We construct a new equation of state (EOS) for numerical simulations of core-collapse supernovae and neutron-star mergers based on an extended relativistic mean-field model with a small symmetry energy slope L, which is compatible with both experimental nuclear data and recent observations of neutron stars. The new EOS table (EOS4) based on the extended TM1 (TM1e) model with L = 40 MeV is designed in the same tabular form and compared with the commonly used Shen EOS (EOS2) based on the original TM1 model with . This is convenient and useful for performing numerical simulations and examining the influences of symmetry energy and its density dependence on astrophysical phenomena. In comparison with the TM1 model used in EOS2, the TM1e model provides a similar maximum neutron-star mass but smaller radius and tidal deformability for a 1.4M _⊙ neutron star, which is more consistent with current constraints. By comparing the phase diagram and thermodynamic quantities between EOS4 and EOS2, it is found that the TM1e model predicts a relatively larger region of nonuniform matter and softer EOS for neutron-rich matter. Significant differences between EOS4 and EOS2 are observed in the case with low proton fraction, while the properties of symmetric matter remain unchanged.

A compact object was observed with a mass of by LIGO Scientific and Virgo collaborations (LVC) in GW190814, which provides a great challenge to investigations of supranuclear matter. To study this object, the properties of the neutron star are systematically calculated within the latest density-dependent relativistic mean-field (DDRMF) parameterizations, which are determined by the ground-state properties of spherical nuclei. The maximum masses of the neutron star calculated by DD-MEX and DD-LZ1 sets can be around with quite stiff equations of state generated by their strong repulsive contributions from vector potentials at high densities. Their maximum speeds of sound c _s /c are smaller than at the center of the neutron star, and the dimensionless tidal deformabilities at are less than 800. Furthermore, the radii of also satisfy the constraint from the observation of simultaneous mass–radius measurements (Neutron star Interior Composition Explorer). Therefore, we conclude that one cannot exclude the possibility of the secondary object in GW190814 as a neutron star composed of hadron matter from DDRMF models.

The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include $\mathrm{\Delta }$ isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the $\mathrm{\Delta }$ isobars' self-energies are evaluated in detail. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of $\mathrm{\Delta }$ isobars is recognized at ${\rho }_B\sim 0.28{\mathrm{fm}}^{-3}$, comparable with that of hyperons. Also, we find that the $\mathrm{\Delta }$ isobars' softening of the equation of state is mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are negligibly small. We finally conclude that with typical parameter sets, neutron stars with $\mathrm{\Delta }$ isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly smaller radii than normal neutron stars.

The radii and tidal deformabilities of neutron stars are investigated in the framework of the relativistic mean-field (RMF) model with different density-dependent behaviors of symmetry energy. To study the effects of symmetry energy on the properties of neutron stars, $\omega$ meson and $\rho$ meson coupling terms are included in a popular RMF Lagrangian, i.e., the TM1 parameter set, which is adopted for the widely used supernova equation of state (EoS) table. The coupling constants relevant to the vector–isovector meson, $\rho$, are refitted by a fixed symmetry energy at subsaturation density and its slope at saturation density, while other coupling constants remain the same as the original ones in TM1 so as to update the supernova EoS table. The radius and mass of maximum neutron stars are not so sensitive to the symmetry energy in these family TM1 parameterizations. However, the radii in the intermediate-mass region are strongly correlated with the slope of symmetry energy. Furthermore, the dimensionless tidal deformabilities of neutron stars are also calculated within the associated Love number, which is related to the quadrupole deformation of the star in a static external tidal field and can be extracted from the observation of a gravitational wave generated by a binary star merger. We find that its value at $1.4 \mathrm{M}_\odot$ has a linear correlation to the slope of symmetry energy, unlike that previously studied. With the latest constraints of tidal deformabilities from the GW170817 event, the slope of symmetry energy at nuclear saturation density should be smaller than $60$ MeV in the family TM1 parameterizations. This fact supports the usage of a lower symmetry energy slope for the updated supernova EoS, which is applicable to simulations of neutron star mergers. Furthermore, an analogous analysis is also done within the family IUFSU parameter sets. It is found that the correlations between the symmetry energy slope with the radius and tidal deformability at $1.4 \mathrm{M}_\odot$ have very similar linear relations in these RMF models.

The properties of nuclear matter are studied using state-of-the-art nucleon-nucleon forces up to fifth order in chiral effective field theory. The equations of state of symmetric nuclear matter and pure neutron matter are calculated in the framework of the Brueckner-Hartree-Fock theory. We discuss in detail the convergence pattern of the chiral expansion and the regulator dependence of the calculated equations of state and provide an estimation of the truncation uncertainty. For all employed values of the regulator, the fifth-order chiral two-nucleon potential is found to generate nuclear saturation properties similar to the available phenomenological high precision potentials. We also extract the symmetry energy of nuclear matter, which is shown to be quite robust with respect to the chiral order and the value of the regulator.