X-ray guided gravitational-wave search for binary neutron star merger remnants

X-ray observations of some short gamma-ray bursts indicate that a long-lived neutron star can form as a remnant of a binary neutron star merger. We develop a gravitational-wave detection pipeline for a long-lived binary neutron star merger remnant guided by these counterpart electromagnetic observations. We determine the distance out to which a gravitational-wave signal can be detected with Advanced LIGO at design sensitivity and the Einstein Telescope using this method, guided by X-ray data from GRB140903A as an example. Such gravitational waves can in principle be detected out to $\sim$ 20 Mpc for Advanced LIGO and $\sim$ 450 Mpc for the Einstein Telescope assuming a fiducial ellipticity of $10^{-2}$. However, in practice we can rule out such high values of the ellipticity as the total energy emitted in gravitational waves would be greater than the total rotational energy budget of the system. We show how these observations can be used to place upper limits on the ellipticity using these energy considerations. For GRB140903A, the upper limit on the ellipticity is $10^{-3}$, which lowers the detectable distance to $\sim$ 2 Mpc and $\sim$ 45 Mpc for Advanced LIGO and the Einstein Telescope, respectively.