Missing Red Supergiants and Carbon Burning

Recent studies on direct imaging of Type II core-collapse supernova progenitors indicate a possible threshold around $M_{\rm ZAMS}\sim 16-20$ M$_\odot$, where red supergiants with larger birth masses do not appear to result in supernova explosions and instead implode directly into a black hole. In this study we argue that it is not a coincidence that this threshold closely matches the critical transition of central Carbon burning in massive stars from the convective to radiative regime. In lighter stars, Carbon burns convectively in the center and result in compact final presupernova cores that are likely to result in explosions, while in heavier stars after the transition, it burns as a radiative flame and the stellar cores become significantly harder to explode. Using the KEPLER code we demonstrate the sensitivity of this transition to the rate of $^{12}$C$(\alpha,\gamma)^{16}$O reaction and the overshoot mixing efficiency, and we argue that the upper mass limit of exploding red supergiants could be employed to constrain uncertain input physics of massive stellar evolution calculations. The initial mass corresponding to the central Carbon burning transition range from 14 to 26 M$_\odot$ in recently published models from various groups and codes, and only a few are in agreement with the estimates inferred from direct imaging studies.