Distances, Radial Distribution and Total Number of Galactic Supernova Remnants

We present a table of 215 SNRs with distances. New distances are found to SNR G$51.26+0.11$ of $6.6 \pm 1.7$ kpc using HI absorption spectra, and to 5 other SNRs using maser/molecular cloud associations. We recalculate the distances and errors to all SNRs using a consistent rotation curve and provide errors where they were not previously estimated. This results in a significant distance revisions for 20 SNRs. Because of observational constraints and selection effects, there to be is an apparent deficit of observed number of Galactic supernova remnants (SNRs). To investigate this, we employ two methods. The first method applies correction factors for the selection effects to derive the radial density distribution. The second method compares functional forms for the SNR surface density and selection function against the data to find which functions are consistent with the data. The total number of SNRs in the Galaxy is $\sim3500$ (Method 1) or in the range $\sim2400$ to $\sim5600$ (Method 2). We conclude that the current observed number of SNRs is not yet complete enough to give a well-determined total SNR number or radial density function.