Towards understanding the planetary nebula luminosity function

We report on a theoretical work in progress about the planetary nebula luminosity function. A new synthetic model is developed to follow the evolution of a planetary nebula and its central star, starting from the onset of AGB phase up to the white dwarf cooling sequence. Both H- and He-burning Post-AGB tracks are used. Basic properties of the circumstellar nebula are predicted, namely: the dynamics and chemical composition of the stellar ejecta, the photoionisation of H and He by the central star, the formation of a few relevant optical emission lines (e.g. Hβ;HeIIλ4686; [OIII]λ5007). As a first application, the planetary nebula luminosity function in the LMC is analysed adopting a population synthesis approach. It turns out that a reasonable reproduction of the observed bright end in the [OIII]λ5007 luminosity cannot be obtained assuming that all central stars are H-burners, but rather considering that the observed population of PNe is excited by a mixture of H- and He-burner central stars.