Camille Ducoin

Core-crust transition in neutron stars: Predictivity of density developments

The possibility to draw links between the isospin properties of nuclei and the structure of compact stars is a stimulating perspective. In order to pursue this objective on a sound basis, the correlations from which such links can be deduced have to be carefully checked against model dependence. Using a variety of nuclear effective models and a microscopic approach, we study the relation between the predictions of a given model and those of a Taylor density development of the corresponding equation of state: this establishes to what extent a limited set of phenomenological constraints can determine the core-crust transition properties. From a correlation analysis, we show that (a) the transition density {rho}{sub t} is mainly correlated with the symmetry energy slope L, (b) the proton fraction Y{sub p,t} with the symmetry energy and symmetry energy slope (J,L) defined at saturation density, or, even better, with the same quantities defined at {rho}=0.1 fm{sup -3}, and (c) the transition pressure P{sub t} with the symmetry energy slope and curvature (L,K{sub sym}) defined at {rho}=0.1 fm{sup -3}.

Role of isospin in the nuclear liquid-gas phase transition

Abstract We study the thermodynamics of asymmetric nuclear matter using a mean-field approximation with a Skyrme effective interaction, in order to establish its phase diagram and more particularly the influence of isospin on the order of the transition. A new statistical method is introduced to study the thermodynamics of a multifluid system, keeping only one density fixed, the others being replaced by their intensive conjugated variables. In this ensemble, phase coexistence reduces to a simple one-dimensional Maxwell construction. For a fixed temperature under a critical value, a coexistence line is obtained in the plane of neutron and proton chemical potentials. Along this line, the grand potential presents a discontinuous slope, showing that the transition is first order except at the two ending points where it becomes second order. This result is not in contradiction with the already reported occurrence of a continuous transformation when a constant proton fraction is imposed. Indeed, the proton fraction being an order parameter in asymmetric matter, the constraint can only be fulfilled by gradual phase mixing along the first-order phase-transition line, leading to a continuous pressure.

Nuclear symmetry energy and core-crust transition in neutron stars: A critical study

The slope of the nuclear symmetry energy at saturation density L is pointed out as a crucial quantity to determine the mass and width of neutron-star crusts. This letter clarifies the relation between L and the core-crust transition. We confirm that the transition density is soundly correlated with L despite differences between models, and we propose a clear understanding of this correlation based on a generalised liquid-drop model. Using a large number of nuclear models, we evaluate the dispersion affecting the correlation between the transition pressure Pt and L. From a detailed analysis it is shown that this correlation is weak due to a cancellation between different terms. The correlation between the isovector coefficients Ksym and L plays a crucial role in this discussion.

Isospin-dependent clusterization of neutron-star matter

Abstract Because of the presence of a liquid-gas phase transition in nuclear matter, compact-star matter can present a region of instability against the formation of clusters. We investigate this phase separation in a matter composed of neutrons, protons and electrons, within a Skyrme–Lyon mean-field approach. Matter instability and phase properties are characterized through the study of the free-energy curvature. The effect of β -equilibrium is also analyzed in detail, and we show that the opacity to neutrinos has an influence on the presence of clusterized matter in finite-temperature proto-neutron stars.

Cluster formation in compact stars: Relativistic versus Skyrme nuclear models

We present various properties of nuclear and compact-star matter, comparing the predictions from two kinds of phenomenological approaches: relativistic models (with both constant and density-dependent couplings) and nonrelativistic Skyrme-type interactions. We mainly focus on the liquid-gas instabilities that occur at subsaturation densities, leading to the decomposition of the homogeneous matter into a clusterized phase. Such study is related to the description of neutron-star crust (at zero temperature) and supernova dynamics (at finite temperature).

Cluster formation in asymmetric nuclear matter: Semi-classical and quantal approaches

Abstract The nuclear-matter liquid–gas phase transition induces instabilities against finite-size density fluctuations. This has implications for both heavy-ion-collision and compact-star physics. In this paper, we study the clusterization properties of nuclear matter in a scenario of spinodal decomposition, comparing three different approaches: the quantal RPA, its semi-classical limit (Vlasov method), and a hydrodynamical framework. The predictions related to clusterization are qualitatively in good agreement varying the approach and the nuclear interaction. Nevertheless, it is shown that (i) the quantum effects reduce the instability zone, and disfavor short-wavelength fluctuations; (ii) large differences appear between the two semi-classical approaches, which correspond respectively to a collisionless (Vlasov) and local equilibrium description (hydrodynamics); (iii) the isospin-distillation effect is stronger in the local equilibrium framework; (iv) important variations between the predicted time-scales of cluster formation appear near the borders of the instability region.

Imprint of the symmetry energy on the inner crust and strangeness content of neutron stars

In this work we study the effect of the symmetry energy on several properties of neutron stars. First, we discuss its effect on the density, proton fraction and pressure of the neutron star crust-core transition. We show that whereas the first two quantities present a clear correlation with the slope parameter L of the symmetry energy, no satisfactory correlation is seen between the transition pressure and L . However, a linear combination of the slope and curvature parameters at ρ = 0.1 fm−3 is well correlated with the transition pressure. In the second part we analyze the effect of the symmetry energy on the pasta phase. It is shown that the size of the pasta clusters, number of nucleons and the cluster proton fraction depend on the density dependence of the symmetry energy: a small L gives rise to larger clusters. The influence of the equation of state at subsaturation densities on the extension of the inner crust of the neutron star is also discussed. Finally, the effect of the density dependence of the symmetry energy on the strangeness content of neutron stars is studied in the last part of the work. It is found that charged (neutral) hyperons appear at smaller (larger) densities for smaller values of the slope parameter L. A linear correlation between the radius and the strangeness content of a star with a fixed mass is also found.

Anomalous thermodynamics and phase transitions in neutron star matter

The presence of the long-range Coulomb force in dense stellar matter implies that the total charge cannot be associated with a chemical potential, even if it is a conserved quantity. As a consequence, the analytical properties of the partition sum are modified, changing the order of the phase transitions and affecting the possible occurrence of critical behaviors. The peculiar thermodynamic properties of this system can be understood introducing a model Hamiltonian where each charge is independently neutralized by a uniform background of opposite charge. Some consequences on the characteristics of mixed-phase structures in neutron star crusts and supernova cores are discussed.

Isospin fractionation : equilibrium versus spinodal decomposition

Abstract This paper focuses on the isospin properties of the asymmetric nuclear-matter liquid–gas phase transition analyzed in a mean-field approach, using Skyrme effective interactions. We compare two different mechanisms of phase separation for low-density matter: equilibrium and spinodal decomposition. The isospin properties of the phases are deduced from the free-energy curvature, which contains information both on the average isospin content and on the system fluctuations. Some implications on experimentally accessible isospin observables are presented.

Plasmons in strong superconductors

We present a study of the possible plasmon excitations that can occur in systems where strong superconductivity is present. In these systems the plasmon energy is comparable to or smaller than the pairing gap. As a prototype of these systems we consider the proton component of Neutron Star matter just below the crust when electron screening is not taken into account. For the realistic case we consider in detail the different aspects of the elementary excitations when the proton, electron components are considered within the Random-Phase Approximation generalized to the superfluid case, while the influence of the neutron component is considered only at qualitative level. Electron screening plays a major role in modifying the proton spectrum and spectral function. At the same time the electron plasmon is strongly modified and damped by the indirect coupling with the superfluid proton component, even at moderately low values of the gap. The excitation spectrum shows the interplay of the different components and their relevance for each excitation modes. The results are relevant for neutrino physics and thermodynamical processes in neutron stars. If electron screening is neglected, the spectral properties of the proton component show some resemblance with the physical situation in high-Tc superconductors, and we briefly discuss similarities and differences in this connection. In a general prospect, the results of the study emphasize the role of Coulomb interaction in strong superconductors.