Constraining the Equation of State of Neutron Stars with third-generation Gravitational Wave detectors

Abstract

We investigated the impact of the number of binary neutron star merger events and neutron star (NS) mass distributions on constraining the equation of state (EoS), tidal deformability and radius of NSs, as well as the nuclear parameters, using binary neutron star inspiral gravitational wave signals with third-generation detectors. We generate simulated gravitational wave signals and compute the Fisher information matrix for each event after the number of events and mass distribution models are given. The covariance of EoS parameters is obtained by holding the non-EoS waveform parameters fixed at their injected values and accumulating the Fisher matrix over all events. Finally, the posterior samples of EoS, tidal deformability, radius and nuclear parameters are generated based on this covariance matrix. We find that larger number of events lead to tighter constraints due to more observed events and data accumulation, as expected given the increased number of detections. Meanwhile, we note that the mass distribution plays a more important role in constraining the EoS. We compare a realistic bimodal Gaussian distribution, a uniform distribution and another uniform including sub-solar mass NSs. The results show that the uniform distribution yields tighter constraints than bimodal models because it includes more low-mass and massive NSs. This also implies that events near $1.4\text{Msun}$ provide partly redundant information about the EoS. Additionally, including sub-solar mass NSs can further improve the constraints by significantly reducing the EoS uncertainties at sub-saturation densities and inner-crust, highlighting the importance of sub-saturation density EoS.

Comments: 21 pages, 10 figures