1999ApJ...510..232B

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 <sup>12</sup>C/<sup>13</sup>C 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 H-burning shell and that CBP begins when the H-burning shell erases the molecular weight discontinuity (``µ-barrier'') established by first dredge-up. For Population I stars, none of the other CNO isotopes except ¹⁵N are expected to be altered by CBP. (If ¹⁸O 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 AGB than on the red giant branch [RGB]–and should also result in a much lower ¹²C/¹³C ratio than is observed in the relevant AGB 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 H-shell burning temperatures of low-metallicity stars. In low-mass Population II 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 ``µ-barrier''). For the CNO isotopes ¹²C, ¹³C, ¹⁴N, ¹⁶O, ¹⁷O, and ¹⁸O, 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 AGB 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 ¹³C, ¹⁴N, and ¹⁷O in the universe. The light elements (³He, ⁴He, ⁷Li, ⁹Be, ¹⁰B, and ¹¹B) are discussed in a companion paper.