Nonlinear Walecka Model Research Articles

Anisotropic electron transport in the nuclear pasta phase

ABSTRACTThe presence of nuclear pasta is expected to modify the transport properties in the mantle of neutron stars. The non-spherical geometry of the pasta nuclear clusters leads to anisotropies in the collision frequencies, impacting the thermal and electrical conductivity. We derive analytical expressions for the anisotropic collision frequencies using the Boltzmann equation in the relaxation time approximation. The average parallel, perpendicular, and Hall electrical conductivities are computed in the high-temperature regime above crustal melting, considering incoherent elastic electron-pasta scattering and randomly oriented pasta structures. Numerical values are obtained at different densities and temperatures by using the Indiana University–Florida State University (IUFSU) parametrization of the non-linear Walecka model to determine the crustal structure. We find that the anisotropy of the collision frequencies grows with the length of the pasta structures and, independently of the magnetic field, the presence of rod and slab phases decreases the conductivity by more than one order of magnitude. Our numerical results indicate that, even if the pasta structures might survive above the crustal melting point, no strong anisotropies are to be expected in the conduction properties in this temperature regime, even in the presence of a very high magnetic field.

Speed of sound and liquid-gas phase transition in nuclear matter

We investigate the speed of sound in nuclear matter at finite temperature and density (chemical potential) in the nonlinear Walecka model. The numerical results suggest that the behaviors of sound speed are closely related to the the nuclear liquid-gas (LG) phase transition and the associated spinodal structure. The adiabatic sound speed is nonzero at the critical endpoint (CEP) in the mean-field approximation. We further derive the boundary of vanishing sound velocity in the temperature-density phase diagram, and point out the region where the sound wave equation is broken. The distinction between the speed of sound in nuclear matter and that in quark matter contains important information about the equation of state of strongly interacting matter at intermediate and high density. We also formulate the relations between differently defined speeds of sound using the fundamental thermodynamic relations.

Neutron star matter equation of state including d*-hexaquark degrees of freedom

We present the extension of a previous study where, assuming a simple free bosonic gas supplemented with a relativistic mean-field model to describe the pure nucleonic part of the equation of state, we studied the consequences that the first non-trivial hexaquark d*(2380) could have on the properties of neutron stars. Compared to that exploratory work, we employ a standard non-linear Walecka model including additional terms that describe the interaction of the d*(2380) di-baryon with the other particles of the system through the exchange of σ- and ω-meson fields. Our results show that the presence of the d*(2380) leads to maximum masses compatible with recent observations of ∼2 M⊙ millisecond pulsars if the interaction of the d*(2380) is slightly repulsive or the d*(2380) does not interact at all. An attractive interaction makes the equation of state too soft to be able to support a 2 M⊙ neutron star whereas an extremely repulsive one induces the collapse of the neutron star into a black hole as soon as the d*(2380) appears.

The effect of the delta-rich hadronic stellar matter in the maximum neutron star mass using the nonlinear Walecka and Zimanyi-Moszkowski models

In this work, the delta-rich hadronic stellar matter condensate is studied in the context of a relativistic mean field calculation for hadrons and mesons using the nonlinear Walecka (NLW) and Zimanyi-Moszkowski (ZM) models. Considering different values of delta-mesons coupling constants we present the delta matter effect in the equation of state in each of these models. Solving numerically the Tolman-Oppenheimer-Volkoff (TOV) equation, we obtain the maximum neutron star mass. We note that the NLW model provides a stiffer equation of state when compared to the ZM model for the same values of delta-mesons coupling constants, and as a consequence gives more massive neutron stars.

Instability of baryonic matter in relativistic mean-field models

In this article we evaluate some of the properties of strongly interacting hadronic matter using non-linear Walecka model in relativistic mean-field approximation. We find that due to the coupling of baryons and bosons, baryonic matter develops instability that is characterised by the appearance of baryonic state with negative entropy density. In the region of instability of baryonic matter we find no evidence of negative in-medium mass of baryons or any signal of kaon condensation. Further we find that this instability of baryonic matter can halt the process of first order phase transition from strongly interacting hadronic matter consisting of coupled baryons and bosons to a weakly interacting quark–gluon plasma phase.

Delta Resonance Coupling with Walecka’s Mesons: Implications to Stellar Matter EoS

In this work we have obtained the equation of state to the highly asymmetric dense stellar matter, using the nonlinear Walecka model in the mean field approximation. We discussed the implication of changes in coupling constant of the delta baryonic resonance on the observable of the neutron star. A detailed analysis of the equation of state and of the baryonic effective mass in respect to changes in the delta coupling constants is carried out. We focus attention on a new aspect observed for pressure when varying the baryonic density of the medium; a first order phase transition like a liquid-gas phase transition was observed for an acceptable range of delta coupled constant values. We have explored the implication of this aspect for the neutron star structure and their maximum masses.

Particle Ratios from Strongly Interacting Hadronic Matter

We calculate the particle ratios K+/π+, K-/π-, and Λ/π- for a strongly interacting hadronic matter using nonlinear Walecka model (NLWM) in relativistic mean field (RMF) approximation. It is found that interactions among hadrons modify K+/π+ and Λ/π- particle ratios, while K-/π- is found to be insensitive to these interactions.

Neutrino diffusion in the pasta phase matter within the Thomas-Fermi approach

The behavior and properties of neutrinos in non-uniform nuclear matter, surrounded by electrons and other neutrinos are studied. The nuclear matter itself is modeled by the non-linear Walecka model, where the so-called nuclear pasta phase is described using the Thomas-Fermi approximation, solved in a Wigner-Seitz cell. We obtain the total cross-section and mean-free path for the neutrinos, taking into account scattering and neutrino absorption, and compare the final results for two known kind of model parametrizations: one in which non-linear effects in the strong sector are explicitly written in the model Lagrangian and another one in which the coupling constants are density dependent. The solution for this problem is important for the understanding of neutrino diffusion in a newly born neutron star after a supernova explosion.

Properties of strongly magnetized ultradense matter and its effects on magnetar pulsations

We investigate the effect of strong magnetic fields on the adiabatic radial oscillations of hadronic stars. We describe magnetized hadronic matter within the framework of the relativistic nonlinear Walecka model and integrate the equations of relativistic radial oscillations to determine the fundamental pulsation mode. We consider that the magnetic field increases, in a density dependent way, from the surface, where it has a typical magnetar value of ${10}^{15}\phantom{\rule{4pt}{0ex}}\mathrm{G}$, to the interior of the star, where it can be as large as $3\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{4pt}{0ex}}\mathrm{G}$. We show that magnetic fields of the order of ${10}^{18}\phantom{\rule{4pt}{0ex}}\mathrm{G}$ at the stellar core produce a significant change in the frequency of neutron star pulsations with respect to unmagnetized objects. If radial pulsations are excited in magnetar flares, they can leave an imprint in the flare lightcurves and open a new window for the study of highly magnetized ultradense matter.

Bubble dynamics and the quark-hadron phase transition in nuclear collisions

We study the nucleation of a quark gluon plasma (QGP) phase in a hadron gas at low temperatures and high baryon densities. This kind of process will presumably happen very often in nuclear collisions at FAIR and NICA. When the appropriate energy densities (or baryon densities) and temperatures are reached the conversion of one phase into another is not instantaneous. It is a complex process, which involves the nucleation of bubbles of the new phase. One important element of this transition process is the rate of growth of a QGP bubble. In order to estimate it we solve the Relativistic Rayleigh$-$Plesset equation which governs the dynamics of a relativistic spherical bubble in a strongly interacting medium. The baryon rich hadron gas is represented by the nonlinear Walecka model and the QGP is described by the MIT bag model and also by a mean field model of QCD.

Cold pasta phase in the extended Thomas–Fermi approximation

In this paper, we aim to obtain more accurate values for the transition density to the homogenous phase in the nuclear pasta that occurs in the inner crust of neutron stars. To that end, we use the nonlinear Walecka model at zero temperature and an approach based on the extended Thomas–Fermi (ETF) approximation.

Effects of the symmetry energy on the kaon condensates in the quark-meson coupling model

In this work we investigate protoneutron star properties within a modified version of the quark-meson coupling (QMC) model that incorporates an $\ensuremath{\omega}\text{\ensuremath{-}}\ensuremath{\rho}$ interaction plus kaon condensed matter at finite temperature. Fixed entropy and trapped neutrinos are taken into account. Our results are compared with the ones obtained with the GM1 parametrization of the nonlinear Walecka model for similar values of the symmetry energy slope. Contrary to GM1, within the QMC model the formation of low mass black holes during cooling are not probable. It is shown that the evolution of the protoneutron star may include the melting of the kaon condensate driven by the neutrino diffusion, followed by the formation of a second condensate after cooling. The signature of this complex process could be a neutrino signal followed by a gamma ray burst. We have seen that both models can, in general, describe very massive stars.

Hadronic and hybrid stars subject to density-dependent magnetic fields

In this work we present a study of magnetars composed of hadronic and quark matter, under the influence of strong magnetic fields. We present our results for hadronic matter taking into account the effects that the inclusion of anomalous magnetic moment corrections may cause on the equations of state (EOS). Particle abundances are also presented and discussed. Additionally, the case of hybrid stars under the influence of strong magnetic fields is considered. We study the structure of hybrid stars based on the Maxwell condition (without a mixed phase), where the hadron phase is described by the non-linear Walecka model (NLW) and the quark phase by the Nambu-Jona-Lasinio model (NJL). The EOS and the mass-radius relation for each case are calculated and discussed. We show that the recently observed high mass neutron stars can be described by both hadronic and hybrid equations of state subject to strong magnetic fields.

Quark deconfinement in protoneutron star cores: Effect of color superconductivity within the MIT bag model

We analyze the effect of color superconductivity in the transition from hot hadron matter to quark matter in the presence of a gas of trapped electron neutrinos. To describe the strongly interacting matter we adopt a two-phase picture in which the hadronic phase is described by means of a non-linear Walecka model and just deconfined matter through the MIT bag model including color superconductivity. We impose flavor conservation during the transition in such a way that just deconfined quark matter is transitorily out of equilibrium with respect to weak interactions. Our results show that color superconductivity facilitates the transition for temperatures below Tc. This effect may be strong if the superconducting gap is large enough. As in the previous work, we find that the trapped neutrinos increase the critical density for deconfinement; however, if the just deconfined phase is color superconducting this effect is weaker than if deconfined matter is unpaired. We also explore the effect of different parametrizations of the hadronic equation of state (GM1 and NL3) and the effect of hyperons in the hadronic phase. We compare our results with those previously obtained employing the Nambu–Jona–Lasinio model in the description of just deconfined matter and show that they are in excellent agreement if the bag constant B is properly chosen.

Viscosity, wave damping, and shock-wave formation in cold hadronic matter

We study linear and nonlinear wave propagation in a dense and cold hadron gas and also in a cold quark-gluon plasma, taking viscosity into account and using the Navier-Stokes equation. The equation of state of the hadronic phase is derived from the nonlinear Walecka model in the mean-field approximation. The quark-gluon plasma phase is described by the MIT equation of state. We show that in a hadron gas viscosity strongly damps wave propagation and also hinders shock-wave formation. This marked difference between the two phases may have phenomenological consequences and lead to new quark-gluon plasma signatures.

Nucleation rate of colour superconducting droplets in protoneutron stars

We analyse the nucleation of quark matter droplets under protoneutron star conditions. We adopt a two-phase framework in which the hadronic phase is described through a nonlinear Walecka model and the just deconfined matter by the MIT bag model including colour superconductivity. Surface tension and curvature energy are calculated self-consistently within the multiple reflection expansion formalism. We impose flavour conservation during the transition, which means that the just deconfined quark droplet is transiently out of equilibrium with respect to weak interactions. Our results show that trapped neutrinos slightly increase the critical density for deconfinement and that colour superconductivity significantly decreases such density at low temperatures. We also show that the nucleation rate is negligible for droplets larger than 100–200 fm and is huge for smaller droplets provided that the temperature is low enough. We compare our results with previous calculations using the Nambu–Jona–Lasinio model with colour superconductivity and the MIT bag model without colour superconductivity. We conclude that the deconfinement transition should be triggered instantaneously when a density slightly larger than the bulk transition density is reached at some layer of a protoneutron star. Since colour superconductivity lowers the transition density at low temperatures, the transition is likely to occur after significant cooling in a massive enough protoneutron star.

Point-coupling Models from Mesonic Hypermassive Limit and Mean-field Approaches

In this work, we show how nonlinear point-coupling models, described by a Lagrangian density containing only terms up to fourth order in the fermion condensate \((\bar{\psi}\psi)\), are derived from a modified meson-exchange nonlinear Walecka model. We present two methods of derivation, namely the hypermassive meson limit within a functional integral approach and the mean-field approximation, in which equations of state at zero temperature of the nonlinear point-coupling models are directly obtained.

Chiral model approach to quark matter nucleation in neutron stars

The nucleation process of quark matter in both cold and hot dense hadronic matter is investigated using a chiral approach to describe the quark phase. We use the Nambu--Jona--Lasinio and the chromo dielectric models to describe the deconfined phase and the nonlinear Walecka model for the hadronic one. The effect of hyperons on the transition phase between hadronic and quark matter is studied. The consequences of the nucleation process for neutron star physics are outlined.

Critical spectrum of fluctuations for deconfinement at protoneutron star cores

We study the deconfinement of hadronic matter into quark matter in a protoneutron star focusing on the effects of the finite size on the formation of just-deconfined color superconducting quark droplets embedded in the hadronic environment. The hadronic phase is modeled by the non-linear Walecka model at finite temperature including the baryon octet and neutrino trapping. For quark matter we use an $SU(3)_f$ Nambu-Jona-Lasinio model including color superconductivity. The finite size effects on the just deconfined droplets are considered in the frame of the multiple reflection expansion. In addition, we consider that just deconfined quark matter is transitorily out of equilibrium respect to weak interaction, and we impose color neutrality and flavor conservation during the transition. We calculate self-consistently the surface tension and curvature energy density of the quark hadron inter-phase and find that it is larger than the values typically assumed in the literature. The transition density is calculated for drops of different sizes, and at different temperatures and neutrino trapping conditions. Then, we show that energy-density fluctuations are much more relevant for deconfinement than temperature and neutrino density fluctuations. We calculate the critical size spectrum of energy-density fluctuations that allows deconfinement as well as the nucleation rate of each critical bubble. We find that drops with any radii smaller than 800 fm can be formed at a huge rate when matter achieves the bulk transition limit of 5-6 times the nuclear saturation density.

Phase diagrams in the hadron–Polyakov–Nambu–Jona-Lasinio model

The two-Equation of State (Two-EoS) model is used to describe the hadron-quark phase transition in dense-hot matter formed in heavy-ion collisions. The non-linear Walecka model is used to describe the hadronic phase. For the quark phase, the Nambu--Jona-Lasinio model coupled to Polyakov-Loop fields (PNJL) is used to include both the chiral and (de)confinement dynamics. The phase diagrams are derived from the Gibbs conditions and compared with the results obtained in the Hadron-NJL model without confinement. As in the Hadron-NJL case a first order transition is observed, but with a Critical-End-Point at much higher temperature, consequence of the confinement mechanism that reduces the degrees of freedom of the quark matter in proximity of the phase transition. Particular attention is devoted to the phase transition in isospin asymmetric matter. Interesting isospin effects are found at high baryon density and reduced temperatures, in fact common also to other quark models, like MIT-Bag and NJL model. Some possible observation signals are suggested to probe in Heavy-Ion Collision (HIC) experiments at intermediate energies.