This paper presents a detailed assessment of the ability of the 240 Skyrme interaction parameter sets in the literature to satisfy a series of criteria derived from macroscopic properties of nuclear matter in the vicinity of nuclear saturation density at zero temperature and their density dependence, derived by the liquid-drop model, in experiments with giant resonances and heavy-ion collisions. The objective is to identify those parametrizations which best satisfy the current understanding of the physics of nuclear matter over a wide range of applications. Out of the 240 models, only 16 are shown to satisfy all these constraints. Additional, more microscopic, constraints on the density dependence of the neutron and proton effective mass $\beta$-equilibrium matter, Landau parameters of symmetric and pure neutron nuclear matter, and observational data on high- and low-mass cold neutron stars further reduce this number to 5, a very small group of recommended Skyrme parametrizations to be used in future applications of the Skyrme interaction of nuclear-matter-related observables. Full information on partial fulfillment of individual constraints by all Skyrme models considered is given. The results are discussed in terms of the physical interpretation of the Skyrme interaction and the validity of its use in mean-field models. Future work on application of the Skyrme forces, selected on the basis of variables of nuclear matter, in the Hartree-Fock calculation of properties of finite nuclei, is outlined.

Background: The microscopic composition and properties of infinite hadronic matter at a wide range of densities and temperatures have been subjects of intense investigation for decades. The equation of state (EoS) relating pressure, energy density, and temperature at a given particle number density is essential for modeling compact astrophysical objects such as neutron stars, core-collapse supernovae, and related phenomena, including the creation of chemical elements in the universe. The EoS depends not only on the particles present in the matter, but, more importantly, also on the forces acting among them. Because a realistic and quantitative description of infinite hadronic matter and nuclei from first principles in not available at present, a large variety of phenomenological models has been developed in the past several decades, but the scarcity of experimental and observational data does not allow a unique determination of the adjustable parameters.

The QCD phase diagram at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three-flavor Nambu\char21{}Jona-Lasinio (NJL) model and the NJL model with the Polyakov loop. A scalar coupling parameter dependent on the magnetic field intensity is considered. The scalar coupling has been fitted so that the lattice QCD pseudocritical chiral transition temperatures are reproduced and in the limit of large magnetic field decreases with the inverse of the magnetic field intensity. This dependence of the coupling allows us to reproduce the lattice QCD results with respect to the quark condensates and Polyakov loop: due to the magnetic field the quark condensates are enhanced at low and high temperatures and suppressed for temperatures close to the transition temperatures and the Polyakov loop increases with the magnetic field.

We analyze the stellar properties of the relativistic mean-field (RMF) parametrizations shown to be consistent with the recently studied constraints related to nuclear matter, pure neutron matter, symmetry energy, and its derivatives [ Phys. Rev. C 90, 055203 (2014)]. Our results show that only two RMF parametrizations do not allow the emergence of the direct Urca process, important aspect regarding the evolution of a neutron star. Moreover, among all approved RMF models, fourteen of them produce neutron stars with maximum masses inside the range $1.93\le M/M_{\odot }\le 2.05$, with $M_{\odot }$ being the solar mass. Only three models yield maximum masses above this range and a discussion on the inclusion of hyperons is presented. Finally, we verified that the models satisfying the neutron star maximum mass constraint do not observe the squared sound velocity bound; namely, $v_s^2<1/3$, corroborating recent findings. However, the recently proposed $\sigma$-cut scheme can make the RMF models consistent with both constraints, depending on the isoscalar-vector interaction of each parametrization.

We have obtained the Love number and corresponding tidal deformabilities $\left(\mathrm{\Lambda }\right)$ associated with the relativistic mean-field parametrizations shown to be consistent (CRMF) with the nuclear matter, pure neutron matter, symmetry energy, and its derivatives [Dutra et al., Phys. Rev. C 90, 055203 (2014)]. Our results show that CRMF models present very good agreement with the recent data from binary neutron star merger event GW170817. They also confirm the strong correlation between ${\mathrm{\Lambda }}_{1.4}$ and the radius of canonical stars $\left(R_{1.4}\right)$. When a recent GW170817 constraint on ${\mathrm{\Lambda }}_{1.4}$ and the corresponding radius $R_{1.4}$ is used, the majority of the models tested are shown to satisfy it.