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Abstract
We investigate the possible origin of extended emissions (EE) of short
gamma-ray bursts (SGRBs) with an isotropic energy of $\sim
10^{50\mbox{-}51} \ \rm erg$ and a duration of $\sim 100 \ \rm s$, based
on the compact binary (neutron star (NS
)-NS or NS-black hole (BH))
merger scenario. We analyze the evolution of magnetized
neutrino-dominated accretion disks of mass $\sim 0.1 \ M_\odot$ around
BHs formed after the mergers, and estimate the power of relativistic
outflows via the Blandford-Znajek (BZ) process. We show that a
rotation
energy of the BH up to $\sim 10^
{53} \ \rm erg$ can be extracted with a
time scale of $\sim 100 \ \rm s$ with a disk viscosity parameter of
$\alpha \sim 0.01$. Such a BZ power dissipates by clashing with
non-relativistic pre-ejected matter of mass $M \sim 10^{-(2\mbox{-}4)} \
M_\odot$, and form a mildly relativistic fireball. We show that the
dissipative photospheric emissions from such fireballs are likely in
soft X-ray band ($1\mbox{-}10 \ \rm keV$) for $M \sim 10^
{-2} M_\odot$
possibly in NS-NS mergers, and in the BAT band ($15\mbox{-}150 \ \rm
keV$) for $M \sim 10^
{-4} M_\odot$ possibly in NS-BH mergers. In the
former case, such soft EEs can provide a good chance of $\sim {\rm 6 \
yr^
{-1}} \ (\Delta \Omega_{softEE}/4\pi) \ ({\cal R
}_
{GW
}/40 \ {\rm
yr^
{-1}}
)$ for simultaneous detections of the gravitational waves with a
$\sim 0.1^\circ$ angular resolution by soft X-ray survey facilities like
Wide-Field MAXI. Here, $\Delta \Omega_{softEE}$ is the beaming factor of
the soft EEs and ${\cal R
}_
{GW
}$ is the NS-NS merger rate detectable by
advanced LIGO, advanced Virgo, and KAGRA. While in the latter case, the
observed EEs, which are associated with $\sim 25\%$ of {\it Swift}
SGRBs, can be well explained although the simultaneous detection rate
with the GWs is expected to be very low $\lesssim 10^
{-3} \ {\rm
yr
}^
{-1} $.
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