The mysterious cut-off of the Planetary Nebula Luminosity Function

Abstract: Planetary Nebulae (PN) emit enormous amount of energy in several emission lines. Measuring the line-flux for PNe in a given stellar population, the Planetary Nebula Luminosity Function (PNLF) can be compiled. Surveys of PNe revealed that the faint-end of the PNLF can be approximated by a simple exponential dependency expected for an expanding spherical shell. However at the bright-end there exists a steep cut-off which was unexpected and remains unexplained. Interestingly, the cut-off value appears to be nearly the same for different stellar populations as young spiral galaxies and old elliptical galaxies and, despite the lack of understanding, became an extragalactic distance estimator. Here we show that the recently computed post-AGB evolutionary tracks are capable to explain the decades old mystery. All new models with ages between 1 and 7 Gyr (progenitor masses between 2.0 and 1.1 of solar mass) evolve fast enough to ionize the PN, and at similar post-AGB luminosity which allows the [O III] 500.7nm line to reach nearly the same magnitude. The new models predict that the Sun at the end of its life will form a rather faint PN.