Evolution of planetary nebulae.II. Population effects on the bright cut-off of the PNLF

We investigate the bright cut-off of the [OIII] 5007 planetary nebula luminosity function (PNLF), that has been suggested as a powerful extragalactic distance indicator in virtue of its observed invariance against populations effects. Theoretical PNLFs are constructed via Monte-Carlo simulations of populations of PNe, whose individual properties are described with the aid of recent PN synthetic models (Marigo et al. 2001, A&A, 378, 958), coupled to a detailed photoionisation code (CLOUDY). The basic dependences of the cut-off magnitude M* are then discussed. We find that : (i) In galaxies with recent or ongoing star formation, the modelled PNLF present M* values between -4 and -5, depending on model details. These are very close to the observationally-calibrated value for the LMC. (ii) In these galaxies, the PNLF cut-off is produced by PNe with progenitor masses of about 2.5 Msun, while less massive stars give origin to fainter PNe. As a consequence M* is expected to depend strongly on the age of the last burst of star formation, dimming by as much as 5 mag as we go from young to 10-Gyr old populations. (iii) Rather than on the initial metallicity of a stellar population, M* depends on the actual [O/H] of the observed PNe, a quantity that may differ significantly from the initial value (due to dredge-up episodes), especially in young and intermediate-age PN populations. (iv) Also the transition time from the end of AGB to the PN phase, and the nuclear-burning properties (i.e. H- or He-burning) of the central stars introduce non-negligible effects on M*. The strongest indication derived from the present calculations is a serious difficulty to explain the age-invariance of the cut-off brightness over an extended interval, say from 1 to 13 Gyr, that observations of PNLFs in galaxies of late-to-early type seem to suggest. We discuss the implications of our findings, also in relation to other interpretative pictures proposed in the past literature.