Phase-transition-induced collapse of proto-compact stars and its implication for supernova explosions

A hadron-quark phase transition (PT) may trigger supernova explosions during stellar core collapse. However, both success and failure have occurred in previous attempts to explode dying stars via this mechanism. We systematically explore the outcomes of the PT-induced collapse of mock proto-compact stars (PCSs) with a constant entropy and lepton fraction, with spherically symmetric general relativistic hydrodynamic simulations and a controlled series of hybrid equations of state. Our results reveal the qualitative dependence of successful and failed explosions on the PT and quark matter characteristics. A small portion ($\sim\!0.04\%\!-\!1\%$) of the released binding energy $\Delta E_B$ transforms into the diagnostic explosion energy $E_{\rm exp,diag}$, which saturates at $\sim\!6\times10^{51}$ erg near the black hole formation. Note that our $E_{\rm exp,diag}$ represents an upper limit of the final explosion energies in realistic supernova simulations. We draw the phase diagrams indicative of the possible fates of supernova explosions driven by hadron-quark PTs, where the control parameters are the onset density, energy gap of the PT, and the quark matter speed of sound. Our findings can guide further self-consistent investigations on PT-driven core-collapse supernovae and help identify hadron-quark PT-induced PCS collapse from future observations.