In the classical picture, electron-capture supernovae and the accretion-induced collapse of oxygen-neon white dwarfs (ONeWDs) undergo an oxygen deflagration phase before gravitational collapse produces a neutron star (NS). These types of core collapse events are postulated to explain several astronomical phenomena. In this work, the deflagration phase is simulated for the first time using multidimensional hydrodynamics, with the aim of gaining new insight into the explosive deaths of $8-10~M_odot$ stars and ONeWDs that accrete material from a binary companion star. The main aim is to determine whether these events are thermonuclear or core-collapse supernova explosions, and hence whether NSs are formed by such phenomena. The deflagration is simulated in ONe cores with three different central ignition densities. The intermediate density case is perhaps the most realistic, being based on recent nuclear physics calculations and 1D stellar models. The 3D hydrodynamic simulations presented in this work begin from a centrally confined flame structure using a level-set-based flame approach and are performed in $256^3$ and $512^3$ numerical resolutions. In the simulations with intermediate and low ignition density, the cores do not appear to collapse into NSs. Instead, almost a solar mass of material becomes unbound from the cores, leaving bound remnants. These simulations represent the case in which semiconvective mixing during the electron-capture phase preceding the deflagration is inefficient. The masses of the bound remnants double when Coulomb corrections are included in the EoS, however they still do not exceed the effective Chandrasekhar mass and, hence, would not collapse into NSs. The simulations with the highest ignition density ($log_{10}rho_{rm c}=10.3$), representing the case where semiconvective mixing is very efficient, show clear signs that the core will collapse into a NS.
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