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We conducted a study on the thermal properties of stellar matter with the nuclear energy density functional BCPM. This functional is based on microscopic Brueckner-Hartree-Fock calculations and has demonstrated success in describing cold neutron stars. To enhance its applicability in astrophysics, in this study we extend the BCPM equation of state to finite temperature for $\beta$-stable neutrino-free matter, taking into consideration the hot inner crust. Such an equation of state holds significant importance for hot compact objects, particularly those resulting from a binary neutron star merger event. Our exploration has shown that with increasing temperature there is a fast decrease of the crust-core transition density, suggesting that for hot stars it is not realistic to assume a fixed value of this density. The microscopic calculations also reveal that the presence of nuclear clusters persists up to $T=7.21$ MeV, identified as the limiting temperature of the crust. Above this threshold, the manifestation of clusters is not anticipated. Below this temperature, clusters within the inner crust are surrounded by uniform matter with varying densities, allowing for the distinction between the upper and lower transition density branches. Moreover, we computed mass--radius relations of neutron stars, assuming an isothermal profile for $\beta$-stable neutron star matter at various temperature values. Our findings highlight the significant influence of the hot inner crust on the mass--radius relationship, leading to the formation of larger and more inflated neutron stars. Consequently, under our prescription, the final outcome is a unified equation of state at finite temperature., Comment: Submitted to A&A, 9 pages, 6 figures

The most popular Gogny parametrizations, namely D1S, D1N and D1M, describe accurately the ground-state properties of spherical and deformed finite nuclei all across the mass table obtained with Hartree--Fock--Bogoliubov (HFB) calculations. However, these forces produce a rather soft equation of state (EoS) in neutron matter, which leads to predict maximum masses of neutron stars well below the observed value of two solar masses. To remove this limitation, we built new Gogny parametrizations by modifying the density dependence of the symmetry energy predicted by the force in such a way that they can be applied to the neutron star domain and can also reproduce the properties of finite nuclei as good as their predecessors. These new parametrizations allow us to obtain stiffer EoS's based on the Gogny interactions, which predict maximum masses of neutron stars around two solar masses. Moreover, other global properties of the star, such as the moment of inertia and the tidal deformability, are in harmony with those obtained with other well tested EoSs based on the SLy4 Skyrme force or the Barcelona--Catania--Paris--Madrid (BCPM) energy density functional. Properties of the core-crust transition predicted by these Gogny EoSs are also analyzed. Using these new Gogny forces, the EoS in the inner crust is obtained with the Wigner--Seitz approximation in the Variational Wigner--Kirkwood approach along with the Strutinsky integral method, which allows one to estimate in a perturbative way the proton shell and pairing corrections. For the outer crust, the EoS is determined basically by the nuclear masses, which are taken from the experiments, wherever they are available, or by HFB calculations performed with these new forces if the experimental masses are not known., Comment: 31 pages, 13 figures

We analyze the effects of including $\Delta(1232)$ isobars in an equation of state (EoS) for cold, $\beta$-stable neutron star matter, employing relativistic nuclear mean field theory. The selected EoS reproduces the properties of nuclear matter and finite nuclei and, in the astrophysical context, allows for the presence of hyperons in neutron stars having masses larger than 2$M_{\odot}$. We find that the composition and structure of neutron stars is critically influenced by the addition of the $\Delta$ isobars, which allows us to constrain their interaction with the meson fields taking into account astrophysical information. Imposing that the EoS is stable and ensures the existence of 2$M_{\odot}$ neutron stars, as well as requiring agreement with data of $\Delta$ excitation in nuclei, we find that, in the absence of other mechanisms stiffening the EoS at high densities, the interaction of the $\Delta$ isobars with the sigma and omega meson fields must be at least 10\% stronger than that of the nucleons. Moreover, the neutron star moment of inertia turns out to be sensitive to the presence of $\Delta$ isobars, whereas the inclusion of $\Delta$ isobars in the EoS allows for smaller stellar radii and for a lower value of the tidal deformability consistent with the analysis of the GW170817 merger event., Comment: 13 pages, 9 figures, 1 table

We present two recent parametrizations of the equation of state (FSU2R and FSU2H models) that reproduce the properties of nuclear matter and finite nuclei, fulfill constraints on high-density matter stemming from heavy-ion collisions, produce 2$M_{\odot}$ neutron stars, and generate neutron star radii below 13 km. Making use of these equations of state, cooling simulations for isolated neutron stars are performed. We find that two of the models studied, FSU2R (with nucleons) and, in particular, FSU2H (with nucleons and hyperons), show very good agreement with cooling observations, even without including nucleon pairing. This indicates that cooling observations are compatible with an equation of state that produces a soft nuclear symmetry energy and, thus, generates small neutron star radii. Nevertheless, both schemes produce cold isolated neutron stars with masses above $1.8 M_{\odot}$., Comment: 6 pages, 4 figures, 1 table, invited parallel talk at Fifteenth Marcel Grossmann Meeting, University of Rome "La Sapienza" - Rome, July 1-7, 2018

We perform cooling simulations for isolated neutron stars using recently developed equations of state for their core. The equations of state are obtained from new parametrizations of the FSU2 relativistic mean-field functional that reproduce the properties of nuclear matter and finite nuclei, while fulfilling the restrictions on high-density matter deduced from heavy-ion collisions, measurements of massive 2$M_{\odot}$ neutron stars, and neutron star radii below 13 km. We find that two of the models studied, FSU2R (with nucleons) and in particular FSU2H (with nucleons and hyperons), show very good agreement with cooling observations, even without including extensive nucleon pairing. This suggests that the cooling observations are more compatible with an equation of state that produces a soft nuclear symmetry energy and, hence, generates small neutron star radii. However, both models favor large stellar masses, above $1.8 M_{\odot}$, to explain the colder isolated neutron stars that have been observed, even if nucleon pairing is present., Comment: 15 pages, 13 figures, 3 tables, accepted version in The Astrophysical Journal

We reexamine the equation of state for the nucleonic and hyperonic inner core of neutron stars that satisfies the 2$M_{\odot}$ observations as well as the recent determinations of stellar radii below 13 km, while fulfilling the saturation properties of nuclear matter and finite nuclei together with the constraints on the high-density nuclear pressure coming from heavy-ion collisions. The recent nucleonic FSU2R and hyperonic FSU2H models are fine tuned improving the density dependence of pure neutron matter at subsaturation densities. The corresponding nuclear matter properties at saturation, the symmetry energy and its slope turn out to be compatible with recent experimental and theoretical determinations. We obtain the mass, radius and composition of neutron stars for the two updated models and study the impact on these properties of the uncertainties in the hyperon-nucleon couplings estimated from hypernuclear data. We find that the onset of appearance of each hyperon strongly depends on the hyperon-nuclear uncertainties, whereas the maximum masses for neutron stars differ by at most 0.1 $M_{\odot}$, although a larger deviation should be expected tied to the lack of knowledge of the hyperon potentials at the high densities present in the center of $2 M_\odot$ stars. For easier use, we provide tables with the results from the FSU2R and FSU2H models for the equation of state and the neutron star mass-radius relation., Comment: 15 pages, 5 figures, 5 tables, published in PASA special issue based on NewCompStar annual meeting, March 27-31, 2017, Warsaw, Poland

We obtain a new equation of state for the nucleonic and hyperonic inner core of neutron stars that fulfills the 2$M_{\odot}$ observations as well as the recent determinations of stellar radii below 13 km. The nucleonic equation of state is obtained from a new parametrization of the FSU2 relativistic mean-field functional that satisfies these latest astrophysical constraints and, at the same time, reproduces the properties of nuclear matter and finite nuclei while fulfilling the restrictions on high-density matter deduced from heavy-ion collisions. On the one hand, the equation of state of neutron star matter is softened around saturation density, which increases the compactness of canonical neutron stars leading to stellar radii below 13 km. On the other hand, the equation of state is stiff enough at higher densities to fulfill the 2$M_{\odot}$ limit. By a slight modification of the parametrization, we also find that the constraints of 2$M_{\odot}$ neutron stars with radii around 13 km are satisfied when hyperons are considered. The inclusion of the high magnetic fields present in magnetars further stiffens the equation of state. Hyperonic magnetars with magnetic fields in the surface of $ \sim 10^{15}$ G and with values of $\sim 10^{18}$ G in the interior can reach maximum masses of 2$M_{\odot}$ with radii in the 12-13 km range., Comment: 18 pages, 9 figures, 2 tables, accepted for publication in The Astrophysical Journal

The Garvey-Kelson relations (GKRs) are algebraic expressions originally developed to predict nuclear masses. In this letter we show that the GKRs provide a fruitful framework for the prediction of other physical observables that also display a slowly-varying dynamics. Based on this concept, we extend the GKRs to the study of nuclear charge radii. The GKRs are tested on 455 out of the approximately 800 nuclei whose charge radius is experimentally known. We find a rms deviation between the GK predictions and the experimental values of only 0.01 fm. This should be contrasted against some of the most successful microscopic models that yield rms deviations almost three times as large. Predictions - with reliable uncertainties - are provided for 116 nuclei whose charge radius is presently unknown., Comment: 4 pages and 3 figures