We assess the occurrence of fast neutrino flavor instabilities in two three-dimensional state-of-the-art core-collapse supernova simulations performed using a two-moment three-species neutrino transport scheme: one with an exploding 9$mathrm{M_{odot}}$ and one with a non-exploding 20$mathrm{M_{odot}}$ model. Apart from confirming the presence of fast instabilities occurring within the neutrino decoupling and the supernova pre-shock regions, we detect flavor instabilities in the post-shock region for the exploding model. These instabilities are likely to be scattering-induced. In addition, the failure in achieving a successful explosion in the heavier supernova model seems to seriously hinder the occurrence of fast instabilities in the post-shock region. This is a consequence of the large matter densities behind the stalled or retreating shock, which implies high neutrino scattering rates and thus more isotropic distributions of neutrinos and antineutrinos. Our findings suggest that the supernova model properties and the fate of the explosion can remarkably affect the occurrence of fast instabilities. Hence, a larger set of realistic hydrodynamical simulations of the stellar collapse is needed in order to make reliable predictions on the flavor conversion physics.
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