2006A&A...451..937S

This paper is the first in a short series dedicated to the long-standing astronomical problem of de-projecting the bi-dimensional, apparent morphology of a three-dimensional mass of gas. We focus on the density distribution in real planetary nebulae (and all types of expanding nebulae). We introduce some basic theoretical notions, discuss the observational methodology, and develop an accurate procedure for determining the matter radial profile within the sharp portion of nebula in the plane of the sky identified by the zero-velocity-pixel-column (zvpc) of high-resolution spectral images. The general and specific applications of the method (and some caveats) are discussed. Moreover, we present a series of evolutive snapshots, combining illustrative examples of both model and true planetary nebulae. The zvpc radial-density reconstruction - added to tomography and 3D recovery developed at the Astronomical Observatory of Padua (Italy) - constitutes a very useful tool for looking more closely at the spatio-kinematics, physical conditions, ionic structure, and evolution of expanding nebulae.