Bayesian nonparametric inference of neutron star equation of state via neural network

TL;DR

This paper introduces a neural network-based nonparametric method to infer the neutron star equation of state from multimessenger data, providing new insights into neutron star properties and the sound speed limit.

Contribution

It develops a neural network approach for nonparametric EoS inference and applies it to real multimessenger data, improving understanding of neutron star internal physics.

Findings

Estimated neutron star radius R_{1.4} = 11.83 km with uncertainties

Derived tidal deformability Λ_{1.4} = 323 with uncertainties

Found high-density sound speed exceeds conformal limit in neutron stars

Abstract

We develop a new nonparametric method to reconstruct the Equation of State (EoS) of Neutron Star with multimessenger data. As an universal function approximator, the Feed-Forward Neural Network (FFNN) with one hidden layer and a sigmoidal activation function can approximately fit any continuous function. Thus we are able to implement the nonparametric FFNN representation of the EoSs. This new representation is validated by its capabilities of fitting the theoretical EoSs and recovering the injected parameters. Then we adopt this nonparametric method to analyze the real data, including mass-tidal deformability measurement from the Binary Neutron Star (BNS) merger Gravitational Wave (GW) event GW170817 and mass-radius measurement of PSR J0030+0451 by {\it NICER}. We take the publicly available samples to construct the likelihood and use the nested sampling to obtain the posteriors of the parameters of FFNN according to the Bayesian theorem, which in turn can be translated to the posteriors of EoS parameters. Combining all these data, for a canonical 1.4 $M_\odot$ neutron star, we get the radius $R_{1.4}=11.83^{+1.25}_{-1.08}$ km and the tidal deformability $\Lambda_{1.4} = 323^{+334}_{-165}$ (90\% confidence interval).Furthermore, we find that in the high density region ($\geq 3\rho_{\rm sat}$), the 90\% lower limits of the $c_{\rm s}^2/c^2$ ($c_{\rm s}$ is the sound speed and $c$ is the velocity of light in the vacuum) are above $1/3$, which means that the so-called conformal limit (i.e., $c_{\rm s}^2/c^2<1/3$) is not always valid in the neutron stars.