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 & 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 M-min = 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 M-min = 1.2 M., at a 2 sigma confidence level (M-min = 1.3 M. at 1 sigma). By contrast, current AGB models for single stars can account neither for the continuous range of N enrichment (Leisy & 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 inf(O) with Galactocentric radius, as reported in Paper I, is a strong property of the synthetic distribution, independent of M-min. 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.