Gamma-ray emission from Cassiopeia A produced by accelerated cosmic rays

This paper discusses the location of a sample of planetary nebulae on the HR diagram. We determine the internal velocity fields of 14 planetary nebulae from high-resolution echelle spectroscopy, with the help of photoionization models. The mass averaged velocity is shown to be a robust, simple parameter describing the outflow. The expansion velocity and radius are used to define the dynamical age; together with the stellar temperature, this gives a measurement of the luminosity and core mass of the central star. The same technique is applied to other planetary nebulae with previously measured expansion velocities, giving a total sample of 73 objects. The objects cluster closely around the Sch?nberner track of 0.61 M, with a very narrow distribution of core masses. The masses are higher than found for local white dwarfs. The luminosities determined in this way tend to be higher by a factor of a few than those derived from the nebular luminosities. The discrepancy is highest for the hottest (most evolved) stars. We suggest photon leakage as the likely cause. The innermost regions of the non-[WC] nebulae tend to show strong acceleration. Together with the acceleration at the ionization front, the velocity field becomes "U"-shaped. The presence of strong turbulent motions in [WC] nebulae is confirmed. Except for this, we find that the [WC] stars evolve on the same tracks as non-[WC] stars.