We investigate the possible progenitors of the planetary nebulae (PNs) which populate the top 0.5 mag of the [O III] 5007 planetary nebula luminosity function (PNLF). We show that the absolute luminosity of the PNLF cutoff demands that the central stars of these most luminous planetaries be greater than 0.6 Msun, and that such high-mass PN cores must exist in every galaxy. We also use the bolometric-luminosity specific PN number density to show that in early-type galaxies, [O III]-bright planetaries are relatively rare, with only about 10% of stars evolving to these bright magnitudes. We demonstrate that the combination of these two facts implies that either all early-type systems contain a small, smoothly distributed component of young (< 1 Gyr old) stars, or another mechanism exists for creating high-core mass planetaries. We argue that binary-star evolution is this second mechanism, and demonstrate that blue stragglers have the appropriate core properties and number density to explain the observations. We discuss the implications of this alternative mode of stellar evolution, and speculate on how coalesced binaries might affect the use of PNs for measuring a galaxys star-formation history and chemical evolution.
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