  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 galaxy's star-formation history and chemical evolution.
