Final compact remnants in core-collapse supernovae from 20 to 40 $M_\odot$: the lower mass gap

A mass paucity of compact objects in the range of $\sim 2-5 ~M_\odot$ has been suggested by X-ray binary observations, namely, the "lower mass gap". Gravitational wave detections have unlocked another mass measurement method, and aLIGO/Virgo has observed some candidates in the gap. We revisit the numerical simulations on the core-collapse supernovae (CCSNe) for $\sim 20-40~M_\odot$ progenitor stars with differently initial explosion energies. As a result, the lower explosion energy naturally causes more efficient fallback accretion for low-metallicity progenitors, and then the newborn black holes (BHs) in the center of the CCSNe can escape from the gap, but neutron stars cannot easily collapse into BHs in the gap; nevertheless, the final remnants of the solar-metallicity progenitors stick to the gap. If we consider that only drastic CCSNe can be observed and that those with lower explosion energies are universal, the lower mass gap can be reasonably built. The width and depth of the gap are mainly determined by the typical CCSN initial explosion energy and metallicity. One can expect that the future multi-messenger observations of compact objects delineate the shape of the gap, which might constrain the properties of the CCSNe and their progenitors.