Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics

This paper gives an overview of the model of a neutron star with non-zero strangeness constructed within the framework of the nonlinear realization of the chiral symmetry. The emphasis is put on the physical properties of the matter of a neutron star as well as on its internal structure. The obtained solution is particularly aimed at the problem of the construction of a theoretical model of a neutron star matter with hyperons that will give high value of the maximum mass.

The symmetry energy is an invaluable tool for studying dense nuclear matter. Unfortunately, its definition is somewhat implicit, and therefore, phenomenological methods are necessary to describe experimental facts. This paper discusses the differences arising from the use of Taylor series expansion and Padé approximation to determine theoretically the symmetry energy and the possible consequences for neutron stars. For this purpose, a form of the nuclear matter equation of state that explicitly depends on the symmetry energy is used. The obtained results point out that the applied approximations lead to modifications of the equilibrium proton fractions and equation of state, especially in their high-density limit. However, this effect is small near the saturation density $n_0$ .

There are generally two factors on which the form of the symmetry energy depends. The first one is the model involved in determining the nuclear matter equation of state, and the second the accuracy of the approximation of the symmetry energy function given by a Taylor series. Including the fourth-order term in the Taylor series accounts for a more reasonable representation of the symmetry energy. This paper focuses on understanding the symmetry energy influence on the neutron star crust-core phase boundary characteristics in terms of the above factors. All calculations were based on selected models of the relativistic mean field theory. The analysis begins with determining the analytical form of the fourth-order symmetry energy. The applied method allows for deriving the potential part of the fourth-order symmetry energy when the model contains various nonlinear couplings between mesons. The presence of the fourth-order term in the symmetry energy description affects the neutron star crust-core phase boundary characteristics by changing the transition density $n_t$, the corresponding pressure $P_t$, and the equilibrium proton fraction $Y_p^{\mathrm{eq}}\left(n_t\right)$ value. The performed statistical analysis clarifies the role of the second- and fourth-order symmetry energy in determining the relationships between the transition density $n_t$ and the leading coefficients characterizing the density dependence of the symmetry energy $[E_{\mathrm{sym}}\left(n_0\right),$ $L_{\mathrm{sym}},$ $K_{\mathrm{sym}}]$, where $L_{\mathrm{sym}}$ is the slope and $K_{\mathrm{sym}}$ is the curvature. It is shown that the regression analysis makes it possible to identify $(P_t,L_{\mathrm{sym}},K_{\mathrm{sym}})$ as the group of factors that significantly influence the variability of the transition density $n_t$. The results also allow for estimating the effect of the fourth-order symmetry energy term inclusion. Additionally, the correlation analysis points to the individual role of $L_{\mathrm{sym}}$ and $K_{\mathrm{sym}}$. Only when the fourth-order term is included are both variables $K_{\mathrm{sym}}$ and $L_{\mathrm{sym}}$ equally anticorrelated with $n_t$, leading to the increasing role of $L_{\mathrm{sym}}$ in analyzing the variability of $n_t$.

Regression analysis for the symmetry energy within a sample of relativistic mean-field models of nuclear matter is performed. The selected models consistently meet the experimentally obtained limitations. A proposed measure of the importance of adding the fourth-order term to the symmetry energy is analyzed. As a result of the research, it became possible to arrange the models and perform two-dimensional and one-dimensional linear regression analyses. The one-dimensional regression analysis between the input parameters confirms the appropriateness of introducing the division of the sample of considered models into four separate classes representing four statistically different fits. An additional result is the formulation of constraints on the function, which describes the energy density of the system. The performed two-dimensional regression analysis refers to an alternative method of parametrizing the symmetry energy using the power law. It was found that the Akaike information criterion of model selection involving the $\gamma$ exponent is sensitive to splitting the symmetry energy into the kinetic and potential parts. The analysis indicates that the more appropriate way of splitting is the one that does not consider the interaction with the sigma meson in the kinetic part.

The quality of approximation is an important issue in modeling nuclear matter. It is argued that Padé approximants provide a useful tool for theoretical representation of the function that describe...