The Sigma - D relation for planetary nebulae

Abstract

We present an extended analysis of the relation between radio surface brightness and diameter -- the so-called $\Sigma -D$ relation for planetary nebulae (PNe). We revise our previous derivation of the theoretical $\Sigma -D$ 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: $\Sigma \propto D^{-1}$ for the first and second phases of evolution and $\Sigma \propto D^{-3}$ for the final stage of evolution. Also, we analyzed several different Galactic PN samples. All samples are influenced by severe selection effects, but Malmquist bias seems to be less influential here than in the supernova remnant (SNR) samples. We derived empirical $\Sigma -D$ 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 $\beta \approx 2$. However, we obtain one empirical $\Sigma -D$ relation that may be useful for determining distances to PNe. This relation is obtained by extracting a recent nearby (< 1 kpc) Galactic PN sample.

12 pages, 3 tables, 4 figures. Accepted for publication in Astronomy & Astrophysics

References in corpus (6)

• The Magellanic Cloud Calibration of the Galactic Planetary Nebula Distance Scale
• Trigonometric Parallaxes of Central Stars of Planetary Nebulae
• Morphology and Composition of the Helix Nebula
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• Hubble Space Telescope Images of Magellanic Cloud Planetary Nebulae
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Cited by in corpus (7)

• The Hα surface brightness - radius relation: a robust statistical distance indicator for planetary nebulae
• Radio-continuum detections of Galactic Planetary Nebulae I. MASH PNe detected in large-scale radio surveys
• On calibration of some distance scales in astrophysics
• The Sigma-D Analysis of Recently Detected Radio Planetary Nebulae in the Magellanic Clouds
• MeerKAT reveals a ghostly thermal radio ring towards the Galactic Centre
• Radio Planetary Nebulae in the Small Magellanic Cloud
• Supernova remnants in clumpy medium: A model of hydrodynamic and radio synchrotron evolution