Nonlinear Walecka Model Research Articles

Shock wave formation in hot nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density at high temperature. The equation of state is derived from the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations lead to the breaking wave equation for the density perturbation. We solve it numerically for this perturbation and follow the propagation of the initial pulses.

Hadron-quark phase transition in asymmetric matter with boson condensation

In the present work we study the hadron-quark phase transition with boson condensation in asymmetric matter by investigating the binodal surface and extending it to finite temperature to mimic the QCD phase diagram. We consider a system with two conserved charges (isospin and baryon densities) using the Gibbs' criteria for phase equilibrium. To obtain these conditions we use two different models for the two possible phases, namely, the nonlinear Walecka model (NLWM) for the hadron matter (also including hyperons) and the MIT bag model for the quark phase. It is shown that the phase transition is very sensitive to the density dependence of the equation of state and the symmetry energy. For an isospin asymmetry of 0.2 and a mixed phase with a fraction of $20%$ of quarks, a transition density in the interval $2{\ensuremath{\rho}}_{0}<{\ensuremath{\rho}}_{t}<4{\ensuremath{\rho}}_{0}$ was obtained for temperatures $30<T<65$ MeV.

The importance of the mixed phase in hybrid stars built with the Nambu-Jona-Lasinio model

We investigate the structure of hybrid stars based on two different constructions: one is based on the Gibbs condition for phase coexistence and considers the existence of a mixed phase (MP), and the other is based on the Maxwell construction and no mixed phase is obtained. The hadron phase is described by the non-linear Walecka model (NLW) and the quark phase by the Nambu-Jona-Lasinio model (NJL). We conclude that the masses and radii obtained are model dependent but not significantly different for both constructions.

Warm stellar matter within the quark-meson-coupling model

In the present article, we investigate stellar matter obtained within the quark-meson-coupling (QMC) model for fixed temperature and with the entropy of the order of $1$ or $2$ Boltzmann units per baryon for neutrino-free matter and matter with trapped neutrinos. A new prescription for the calculation of the baryon effective masses in terms of the free energy is used. Comparing the results of the present work with those obtained from the nonlinear Walecka model, smaller strangeness and neutrino fractions are predicted within QMC. As a consequence, QMC has a smaller window of metastability for conversion into a low-mass blackhole during cooling.

EFFECTS OF THE EXISTENCE OF A MIXED PHASE IN HYBRID NEUTRON STARS

In this work we investigate the structure of hybrid stars composed of a hadron phase described by the nonlinear Walecka model and a quark phase described by the Nambu–Jona–Lasinio model. Two constructions are studied: the first one considers the existence of a mixed phase at intermediate stellar densities, between the density where matter is composed of hadrons and the density where matter is composed of quarks. The second construction implies the inexistence of this mixed phase. In this case, the hadron and the quark phases are in direct contact.

DECONFINEMENT TRANSITION IN PROTONEUTRON STARS

In this paper we study the transition from hadron matter to quark matter in the presence of a gas of trapped electron neutrinos assuming color and flavor conservation during the transition. For the hadronic phase we use a parametrization of a nonlinear Walecka model which includes the whole baryon octet. For the quark matter phase we use MIT model including color superconductivity. Deconfinement is considered to be a first-order phase transition that conserves color and flavor. Our results show that neutrino trapping increases the deconfinement density but color superconductivity decreases it. As a consequence, the transition density in the protoneutron star phase is determined by a competition between between temperature, neutrino trapping and quark pairing.

EVOLUTION OF PROTONEUTRON STARS

In this work, we present results obtained from numerical simulations of the Kelvin–Helmholtz phase of the birth of a neutron star. The neutrino transport in the interior of the star is treated in the diffusion approximation. The numerical method we use is based on a scheme in which the transport and hydrostatic equations are solved separately. We use as input an equation of state obtained with the nonlinear Walecka model. Our results show the evolution of several thermodynamical quantities inside the star.

NEUTRON STAR MASS CORRELATION WITH SOUND VELOCITY AND INCOMPRESSIBILITY AT THE STAR CENTER IN THE POLYTROPIC APPROXIMATION

In this paper we use a polytropic approximation to the equation of state for the interior of neutrons stars, described by relativistic hadronic mean field models. In this approximation, it is possible to obtain analytic expressions for the sound velocity and the incompressibility at the star center. We found a correlation between these quantities and the star mass. Using two well-known parametrizations of the nonlinear Walecka model for nuclear matter composed only of protons, neutrons and electron in β equilibrium, we obtain for a star mass of 1.43 M⊙ a central incompressibility Kc = (3000±100), around ten times the nuclear matter incompressibility, and a central sound velocity (v/c)2 ~ 0.3.

Adiabatic index of hot and cold compact objects

In the present work we calculate the adiabatic index of neutron stars formed by hadronic or quarkionic matter, under two possible conditions, with and without trapped neutrinos, and for two values of the entropy per baryon S = 0,2 kB/ baryon. We use the nonlinear Walecka model to describe hadronic stars, and the MIT bag model to describe quark stars. Particle fractions for each case are obtained and the appearance of particles are compared with drops in the adiabatic index, whenever possible.

Deconfinement transition in protoneutron stars: Analysis within the Nambu–Jona-Lasinio model

We study the effect of color superconductivity and neutrino trapping on the deconfinement transition of hadronic matter into quark matter in a protoneutron star. To describe the strongly interacting matter a two-phase picture is adopted. For the hadronic phase we use different parametrizations of a nonlinear Walecka model which includes the whole baryon octet. For the quark-matter phase we use an $SU(3{)}_{f}$ Nambu--Jona-Lasinio effective model which includes color superconductivity. We impose color and flavor conservation during the transition in such a way that just deconfined quark matter is transitorily out of equilibrium with respect to weak interactions. We find that deconfinement is more difficult for small neutrino content and it is easier for lower temperatures although these effects are not too large. In addition they will tend to cancel each other as the protoneutron star cools and deleptonizes, resulting a transition density that is roughly constant along the evolution of the protoneutron star. According to these results the deconfinement transition is favored after substantial cooling and contraction of the protoneutron star.

Nonlinear Walecka models and point-coupling relativistic models

We study hadronic nonlinear point-coupling (NLPC) models which reproduce numerically the binding energy, the incompressibility, and the nucleon effective mass at the nuclear matter saturation obtained by different nonlinear Walecka (NLW) models. We have investigated their behaviors as functions of the nuclear matter density to observe how they deviate from known NLW models. In our study we present a meson-exchange modified nonlinear Walecka model (MNLW) which exactly underlies a nonlinear point-coupling model (NLPC) presenting third- and fourth-order scalar density self-couplings. A discussion about naive dimensional analysis (NDA) and naturalness is also provided for a large class of NLW and NLPC models. At finite temperature, critical and flash parameters of both approaches are presented.

Deconfinement of neutron star matter within the Nambu–Jona-Lasinio model

We study the deconfinement transition of hadronic matter into quark matter under neutron star conditions assuming color and flavor conservation during the transition. We use a two-phase description. For the hadronic phase we use different parametrizations of a nonlinear Walecka model which includes the whole baryon octet. For the quark-matter phase we use an SU(3){sub f} Nambu-Jona-Lasinio effective model including color superconductivity. Deconfinement is considered to be a first order phase transition that conserves color and flavor. It gives a short-lived transitory colorless-quark phase that is not in {beta} equilibrium, and decays to a stable configuration in {tau}{approx}{tau}{sub weak}{approx}10{sup -8} s. However, in spite of being very short lived, the transition to this intermediate phase determines the onset of the transition inside neutron stars. We find the transition free-energy density for temperatures typical of neutron star interiors. We also find the critical mass above which compact stars should contain a quark core and below which they are safe with respect to a sudden transition to quark matter. Rather independently on the stiffness of the hadronic equation of state (EOS) we find that the critical mass of hadronic stars (without trapped neutrinos) is in the range of {approx}1.5-1.8 solar masses. Thismore » is in coincidence with previous results obtained within the MIT bag model.« less

Hadron production in non-linear relativistic mean field models

By using a parametrization of the non-linear Walecka model which takes into account the binding energy of different hyperons, we present a study of particle production yields measured in central Au–Au collision at RHIC. Two sets of different hyperon–meson coupling constants are employed in obtaining the hadron production and chemical freeze-out parameters. These quantities show a weak dependence on the used hyperon–meson couplings. Results are in good overall accordance with experimental data. We have found that the repulsion among the baryons is quite small and, through a preliminary analysis of the effective mesonic masses, we suggest a way to improve the fittings.

Quasielastic electron scattering in nuclear matter

We have investigated the longitudinal response function and the Coulomb sum rule of electron quasielastic scattering in nuclear matter in the relativistic random phase approximation (RPA). It has been shown that the attractive potential between nucleons due to the δ meson in the DDRH model cancels the repulsive contribution of the ρ meson to a certain extent. Comparison among the results calculated in the DDRH model and in other models has been made. The nonlinear items in the nonlinear Walecka model are crucial to obtain a self-contained meson Green's functions in calculations. The effects of ρ and δ mesons on zero sound are also examined.

Nuclear “pasta” phase within density dependent hadronic models

In the present paper, we investigate the onset of the ``pasta'' phase with different parametrizations of the density dependent hadronic model and compare the results with one of the usual parametrizations of the nonlinear Walecka model. The influence of the scalar-isovector virtual $\ensuremath{\delta}$ meson is shown. At zero temperature, two different methods are used, one based on coexistent phases and the other on the Thomas-Fermi approximation. At finite temperature, only the coexistence phases method is used. $\mathit{npe}$ matter with fixed proton fractions and in $\ensuremath{\beta}$ equilibrium are studied. We compare our results with restrictions imposed on the values of the density and pressure at the inner edge of the crust, obtained from observations of the Vela pulsar and recent isospin diffusion data from heavy-ion reactions, and with predictions from spinodal calculations.

Sound waves and solitons in hot and dense nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density perturbation. We solve them numerically for linear and spherical perturbations and follow the propagation of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by “radiation”. Depending on the equation of state a strong damping may occur. We consider also the evolution of perturbations in a medium without dispersive effects. In this case we observe the formation and breaking of shock waves. We study all these equations also for matter at finite temperature. Our results may be relevant for the analysis of RHIC data. They suggest that the shock waves formed in the quark gluon plasma phase may survive and propagate in the hadronic phase.

Warm protoneutron stars with strange mesons

In order to reproduce the observed strongly attractive ΛΛ interaction within relativistic models in a mean-field approximation, strange meson fields, namely the scalar meson field σ*(975) and the vector meson field ϕ(1020) have to be considered. In the present work we study the inclusion of these mesons in the equation of state (EOS) obtained with the nonlinear Walecka model with nucleons and hyperons at finite temperature and also fixed entropy per baryon after the deleptonization stage of the star. The calculations are done in a mean-field approximation and the consequences in the stellar properties are verified.

Warm and cold pasta phase in relativistic mean field theory

In the present article we investigate the onset of the pasta phase with different parametrizations of the nonlinear Walecka model. At zero temperature two different methods are used, one based on coexistent phases and the other on the Thomas-Fermi approximation. At finite temperature only the coexistence phases method is used. $\mathit{npe}$ matter with fixed proton fractions and in $\ensuremath{\beta}$ equilibrium is studied. The pasta phase decreases with the increase of temperature. The internal pasta structure and the beginning of the homogeneous phase vary depending on the proton fraction (or the imposition of $\ensuremath{\beta}$ equilibrium), on the method used, and on the chosen parametrization. It is shown that a good parametrization of the surface tension with dependence on the temperature, proton fraction, and geometry is essential to describe correctly large isospin asymmetries and the transition from pasta to homogeneous matter.

Dynamical instabilities in density-dependent hadronic relativistic models

Unstable modes in asymmetric nuclear matter (ANM) at subsaturation densities are studied in the framework of relativistic mean-field density-dependent hadron models. The size of the instabilities that drive the system are calculated and a comparison with results obtained within the nonlinear Walecka model is presented. The distillation and antidistillation effects are discussed.

Metastability of hadronic compact stars

Pure hadronic compact stars, above a threshold value of their gravitational mass (central pressure), are metastable to the conversion to quark stars (hybrid or strange stars). In this paper, we present a systematic study of the metastability of pure hadronic compact stars using different relativistic models for the equation of state. In particular, we compare results for the quark-meson coupling model with those for the Glendenning-Moszkowski parametrization of the nonlinear Walecka model. For the quark-meson coupling model, we find large values (${M}_{\mathrm{cr}}=1.6--1.9{M}_{\ensuremath{\bigodot}}$) for the critical mass of the hadronic star sequence and we find that the formation of a quark star is only possible with a soft quark matter equation of state. For the Glendenning-Moszkowski parametrization of the nonlinear Walecka model, we explore the effect of different hyperon couplings on the critical mass and on the stellar conversion energy. We find that increasing the value of the hyperon coupling constants shifts the bulk transition point for quark deconfinement to higher densities, increases the stellar metastability threshold mass and the value of the critical mass, and thus makes the formation of quark stars less likely. For the largest values of the hyperon couplings we find a critical mass which may be as high as $1.9--2.1{M}_{\ensuremath{\bigodot}}$. These stellar configurations, which contain a large central hyperon fraction (${f}_{Y,\mathrm{cr}}\ensuremath{\sim}30%$), would be able to describe highly massive compact stars, such as the one associated with the millisecond pulsar PSR $\mathrm{B}1516+02\mathrm{B}$ with a mass $M={1.94}_{\ensuremath{-}0.19}^{+0.17}{M}_{\ensuremath{\bigodot}}$.