2002A&A...390..987B

Following our study of the carbon-rich giants in the HR diagram and of their luminosity function (Paper III, Bergeat et al., 2002A&A...390..967B), we investigate the pulsation data of the long period variables (LPVs) included in our sample. Pulsation modes (fundamental, overtone(s)) for carbon LPVs are identified in the period-radius diagram, making use of observed bi-periodicity in a small subsample of those stars, and of comparison to models. Mean pulsation masses are then deduced from theoretical PMR-relations, with due attention paid to a possible bias while averaging. Mean (present) pulsation masses (0.6-4.0M_☉) are found to increase along the group sequence HC5 to CV6, with still larger masses possibly associated with cool extreme CV7-objects with strong mass loss and thick circumstellar shells. This is consistent with the 0.8-4M_☉ range of initial masses found in Paper III for the majority of carbon-rich giants affected by mass loss during their evolution. The pulsation masses found for a few HC-stars (M≤0.8M_☉) are consistent with their low initial masses (M_i≲1.1M_☉), as inferred from their thick disk membership (age ≃11Gyr?) and locus in the HR diagram. A mean pulsation mass of ≃0.6M_☉ is found for the three population II Cepheids in the sample. A mass-luminosity diagram is proposed for the Galactic carbon giants. The data from observations is found consistent with theoretical predictions from AGB modeling, specially the third dredge-up (TDU) through thermal pulses (TP) with a carbon star formation line (CSFL) for TP-AGB stars. It appears that the CV-giants are close to the tip and end of their evolutionary tracks in the TP-AGB of the HR diagram. It is confirmed that this end shifts toward lower effective temperatures and higher luminosities, with increasing masses. It is shown that the C/O abundance ratios do correlate with effective temperatures, according to three distinct distributions (halo CH stars, thick disk HC-stars, and thin disk CV-stars). The mean stellar density decreases along the HC5-CV7 sequence, while the surface gravity remains nearly constant at about 0.5 CGS unit (logg≃-0.3;5x10^–3SI). The nature of (thin disk) CV-stars as TP-AGB objects being confirmed, the discussion is focused on (thick disk) HC-stars since the origin of these old low-mass giants remains unclear. Unpredicted extra mixing on RGB and/or E-AGB is favored. Evolution from (old, low O/H) dwarf carbon stars is also considered since observations of metal-poor stars and recent calculations point to large supersolar [C/Fe] ratios in Population III objects and contamination through rapid cycling in the interstellar medium.