Constraining the Ellipticity of the Newborn Magnetar with the Observational Data of Long Gamma-Ray Bursts

The X-ray plateau emission observed in many long gamma-ray bursts (LGRBs) has been usually interpreted as the spin-down luminosity of a rapidly spinning, highly magnetized neutron star (millisecond magnetar). If this is true, then the magnetar may emit extended gravitational wave (GW) emission associated with the X-ray plateau due to nonaxisymmetric deformation or various stellar oscillations. The advanced LIGO and Virgo detectors have searched for long-duration GW transients for several years; no evidence of GWs from any magnetar has been found until now. In this work, we attempt to search for signatures of GW radiation in the electromagnetic observation of 30 LGRBs under the assumption of the magnetar model. We utilize the observations of the LGRB plateau to constrain the properties of the newborn magnetar, including the initial spin period P-0, dipole magnetic field strength B-p , and the ellipticity epsilon. We find that there are some tight relations between magnetar parameters, e.g., epsilon proportional to B-p(1.29) and B-p proportional to P-0(1.14) . In addition, we derive the GW strain for the magnetar sample via their spin-down processes, and find that the GWs from these objects may not be detectable by the aLIGO and Einstein Telescope (ET) detectors. For a rapidly spinning magnetar (P similar to 1 ms, B similar to 10(15) G), the detection horizon for the advanced LIGO O5 detector is similar to 180 Mpc. The detection of such a GW signal associated with the X-ray plateau would be a smoking gun that the central engine of a GRB is a magnetar.