Long-duration Gamma-Ray Burst and Associated Kilonova Emission from Fast-spinning Black Hole-Neutron Star Mergers

Gamma-ray bursts (GRBs) have been phenomenologically divided into long- and short-duration populations, generally corresponding to collapsar and compact merger origins, respectively. Here, we collect three unique bursts, GRBs 060614, 211211A, and 211227A, all of which are characterized by a long-duration main emission (ME) phase and a rebrightening extended emission (EE) phase, to study their observed properties and their potential origins as neutron star-black hole (NSBH) mergers. NS-first-born (BH-first-born) NSBH mergers tend to contain fast-spinning (nonspinning) BHs that more easily (hardly) allow tidal disruption to occur, while (without) forming electromagnetic signals. We find that NS-first-born NSBH mergers can well interpret the origins of these three GRBs, supported by the following. (1) Their X-ray MEs and EEs show unambiguous fallback accretion signatures, decreasing as t -5/3, which might account for their long durations. The EEs could result from the fallback accretion of r-process heating materials, which is predicted to occur after NSBH mergers. (2) The beaming-corrected local event-rate density for these types of merger-origin long-duration GRBs is .4-1.3+2.3Gpc-3yr-1, consistent with that of NS-first-born NSBH mergers. (3) Our detailed analysis of the EE, afterglow, and kilonova of the recent high-impact event GRB 211211A reveals that it could be a merger between a .23-0.07+0.06M NS and a.21-0.75+0.77M⊙ BH, with an aligned spin of χBH 62-0.07+0.06, supporting an NS-first-born NSBH formation channel. A long-duration burst, with a rebrightening fallback accretion signature after the ME, and a bright kilonova, might be commonly observed features for on-axis NSBH mergers. We estimate the multimessenger detection rate between gravitational waves, GRBs, and kilonova emissions from NSBH mergers in O4 (O5) to be 1 yr-1 ( yr-1).