Planetary nebulae as standard candles. I - Evolutionary models

We use a series of models of evolving planetary nebulae to derive their time-dependent luminosity history for a selection of central star masses. We then simulate observations of ensembles of planetary nebulae (PNs) using Monte Carlo methods to derive theoretical luminosity functions. The generated [O III] λ5007 luminosity functions agree very well with observations of M31, M81, and Leo Group (NGC 3377, NGC 3379, NGC 3384) galaxies, exhibiting a sharp cutoff over 0.8 mag at the bright end. This cutoff strongly implies that the distribution of central star masses for bright PNs is centered near 0.61 M_sun_ and has a narrow high-side Gaussian width (σ) near 0.02 M_sun_. The Hβ luminosity function also exhibits a bright cutoff, but at a flux level 1.7 mag fainter than the [O III] luminosity function. We propose deriving extragalactic distances by comparing the shapes of the luminosity functions of PNs in distant galaxies with those found for nearby reference galaxies. The simpler, but less accurate, standard candle method, whereby one simply compares the luminosities of the brightest PN(s) in a galaxy to the brightest PNs in reference galaxies such as those in the Local Group can also be used to obtain distances.