A Bound on the Light Emitted during the Thermally Pulsing Asymptotic Giant Branch Phase

The integrated luminosity of the thermally pulsing asymptotic giant branch (TP-AGB) phase is a major uncertainty in stellar population synthesis models. We revise the white dwarf initial-final mass relation (IFMR), incorporating the latest composition and distance measurements for several clusters. Using this IFMR and stellar interiors models, we demonstrate that a significant fraction of the core mass growth for intermediate (1.5 < M _sun < 6) mass stars must take place during the TP-AGB phase. This conclusion holds using models both with and without convective overshoot. We find evidence that the peak fractional core mass contribution for TP-AGB stars is ~20% and occurs for stars between 2 M _sun and 3.5 M _sun. Using a simple fuel consumption argument we couple this core mass increase to a lower limit on the TP-AGB phase energy output. We demonstrate that the current TP-AGB models of Pietrinferni et al. and Bertelli et al. systematically grow the core less than we require while the latter predict sufficient integrated light. Our calculated lower bound, coupled with chemical evolution constraints, may provide an upper limit to the integrated luminosity of stars in the TP-AGB phase. Alternatively, a robust measurement of the emitted light in this phase and our constraints could set strong constraints on helium enrichment from TP-AGB stars. We estimate the yields predicted by current models as a function of initial mass. Implications for stellar population studies and prospects for improvements are discussed.