Breakdown of the core mass-luminosity relation at high luminosities on the asymptotic giant branch

Hot bottom burning in asymptotic giant branch stars causes a breakdown of the core mass-luminosity (MC-L) relation. For stellar models with up-to-date input physics, including molecular opacities and the associated higher mixing length, the breakdown takes place at core masses greater than or approximately equal to 0.85 solar luminosity, i.e., luminosities brighter than Mbol of about -6. This occurs in stars of initial mass greater than or approximately equal to 5 solar luminosities for Population I (Z = 0.02) compositions, and greater than or approximately equal to 4 solar luminosities for Population II (Z = 0.001). For these stars, the luminosity increases much more steeply than the MC-L relation would predict, and is no longer independent of the stellar mass. Large mass loss rates can turn off hot bottom burning by significantly reducing the star's mass (and thus the temperature at the base of the convective envelope), causing the star's luminosity to decline toward the standard MC-L relation; such mass-loss rates are still an order of magnitude less than that observed in some OH/IR stars. Uncertainties in molecular opacities can significantly affect the extent of hot bottom burning, and thus the luminosities attained.