The general behavior of the nuclear equation of state (EOS), relevant for the description of neutron stars (NSs), is studied within a Bayesian approach applied to a set of models based on a density-dependent relativistic mean-field description of nuclear matter. The EOS is subjected to a minimal number of constraints based on nuclear saturation properties and the low-density pure neutron matter EOS obtained from a precise next-to-next-to-next-to-leading order (N³LO) calculation in chiral effective field theory (χEFT). The posterior distributions of the model parameters obtained under these minimal constraints are employed to construct the distributions of various nuclear matter properties and NS properties such as radii, tidal deformabilities, central energy densities, speeds of sound, etc. We found that a 90% confidence interval for the allowed NS mass–radius relationship and tidal deformabilities is compatible with GW170817 and recent Neutron star Interior Composition ExploreR observations, without invoking the exotic degrees of freedom. A central speed of sound of the order of 2 / 3 c is obtained. The maximum NS mass allowed by the model is 2.5 M _⊙.

The density dependence of the symmetry energy, instrumental in understanding the behavior of the asymmetric nuclear matter, is investigated within the extended relativistic mean-field (ERMF) model, which includes the contributions from the self- and mixed-interaction terms for the scalar-isoscalar ($\sigma${}), vector-isoscalar ($\omega${}), and vector-isovector ($\rho${}) mesons up to the quartic order. Each of the 26 different parametrizations of the ERMF model employed is compatible with the bulk properties of the finite nuclei. The behavior of the symmetry energy for several parameter sets is found to be consistent with the empirical constraints on them as extracted from the analyses of the isospin diffusion data. The neutron-skin thickness in the Pb208 nucleus for these parameter sets of the ERMF model lies in the range of ~0.20-0.24\,fm, which is in harmony with the thickness predicted by the Skyrme Hartree-Fock model. We also investigate the role of various mixed-interaction terms that are crucial for the density dependence of the symmetry energy.

The density dependence of nuclear symmetry energy remains poorly constrained. Starting from precise empirical values of the nuclear volume and surface symmetry energy coefficients and the nuclear saturation density, we show how in the ambit of microscopic calculations with different energy density functionals, the value of the symmetry energy slope parameter L along with that for neutron skin can be put in tighter bounds. The value of L is found to be L=64\ifmmode\pm\else\textpm\fi{}5\,\,MeV. For Pb208, the neutron skin thickness comes out to be 0.188\ifmmode\pm\else\textpm\fi{}0.014\,\,fm. Knowing L, the method can be applied to predict neutron skin thicknesses of other nuclei.

Relations between the nuclear symmetry energy coefficient and its density derivatives are derived. The relations hold for a class of interactions with quadratic momentum dependence and a power-law density dependence. The structural connection between the different symmetry energy elements as obtained seems to be followed by almost all reasonable nuclear energy density functionals, both relativistic and nonrelativistic, suggesting a universality in the correlation structure. This, coupled with known values of some well-accepted constants related to nuclear matter, helps in constraining values of different density derivatives of the nuclear symmetry energy, shedding light on the isovector part of the nuclear interaction.

We investigate the impact of the neutron-star matter equation of state on the $f$- and $p_1$-mode oscillations of neutron stars obtained within the Cowling approximation and linearized general relativity. The $f$- and $p_1$-mode oscillation frequencies, and their damping times are calculated using representative sets of Skyrme Hartree-Fock and relativistic mean-field models, all of which reproduce nuclear systematics and support $2M_{\odot }$ neutron stars. Our study shows strong correlations between the frequencies of $f$- and $p_1$-modes and their damping times with the pressure of $\beta$-equilibrated matter at densities equal to or slightly higher than the nuclear saturation density ${\rho }_0$. Such correlations are found to be almost independent of the composition of the stars. The frequency of the $p_1$-mode of $1.4M_{\odot }$ star is strongly correlated with the slope of the symmetry energy $L_0$ and $\beta$-equilibrated pressure at density ${\rho }_0$. Compared to GR calculations, the error in the Cowling approximation for the $f$-mode is about 30% for neutron stars of low mass, whereas it decreases with increasing mass. The accuracy of the $p_1$-mode is better than 15% for neutron stars of maximum mass, and improves for lower masses and higher number of radial nodes.

We apply a Bayesian approach to construct a large number of minimally constrained equations of state (EOSs) and study their correlations with a few selected properties of a neutron star (NS). Our set of minimal constraints includes a few basic properties of saturated nuclear matter and low-density pure neutron matter EOS which is obtained from a precise next-to-next-to-next-to-leading-order (${\mathrm{N}}^3\mathrm{LO}$) calculation in chiral effective field theory. The tidal deformability and radius of a NS with mass $1–2M_{\odot }$ are found to be strongly correlated with the pressure of $\beta$-equilibrated matter at densities higher than the saturation density (${\rho }_0=0.16{\mathrm{fm}}^{-3}$) in a nearly model-independent manner. These correlations are employed to parametrize the pressure for $\beta$-equilibrated matter, around $2{\rho }_0$, as a function of neutron star mass and the corresponding tidal deformability. The maximum mass of the neutron star is also found to be strongly correlated with the pressure of $\beta$-equilibrated matter at densities $\sim 4.5{\rho }_0$.