Envelope burning over-luminosity: a challenge to synthetic TP-AGB models

Until recently synthetic AGE models had not taken into account the break-do wn of the core mass-luminosity (M-c-, L) relation due to the occurrence of envelope burning in the most massive (M greater than or similar to 3.5 M. f or Pop. II and M greater than or similar to 4.5 M. for Pop. I) and luminous (M-bol less than or similar to -6) stars. Marigo et al. (1998) made the first attempt to consistently include the rel ated over-luminosity effect (i.e. above the M-c - L relation) in synthetic TP-AGB calculations. The method couples complete envelope integrations with analytical prescriptions, these latter being presently updated with the hi ghly detailed relations by Wagenhuber & Groenewegen (1998). In this paper the reliability of the solution scheme is tested by compariso n with the results of complete evolutionary calculations for a 7 M. AGE sta r undergoing envelope burning (Blocker & Schonberner 1991; Blocker 1995). Indeed, the method proves to be valid as it is able to reproduce with remar kable accuracy several evolutionary features of the 7 M. star (e.g, rate of brightening, luminosity evolution as a function of the core mass and envel ope mass for different mass-loss prescriptions) as predicted by full AGB mo dels. Basing on the new solution method, we present extensive synthetic TP-AGB ca lculations for stars with initial masses of 3.5, 4.0, 4.5, and 5.0 M-., and three choices of the initial metallicity, i.e. Z = 0.019, Z = 0.008, and Z = 0.004. Three values of the mixing-length parameter are used, i.e. alpha = 1.68, 2.0, 2.5. We investigate the dependence of envelope burning on such stellar parameter s (M, Z, and alpha). The comparison between different cases gives hints on the interplay between envelope burning over-luminosity and mass loss, and r elated effects on TP-AGB lifetimes.