A hydrodynamical study of multiple-shell planetary nebulae. III. Expansion properties and internal kinematics: Theory versus observation

We present the result of a study on the expansion properties and internal kinematics of round/elliptical planetary nebulae of the Milky Way disk, the halo, and of the globular cluster M 15. The purpose of this study is to considerably enlarge the small sample of nebulae with precisely determined expansion properties (Schönberner et al. \cite{SJSPCA.05}). To this aim, we selected a representative sample of objects with different evolutionary stages and metallicities and conducted high-resolution échelle spectroscopy. In most cases we succeeded in detecting the weak signals from the outer nebular shell which are attached to the main line emission from the bright nebular rim. Next to the measurement of the motion of the rim gas by decomposition of the main line components into Gaussians, we were able to measure separately, for most objects for the first time, the gas velocity immediately behind the leading shock of the shell, i.e. the post-shock velocity. We more than doubled the number of objects for which the velocities of both rim and shell are known and confirm that the overall expansion of planetary nebulae is accelerating with time. There are, however, differences between the expansion behaviour of the shell and the rim: The post-shock velocity is starting at values as low as around 20 km s^-1 for the youngest nebulae, just above the AGB wind velocity of ∼ 10-15 km s^-1, and is reaching values of about 40 km s^-1 for the nebulae around hotter central stars. Contrarily, the rim matter is at first decelerated below the typical AGB-wind velocity and remains at about 5-10 km s^-1 for a while until finally a typical flow velocity of up to 30 km s^-1 is reached. This observed distinct velocity evolution of both rim and shell is explained by radiation-hydrodynamics simulations, at least qualitatively: It is due to the ever changing stellar radiation field and wind-wind interaction together with the varying density profile ahead of the leading shock during the progress of evolution. The wind-wind interaction works on the rim dynamics while the radiation field and upstream density gradient is responsible for the shell dynamics. Because of these time-dependent boundary conditions, a planetary nebula will never evolve into a simple self-similar expansion. Also the metal-poor objects behave as theory predicts: The post-shock velocities are higher and the rim flow velocities are equal or even lower compared to disk objects at similar evolutionary stage. The old nebula around low-luminosity central stars contained in our sample expand still fast and are dominated by reionisation. We detected, for the first time, in some objects an asymmetric expansion behaviour: The relative expansions between rim and shell appear to be different for the receding and approaching parts of the nebular envelope.

Based partly on observations obtained at the European Southern Observatory, Paranal, Chile (ESO programme No. 077.D-0652).