Revisiting black hole hyperaccretion in the center of gamma-ray bursts for the lower mass gap

The ultrarelativistic jets triggered by neutrino annihilation processes or Blandford-Znajek (BZ) mechanisms in stellar-mass black hole (BH) hyperaccretion systems are generally considered to power gamma-ray bursts (GRBs). Due to the high accretion rate, the central BHs might grow rapidly on a short timescale, providing a new way to understand "the lower mass gap" problem. In this paper, we use the BH hyperaccretion model to investigate BH mass growth based on observational GRB data. The results show that (i) if the initial BH mass is set as $3~M_\odot$, the neutrino annihilation processes are capable of fueling the BHs to escape the lower mass gap for more than half of long-duration GRBs (LGRBs), while the BZ mechanism is inefficient on triggering BH growths for LGRBs; (ii) the mean BH mass growths in the case of LGRBs without observable supernova (SN) association are much larger than these in the case of LGRBs associated with SNe for both mechanisms, which imply that more massive progenitors or lower SN explosion energies prevail throughout the former cases; (iii) for the short-duration GRBs, the mean BH mass growths are satisfied with the mass supply limitation in the scenario of compact object mergers, but the hyperaccretion processes are unable to rescue BHs from the gap in binary neutron star (NS) mergers or the initial BH mass being $3~M_\odot$ after NS-BH mergers.