arXiv subjects

J. M. Pearson

Publications and source records attributed to J. M. Pearson.

At least 19 recordsLinked to original sources

arXiv2024

Unified equations of state for cold nonaccreting neutron stars with Brussels-Montreal functionals. V. Improved parametrization of the nucleon density distributions

We previously studied the inner crust and the pasta mantle of a neutron star within the 4th-order extended Thomas-Fermi (ETF) approach with consistent proton shell corrections added perturbatively via the Strutinsky integral (SI) theorem together with the contribution due to pairing. To speed up the computations and avoid numerical problems, we adopted parametrized nucleon density distributions. However, the errors incurred by the choice of the parametrization are expected to become more significant as the mean baryon number density is increased, especially in the pasta mantle where the differences in the energy per nucleon of the different phases are very small, typically a few keV. To improve the description of these exotic structures, we discuss the important features that a nuclear profile should fulfill and introduce two new parametrizations. Performing calculations using the BSk24 functional, we find that these parametrizations lead to lower ETF energy solutions for all pasta phases than the parametrization we adopted before and more accurately reproduce the exact equilibrium nucleon density distributions obtained from unconstrained variational calculations. Within the ETFSI method, all parametrizations predict the same composition in the region with quasi-spherical clusters. However, the two new parametrizations lead to a different mantle structure at mean baryon densities above about 0.07 fm^-3, at which point lasagna is energetically favored. Interestingly, spherical clusters reappear in the pasta region. The inverted pasta phases such as bucatini and Swiss cheese are still found in the densest region above the core in all cases.

astro-ph.HE↗

arXiv2023

Unified equations of state for cold non-accreting neutron stars with Brussels-Montreal functionals. IV. Role of the symmetry energy in pasta phases

Our previous investigation of neutron-star crusts, based on the functional BSk24, led to a substantial reduction of the pasta mantle when Strutinsky integral and pairing corrections were added on top of the fourth-order extended Thomas-Fermi method (ETF). Here, our earlier calculations are widened to a larger set of functionals within the same family, and we find that the microscopic corrections weaken significantly the influence of the symmetry energy. In particular, the correlation observed at the pure ETF level between the density for the onset of pasta formation and the symmetry energy vanishes, not only for the $L$ coefficient but also for the symmetry-energy values at the relevant densities. Moreover, the inclusion of microscopic corrections results in a much lower abundance of pasta for all functionals.

astro-ph.HE↗

arXiv2022

Accreting neutron stars from the nuclear energy-density functional theory. II. Equation of state and global properties

The accretion of matter onto the surface of a neutron star in a low-mass X-ray binary triggers X-ray bursts, whose ashes are buried and further processed thus altering the composition and the properties of the stellar crust. In this second paper of a series, the impact of accretion on the equation of state and on the global properties of neutron stars is studied in the framework of the nuclear energy-density functional theory. Considering ashes made of $^{56}$Fe, we calculated the equations of state using the same Brussels-Montreal nuclear energy-density functionals BSk19, BSk20, and BSk21, as those already employed for determining the crustal heating in our previous study for the same ashes. All regions of accreting neutron stars were treated in a unified and thermodynamically consistent way. With these equations of state, we determined the mass, radius, moment of inertia, and tidal deformability of accreted neutron stars and compared with catalyzed neutron stars for which unified equations of state based on the same functionals are available. The equation of state of accreted neutron stars is found to be significantly stiffer than that of catalyzed matter, with an adiabatic index $Γ\approx 4/3$ throughout the crust. For this reason, accreting neutron stars have larger radii. However, their crustal moment of inertia and their tidal deformability are hardly changed provided density discontinuities at the interface between adjacent crustal layers are properly taken into account. The enhancement of the stiffness of the equation of state of accreting neutron stars is mainly a consequence of nuclear shell effects, thus confirming the importance of a quantum treatment as stressed in our first study. With our previous calculations of crustal heating using the same functionals, we have thus obtained consistent microscopic inputs for simulations of accreting neutron stars.

astro-ph.HE↗

arXiv2020

Unified equations of state for cold non-accreting neutron stars with Brussels-Montreal functionals. II. Pasta phases in semi-classical approximation

We generalize our earlier work on neutron stars (arXiv:1903.04981), which assumed spherical Wigner-Seitz cells in the inner crust, to admit the possibility of pasta phases, i.e., non-spherical cell shapes. Full fourth-order extended Thomas-Fermi calculations using the density functional BSk24 are performed for cylindrical and plate-like cells. Unlike in our spherical-cell calculations, we do not include shell and pairing corrections, but there are grounds for expecting these corrections for pasta to be significantly smaller. It is therefore meaningful to compare the ETF pasta results with the full spherical-cell results, i.e., with shell and pairing corrections included. However, in view of the many previous studies in which shell and pairing corrections were omitted entirely, it is of interest to compare our pasta results with the ETF part of the corresponding spherical calculations. Making this latter comparison we find that as the density increases the cell shapes pass through the usual sequence sphere $\to$ cylinder $\to$ plate before the transition to the homogeneous core. The filling fractions found at the phase transitions are in close agreement with expectations based on the liquid-drop model. On the other hand, when we compare with the full spherical-cell results, we find the sequence to be sphere $\to$ cylinder $\to$ sphere $\to$ cylinder $\to$ plate. In neither case do any "inverted", i.e., bubble-like, configurations appear. We provide accurate fitting formulas to all our essential numerical results for each of the three phases, designed especially for the density range where the nonspherical shapes are expected, which enable one to capture not only the general behavior of the fitted functions, but also the differences between them in different phases.

astro-ph.HE↗

arXiv2019

Crystallization of the inner crust of a neutron star and the influence of shell effects

Context. In the cooling process of a non-accreting neutron star, the composition and properties of the crust are thought to be fixed at the finite temperature where nuclear reactions fall out of equilibrium. A lower estimation for this temperature is given by the crystallization temperature, which can be as high as $\approx 7\times 10^9$ K in the inner crust, potentially leading to sizeable differences with respect to the simplifying cold-catalyzed matter hypothesis. Aims. We extend the recent work by Fantina et al. (2019) on the outer crust, to the study of the crystallization of the inner crust and the associated composition in the one-component plasma approximation. Methods. The finite temperature variational equations for non-uniform matter in both the liquid and the solid phases are solved using a compressible liquid-drop approach with parameters optimized on four different microscopic models which cover the present uncertainties in nuclear modeling. Results. We consider separately the effect of the different nuclear ingredients with their associated uncertainties, namely the nuclear equation of state, the surface properties in the presence of a uniform gas of dripped neutrons, and the proton shell effects arising from the ion single-particle structure. Our results suggest that the highest source of model dependence comes from the smooth part of the nuclear functional. Conclusions. We show that shell effects play an important role at the lowest densities close to the outer crust, but the most important physical ingredient to be settled for a quantitative prediction of the inner crust properties is the surface tension at extreme isospin values.

astro-ph.HE↗

arXiv2019

Role of Landau-Rabi quantization of electron motion on the crust of magnetars within the nuclear energy density functional theory

Magnetic fields of order $10^{15}$ G have been measured at the surface of some neutron stars, and much stronger magnetic fields are expected to be present in the solid region beneath the surface. The effects of the magnetic field on the equation of state and on the composition of the crust due to Landau-Rabi quantization of electron motion are studied. Both the outer and inner crustal regions are described in a unified and consistent way within the nuclear-energy density functional theory.

astro-ph.HE↗

arXiv2019

Unified equations of state for cold non-accreting neutron stars with Brussels-Montreal functionals. I. Role of symmetry energy

The theory of the nuclear energy-density functional is used to provide a unified and thermodynamically consistent treatment of all regions of cold non-accreting neutron stars. In order to assess the impact of our lack of complete knowledge of the density dependence of the symmetry energy on the constitution and the global structure of neutron stars, we employ four different functionals. All of them were precision fitted to essentially all the nuclear-mass data with the Hartree-Fock-Bogoliubov method and two different neutron-matter equations of state based on realistic nuclear forces. For each functional, we calculate the composition, the pressure-density relation, and the chemical potentials throughout the star. We show that uncertainties in the symmetry energy can significantly affect the theoretical results for the composition and global structure of neutron stars. To facilitate astrophysical applications, we construct analytic fits to our numerical results.

astro-ph.HE↗

arXiv2018

Crustal heating in accreting neutron stars from the nuclear energy-density functional theory. I. Proton shell effects and neutron-matter constraint

Observations of soft X-ray transients in quiescence suggest the existence of heat sources in the crust of accreting neutron stars. Heat is thought to be released by electroweak and nuclear processes triggered by the burying of ashes of X-ray bursts. The heating is studied using a fully quantum approach taking consistently into account nuclear shell effects. We have followed the evolution of ashes made of $^{56}$Fe employing the nuclear energy-density functional theory. Both the outer and inner crusts are described using the same functional, thus ensuring a unified and thermodynamically consistent treatment. To assess the role of the neutron-matter constraint, we have employed the set of accurately calibrated Brussels-Montreal functionals BSk19, BSk20, and BSk21 and for comparison the SLy4 functional. Due to nuclear shell effects, the fully accreted crust is found to be much less stratified than in previous studies. In particular, large regions of the inner crust contain clusters with the magic number $Z=14$. The heat deposited in the outer crust is tightly constrained by experimental atomic mass data. The shallow heating we obtain does not exceed $0.2$~MeV and is therefore not enough to explain the cooling of some soft X-ray transients. The total heat released in the crust is very sensitive to details of the nuclear structure and is predicted to lie in the range from $1.5$~MeV to $1.7$~MeV. The evolution of an accreted matter element and therefore the location of heat sources are governed to a large extent by the existence of nuclear shell closures. Ignoring these effects in the inner crust, the total heat falls to $\sim 0.6$~MeV. The neutron-matter constraint is also found to play a key role. The large amount of heat obtained by Steiner et al. (2012) could thus be traced back to unrealistic neutron-matter equations of state.

astro-ph.HE↗

arXiv2016

Giant Pulsar Glitches and the Inertia of Neutron-Star Crusts

Giant pulsar frequency glitches as detected in the emblematic Vela pulsar have long been thought to be the manifestation of a neutron superfluid permeating the inner crust of a neutron star. However, this superfluid has been recently found to be entrained by the crust, and as a consequence it does not carry enough angular momentum to explain giant glitches. The extent to which pulsar-timing observations can be reconciled with the standard vortex-mediated glitch theory is studied considering the current uncertainties on dense-matter properties. To this end, the crustal moment of inertia of glitching pulsars is calculated employing a series of different unified dense-matter equations of state.

astro-ph.HE↗

arXiv2015

Analytical representations of unified equations of state for neutron-star matter

Context. A unified equation of state (EoS) should describe the crust and the core of a neutron star using the same physical model. The Brussels-Montreal group has recently derived a family of such EoSs based on the nuclear energy-density functional theory with generalized Skyrme effective forces, fitted to the available mass data. At the same time, these forces were constrained to reproduce microscopic calculations of homogeneous neutron matter based on realistic two- and three-nucleon forces. Aims. We represent basic physical characteristics of the latest Brussels-Montreal EoS models by analytical expressions to facilitate their inclusion in astrophysical simulations. Methods. We consider three EoS models, which significantly differ by stiffness: BSk19, BSk20, and BSk21. For each of them we constructed two versions of the EoS parametrization. In the first version, pressure P and gravitational mass density ρare given as functions of the baryon number density n_b. In the second version, P, ρ, and n_b are given as functions of pseudo-enthalpy, which is useful for two-dimensional calculations of stationary rotating configurations of neutron stars. In addition to the EoS, we derived analytical expressions for several related quantities that are required in neutron-star simulations: number fractions of electrons and muons in the stellar core, nucleon numbers per nucleus in the inner crust, and equivalent radii and shape parameters of the nuclei in the inner crust. Results. We obtain analytical representations for the basic characteristics of the models of cold dense matter, which are most important for studies of neutron stars. We demonstrate the usability of our results by applying them to calculations of neutron-star mass-radius relations, maximum and minimum masses, thresholds of direct Urca processes, and the electron conductivity in the neutron-star crust.

astro-ph.SR↗

arXiv2013

Symmetry energy: nuclear masses and neutron stars

We describe the main features of our most recent Hartree-Fock-Bogoliubov nuclear mass models, based on 16-parameter generalized Skyrme forces. They have been fitted to the data of the 2012 Atomic Mass Evaluation, and favour a value of 30 MeV for the symmetry coefficient J, the corresponding root-mean square deviation being 0.549 MeV. We find that this conclusion is compatible with measurements of neutron-skin thickness. By constraining the underlying interactions to fit various equations of state of neutron matter calculated {\it ab initio} our models are well adapted to a realistic and unified treatment of all regions of neutron stars. We use our models to calculate the composition, the equation of state, the mass-radius relation and the maximum mass. Comparison with observations of neutron stars again favours a value of J = 30 MeV.

nucl-th↗

arXiv2013

Properties of the outer crust of strongly magnetized neutron stars from Hartree-Fock-Bogoliubov atomic mass models

The equilibrium properties of the outer crust of cold nonaccreting magnetars (i.e. neutron stars endowed with very strong magnetic fields) are studied using the latest experimental atomic mass data complemented with a microscopic atomic mass model based on the Hartree-Fock-Bogoliubov method. The Landau quantization of electron motion caused by the strong magnetic field is found to have a significant impact on the composition and the equation of state of crustal matter. It is also shown that the outer crust of magnetars could be much more massive than that of ordinary neutron stars.

astro-ph.HE↗

arXiv2013

Does a hadron-quark phase transition in dense matter preclude the existence of massive neutron stars ?

We study the impact of a hadron-quark phase transition on the maximum neutron-star mass. The hadronic part of the equation of state relies on the most up-to-date Skyrme nuclear energy density functionals, fitted to essentially all experimental nuclear mass data and constrained to reproduce the properties of infinite nuclear matter as obtained from microscopic calculations using realistic forces. We show that the softening of the dense matter equation of state due to the phase transition is not necessarily incompatible with the existence of massive neutron stars like PSR J1614-2230.

astro-ph.HE↗

arXiv2013

Phase transitions in dense matter and the maximum mass of neutron stars

The recent precise measurement of the mass of pulsar PSR J1614$-$2230, as well as observational indications of even more massive neutron stars, has revived the question of the composition of matter at the high densities prevailing inside neutron-star cores. We study the impact on the maximum possible neutron-star mass of an "exotic" core consisting of non-nucleonic matter. For this purpose, we study the occurrence of a first-order phase transition in nucleonic matter. Given the current lack of knowledge of non-nucleonic matter, we consider the stiffest possible equation of state subject only to the constraints of causality and thermodynamic stability. The case of a hadron-quark phase transition is discussed separately. The purely nucleonic matter is described using a set of unified equations of state that have been recently developed to permit a consistent treatment of both homogeneous and inhomogeneous phases. We then compute the mass-radius relation of cold nonaccreting neutron stars with and without exotic cores from the Tolman-Oppenheimer-Volkoff equations. We find that even if there is a significant softening of the equation of state associated with the actual transition to an exotic phase, there can still be a stiffening at higher densities closer to the center of the star that is sufficient to increase the maximum possible mass. However with quarks the maximum neutron-star mass is always reduced by assuming that the sound speed is limited by $c/\sqrt{3}$ as suggested by QCD calculations. In particular, by invoking such a phase transition, it becomes possible to support PSR J1614$-$2230 with a nucleonic equation of state that is soft enough to be compatible with the kaon and pion production in heavy-ion collisions.

nucl-th↗

arXiv2013

Unified description of dense matter in neutron stars and magnetars

We have recently developed a set of equations of state based on the nuclear energy density functional theory providing a unified description of the different regions constituting the interior of neutron stars and magnetars. The nuclear functionals, which were constructed from generalized Skyrme effective nucleon-nucleon interactions, yield not only an excellent fit to essentially all experimental atomic mass data but were also constrained to reproduce the neutron-matter equation of state as obtained from realistic many-body calculations.

astro-ph.HE↗

arXiv2012

Equation of state of magnetar crusts from Hartree-Fock-Bogoliubov atomic mass models

The equation of state (EoS) of the outer crust of a cold non-accreting magnetar has been determined using the model of Lai and Shapiro (1991). For this purpose, we have made use of the latest experimental atomic mass data complemented with a Hartree-Fock-Bogoliubov (HFB) mass model. Magnetar crusts are found to be significantly different from the crusts of ordinary neutron stars.

astro-ph.HE↗

arXiv2012

Structure of neutron stars with unified equations of state

We present a set of three unified equations of states (EoSs) based on the nuclear energy-density functional (EDF) theory.These EoSs are based on generalized Skyrme forces fitted to essentially all experimental atomic mass data and constrained to reproduce various properties of infinite nuclear matter as obtained from many-body calculations using realistic two- and three-body interactions. The structure of cold isolated neutron stars is discussed in connection with some astrophysical observations.

astro-ph.HE↗

arXiv2012

Superfluidity and entrainment in neutron-star crusts

Despite the absence of viscous drag, the neutron superfluid permeating the inner crust of a neutron star can still be strongly coupled to nuclei due to non-dissipative entrainment effects. Neutron superfluidity and entrainment have been systematically studied in all regions of the inner crust of a cold non-accreting neutron star in the framework of the band theory of solids. It is shown that in the intermediate layers of the inner crust a large fraction of "free" neutrons are actually entrained by the crust. The results suggest that a revision of the interpretation of many observable astrophysical phenomena might be necessary.

astro-ph.HE↗