An analysis of the observed radio emission from planetary nebulae

We have analysed the radio fluxes for 264 planetary nebulae for which reliable measurements of fluxes at 1.4 and 5 GHz, and of nebular diameters are available. For many of the investigated nebulae, the optical thickness is important, especially at 1.4 GHz. Simple models like the one specified only by a single optical thickness or spherical, constant density shells do not account satisfactorily for the observations. Also an r(-2) density distribution is ruled out. A reasonable representation of the observations can be obtained by a two-component model having regions of two different values of optical thickness. We show that the nebular diameters smaller than 10" are uncertain, particularly if they come from photographic plates or Gaussian fitting to the radio profile. While determining the interstellar extinction from an optical to radio flux ratio, caution should be paid regarding optical thickness effects in the radio. We have developed a method for estimating the value of self absorption. At 1.4 GHz self absorption of the flux is usually important and can exceed a factor of 10. At 5 GHz self absorption is negligible for most of the objects, although in some cases it can reach a factor of 2. The Galactic bulge planetary nebulae when used to calibrate the Shklovsky method give a mean nebular mass of 0.14 M-.. The statistical uncertainty of the Shklovsky distances is smaller than a factor of 1.5.