, this implies that most SNRs result from supernovae propagating in the
warm, ionized medium. However, it is also likely that either SNR evolution is
not dominated by the simple Sedov evolution or SNR samples are biased to the
warm, ionized medium (WIM).