Luminosities of carbon-rich asymptotic giant branch stars in the Milky Way

Context.Stars evolving along the asymptotic giant branch can become carbon-rich in the final part of their evolution. They replenish the inter-stellar medium with nuclear processed material via strong radiative stellar winds. The determination of the luminosity function of these stars, even if far from being conclusive, is extremely important for testing the reliability of theoretical models. In particular, strong constraints on the mixing treatment and the mass-loss rate can be derived. Aims. We present an updated luminosity function of Galactic carbon stars (LFGCS) obtained from a re-analysis of available data already published in previous papers. Methods. Starting from available near-and mid-infrared photometric data, we re-determined the selection criteria. Moreover, we took advantage of updated distance estimates and period-luminosity relations and we adopted a new formulation for the computation of bolometric corrections (BCs). This led us to collect an improved sample of carbon-rich sources from which we constructed an updated luminosity function. Results. The LFGCS peaks at magnitudes around -4.9, confirming the results obtained in a previous work. Nevertheless, the luminosity function presents two symmetrical tails instead of the larger high-luminosity tail characterizing the former luminosity function. Conclusions. The derived LFCGS matches the indications from recent theoretical evolutionary asymptotic giant branch models, thus confirming the validity of the choices of mixing treatment and mass-loss history. Moreover, we compare our new luminosity function with its counterpart in the Large Magellanic Cloud finding that the two distributions are very similar for dust-enshrouded sources, as expected from stellar evolutionary models. Finally, we derive a new fitting formula aimed to better determine BCs for C-stars.