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 ZAMS mass, initial rotation rate, and mixing parameters such as convective overshoot, semiconvection, thermohaline and angular momentum transport. In general terms, we find 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, $rho_{ign} approx 2.1 times 10^6$ 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 $Delta M_{rm ZAMS}$/$Delta f_{rm{ov}}approx$ 1.6 $M_{odot}$. For zero overshoot, $f_{rm{ov}}$=0.0, our models in the ZAMS mass range $approx$ 8.9 to 11 $M_{odot}$ show off-center carbon ignition. For canonical amounts of overshooting, $f_{rm{ov}}$=0.016, the off-center carbon ignition range shifts to $approx$ 7.2 to 8.8 $M_{odot}$. Only systems with $f_{rm{ov}}$ $geq 0.01$ and ZAMS mass $approx$ 7.2-8.0 $M_{odot}$ 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.
Using population synthesis tools we create a synthetic Kepler Input Catalogue (KIC) and subject it to the Kepler Stellar Classification Program (SCP) method for determining stellar parameters such as the effective temperature Teff and surface gravity
g. We achieve a satisfactory match between the synthetic KIC and the real KIC in the log g vs log Teff diagram, while there is a significant difference between the actual physical stellar parameters and those derived by the SCP of the stars in the synthetic sample. We find a median difference Delta Teff=+500K and Delta log g =-0.2dex for main-sequence stars, and Delta Teff=+50K and Delta log g =-0.5dex for giants, although there is a large variation across parameter space. For a MS star the median difference in g would equate to a ~3% increase in stellar radius and a consequent ~3% overestimate of the radius for any transiting exoplanet. We find no significant difference between Delta Teff and Delta log g for single stars and the primary star in a binary system. We also re-created the Kepler target selection method and found that the binary fraction is unchanged by the target selection. Binaries are selected in similar proportions to single star systems; the fraction of MS dwarfs in the sample increases from about 75% to 80%, and the giant star fraction decreases from 25% to 20%.
