The role of mass loss in constraining quenching time in dwarf galaxies from asymptotic-giant-branch and red-giant-branch star counts

Context . The possibility of reconstructing the past star formation history of dwarf elliptical galaxies out of the Local Volume relies on modelling bright stellar populations currently evolving through the red-giant-branch (RGB) and asymptotic-giant-branch (AGB) phases. Recent studies proposed the use of the relative fractions of RGB and AGB stars populating specific boxes in the observational colour-magnitude plane to infer the epoch within which 90% of the stellar population of the galaxy formed (T90). Aims . We aim to understand the physical processes of stellar evolution that are constrained by the relationship between the relative fraction of AGB and RGB stars of dwarf galaxies and the T90 epoch. Methods . We used updated stellar models that include the description of dust formation in the wind to undertake a population synthesis approach that would allow us to monitor the variation of the N AGB /N RGB ratio with time. The effects of some specific ingredients, such as the mass loss experienced by low-mass stars during the RGB phase, and the details of the time variation of the star formation rate, were extensively explored and tested against data in this study. Results . The mass lost by low-mass stars during the RGB evolution proves the most relevant ingredients affecting the time variation of N AGB /N RGB : at metallicities ~1/10 solar, a mass loss of ~0.25 M ⊙ is required to reproduce the observations. This analysis allowed us to derive a relationship between N AGB /N RGB and T90, with a ~1 Gyr uncertainty on T90.