The Galactic disc distribution of planetary nebulae with warm dust emission features - II

We address the question of whether the distribution of warm-dust compositions in IR-bright Galactic disc PNe (Paper I, Casassus et al.) can be linked to the underlying stellar population. The PNe with warm dust emission represent a homogeneous population, which is presumably young and minimally affected by a possible dependence of PN lifetime on progenitor mass. The sample in Paper I thus allows testing of the predictions of single-star evolution, through a comparison with synthetic distributions and under the assumption that tip-of-the-AGB and PN statistics are similar. We construct a schematic model for AGB evolution (adapted from Groenewegen and de Jong), the free parameters of which are calibrated with the luminosity function (LF) of C stars in the LMC, the initial-final mass relation and the range of PN compositions. The observed metallicity gradient and distribution of star-forming regions with Galactocentric radius (Bronfman et al.) allow us to synthesize the Galactic disc PN progenitor population. We find that the fraction of O-rich PNe, f(O), is a tight constraint on AGB parameters. For our best model, a minimum PN progenitor mass Mmin = 1 M⊙ predicts that about 50 per cent of all young PNe should be O-rich compared with an observed fraction of 22 per cent; thus Mmin = 1.2 M⊙, at a 2σ confidence level (Mmin = 1.3 M⊙ at 1σ). By contrast, current AGB models for single stars can account neither for the continuous range of N enrichment (Leisy and Dennefeld) nor for the observation that the majority of very C-rich PNe have Peimbert type I (Paper I). f(O) is thus an observable quantity much easier to model. The decrease in f(O) with Galactocentric radius as reported in Paper I, is a strong property of the synthetic distribution, independent of Mmin. This trend reflects the sensitivity of the surface temperature of AGB stars and of the core mass at the first thermal pulse to the Galactic metallicity gradient