Analytical and Monte Carlo results for the surface-brightness diameter   relationship in supernova remnants
  The surface brightness diameter relationship for supernovae remnants (SNRs) is explained by adopting a model of direct conversion of the flux of kinetic energy into synchrotron luminosity. Two laws of motion are adopted, a power law model for the radius-time relationship, and a model which uses the thin layer approximation. The fluctuations on the log-log surface diameter relationship are modeled by a Monte Carlo simulation. In this model a new probability density function for the density as function of the galactic height is introduced. 
L. Zaninetti
astro-ph.GA