We perform hydrodynamical calculations of core-collapse supernovae (SNe) with low explosion energies. These SNe do not have enough energy to eject the whole progenitor and most of the progenitor falls back to the central remnant. We show that such fallback SNe can have a variety of light curves (LCs) but their photospheric velocities can only have some limited values with lower limits. We also perform calculations of nucleosynthesis and LCs of several fallback SN models, and find that a fallback SN from the progenitor with a main-sequence mass of 13 M⊙ can account for the properties of the peculiar Type Ia supernova SN 2008ha. The kinetic energy and ejecta mass of the model are 1.2 × 1048 erg and 0.074 M⊙, respectively, and the ejected 56Ni mass is 0.003 M⊙. Thus, SN 2008ha can be a core-collapse SN with a large amount of fallback. We also suggest that SN 2008ha could have been accompanied by long gamma-ray bursts, and long gamma-ray bursts without associated SNe may be accompanied by very faint SNe with significant amount of fallback, which are similar to SN 2008ha.
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