The ACS Nearby Galaxy Survey Treasury IX. Constraining asymptotic giant branch evolution with old metal-poor galaxies

In an attempt to constrain evolutionary models of the asymptotic giant branch (AGB) phase at the limit of low masses and low metallicities, we have examined the luminosity functions and number ratio between AGB and red giant branch (RGB) stars from a sample of resolved galaxies from the ACS Nearby Galaxy Survey Treasury (ANGST). This database provides HST optical photometry together with maps of completeness, photometric errors, and star formation histories for dozens of galaxies within 4 Mpc. We select 12 galaxies characterized by predominantly metal-poor populations as indicated by a very steep and blue RGB, and which do not present any indication of recent star formation in their color--magnitude diagrams. Thousands of AGB stars brighter than the tip of the RGB (TRGB) are present in the sample (between 60 and 400 per galaxy), hence the Poisson noise has little impact in our measurements of the AGB/RGB ratio. We model the photometric data with a few sets of thermally pulsing AGB (TP-AGB) evolutionary models with different prescriptions for the mass loss. This technique allows us to set stringent constraints to the TP-AGB models of low-mass metal-poor stars (with M<1.5 Msun, [Fe/H]<~-1.0). Indeed, those which satisfactorily reproduce the observed AGB/RGB ratios have TP-AGB lifetimes between 1.2 and 1.8 Myr, and finish their nuclear burning lives with masses between 0.51 and 0.55 Msun. This is also in good agreement with recent observations of white dwarf masses in the M4 old globular cluster. These constraints can be added to those already derived from Magellanic Cloud star clusters as important mileposts in the arduous process of calibrating AGB evolutionary models.