The Relation Between the Surface Brightness and the Diameter for Galactic Supernova Remnants

In this work, we have constructed a relation between the surface brightness ($\Sigma$) and diameter (D) of Galactic C- and S-type supernova remnants (SNRs). In order to calibrate the $\Sigma$-D dependence, we have carefully examined some intrinsic (e.g. explosion energy) and extrinsic (e.g. density of the ambient medium) properties of the remnants and, taking into account also the distance values given in the literature, we have adopted distances for some of the SNRs which have relatively more reliable distance values. These calibrator SNRs are all C- and S-type SNRs, i.e. F-type SNRs (and S-type SNR Cas A which has an exceptionally high surface brightness) are excluded. The Sigma-D relation has 2 slopes with a turning point at D=36.5 pc: $\Sigma$(at 1 GHz)=8.4$^{+19.5}_{-6.3}$$\times10^{-12}$ D$^{{-5.99}^{+0.38}_{-0.33}}$ Wm$^{-2}$Hz$^{-1}$ster$^{-1}$ (for $\Sigma$$\le3.7\times10^{-21}$ Wm$^{-2}$Hz$^{-1}$ster$^{-1}$ and D$\ge$36.5 pc) and $\Sigma$(at 1 GHz)=2.7$^{+2.1}_{-1.4}$$\times$ 10$^{-17}$ D$^{{-2.47}^{+0.20}_{-0.16}}$ Wm$^{-2}$Hz$^{-1}$ster$^{-1}$ (for $\Sigma$$>3.7\times10^{-21}$ Wm$^{-2}$Hz$^{-1}$ster$^{-1}$ and D$<$36.5 pc). We discussed the theoretical basis for the $\Sigma$-D dependence and particularly the reasons for the change in slope of the relation were stated. Added to this, we have shown the dependence between the radio luminosity and the diameter which seems to have a slope close to zero up to about D=36.5 pc. We have also adopted distance and diameter values for all of the observed Galactic SNRs by examining all the available distance values presented in the literature together with the distances found from our $\Sigma$-D relation.Comment: 45 pages, 2 figures, accepted for publication in Astronomical and Astrophysical Transaction