A two-parameter criterion for classifying the explodability of massive stars by the neutrino-driven mechanism

Thus far, judging the fate of a massive star (either a neutron star [NS] or a black hole) solely by its structure prior to core collapse has been ambiguous. Our work and previous attempts find a nonmonotonic variation of successful and failed supernovae with zero-age main-sequence mass, for which no single structural parameter can serve as a good predictive measure. However, we identify two parameters computed from the pre-collapse structure of the progenitor, which in combination allow for a clear separation of exploding and nonexploding cases with only a few exceptions (∼1%–2.5%) in our set of 621 investigated stellar models. One parameter is M₄, defining the normalized enclosed mass for a dimensionless entropy per nucleon of s = 4, and the other is ${\mu }_4\equiv \left(dm/M_{\odot }\right)/\left(dr/1000km\right){|}_{s=4}$, being the normalized mass derivative at this location. The two parameters μ₄ and M₄μ₄ can be directly linked to the mass-infall rate, $\dot{M}$, of the collapsing star and the electron-type neutrino luminosity of the accreting proto-NS, $L_{{\nu }_e}\propto M_{ns}\dot{M}$, which play a crucial role in the "critical luminosity" concept for the theoretical description of neutrino-driven explosions as runaway phenomena of the stalled accretion shock. All models were evolved employing the approach of Ugliano et al. for simulating neutrino-driven explosions in spherical symmetry. The neutrino emission of the accretion layer is approximated by a gray transport solver, while the uncertain neutrino emission of the 1.1 M_⊙ proto-NS core is parameterized by an analytic model. The free parameters connected to the core-boundary prescription are calibrated to reproduce the observables of SN 1987A for five different progenitor models.