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

Here we collect three unique bursts, GRBs\,060614, 211211A and 211227A, all characterized by a long-duration main emission (ME) phase and a rebrightening extended emission (EE) phase, to study their observed properties and the potential origin as neutron star-black hole (NSBH) mergers. NS-first-born (BH-first-born) NSBH mergers tend to contain fast-spinning (non-spinning) BHs that more easily (hardly) allow tidal disruption to happen with (without) forming electromagnetic signals. We find that NS-first-born NSBH mergers can well interpret the origins of these three GRBs, supported by that: (1) Their X-ray MEs and EEs show unambiguous fall-back accretion signatures, decreasing as \(\propto{t}^{-5/3}\), which might account for their long duration. The EEs can result from the fall-back accretion of \(r\)-process heating materials, predicted to occur after NSBH mergers. (2) The beaming-corrected local event rate density for this type of merger-origin long-duration GRBs is \(\mathcal{R}_0\sim2.4^{+2.3}_{-1.3}\,{\rm{Gpc}}^{-3}\,{\rm{yr}}^{-1}\), consistent with that of NS-first-born NSBH mergers. (3) Our detailed analysis on the EE, afterglow and kilonova of the recently high-impact event GRB\,211211A reveals it could be a merger between a \(\sim1.23^{+0.06}_{-0.07}\,M_\odot\) NS and a \(\sim8.21^{+0.77}_{-0.75}\,M_\odot\) BH with an aligned-spin of \(\chi_{\rm{BH}}\sim0.62^{+0.06}_{-0.07}\), supporting an NS-first-born NSBH formation channel. Long-duration burst with rebrightening fall-back accretion signature after ME, and bright kilonova might be commonly observed features for on-axis NSBHs. We estimate the multimessenger detection rate between gravitational waves, GRBs and kilonovae from NSBH mergers in O4 (O5) is \(\sim0.1\,{\rm{yr}}^{-1}\) (\(\sim1\,{\rm{yr}}^{-1}\)).