We perform hydrodynamical calculations of core-collapse supernovae (SNe) withlow explosion energies. These SNe do not have enough energy to eject the wholeprogenitor and most of the progenitor falls back to the central remnant. Weshow that such fallback SNe can have a variety of light curves (LCs) but theirphotospheric velocities can only have some limited values with lower limits. Wealso perform calculations of nucleosynthesis and LCs of several fallback SNmodel, and find that a fallback SN from the progenitor with a main-sequencemass of 13 Msun can account for the properties of the peculiar Type Iasupernova SN 2008ha. The kinetic energy and ejecta mass of the model are1.2*10^{48} erg and 0.074 Msun, respectively, and the ejected 56Ni mass is0.003 Msun. Thus, SN 2008ha can be a core-collapse SN with a large amount offallback. We also suggest that SN 2008ha could have been accompanied with longgamma-ray bursts and long gamma-ray bursts without associated SNe may beaccompanied with very faint SNe with significant amount of fallback which aresimilar to SN 2008ha.
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