The ∑ - D relation for planetary nebulae: Preliminary analysis

Abstract

An analysis of the relation between radio surface brightness and diameter, so-called ∑ - D relation, for planetary nebulae (PNe) is presented: i) the theoretical ∑ - D relation for the evolution of bremsstrahlung surface brightness is derived; ii) contrary to the results obtained earlier for the Galactic supernova remnant (SNR) samples, our results show that the updated sample of Galactic PNe does not severely suffer from volume selection effect - Malmquist bias (same as for the extragalactic SNR samples) and; iii) we conclude that the empirical ∑ - D relation for PNe derived in this paper is not useful for valid determination of distances for all observed PNe with unknown distances.