The CNO isotopes: Deep circulation in red giants and first and second dredge-up

It is demonstrated that deep circulation mixing below the base of the standard convective envelope, and the consequent '"cool bottom processing" (CBP) of the CNO isotopes, can reproduce the trend with stellar mass of the C-12/C-13 observations in low-mass red giants. (This trend is opposite to what is expected from standard first dredge-up.) Our models assume that extra mixing always reaches to the same distance in temperature from the II-burning shell and that CBP begins when the II-burning shell erases the molecular weight discontinuity ("mu-barrier") established by first dredge-up. For Population I stars, none of the other CNO isotopes except N-15 are expected to be altered by CBP. (If O-18 depletion occurs on the asymptotic giant branch [AGB], as some observations suggest, it would require that extra mixing reach closer to the H-burning shell on the AGE than on the red giant branch [RGB]-and should also result in a much lower C-12/C-13 ratio than is observed in the relevant AGE stars.) CBP increases dramatically as one reduces the stellar mass or metallicity-roughly as M-2 on the RGB, because of the longer RGB of low-mass stars, and roughly as Z(-1), because of the higher II-shell burning temperatures of low-metallicity stars. In low-mass Population IT stars, all the CNO isotopes are expected to be significantly altered by CBP. Field Population II stars exhibit RGB abundances consistent with the predictions of our CBP models that have been normalized to reproduce the Population I RGB abundances. On the other hand, globular cluster stars are observed to encounter much more extensive processing; additionally, CBP is observed to start near the base of the globular cluster RGB (overcoming any "mu-barrier"). For the CNO isotopes C-12, C-13, N-14, O-16, O-17, and O-18, we also present self-consistent calculations of the consequences of both first and second dredge-up, i.e., of standard convection during the RGB and AGE stages, over a wide range of stellar masses (0.8-9 M-.) and metallicities (Z = 0.02-0.0001). We demonstrate that the common low- and intermediate-mass stars are a prime source of C-13, N-14, and O-17 in the universe. The light elements (He-3, He-4, Li-7, Be-9, B-10, and B-11) are discussed in a companion paper.