Radio-continuum spectrum, brightness temperature, and planetary nebulae properties

Abstract

Context. Radio-continuum spectra are frequently used to infer the density distribution of ionized gaseous regions, while observed correlations between the brightness temperature and other distance-independent parameters are used to test evolutionary models of planetary nebulae. Aims. We check empirical correlations among features derived from the observed radio data and the inferred conclusions available in the literature, using self-consistent photoionization models. Methods. Photoionization models are computed for the physical conditions of planetary nebulae in order to derive self-consistent radio-continuum spectra, as well as the brightness temperature. Results. The temperature and ionization distributions throughout the nebulae explain the observed range of spectral indexes in the thick region of the spectrum, even for a uniform density distribution, usually challenged in the literature. The obtained models fit the observed radio spectra for planetary nebulae in a large range of spectral indexes. Our calculations show a correlation between the spectral index obtained in a given frequency range and the nebula size, as well as reproduce the observed relations between the brightness temperature and other distance-independent parameters. Such diagrams are frequently used to check evolutionary models of the central star and/or of the nebula. Conclusions. Since PNe images clearly show that the density is not constant inside the nebulae, and models with uniform and nonuniform density distributions can both reproduce the observed radio spectra, we conclude that it is not possible to favour one of them from the radio data, or to infer a particular density distribution for planetary nebulae.