Hydrostatic evolutionary sequences for the nuclei of planetary nebulae

Abstract

This paper describes a set of evolutionary calculations for nuclei of planetary nebulae. The properties of the nuclei are studied as a function of the following three input parameters: (i) mass of the nucleus, which is set equal to 0.60, 0.70, 0.76, and 0.89 M 0 ; (ii) departure phase from the asymptotic giant branch (AGB), which is set at four equally spaced values within the helium shell flash cycle; and (iii) mass loss, which takes a range of forms. We have found evidence for a critical AGB core mass and planetary nebula nucleus mass above which radiation pressure removes all the hydrogen-rich material from the nucleus. We argue that every AGB star capable of producing a core mass greater than 0.86 M 0 will produce a planetary nebula with a helium-rich nucleus (or a supernova if the core mass'reaches the Chandrasekhar limiting mass of ~1.4 M 0). Such nuclei will evolve through the planetary nebula phase burning helium before cooling off to become non-DA white dwarfs, unless accretion of hydrogen from the interstellar medium can hide the helium-rich layers. The radiation pressure mechanism may help explain a deficiency in the number of high-luminosity AGB stars apparent in some recent surveys in Magellanic Cloud fields. For the less massive stars that leave the AGB during the interflash phase, the transition time from the AGB to the planetary nebula region is shown to vary strongly with the phase of the shell flash cycle at which the star leaves the AGB. The transition time can be a large fraction of the post-AGB expansion lifetime of a nebula whose ejection ceased when the star was near a post-flash luminosity minimum. A detailed comparison of our evolutionary results with observational data is given. There is strong evidence that some recent determinations of the luminosities of planetary nebula nuclei systematically underestimate them by a factor of ~3. The masses of planetary nebula nuclei vary from ~0.6 M© to greater than ~0.8 M©. There is little evidence for or against the supposition that planetary nebulae are ejected primarily at a helium shell flash.