Theoretical models of the planetary nebula populations in galaxies: The ISM oxygen abundance when star formation stops

Using theoretical models of the planetary nebula populations in galaxies, we investigate whether the current oxygen abundances in bright planetary nebulae can be used to predict the oxygen abundance in the interstellar medium when star formation stopped. These models successfully reproduce a constant planetary nebula luminosity function (PNLF) peak luminosity, the PNLF shape in galaxies with and without star formation, and the mean densities and oxygen abundances observed in bright planetary nebulae in the Magellanic Clouds. To accomplish this, we had to couple the evolution of the nebular shell and the central star, and impose a mass-dependent nebular covering factor. In all galaxies, these models predict that a gap develops between the abundances observed in bright planetary nebulae and those in the interstellar medium when star formation stopped. This abundance gap depends primarily upon the oxygen abundance achieved in the interstellar medium when star formation stopped, though it also has some sensitivity to the history of star formation. The abundance gap is always less than 0.35dex in these models. For the Milky Way, the predicted abundance gap, O.14dex, is identical to that observed. We also re-examined spectroscopic observations of planetary nebulae in diffuse elliptical galaxies to determine their interstellar medium oxygen abundances when they stopped forming stars. Allowing for the abundance gap magnifies the chemical differences between diffuse ellipticals and dwarf irregulars found by Richer & McCall (1995). Diffuse ellipticals are confirmed to have larger oxygen abundances than similarly luminous dwarf irregulars, and to have larger [O/Fe] ratios than dwarf irregulars with the same oxygen abundance. The simplest explanation for both of these observations is that diffuse ellipticals formed the majority of their stars on shorter time scales than dwarf irregulars, so diffuse ellipticals cannot be the faded remnants of dwarf irregulars.