The ∑ - D relation for planetary nebulae

D. Urošević*, B. Vukotić, B. Arbutina, D. Ilić, M. Filipović, I. Bojičić, S. Šegan, S. Vidojević

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


We present an extended analysis of the relation between radio surface brightness and diameter - the so-called ∑ - D relation for planetary nebulae (PNe). We revise our previous derivation of the theoretical ∑ - D 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: ∑ α D-1 for the first and second phases of evolution and ∑ α D-3 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 ∑ - D 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 β ≈ 2. However, we obtain one empirical ∑ - D relation that may be useful for determining distances to PNe. This relation is obtained by extracting a recent nearby (<1 kpc) Galactic PN sample.

Original languageEnglish
Pages (from-to)537-546
Number of pages10
JournalAstronomy and Astrophysics
Issue number2
Publication statusPublished - Feb 2009


  • ISM: supernova remnants
  • Methods: analytical
  • Methods: statistical
  • planetary nebulae: general
  • Radio continuum: general
  • Radio continuum: ISM


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