Ages and masses of asymptotic giant branch stars from the period--luminosity diagram

Abstract

A method of determining ages and masses of asymptotic giant branch (AGB) stars between 0.8 and $\sim$6 M$_\odot$ is demonstrated, based on comparing the star's position in the period--absolute-magnitude diagram to theoretical evolutionary models. For samples of Milky Way stars, the method provides errors (statistical and systematic, respectively) of order of $^{+29}_{-35} \pm 15$ per cent in age, $^{+14}_{-7} \pm 7$ per cent in initial mass and $^{+17}_{-11} \pm 27$ per cent in current mass. However, its applicability to individual stars depends strongly on both their position in the $P-L$ diagram and the uncertainty of that position. This method is applied to published samples of AGB stars from the \emph{Gaia}, NESS, DEATHSTAR and ATOMIUM surveys. These surveys' statistical ensembles are compared to expectations from stellar evolutionary models, finding that most AGB samples are biased towards stars of younger ages and higher masses. An average mass for Milky Way AGB stars is found to be $\sim$1.1 M$_\odot$, while mass returned to the interstellar medium by AGB stars typically comes from $\sim$1.2 M$_\odot$ stars with mass-loss rates of order $2-3 \times 10^{-6}$ M$_\odot$ yr$^{-1}$.