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

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