The PICS Project. I. The impact of metallicity and helium abundance on the bright end of the planetary nebula luminosity function

Abstract: Planetary nebulae (PNe) and their luminosity function (PNLF) in galaxies have been used as a cosmic distance indicator for decades, yet a fundamental understanding is still lacking to explain the universality of the PNLF among different galaxies. Models for the PNLF have generally assumed solar metallicities and artificial stellar populations. In this work, we investigate how metallicity and helium abundances affect the PNe and PNLF, and the importance of the initial-to-final mass relation (IFMR), to resolve the tension between PNLF observations and models. We introduce PICS (PNe In Cosmological Simulations), a PN model framework that accounts for metallicity and is applicable to realistic stellar populations from cosmological simulations and observations. The framework combines stellar evolution models with post-AGB tracks, PN models, and circumnebular extinction to obtain PNe from a parent stellar population. We find that metallicity plays an important role for the resulting PNe: old metal-rich populations can harbor much brighter PNe than old metal-poor ones. We show that the helium abundance is a vital ingredient at high metallicities and explore the impact on the PNLF of a possible saturation of helium at high metallicities. We present PNLF grids for different stellar ages and metallicities, where the observed PNLF bright end can be reached even for old stellar populations of 10 Gyr at high metallicities. Finally, we find that the PNLFs of old stellar populations are sensitive to the IFMR, allowing for the production of bright PNe. With PICS, we have laid the groundwork for studying how different models affect the PNe and PNLF. Two central ingredients for this are the metallicity and helium abundance. Future applications of PICS include modeling PNe in a cosmological framework to explain the origin of the universal PNLF cutoff and using it as a diagnostic tool for galaxy formation.