Constraining the Equation of State of Neutron Stars through GRB X-Ray Plateaus

The unknown equation of state (EoS) of neutron stars (NSs) is puzzling because of rich non-perturbative effects of strong interaction there. A method to constrain the EoS by using the detected X-ray plateaus of gamma-ray bursts (GRBs) is proposed in this paper. Observations show some GRB X-ray plateaus may be powered by strongly magnetized millisecond NSs. The properties of these NSs should then satisfy: (i) the spin-down luminosity of these NSs should be brighter than the observed luminosity of the X-ray plateaus; (ii) the total rotational energy of these NSs should be larger than the total energy of the X-ray plateaus. Through the case study of GRB 170714A, the moment of inertia of NSs is constrained as $I>1.0\times 10^{45}\left ( \frac{P_{\rm cri}}{1;\rm ms} \right )^{2} ;\rm g\cdot cm^{2}$,where$P_{\rm cri}$ is the critical rotational period that an NS can achieve. The constraint of the radii of NSs according to GRB 080607 is shown in Table 1.