The relation for planetary nebulae

¹ Department of Astronomy, Faculty of Mathematics, University of Belgrade, Studentski trg 16, PO 550, 11000 Belgrade, Serbia e-mail: dejanu@matf.bg.ac.yu
² Isaac Newton Institute of Chile, Yugoslavia Branch, Yugoslavia
³ Astronomical Observatory, Volgina 7, 11160 Belgrade 74, Serbia
⁴ University of Western Sydney, Locked Bag 1797, Penrith South DC, NSW 1797, Australia
⁵ Department of Physics, Macquarie University, Sydney, NSW 2109, Australia

Received: 1 February 2008
Accepted: 10 January 2009

Abstract

We present an extended analysis of the relation between radio surface brightness and diameter – the so-called relation for planetary nebulae (PNe). We revise our previous derivation of the theoretical relation for the evolution of bremsstrahlung surface brightness in order to include the influence of the fast wind from the central star. Different theoretical forms are derived: for the first and second phases of evolution and for the final stage of evolution. Also, we analyzed several different Galactic PN samples. All samples are influenced by severe selection effects, but the Malmquist bias seems to be less influential here than in the supernova remnant (SNR) samples. We derived empirical relations for 27 sample sets using 6 updated PN papers from which an additional 21 new sets were extracted. Twenty four of these have a trivial form of . However, we obtain one empirical relation that may be useful for determining distances to PNe. This relation is obtained by extracting a recent nearby (<1 kpc) Galactic PN sample.