ar X iv : a st ro - p h / 06 06 35 4 v 1 1 4 Ju n 20 06

We present a population synthesis calculation to derive the total number of planetary nebulae (PN) in the Galaxy that descend from single stars and stars in binary systems. Using the most recent literature results on galactic and stellar formation as well as stellar evolution, we predict the total number of galactic PNe with radii <0.9 pc to be (4.6 ± 1.3) × 10. We do not claim this to be the complete population, since there can be visible PNe with radii larger than this limit. However, by taking this limit, we make our predicted population inherently comparable to the observationally-based value of Peimbert, who determined (7200 ± 1800) PNe should reside in the Galaxy today. Our prediction is discrepant with the observations at the 2.9 σ level, a disagreement which we argue is meaningful in view of our specific treatment of the uncertainty. We conclude that it is likely that only a subset of the stars thought to be capable of making a visible PN, actually do. In the second paper in this series, an argument will be presented that the bulk of the galactic PN population might be better explained if only binaries produce PNe. The predicted PN formation rate density from single stars and binaries is (1.1±0.5)×10−12 PN yr pc in the local neighborhood. This number is lower than the most recent PN birthrate density estimates (2.1 ×10−12 PN yr pc), which are based on local PN counts and the PN distance scale, but more in line with the white dwarf birthrate densities determined by Liebert et al. ((1.0 ± 0.25)×10−12 WD yr pc). The predicted PN birthrate density will be revised down, if we assume that only binaries make PNe. This revision will imply that the PN distance scale has to be revised to larger values. Department of Astrophysical and Planetary Sciences and CASA, University of Colorado, 389-UCB, Boulder, CO 80309 REU student at the Astrophysics Department of the American Museum of Natural History Astrophysics Department, American Museum of Natural History, Central Park West at 79 Street, New York, NY 10024