Identifying gravitational wave emission signature in electromagnetic observations of short gamma-ray bursts

Observations of the long-lived X-ray plateau in short gamma-ray burst (SGRB) afterglow suggest that a portion of binary neutron star mergers would leave behind a rapidly spinning, strongly magnetized neutron star (millisecond magnetar). The new-born magnetar may undergo large deformation due to magnetic distortion or unstable oscillation, which would emit the extended gravitational wave (GW) associated with the SGRB X-ray plateau. In this work, we focus on the spin-down luminosity evolution of magnetar by considering the spin energy loss due to the GW and magnetic dipole radiation, and systematically analyse the SGRB light curves of our magnetar sample. The results show that GW emission signatures have existed in the spin-down stage of GRB 090426 and GRB 150424A. We also present constraints on the ellipticity of the new-born magnetar as epsilon < 1.58 x 10(-3)(B/10(15) G)(P/1 ms). The magnetar can lose significant spin energy via GW radiation if the ellipticity epsilon >= 10(-3) and magnetic field strength B similar to 10(15) G. In addition, we derive the evolution of GW strain for magnetars through their spin-down processes. This result shows that the GW signals from these magnetars may be detectable for the Einstein Telescope (ET). For a rapidly spinning magnetar (P similar to 1 ms), the detection horizons for aLIGO O3, aLIGO O5, and ET detectors are similar to 60, similar to 210, and similar to 900 Mpc, respectively. The detection of the GW emission from new-born millisecond magnetar may reveal the interior composition of magnetar in the near future.