Shock Revival Energy Budget and the Fraction of Binding Energy Available to Explode a Star

Neutrino heating must revive a stalled shock using only a small share of the gravitational binding energy released at collapse. The paper quantifies that share for representative explosions and asks whether the required efficiency leaves room for additional losses without invoking new energy sources. Using the calculation described in the Methods, the headline results are: typical_efficiency_pct = 0.333, hypernova_efficiency_pct = 2.59, Ebind_typical_erg = 3e+53. An ordinary explosion converts well under one percent of the binding energy into kinetic energy, while a hypernova still uses only a few percent. The budget is therefore comfortable in total energy and tight only in coupling: the difficulty of explosion models lies in transferring energy to the shock, not in any shortage of released energy. This distinction matters because proposals that add energy and proposals that improve coupling predict different neutrino signals. This study is simulated and computed from stated assumptions; it is not a measurement. All headline numbers in this abstract appear in the deposited results file and are reproduced by running the deposited code without modification.