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 $\sim 20\mathrm{Mpc}$ for Advanced LIGO and $\sim 450\mathrm{Mpc}$ 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 $\sim 2\mathrm{Mpc}$ and $\sim 45\mathrm{Mpc}$ for Advanced LIGO and the Einstein Telescope, respectively.

Figure 1

The energy budget of a postmerger remnant inferred from GRB140903A with ellipticity $\epsilon ={10}^{-2}$ (solid curves) and ${10}^{-3}$ (dashed curves) with the red shaded region indicating the $2\sigma$ confidence interval. The grey shaded region above the solid black horizontal line is nonphysical as discussed in Sec. 2a.

Figure 2

Optimal matched-filter signal-to-noise ratio ${\rho }_{\mathrm{opt}}$ for a typical SGRB postmerger signal at a distance of 40 Mpc as a function of the gravitational-wave observation time $t_{\mathrm{obs}}$ and the spin-down timescale of the system. The left panels shows ${\rho }_{\mathrm{opt}}$ for aLIGO with $\epsilon ={10}^{-2}$ (top panel) and $\epsilon ={10}^{-3}$ (bottom panel). The right panels show the same but for ET. The shaded region is nonphysical as the implied gravitational-wave energy emitted by the neutron star is greater than the available energy budget (see Sec. 2a). A ${\rho }_{\mathrm{opt}}>4.4$ is considered detectable.

Figure 3

The optimal matched-filter signal-to-noise ratio ${\rho }_{\mathrm{opt}}$ as a function of distance for a millisecond magnetar inferred from GRB140903A for aLIGO (top panel) and ET (bottom panel) for two different ellipticities; $\epsilon ={10}^{-2}$ (solid curves) and $\epsilon ={10}^{-3}$ (dashed curves). The red shaded region indicates the $2\sigma$ confidence interval from the posteriors shown in Fig. 5. A threshold ${\rho }_{\mathrm{opt}}=4.4$ is indicated by a black horizontal dotted line. Any value above this threshold is detectable by aLIGO at design sensitivity. All curves are constructed using an observation time of $5\times {10}^4\mathrm{s}$.

Figure 4

$\gamma$ and x-ray lightcurves for GRB140903A. Black points are data from Swift and Chandra satellites. The blue curve shows the maximum likelihood model described in Sec. 3. The dark red band is the superposition of 800 models randomly drawn from the posterior distribution (shown in Fig. 5). The dashed black curve is the model for the luminosity from the nascent neutron star [Eq. (16)].

Figure 5

Posterior distribution for $f_{\mathrm{gw},0}$, $n$, and $\tau$ for GRB140903A. These posteriors are used as priors to build a GRB specific template bank. Shown are one-,two-, and three-sigma confidence levels. This figure is generated using the ChainConsumer software package [43].

Figure 6

The fitting factor ($FF$) as a function of the number of templates with unconstrained parameter priors (left panel) and priors constrained by x-ray afterglow observations (right panel) for observation times $t_{\mathrm{obs}}=10$ seconds (solid lines), $t_{\mathrm{obs}}=100$ seconds (dashed lines), and $t_{\mathrm{obs}}=500$ seconds (dotted lines). The error-bars indicate one sigma.