Title: Supernova Explosions of the Lowest-Mass Massive Star Progenitors

Abstract: We here focus on the behavior of supernovae that technically explode in 1D (spherical symmetry). When simulated in 3D, however, the outcomes of representative progenitors of this class are quite different in almost all relevant quantities. In 3D, the explosion energies can be two to ten times higher, and there are correspondingly large differences in the $^{56}$Ni yields. These differences between the 3D and 1D simulations reflect in part the relative delay to explosion of the latter and in the former the presence of proto-neutron star convection that boosts the driving neutrino luminosities by as much as $\sim$50\% at later times. In addition, we find that the ejecta in 3D models are more neutron-rich, resulting in significant weak r-process and $^{48}$Ca yields. Furthermore, we find that in 3D the core is an interesting, though subdominant, source of acoustic power. In summary, we find that though a model might be found theoretically to explode in 1D, one must perform supernova simulations in 3D to capture most of the associated observables. The differences between 1D and 3D models are just too large to ignore.