Prevention of High-Luminosity Carbon Stars by Hot Bottom Burning

CNO abundances are presented for theoretical models of asymptotic giant branch stars of 4, 5, and 6 Msun with Z = 0.02 and Z = 0.001. Self-consistent stellar evolutionary models were computed, starting on the pre-main sequence and terminating after a series of helium shell flashes on the asymptotic giant branch (AGB). The 5 and 6 Msun cases encountered hot bottom burning, with temperatures at the base of the convective envelope reaching (60-80) × 10⁶ K for Z = 0.02 and (80-100) × 10⁶ K for Z = 0.001. A luminosity boundary near MCbol ∼ -6.4 is predicted; for brighter luminosities, hot bottom burning will prevent carbon star formation (these will be S stars, with 3 ≲ ¹²C/¹³C ≲ 18, and for a period they will be super lithium-rich). For luminosities fainter than MCbol, carbon stars can be formed as well as S stars, with values of ¹²C/¹³C ≳ 14. This luminosity boundary MCbol is rather insensitive to metallicity, to changes in low-temperature molecular opacities, to changes in the mass-loss rate, and to the presence or absence of helium core breathing pulses during the earlier core helium burning stage. To burn envelope carbon significantly requires base temperatures ∼80 × 10⁶ K. Since only ∼50 × 10⁶ K is required to produce super-rich lithium stars, some of the most luminosity carbon can be super lithium-rich. The higher metallicity stars spend a larger fraction of their time on the asymptotic giant branch passing through this base temperature range of (50-80) × 10⁶ K; thus super lithium-rich carbon stars are more probable for higher metallicities. The above predictions are in excellent agreement with observations of carbon stars and super-rich lithium stars in the galaxy and the Magellanic Clouds.