The carbon star luminosity functions in the Magellanic Clouds

We address the question of reproducing the observed luminosity functions of carbons stars in both the LMC and SMC, characterized by quite different features (i.e. faint end and peak location). To this aim, we use recent synthetic TP-AGB evolutionary calculations for a dense grid of stellar masses in the range 0.8 Mo ~< M ~< 5 Mo and metallicities Z = 0.008 and Z = 0.004. These models rely on updated inputs, treating envelope burning and dregde-up in detail by means of envelope integrations (Marigo et al. 1996, 1998ab). The observed carbon star luminosity functions turn out to be strong calibrators of the dredge-up parameters, namely: the minimum temperature at the base of the convective envelope, Tbdred, and the efficiency, lambda. Both distributions are reproduced remarkably well. We also investigate the sensitiveness of the predictions to the star formation history (SFR). The peak location results essentially invariant with respect to the SFR, whereas the shape of the bright wing may give hints on the recent epochs.