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Long-lasting emission of short gamma-ray bursts (GRBs) is crucial to revealthe physical origin of the central engine as well as to detect electromagnetic(EM) counterparts to gravitational waves (GWs) from neutron star binarymergers. We investigate 65 X-ray light curves of short GRBs, which is six timesmore than previous studies, by combining both Swift/BAT and XRT data. The lightcurves are found to consist of two distinct components at $>5\sigma$ withbimodal distributions of luminosity and duration, i.e., extended (withtimescale $\lesssim10^3$ s) and plateau emission (with timescale $\gtrsim10^3$s), which are likely the central engine activities but not afterglows. Theextended emission has an isotropic energy comparable to the prompt emission,while the plateau emission has $\sim0.01-1$ times of that energy. A half (50\%)of our sample has both components, while the other half is consistent withhaving both components. This leads us to conjecture that almost all short GRBshave both the extended and plateau emission. The long-lasting emission can beexplained by the jets from black holes with fallback ejecta, and could powermacronovae (or kilonovae) like GRB 130603B and GRB 160821B. Based on theobserved properties, we quantify the detectability of EM counterparts to GWs,including the plateau emission scattered to the off-axis angle, with CALET/HXM,INTEGRAL/SPI-ACS, Fermi/GBM, MAXI/GSC, Swift/BAT, XRT, future ISS-Lobster/WFI,Einstein Probe/WXT, and eROSITA.

Bimodal Long-Lasting Components in Short Gamma-Ray Bursts: Promising Electromagnetic Counterparts to Neutron Star Binary Mergers