Stars of $sim$ 8 - 10 $M_{odot}$ on the main-sequence form strongly electron-degenerate O+Ne+Mg core and become super-AGB stars. If such an O+Ne+Mg core grows to 1.38 $M_odot$, electron captures on $^{20}$Ne$(e, u_e)^{20}$F$(e, u_e)^{20}$O take place and ignite O-Ne deflagration around the center. In this paper, we perform two-dimensional hydrodynamics simulations of the propagation of the O-Ne flame to see whether such a flame induces a collapse of the O+Ne+Mg core due to subsequent electron capture behind the flame or triggers a thermonuclear explosion. We present a series of models to explore how the outcome depends on model parameters for the central density in the range from $10^{9.80}$ to $10^{10.20}$ g cm$^{-3}$, flame structure of both centered and off-centered ignition kernels, special and general relativistic effects, turbulent flame speed formula and the treatments of laminar burning phase. We find that the O+Ne+Mg core obtained from stellar evolutionary models has a high tendency to collapse into a neutron star. We obtain the bifurcation between the electron-capture collapse and thermonuclear explosion. We discuss the implication in nucleosynthesis and the possible observational signals of this class of supernovae.
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