Updated radio $\Sigma-D$ relation for Galactic supernova remnants -- II

Abstract

In this paper we present the updated empirical radio surface-brightness-to-diameter ($\Sigma$--$D$) relation for Galactic supernova remnants (SNRs) calibrated using $110$ SNRs with reliable distances. We apply orthogonal fitting procedure and kernel density smoothing in $\Sigma-D$ plane and compare the results with the latest theoretical $\Sigma-D$ relations derived from simulations of radio evolution of SNRs. We argue that the best agreement between the empirical and simulated $\Sigma-D$ relations is achieved if the mixed-morphology SNRs and SNRs of both, low brightness and small diameter, are filtered out from the calibration sample. The distances to $5$ newly discovered remnants and $27$ new candidates for shell SNRs are estimated from our full and filtered calibration samples.