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 similar to 1.5 to 2.8 M-circle dot. There is also an indication that the peak of C-star lifetime shifts to lower masses (from slightly above to slightly below 2 M-circle dot) as we move from LMC to SMC metallicities. The M-giant lifetimes also peak at similar to 2 M-circle dot 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.