Soft X-ray extended emissions of short gamma-ray bursts as electromagnetic counterparts of compact binary mergers: Possible origin and detectability

We investigate the possible origin of extended emissions (EEs) of short gamma-ray bursts with an isotropic energy of ∼10^50-51 erg and a duration of a few 10 s to ∼100 s, based on a 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 ∼0.1 M _⊙ 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 ≳ 10⁵² erg can be extracted with an observed timescale of ≳ 30(1 + z) s with a relatively small disk viscosity parameter of α < 0.01. Such a BZ power dissipates by clashing with non-relativistic pre-ejected matter of mass M ∼ 10^-(2-4) M _⊙, and forms a mildly relativistic fireball. We show that the dissipative photospheric emissions from such fireballs are likely in the soft X-ray band (1-10 keV) for M ∼ 10^-2 M _⊙, possibly in NS-NS mergers, and in the BAT band (15-150 keV) for M ∼ 10^-4 M _⊙, possibly in NS-BH mergers. In the former case, such soft EEs can provide a good chance of ∼6 yr^-1 (ΔΩ_softEE/4π) (script R_GW/40 yr^-1) for simultaneous detections of the gravitational waves with a ∼0small letter o with dot below.1 angular resolution by soft X-ray survey facilities like the Wide-Field MAXI. Here, ΔΩ_softEE is the beaming factor of the soft EEs and script R_GW is the NS-NS merger rate detectable by the advanced LIGO, the advanced Virgo, and KAGRA.