Quantifying the Impact of the Si/O Interface in CCSN Explosions Using the Force Explosion Condition

The explosion mechanism of a core-collapse supernova is a complex interplay between neutrino heating and cooling (including the effects of neutrino-driven convection), the gravitational potential, and the ram pressure of the infalling material. To analyze the post-bounce phase of a supernova, one can use the generalized Force Explosion Condition (FEC+), which succinctly formalizes the interplay among these four phenomena in an analytical condition, consistent with realistic simulations. In this paper, we use the FEC+ to study the post-bounce phase of 341 spherically symmetric simulations, where convection is included through a time-dependent mixing length approach. We find that the accretion of the Si/O interface through the expanding shock can significantly change the outcome of the supernova by driving the FEC+ above the explosion threshold. We systematically explore this by (i) artificially smoothing the pre-supernova density profile, and (ii) artificially varying the mixing length. In both cases, we find that large-enough density contrasts at the Si/O interface lead to successful shock revival only if the FEC+ is already close to the explosion threshold. Furthermore, we find that the accretion of the Si/O interface has a substantial effect on the critical condition for supernova explosions, contributing between 5\% and 15\%, depending on how pronounced the density contrast at the interface is. Earlier studies showed that convection affects the critical condition by 25--30\%, which demonstrates that the accretion of the Si/O interface through the shock can play a nearly comparable role in influencing shock dynamics.