ON CARBON BURNING in SUPER ASYMPTOTIC GIANT BRANCH STARS

We explore the detailed and broad properties of carbon burning in Super Asymptotic Giant Branch (SAGB) stars with 2755 MESA stellar evolution models. The location of first carbon ignition, quenching location of the carbon-burning flames and flashes, angular frequency of the carbon core, and carbon core mass are studied as a function of the zero-age main sequence (ZAMS) mass, initial rotation rate, and mixing parameters such as convective overshoot, semiconvection, thermohaline, and angular momentum transport. In general terms, we find that these properties of carbon burning in SAGB models are not a strong function of the initial rotation profile, but are a sensitive function of the overshoot parameter. We quasi-analytically derive an approximate ignition density, ρ_ign ≈ 2.1 × 10⁶ g cm^-3, to predict the location of first carbon ignition in models that ignite carbon off-center. We also find that overshoot moves the ZAMS mass boundaries where off-center carbon ignition occurs at a nearly uniform rate of ΔM_ZAMS/Δf_ov ≈ 1.6 . For zero overshoot, f_ov = 0.0, our models in the ZAMS mass range ≈8.9-11 show off-center carbon ignition. For canonical amounts of overshooting, f_ov = 0.016, the off-center carbon ignition range shifts to ≈7.2-8.8 . Only systems with f_ov ≥ 0.01 and ZAMS mass ≈7.2-8.0 show carbon burning is quenched a significant distance from the center. These results suggest a careful assessment of overshoot modeling approximations on claims that carbon burning quenches an appreciable distance from the center of the carbon core.