Do most planetary nebulae derive from binaries? I. Population synthesis model of the Galactic planetary nebula population produced by single stars and binaries

We present a population synthesis calculation to derive the total number of planetary nebulae (PNs) in the Galaxy that descend from single stars and stars in binary systems. Using the most recent literature results on Galactic and stellar formation and stellar evolution, we predict the total number of Galactic PNs with radii < 0.9 pc to be (4.6 +/- 1.3); 10(4). We do not claim this to be the complete population, since there can be visible PNs 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 and Jacoby (8000 +/- 2000 objects). Our prediction is discrepant with the observations at the 2.9 sigma level, a disagreement that 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 PNs. The predicted local PN formation rate density from single stars and binaries is (1.1 +/- 0.5); 10(-12) PNs yr(-1) pc(-3), lower than recent estimates (2.1 x 10(-12) PNs yr(-1) pc(-3)), which are based on local PN counts and the PN distance scale, but more in line with the white dwarf (WD) birthrate densities [(1.0 +/- 0.25) x 10(-12) WDs yr(-1) pc(-3)]. The predicted PN birthrate density will be revised down if we assume that only binaries make PNs, implying that the PN distance scale has to be revised to larger values.