The Hadron-Quark Crossover in Neutron Star within Gaussian Process Regression Method

TL;DR

This paper employs Gaussian process regression to interpolate the neutron star equation of state across the hadron-quark crossover, integrating models and observational constraints to refine the understanding of neutron star properties.

Contribution

It introduces a novel application of Gaussian process regression to interpolate neutron star equations of state, incorporating multiple models and observational data for improved accuracy.

Findings

The slope of symmetry energy, L, should be around 50-90 MeV.

The crossover window is (0.3, 0.6) fm^{-3}.

Uncertainties in neutron star masses and radii are predicted.

Abstract

The equations of state of the neutron star at the hadron-quark crossover region are interpolated with the Gaussian process regression (GPR) method, which can reduce the randomness of present interpolation schemes. The relativistic mean-field (RMF) model and Nambu-Jona-Lasinio (NJL) model are employed to describe the hadronic phase and quark phase, respectively. In the RMF model, the coupling term between $\omega$ and $\rho$ mesons is considered to control the density-dependent behaviors of symmetry energy, i.e. the slope of symmetry energy, $L$. Furthermore, the vector interaction between quarks is included in the NJL model to obtain the additional repulsive contributions. Their coupling strengths and the crossover windows are discussed in the present framework under the constraints on the neutron star from gravitational wave detections, massive neutron star measurements, mass-radius simultaneous observation of NICER collaboration, and the neutron skin thickness of $^{208}$Pb from PREX-II. It is found that the slope of symmetry energy, $L$ should be around $50-90$ MeV and the crossover window is $(0.3,~0.6)~\rm fm^{-3}$ with these observables. Furthermore, the uncertainties of neutron star masses and radii in the hadron-quark crossover regions are also predicted by the GPR method.