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Some massive stars end their lives as \textit{failed} core-collapsesupernovae (CCSNe) and become black holes (BHs). Although in this class ofphenomena the stalled supernova shock is not revived, the outer stellarenvelope can still be partially ejected. This occurs because the hydrodynamicequilibrium of the star is disrupted by the gravitational mass loss of theprotoneutron star (PNS) due to neutrino emission. We develop a simple modelthat emulates PNS evolution and its neutrino emission and use it to simulatefailed CCSNe in spherical symmetry for a wide range of progenitor stars. Ourmodel allows us to study mass ejection of failed CCSNe where the PNS collapsesinto a BH within $\sim100\,{\rm ms}$ and up to $\sim10^6\,{\rm s}$. We performfailed CCSNe simulations for 262 different pre-SN progenitors and determine howthe energy and mass of the ejecta depend on progenitor properties and theequation of state (EOS) of dense matter. In the case of a future failed CCSNobservation, the trends obtained in our simulations can be used to placeconstraints on the pre-SN progenitor characteristics, the EOS, and on PNSproperties at BH formation time.

A Parameterized Neutrino Emission Model to Study Mass Ejection in Failed Core-collapse Supernovae