The recent detection of gravitational waves and electromagnetic counterpartsfrom the double neutron star merger event GW+EM170817, supports the standardparadigm of short gamma-ray bursts (SGRBs) and kilonovae/macronovae. It isimportant to reveal the nature of the compact remnant left after the merger,either a black hole or neutron star, and their physical link to the origin ofthe long-lasting emission observed in SGRBs. The diversity of the mergerremnants may also lead to different kinds of transients that can be detected infuture. Here we study the high-energy emission from the long-lasting centralengine left after the coalescence, under certain assumptions. In particular, weconsider the X-ray emission from a remnant disk and the non-thermal nebularemission from disk-driven outflows or pulsar winds. We demonstrate thatlate-time X-ray and high-frequency radio emission can provide usefulconstraints on properties of the hidden compact remnants and their connectionsto long-lasting SGRB emission, and we discuss the detectability of nearbymerger events through late-time observations at $\sim30-100$ d after thecoalescence. We also investigate the GeV-TeV gamma-ray emission that occurs inthe presence of long-lasting central engines, and show the importance ofexternal inverse-Compton radiation due to up-scattering of X-ray photons byrelativistic electrons in the jet. We also search for high-energy gamma-raysfrom GW170817 in the Fermi-LAT data, and report upper limits on suchlong-lasting emission. Finally, we consider the implications of GW+EM170817 anddiscuss the constraints placed by X-ray and high-frequency radio observations.
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