The joint detection of the gravitational wave signal and the electromagnetic emission from a binary neutron star merger can place unprecedented constraint on the equation of state of supranuclear matter. Although a variety of electromagnetic counterparts have been observed for GW170817, including a short gamma-ray burst, kilonova, and the afterglow emission, the nature of the merger remnant is still unclear, however. The X-ray plateau is another important characteristics of short gamma-ray bursts. This plateau is probably due to the energy injection from a rapidly rotating magnetar. We investigate what we can learn from the detection of a gravitational wave along with the X-ray plateau. In principle, we can estimate the mass of the merger remnant if the X-ray plateau is caused by the central magnetar. We selected eight equations of state that all satisfy the constraint given by the gravitational wave observation, and then calculated the mass of the merger remnants of four short gamma-ray bursts with a well-measured X-ray plateau. If, on the other hand, the mass of the merger remnant can be obtained by gravitational wave information, then by comparing the masses derived by these two different methods can further constrain the equation of state. We discuss the possibility that the merger product is a quark star. In addition, we estimate the possible mass range for the recently discovered X-ray transient CDF-S XT2 that probably originated from a binary neutron star merger. Finally, under the assumption that the post-merger remnant of GW170817 was a supramassive neutron star, we estimated the allowed parameter space of the supramassive neutron star and find that in this case, the magnetic dipole radiation energy is so high that it may have some effects on the short gamma-ray burst and kilonova emission. The lack of detection of these effects suggests that the merger product of GW170817 may not be a supermassive neutron star.
Short gamma-ray bursts from binary neutron star mergers: the time-reversal scenario