Improved simulations of the planetary nebula luminosity function
  We have developed a new procedure for the generation of a planetary nebula luminosity function (PNLF), improving on previous work. The procedure is based, as before, on an exponential central star mass distribution, on H-burning post-AGB evolutionary tracks, and on the avoidance of nebular models for the calculation of nebular fluxes. We have added new post-AGB evolutionary tracks and introduced the following improvements: (1) the imperfect analytical representation of post-AGB evolutionary tracks has been replaced by an interpolation routine giving a better approximation; (2) we have modified the distribution of the intensities of [O III] lambda 5007 relative to Hbeta, so that it better imitates the observed distribution, which we have taken from data in the Strasbourg-ESO catalogue of Galactic PNs and other sources; (3) we have adjusted the absorbing factor mu along the white dwarf cooling tracks, so as to reproduce the observed PNLF of the Magellanic Clouds and M 31 at fainter magnitudes. In this way we have produced a PNLF which is more consistent with observed PN properties. We use this randomly generated PNLF to: (1) show as convincingly as possible that most PNs in any real population must leak stellar H-ionizing photons; (2) revise our determinations of the parameter mu(max); (3) discuss the shape of the PNLF, hinting at the possible existence of a distinct feature 2 magnitudes fainter than the brightest PNs; (4) attempt estimates of maximum final masses from fits to the PNLFs of the LMC and M 31. There is marginal evidence of a higher maximum final mass in the LMC, but this should be confirmed in other galaxies with recent star formation. A convincing confirmation will require to increase the sample sizes and to extend the PNLFs to at least 1.5 mag fainter than the brightest PNs. 
R.H. M\'endez and T. Soffner (Universit\"atssternwarte M\"unchen)