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Abstract

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
$\sim0.1\,{\rm{yr}}^{-1}$ ($\sim1\,{\rm{yr}}^{-1}$).