A two-mode planetary nebula luminosity function
  We propose a new Planetary Nebula Luminosity Function (PNLF) that includes two populations in the distribution. Our PNLF is a direct extension of the canonical function proposed by Jacoby et al. (1987), in order to avoid problems related with the histogram construction, it is cast in terms of cumulative functions. We are interested in recovering the shape of the faint part of the PNLF in a consistent manner, for galaxies with and without a dip in their PN luminosity functions. The parameters for the two mode PNLF are obtained with a genetic algorithm, which obtains a best fit to the PNLF varying all of the parameters simultaneously in a broad parameter space. We explore a sample of 9 galaxies with various Hubble types and construct their PNLF. All of the irregular galaxies, except one, are found to be consistent with a two-mode population, while the situation is less clear for ellipticals and spirals.For the case of NGC\, 6822, we show that the two-mode PNLF is consistent with previous studies of the star formation history within that galaxy. Our results support two episodes of star formation, in which the latter is significantly stronger. 
A. Rodr\'iguez-Gonz\'alez, L. Hern\'andez-Mart\'inez, A. Esquivel,   A.C. Raga, G. Stasi\'nska, M. Pe\~na and D. Mayya
astro-ph.GA