Predicting the Fate of Binary Red Giants Using the Observed Sequence E   Star Population: Binary Planetary Nebula Nuclei and Post-RGB Stars
  Sequence E variables are close binary red giants that show ellipsoidal light variations. They are likely the immediate precursors of planetary nebulae (PNe) with close binary central. We have made a Monte Carlo simulation to determine the fraction of red giant binaries that go through a common envelope (CE) event leading to the production of a close binary system or a merged star. The novel aspect of this simulation is that we use the observed frequency of sequence E binaries in the LMC to normalize our calculations. In our standard model, we find that in the LMC today the fraction of PNe with close binary central stars is 7-9%, the fraction of PNe with intermediate period binary central stars having separations capable of influencing the nebula shape (P<500 yrs) is 23-27%, the fraction of PNe containing wide binaries that are unable to influence the nebula shape (P>500 yrs) is 46-55%, the fraction of PNe derived from single stars is 3-19% and 5-6% of PNe are produced by previously merged stars. We also predict that the birthrate of post-RGB stars is ~4% of the total PN birthrate, equivalent to ~50% of the production rate of PNe with close binary central stars. These post-RGB stars most likely appear initially as luminous low-mass helium white dwarf binaries. We use our model and the observed number of red giant stars in the top one magnitude of the RGB in the LMC to predict the number of PNe in the LMC. We predict 548 PNe in good agreement with the 541+/-89 PNe observed by Reid & Parker (2006). Since most of these PNe come from single or non-interacting binary stars in our model, this means that most such stars produce PNe contrary to the "Binary Hypothesis" which suggests that binary interaction is required to produce a PN. 
J.D. Nie, P.R. Wood and C.P. Nicholls
astro-ph.SR