Isotropic Detectable X-ray Counterparts to Gravitational Waves from Neutron Star Binary Mergers

Neutron star binary mergers are strong sources of gravitational waves (GWs). Promising electromagnetic counterparts are short gamma-ray bursts (GRBs) but the emission is highly collimated. We propose that the scattering of the long-lasting plateau emission in short GRBs by the merger ejecta produces nearly isotropic emission for $\sim 10^4$ s with flux $10^{-13}-10^{-10}$ erg cm$^{-2}$ s$^{-1}$ at 100 Mpc in X-ray. This is detectable by Swift XRT and wide field X-ray detectors such as ISS-Lobster, Einstein Probe, eROSITA and WF-MAXI, which are desired by the infrared and optical follow-ups to localize and measure the distance to the host galaxy. The scattered X-rays obtain linear polarization, which correlates with the jet direction, X-ray luminosity and GW polarizations. The activity of plateau emission is also a natural energy source of a macronova (or kilonova) detected in short GRB 130603B without the $r$-process radioactivity.