Constraining the Nuclear Equation of State via Gravitational-wave Radiation of Short Gamma-Ray Burst Remnants

The observed internal plateau of X-ray emission in some short gamma-ray bursts (GRBs) suggests the formation of a remnant supramassive magnetar following a double neutron star (NS) merger. In this paper, we assume that the rotational energy is lost mainly via gravitational-wave radiation instead of magnetic dipole (MD) radiation, and present further constraints on the NS nuclear equation of state (EoS) via mass quadrupole deformation and r-mode fluid oscillations of the magnetar. We present two short GRBs with measured redshifts, 101219A and 160821B, whose X-ray light curves exhibit an internal plateau. This suggests that a supramassive NS may survive as the central engine. By considering 12 NS EoSs, within the mass quadrupole deformation scenario we find that the GM1, DD2, and DDME2 models give an M_p band falling within the 2σ region of the proto-magnetar mass distribution for ɛ = 0.01. This is consistent with the constraints from the MD radiation dominated model of rotational energy loss. However, for an r-mode fluid oscillation model with α = 0.1 the data suggest that the NS EOS is close to the Shen and APR models, which is obviously different from the MD radiation dominated and mass quadrupole deformation cases.