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.
