A New $\Sigma-D$ Relation and Its Application to the Galactic Supernova   Remnant Distribution
  Technological advances in radio telescopes and X-ray instruments over the last 20 years have greatly increased the number of known supernova remnants (SNRs) and led to a better determination of their properties. In particular, more SNRs now have reasonably determined distances. However, many of these distances were determined kinematically using old rotation curves (based on $R_{\sun} = 10$ kpc and $V_{\sun} = 250$ km/s). A more modern rotation curve (based on $R_{\sun} = 8.5$ kpc and $V_{\sun} = 220$ km/s) is used to verify or recalculate the distances to these remnants. We use a sample of 36 shell SNRs (37 including Cas A) with known distances to derive a new radio surface brightness-to-diameter ($\Sigma-D$) relation. The slopes derived here ($\beta = -2.64$ including Cas A, $\beta = -2.38$ without Cas A) are significantly flatter than those derived in previous studies. An independent test of the accuracy of the $\Sigma-D$ relation was performed by using the extragalactic SNRs in the Large and Small Magellanic Clouds. The limitations of the $\Sigma-D$ relation and the assumptions necessary for its use are discussed. A revised Galactic distribution of SNRs is presented based on the revised distances as well as those calculated from this $\Sigma-D$ relation. A scaling method is employed to compensate for observational selection effects by computing scale factors based on individual telescope survey sensitivities, angular resolutions and sky coverage. The radial distribution of the surface density of shell SNRs, corrected for selection effects, is presented and compared to previous works. 
Gary L. Case and Dipen Bhattacharya (U. C. Riverside)