Explodability criteria for the neutrino-driven supernova mechanism

Massive stars undergoing iron core-collapse at the end of their evolution terminate their lives either in successful or failed supernovae (SNe). The physics of core-collapse supernovae (CCSNe) is complex, and their understanding requires computationally expensive simulations. Using these to predict CCSN outcomes over large, densely sampled parameter spaces of SN progenitors, as is needed e.g. for population synthesis studies, is thus not feasible. To remedy this situation, we present explodability criteria that allow us to predict the final fates of stars by evaluating stellar structure variables at the onset of core-collapse. The criteria are calibrated to predictions of a semi-analytical SN model, evaluated over a set of $\sim$~3,900 heterogeneous stellar progenitors (single, binary-stripped and accretor stars). Over these, the criteria achieve an accuracy of >99\% agreement with the semi-analytical model. The criteria are tested on 29 state-of-the-art 3D CCSN simulation outcomes from two different groups. Furthermore, we find that all explodability proxies needed for our pre-SN structure-based criteria have two distinct peaks and intervening valleys as a function of the carbon-oxygen (CO) core mass $M_\mathrm{CO}$, which coincide with failed and successful SNe, respectively. The CO core masses of explodability peaks shift systematically with metallicity, $Z$, and with timing of hydrogen-rich envelope removal by binary mass transfer. With these, we identify critical values in $M_\mathrm{CO}$ that define windows over which black holes form by direct collapse and formulate a CCSN recipe based on $M_\mathrm{CO}$ and $Z$, applicable for rapid binary population synthesis and other studies. Our explodability formalism is consistent with observations of Type~IIP, IIb/Ib and Ic supernova progenitors and partially addresses the missing Red Supergiant Problem by direct black hole formation.