The electromagnetic and gravitational-wave radiations of X-ray transient CDF-S XT2

Binary neutron star (NS) mergers may result in remnants of supra-massive or even stable NS, which have been supported indirectly by observed X-ray plateau of some gamma-ray bursts (GRBs) afterglow. Recently, Xue et al. (2019) discovered a X-ray transient CDF-S XT2 that is powered by a magnetar from merger of double NS via X-ray plateau and following stepper phase. However, the decay slope after the plateau emission is a little bit larger than the theoretical value of spin-down in electromagnetic (EM) dominated by losing its rotation energy. In this paper, we assume that the feature of X-ray emission is caused by a supra-massive magnetar central engine for surviving thousands of seconds to collapse black hole. Within this scenario, we present the comparisons of the X-ray plateau luminosity, break time, and the parameters of magnetar between CDF-S XT2 and other short GRBs with internal plateau samples. By adopting the collapse time to constrain the equation of state (EOS), we find that three EOSs (GM1, DD2, and DDME2) are consistent with the observational data. On the other hand, if the most released rotation energy of magnetar is dominated by GW radiation, we also constrain the upper limit of ellipticity of NS for given EOS, and it is range in $[0.32-1.3]\times 10^{-3}$. Its GW signal can not be detected by aLIGO or even for more sensitive Einstein Telescope in the future.