The TP-AGB phase. Lifetimes from C and M star counts in Magellanic Cloud clusters

Using available data for C and M giants with M_bol<-3.6 in Magellanic Cloud clusters, we derive limits to the lifetimes for the corresponding evolutionary phases, as a function of stellar mass. The C-star phase is found to have a duration between 2 and 3 Myr for stars in the mass range from ~1.5 to 2.8 M_sun. There is also an indication that the peak of C-star lifetime shifts to lower masses (from slightly above to slightly below 2 Msun) as we move from LMC to SMC metallicities. The M-giant lifetimes also peak at ~2 Msun in the LMC, with a maximum value of about 4 Myr, whereas in the SMC their lifetimes appear much shorter, but, actually, they are poorly constrained by the data. These numbers constitute useful constraints to theoretical models of the TP-AGB phase. We show that several models in the literature underestimate the duration of the C-star phase at LMC metallicities.