The effect of tides on the population of PN from interacting binaries

We have used the tidal equations of Zahn to determine the maximum orbital distance at which companions are brought into Roche lobe contact with their giant primary, when the primary expands during the giant phases. This is a key step when determining the rates of interaction between giants and their companions. Our stellar structure calculations are presented as maximum radii reached during the red and asymptotic giant branch (RGB and AGB, respectively) stages of evolution for masses between 0.8 and 4.0 M-aS (TM) (Z = 0.001-0.04) and compared with other models to gauge the uncertainty on radii deriving from details of these calculations. We find overall tidal capture distances that are typically 1-4 times the maximum radial extent of the giant star, where companions are in the mass range from 1 M-J to a mass slightly smaller than the mass of the primary. We find that only companions at initial orbital separations between similar to 320 and similar to 630 R-aS (TM) will be typically captured into a Roche lobe-filling interaction or a common envelope on the AGB. Comparing these limits with the period distribution for binaries that will make planetary nebula (PN), we deduce that in the standard scenario where all similar to 1-8 M-aS (TM) stars make a PN, at most 2.5 per cent of all PN should have a post-common envelope central star binary, at odds with the observational lower limit of 15-20 per cent. The observed overabundance of post-interaction central stars of PN cannot be easily explained considering the uncertainties. We examine a range of explanations for this discrepancy.