Constraining the Nuclear Equation of State via Gravitational-wave Radiation of Short Gamma-Ray Burst Remnants
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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 (GW) 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 Mp band falling within the 2σ region of the proto-magnetar mass distribution for ε = 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.