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

## TL;DR

This paper proposes a novel method to constrain the neutron star equation of state by analyzing X-ray plateaus in gamma-ray bursts, using observational data to set limits on neutron star properties.

## Contribution

It introduces a new approach linking GRB X-ray plateau observations to neutron star equations of state, providing constraints on neutron star moments of inertia and radii.

## Key findings

- Constrained neutron star moment of inertia to be greater than 1.0×10^45 g·cm^2.
- Derived radius constraints for neutron stars based on GRB data.
- Established a relationship between X-ray plateau luminosity and neutron star properties.

## Abstract

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.