Dynamical properties of nuclear and stellar matter and the symmetry energy

The effects of density dependence of the symmetry energy on the collective modes and dynamical instabilities of cold and warm nuclear and stellar matter are studied in the framework of relativistic mean-field hadron models. The existence of the collective isovector and possibly an isoscalar collective mode above saturation density is discussed. It is shown that soft equations of state do not allow for a high density isoscalar collective mode, however, if the symmetry energy is hard enough an isovector mode will not disappear at high densities. The crust-core transition density and pressure are obtained as a function of temperature for $\beta$-equilibrium matter with and without neutrino trapping. An estimation of the size of the clusters formed in the non-homogeneous phase as well as the corresponding growth rates and distillation effect is made. It is shown that cluster sizes increase with temperature, that the distillation effect close to the inner edge of the crust-core transition is very sensitive to the symmetry energy, and that, within a dynamical instability calculation, the pasta phase exists in warm compact stars up to 10 - 12 MeV.Comment: 16 pages, 10 figures. Submitted for publication in Phys. Rev.

Light Clusters and Pasta Phases in Warm and Dense Nuclear Matter

The pasta phases are calculated for warm stellar matter in a framework of relativistic mean-field models, including the possibility of light cluster formation. Results from three different semiclassical approaches are compared with a quantum statistical calculation. Light clusters are considered as point-like particles, and their abundances are determined from the minimization of the free energy. The couplings of the light-clusters to mesons are determined from experimental chemical equilibrium constants and many-body quantum statistical calculations. The effect of these light clusters on the chemical potentials is also discussed. It is shown that including heavy clusters, light clusters are present until larger nucleonic densities, although with smaller mass fractions.Comment: 15 pages, 13 figures, accepted for publication in Physical review

Heavy baryons in hot stellar matter with light nuclei and hypernuclei

The production of light nuclei and hypernuclei together with heavy baryons, both hyperons and $\Delta$-baryons, in low density matter as found in stellar environments such as supernova or binary mergers is studied within relativistic mean-field models. Five light nuclei were considered together with three light hypernuclei. The presence of both hyperons and $\Delta$-baryons shift the dissolution of clusters to larger densities and increase the abundance of clusters. This effect is larger the smaller the charge fraction and the higher the temperature. The couplings of the $\Delta$-baryons were chosen imposing that the nucleon effective mass remains finite inside neutron stars.Comment: 11 pages, 8 figures, submitted to Phys. Rev.

Unified neutron star equations of state calibrated to nuclear properties

Recently, in Malik23, a dataset of several EoS for purely nucleonic stellar matter based on a non-linear RMF model prescription, and constrained to properties of nuclear matter, to state-of-the-art chiral effective field theory calculations for low-density neutron matter, and to astrophysical data, were proposed. In this work, twenty one unified neutron star EoS were chosen from that dataset, in such a way that a large range of values of the slope of the symmetry energy at saturation is covered. Several quantities are calculated and discussed, such as the the proton fraction and the direct Urca behavior, the density dependence of the speed of sound and the trace anomaly, the crust-core transition properties, the compatibility with astrophysical observations, and the neutron matter properties from $\chi$EFT calculations and pQCD constraints. We construct unified EoS, where the outer crust is given by the BSk22 functional, and the inner crust is calculated from a CLD approximation. The core is purely nucleonic, made of protons, neutrons, electrons and muons, under charge neutrality and in $\beta-$equilibrium conditions. The correlation of the slope of the symmetry energy at saturation with the crust-core transition density and proton fraction is analysed, and equations that translate these relations are proposed. Moreover, the spectral representation for all the EOS according to the format proposed in Lindblom10 is given, which is a convenient representation to study quasi-periodic oscillations with realistic EOS. It is shown that several of these EoS have in the center of the most massive NS a speed of sound squared of the order of $\lesssim 0.5$. Most of the EoS predict a maximum central density of the order of about 6 times the nuclear saturation density. Three of the EoS satisfy all of the constraints imposed. All these EoS will be made available in the CompOSE platform.Comment: 14 pages, 12 figures, 7 table

Three Dimensional Equation of State for Core-Collapse Supernova Matter

The core-collapse supernova (CCSN) phenomenon, one of the most explosive events in the Universe, presents a challenge to theoretical astrophysics. Stellar matter in supernovae, experiencing most extreme pressure and temperature, undergoes transformations that cannot be simulated in terrestrial laboratories. Construction of astrophysical models is the only way towards comprehension of CCSN. The key microscopic input into CCSN models is the Equation of State (EoS), connecting the pressure of stellar matter to the energy density and temperature, dependent upon its composition. Of the large variety of forms of CCSN matter, we focus on the transitional region between homogeneous and inhomogeneous phases. Here the nuclear structures undergo a series of changes in shape from spherical to exotic deformed forms: rods, slabs, cylindrical holes and bubbles, termed “nuclear pasta”. We perform a three-dimensional, finite temperature Skyrme-Hartree-Fock + BCS (3D-SHF) study of the inhomogeneous nuclear matter, where we calculate self-consistently the nuclear pasta phase and determine the phase transition between pasta and uniform matter and its character. As the nuclear matter properties depend on the effective nucleon-nucleon interaction in the 3D-SHF model, we employ four different parametrizations of the Skyrme interaction, SkM*, SLy4, NRAPR and SQMC700. For each of these interactions we calculate free energy, pressure, entropy and chemical potentials in the space of particle number densities, temperatures and proton fractions, expected to cover the pasta region. The available data analysed are for particle number densities 0.02 - 0.12 fm−3 [reciprocal of cubic fermi], temperatures 0 - 10 MeV and a proton fraction equal to 0.3. The data indicate a distinct discontinuity in the first derivatives of the free energy, which can be interpreted as a fingerprint of the first order transition between inhomogeneous and homogeneous supernova matter. This transition occurs naturally in our model, without a need for thermodynamic constructions. However, the transitions between distinct pasta formations are much less pronounced and hard to detect with certainty