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 M15. The purpose of this study is to considerably enlarge the smal
l sample of nebulae with precisely determined expansion properties. To this aim, we selected a representative sample of objects with different evolutionary stages and metallicities and conducted high-resolution echelle 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. This observed distinct velocity evolution of both rim and shell is explained by radiation-hydrodynamics simulations, at least qualitatively. Because of the 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. 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.
The visibility time of planetary nebulae (PNe) in stellar systems is an essential quantity for estimating the size of a PN population in the context of general population studies. For instance, it enters directly into the PN death rate determination.
The basic ingredient for determining visibility times is the typical nebular expansion velocity, as a suited average over all PN sizes of a PN population within a certain volume or stellar system. The true expansion speed of the outer nebular edge of a PN is, however, not accessible by spectroscopy -- a difficulty that we surmount by radiation-hydrodynamics modelling. We find a mean true expansion velocity of 42 km/s, i.e. nearly twice as high as the commonly adopted value to date. Accordingly, the time for a PN to expand to a radius of, say 0.9 pc, is only 21000 +/- 5000 years. This visibility time of a PN holds for all central star masses since a nebula does not become extinct as the central star fades. There is, however, a dependence on metallicity in the sense that the visibility time becomes shorter for lower nebular metal content. With the higher expansion rate of PNe derived here we determined their local death-rate density as (1.4 +/- 0.5) x E-12 PN pc^{-3} yr^{-1}, using the local PN density advocated by Frew (2008).
Based on time-dependent radiation-hydrodynamics simulations of the evolution of Planetary Nebulae (PNe), we have carried out a systematic parameter study to address the non-trivial question of how the diffuse X-ray emission of PNe with closed central
cavities is expected to depend on the evolutionary state of the nebula, the mass of the central star, and the metallicity of stellar wind and circumstellar matter. We have also investigated how the model predictions depend on the treatment of thermal conduction at the interface between the central `hot bubble and the `cool inner nebula, and compare the results with recent X-ray observations. Our study includes models whose properties resemble the extreme case of PNe with Wolf-Rayet type central stars. Indeed, such models are found to produce the highest X-ray luminosities.
