2007A&A...474..529C

Planetary Nebulae (PNe) display complex radial surface brightness profiles whose understanding is crucial for a correct interpretation of their formation and evolution. In particular, the intermediate shells commonly observed around the bright rims of PNe contain important information for the discussion of the mass loss rate at the end of the AGB, for the determination of the post-AGB age of the central stars and the distance via the expansion parallax method, and for the analysis of line profiles for unresolved, faraway objects like extragalactic PNe. This paper describes the dynamical properties of PNe shells and presents a new practical method to properly determine their expansion velocity. The analysis is guided by realistic radiative-hydrodynamical simulations which allow to test and verify different methods for the kinematical study of PNe shells using high-resolution long-slit spectra. We show that the use of the derivative of the line profile allows us to determine accurately the post-shock gas velocity in the shells. This method is generally superior to other techniques previously used. In addition, if applied to long-slit data, it allows to determine the velocities of the shells even when they are very close to those of the PNe rims. Its application to 10 real PNe confirms the model predictions and previous conclusions about the substantial mass loss increase during the latest AGB evolution. The method and discussion presented in this paper are meant to be used as a guide for a correct determination of some basic kinematic and evolutionary properties of Galactic and extragalactic PNe, including their expansion parallaxes.