  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.
