The role of mass loss in constraining quenching time in dwarf galaxies from AGB and RGB star counts

The capability 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 the 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). We aim at understanding the physical process 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. We use updated stellar models that include the description of dust formation in the wind, to undertake a population synthesis approach, to allow monitoring the variation of the NAGB/NRGB 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, are extensively explored and tested against data. The mass lost by low-mass stars during the RGB evolution proves the most relevant ingredients affecting the time variation of NAGB/NRGB: at metallicities ~ 1/10 solar, a mass loss ~ 0.25Msun is required to reproduce the observations. This analysis allows to derive a relationship between NAGB/NRGB and T90, with a ~ 1 Gyr uncertainty on T90.