The puzzle of the CNO isotope ratios in asymptotic giant branch carbon stars

Context. The abundance ratios of the main isotopes of carbon, nitrogen and oxygen are modified by the CNO-cycle in the stellar interiors. When the different dredge-up events mix the burning material with the envelope, valuable information on the nucleosynthesis and mixing processes can be extracted by measuring these isotope ratios. Aims. Previous determinations of the oxygen isotopic ratios in asymptotic giant branch (AGB) carbon stars were at odds with the existing theoretical predictions. We aim to redetermine the oxygen ratios in these stars using new spectral analysis tools and further develop discussions on the carbon and nitrogen isotopic ratios in order to elucidate this problem. Methods. Oxygen isotopic ratios were derived from spectra in the K -band in a sample of galactic AGB carbon stars of different spectral types and near solar metallicity. Synthetic spectra calculated in local thermodynamic equillibrium (LTE) with spherical carbon-rich atmosphere models and updated molecular line lists were used. The CNO isotope ratios derived in a homogeneous way, were compared with theoretical predictions for low-mass (1.5–3  M ⊙ ) AGB stars computed with the FUNS code assuming extra mixing both during the RGB and AGB phases. Results. For most of the stars the 16 O/ 17 O/ 18 O ratios derived are in good agreement with theoretical predictions confirming that, for AGB stars, are established using the values reached after the first dredge-up (FDU) according to the initial stellar mass. This fact, as far as the oxygen isotopic ratios are concerned, leaves little space for the operation of any extra mixing mechanism during the AGB phase. Nevertheless, for a few stars with large 16 O/ 17 O/ 18 O, the operation of such a mechanism might be required, although their observed 12 C/ 13 C and 14 N/ 15 N ratios would be difficult to reconcile within this scenario. Furthermore, J-type stars tend to have lower 16 O/ 17 O ratios than the normal carbon stars, as already indicated in previous studies. Excluding these peculiar stars, AGB carbon stars occupy the same region as pre-solar type I oxide grains in a 17 O/ 16 O vs. 18 O/ 16 O diagram, showing little spread. This reinforces the idea that these grains were probably formed in low-mass stars during the previous O-rich phases.