Radio observations of planetary nebulae: no evidence for strong radial density gradients

Radio continuum observations trace thermal emission of ionized plasma in planetary nebulae and bring useful information on nebular geometries. A model of homogeneous sphere or shell cannot fit the nebular spectra and brightness temperatures. Two alternative models have been proposed in the literature: the first one consists of two homogeneous components, while the other one is a model of a shell with a significant radial density gradient. On the other side, prolate ellipsoidal shell model can successfully fit the surface brightness distribution of selected objects. We verify the existing models using data collected in radio surveys covering wide range of frequencies. In about 50% cases, density gradient can be excluded, and none of the remaining objects could be confirmed. None of the observed planetary nebulae show the spectral index of 0.6 in the optically thick part of the spectrum, which is a value predicted for a shell containing strong radial density gradient. Radio spectra can be fitted with a model of prolate ellipsoidal shell, but also by a shell containing temperature variations in planetary nebulae. At least eight planetary nebulae show two component spectra, with one compact component showing much higher optical thickness than the other one. Unexpectedly, a group of planetary nebulae with lowest surface brightness show non-negligible optical thickness. Their emission comes from compact and dense structures, comprising only small part of total nebular mass.