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We present chemical abundances for planetary nebulae in M32, NGC 185, and NGC205 based upon spectroscopy obtained at the Canada-France-Hawaii Telescopeusing the Multi-Object Spectrograph. From these and similar data compiled fromthe literature for other Local Group galaxies, we consider the origin andevolution of the stellar progenitors of bright planetary nebulae in galaxieswhere star formation ceased long ago. The ratio of neon to oxygen abundances inbright planetary nebulae is either identical to that measured in theinterstellar medium of star-forming dwarf galaxies or at most changed by a fewpercent, indicating that neither abundance is significantly altered as a resultof the evolution of their stellar progenitors. Several planetary nebulae appearto have dredged up oxygen, but these are the exception, not the rule. Theprogenitors of bright planetary nebulae typically enhance their original heliumabundances by less than 50%. In contrast, nitrogen enhancements can reachfactors of 100. However, nitrogen often shows little or no enhancement,suggesting that nitrogen enrichment is a random process. The helium, oxygen,and neon abundances argue that the typical bright planetary nebulae in all ofthe galaxies considered here are the progeny of stars with initial masses ofapproximately 1.5 Msun or less, based upon the nucleosynthesis predictions ofcurrent theoretical models. These models, however, are unable to explain thenitrogen enrichment or its scatter. Similar conclusions hold for the brightplanetary nebulae in galaxies with ongoing star formation. Thus, thoughcomposition varies significantly, there is unity in the sense that theprogenitors of typical bright planetary nebulae appear to have undergonesimilar physical processes. (Abridged)

Bright Planetary Nebulae and their Progenitors in Galaxies Without Star Formation