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Parametrized nucleon density distributions are widely employed for the calculation of the properties of atomic nuclei and dense inhomogeneous matter in compact stars within the Thomas-Fermi method and its extensions. We show that the use of insufficiently smooth parametrizations may deteriorate the accuracy of this method. We discuss and clarify the smoothness condition using the example of the so-called "nuclear pasta" in the neutron star mantle., Comment: 9 pages, Phys. Usp., accepted

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., Comment: 12 pages, 9 figures, published in Phys. Rev. C

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., Comment: 11 pages, 4 figures

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 $\Gamma \approx 4/3$ 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., Comment: 10 pages, 7 figures. The tables of the equations of state are available at the CDS

Electron captures by atomic nuclei in dense matter are among the most important processes governing the late evolution of stars, limiting in particular the stability of white dwarfs. Despite considerable progress in the determination of the equation of state of dense Coulomb plasmas, the threshold electron Fermi energies are still generally estimated from the corresponding $Q$ values in vacuum. Moreover, most studies have focused on nonmagnetized matter. However, some white dwarfs are endowed with magnetic fields reaching $10^9$ G. Even more extreme magnetic fields might exist in super Chandrasekhar white dwarfs, the progenitors of overluminous type Ia supernovae like SN 2006gz and SN 2009dc. The roles of the dense stellar medium and magnetic fields on the onset of electron captures and on the structure of white dwarfs are briefly reviewed. New analytical formulas are derived to evaluate the threshold density for the onset of electron captures for arbitrary magnetic fields. Their influence on the structure of white dwarfs is illustrated by simple analytical formulas and numerical calculations., Comment: 20 pages, 5 figures, contribution to the Sixteenth Marcel Grossmann Meeting - MG16

In this paper, we study the role of the symmetry energy on the neutron-drip transition in both nonaccreting and accreting neutron stars, allowing for the presence of a strong magnetic field as in magnetars. The density, pressure, and composition at the neutron-drip threshold are determined using the recent set of the Brussels-Montreal microscopic nuclear mass models, which mainly differ in their predictions for the value of the symmetry energy $J$ and its slope $L$ in infinite homogeneous nuclear matter at saturation. Although some correlations between on the one hand the neutron-drip density, the pressure, the proton fraction and on the other hand $J$ (or equivalently $L$) are found, these correlations are radically different in nonaccreting and accreting neutron stars. In particular, the neutron-drip density is found to increase with $L$ in the former case, but decreases in the latter case depending on the composition of ashes from x-ray bursts and superbursts. We have qualitatively explained these different behaviors using a simple mass formula. We have also shown that the details of the nuclear structure may play a more important role than the symmetry energy in accreting neutron-star crusts., Comment: 29 pages, 9 figures

Nonequilibrium conditions imposed by neutrino cooling through the liquid-solid transition lead to disorder in the solid crust of neutron stars. Disorder reduces the superfluid fraction, $\rho_s/\rho$, at densities above that of neutron drip, $\rho_d \approx 4\times 10^{11}\,g/cm^3$. For an amorphous solid crust the suppression of $\rho_s$ is small, except in the highest density regions of the crust. In contrast to the strong reduction in neutron conduction predicted for coherent Bragg scattering in a crystalline crust, the disordered solid crust supports sufficient neutron superfluid density to account for pulsar glitches., Comment: 6 pages, 5 figures

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., Comment: 16 pages, 14 tables, 8 figures, accepted by Phys. Rev. C

The interior of a neutron star (NS) is usually assumed to be made of cold catalyzed matter. However, the outer layers are unlikely to remain in full equilibrium during the formation of the star and its cooling, especially after crystallization. We study the cooling and equilibrium composition of the outer layers of a NS down to crystallization. Here the impurity parameter, usually a free parameter in cooling simulations, is calculated self-consistently using a microscopic model for which a unified equation of state has recently been determined. We follow the evolution of the nuclear distributions of the multi-component Coulomb liquid plasma (MCP) fully self-consistently, adapting a general formalism originally developed for the description of supernova cores. We calculate the impurity parameter at the crystallization as determined in the one-component plasma (OCP) approximation. Our analysis shows that the sharp changes in composition obtained in the OCP approximation are smoothed out when a full nuclear distribution is allowed. The Coulomb coupling parameter at melting is found to be reasonably close to the canonical value of 175, except for specific pressures for which supercooling occurs in the OCP approximation. Our MCP treatment leads to non-monotonic variations of the impurity parameter with pressure. Its values can change by several orders of magnitude reaching about 50, suggesting that the crust may be composed of an alternation of pure (highly conductive) and impure (highly resistive) layers. The results presented here complement the recent unified equation of state obtained with the same model. Our self-consistent approach to hot MCP shows that the presence of impurities in the outer crust of a NS is non-negligible and may have a sizeable impact on transport properties. In turn, this may have important implications for the cooling of NS and their magneto-rotational evolution., Comment: 15 pages, 8 figures, accepted for publication in Astronomy and Astrophysics

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., Comment: 9 pages, 9 figures

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., Comment: 23 pages, 11 figures

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., Comment: 36 pages, 31 figures, 29 tables; corrected according to an erratum (2019, accepted)

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., Comment: 20 pages, 13 figures, submitted to A&A

Neutron stars, the compact stellar remnants of core-collapse supernova explosions, are unique cosmic laboratories for exploring novel phases of matter under extreme conditions. In particular, the occurrence of superfluidity and superconductivity in neutron stars will be briefly reviewed., Comment: Has appeared in Journal of Astrophysics and Astronomy special issue on "Physics of Neutron Stars and Related Objects", celebrating the 75th birth-year of G. Srinivasan

In spite of the absence of viscous drag, the neutron superfluid permeating the inner crust of a neutron star cannot flow freely, and is entrained by the nuclear lattice similarly to laboratory superfluid atomic gases in optical lattices. The role of entrainment on the neutron superfluid dynamics is reviewed. For this purpose, a minimal hydrodynamical model of superfluidity in neutron-star crusts is presented. This model relies on a fully four-dimensionally covariant action principle. The equivalence of this formulation with the more traditional approach is demonstrated. In addition, the different treatments of entrainment in terms of dynamical effective masses or superfluid density are clarified. The nuclear energy density functional theory employed for the calculations of all the necessary microscopic inputs is also reviewed, focusing on superfluid properties. In particular, the microscopic origin of entrainment and the different methods to estimate its importance are discussed., Comment: 30 pages, 4 figures

We develop a detailed and self-consistent numerical model for extremely-magnetised white dwarfs, which have been proposed as progenitors of overluminous Type Ia supernovae. This model can describe fully-consistent equilibria of magnetic stars in axial symmetry, with rotation, general-relativistic effects and realistic equations of state (including electron-ion interactions and taking into account Landau quantisation of electrons due to the magnetic field). We study the influence of each of these ingredients onto the white dwarf structure and, in particular, on their maximum mass. We perform an extensive stability analysis of such objects, with their highest surface magnetic fields reaching $\sim 10^{13}~G$ (at which point the star adopts a torus-like shape). We confirm previous speculations that although very massive strongly magnetised white dwarfs could potentially exist, the onset of electron captures and pycnonuclear reactions may severely limit their stability. Finally, the emission of gravitational waves by these objects is addressed, showing no possibility of detection by the currently planned space-based detector eLISA., Comment: submitted to MNRAS on 24.2.2016

Pulsars are spinning extremely rapidly with periods as short as about $1.4$ milliseconds and delays of a few milliseconds per year at most, thus providing the most accurate clocks in the Universe. Nevertheless, sudden spin ups have been detected in some pulsars like the emblematic Vela pulsar. These abrupt changes in the pulsar's rotation period have long been thought to be the manifestation of a neutron superfluid permeating the inner crust of neutron stars. However, the neutron superfluid has been recently found to be so strongly coupled to the crust that it does not carry enough angular momentum to explain the Vela data. We explore the extent to which pulsar-timing observations can be reconciled with the standard glitch theory considering the lack of knowledge of the dense-matter equation of state., Comment: Proceedings of the conference "The Modern Physics of Compact Stars 2015" held in Erevan, Armenia, from 30 September 2015 to 3 October 2015. To appear in Proceedings of Science

Magnetars are neutron stars endowed with surface magnetic fields of the order of $10^{14}-10^{15}$~G, and with presumably much stronger fields in their interior. As a result of Landau quantization of electron motion, the neutron-drip transition in the crust of a magnetar is shifted to either higher or lower densities depending on the magnetic field strength. The impact of nuclear uncertainties is explored considering the recent series of Brussels-Montreal microscopic nuclear mass models. All these models are based on the Hartree-Fock-Bogoliubov method with generalized Skyrme functionals. They differ in their predictions for the symmetry energy coefficient at saturation, and for the stiffness of the neutron-matter equation of state. For comparison, we have also considered the very accurate but more phenomenological model of Duflo and Zuker. Although the equilibrium composition of the crust of a magnetar and the onset of neutron emission are found to be model dependent, the quantum oscillations of the threshold density are essentially universal., Comment: 7 pages, 2 figures

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., Comment: 11 pages, 6 figures, submitted to PRD

The neutron-drip transition in the dense matter constituting the interior of neutron stars generally refers to the appearance of unbound neutrons as the matter density reaches some threshold density $\rho_\textrm{drip}$. This transition has been mainly studied under the cold catalyzed matter hypothesis. However, this assumption is unrealistic for accreting neutron stars. After examining the physical processes that are thought to be allowed in both accreting and nonaccreting neutron stars, suitable conditions for the onset of neutron drip are derived and general analytical expressions for the neutron drip density and pressure are obtained. Moreover, we show that the neutron-drip transition occurs at lower density and pressure than those predicted within the mean-nucleus approximation. This transition is studied numerically for various initial composition of the ashes from X-ray bursts and superbursts using microscopic nuclear mass models., Comment: 24 pages, accepted for publication in Physical Review C

The heat capacity of neutron matter is studied over the range of densities and temperatures prevailing in neutron-star crusts, allowing for the transition to a superfluid phase at temperatures below some critical temperature $T_{sf}$ and including the transition to the classical limit. Finite temperature Hartree-Fock-Bogoliubov equations (FTHFB) are solved and compared to existing approximate expressions. In particular, the formula given by Levenfish and Yakovlev is found to reproduce the numerical results with a high degree of accuracy for temperatures $T\leq T_{sf}$. In the non-superfluid phase, $T\geq T_{sf}$, the linear approximation is valid only at temperature $T\ll T_{{\rm F} n}$ ($T_{{\rm F} n}$ being the Fermi temperature of the neutron gas) which is rarely the case in the shallow layers of the neutron star's crust. A non-perturbative interpolation between the quantal and the classical regimes is proposed here. The heat capacity, conveniently parametrized solely in terms of $T_{sf}$, $T_{{\rm F} n}$, and the neutron number density $n_n$, can be easily implemented in neutron-star cooling simulations., Comment: Accepted by Monthly Notices of the Royal Astronomical Society

The Galilean (and more generally Milne) invariance of Newtonian theory allows for Killing vector fields of a general kind, whereby the Lie derivative of a field is not required to vanish but only to be cancellable by some infinitesimal Galilean (respectively Milne) gauge transformation. In this paper, it is shown that both the Killing-Milne vector fields, which preserve the background Newtonian space-time structure, and the Killing-Cartan vector fields, which in addition preserve the gravitational field, form a Lie subalgebra., Comment: 8 pages

The Brussels-Montreal Skyrme functionals have been successful to describe properties of both finite nuclei and infinite homogeneous nuclear matter. In their latest version, these functionals have been equipped with two extra density-dependent terms in order to reproduce simultaneously ground state properties of nuclei and infinite nuclear matter properties while avoiding at the same time the arising of ferromagnetic instabilities. In the present article, we extend our previous results of the linear response theory to include such extra terms at both zero and finite temperature in pure neutron matter. The resulting formalism is then applied to derive the neutrino mean free path. The predictions from the Brussels-Montreal Skyrme functionals are compared with ab-initio methods.

We explore the spectrum of low-energy collective excitations in the crust of a neutron star, especially in the inner region where neutron-proton clusters are immersed in a sea of superfluid neutrons. The speeds of the different modes are calculated systematically from the nuclear energy density functional theory using a Skyrme functional fitted to essentially all experimental atomic mass data., Comment: 5 pages, 1 figure, proceeding of the Nuclear Physics in Astrophysics VI conference, Lisbon, May 19-24 2013

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 \rho are given as functions of the baryon number density n_b. In the second version, P, \rho, 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., Comment: 13 pages, 10 figures, 10 tables. In v.2, minor typos in the text and references are fixed. In v.3 and v.4, typos in Table 6 and Eq.(17), respectively, are fixed. In v.5, labels on Fig.7 are corrected

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., Comment: 10 pages, 9 figures, to appear in EPJA special volume on symmetry energy

One of the most intringuing questions about neutron stars concerns their maximum mass. The answer is intimately related to the properties of matter at densities far beyond that found in heavy atomic nuclei. The current view on the internal constitution of neutron stars and on their maximum mass, both from theoretical and observational studies, are briefly reviewed., Comment: 25 pages, 4 figures; revised version with additions, corrections and updated references

It has been recently proposed that very massive white dwarfs endowed with strongly quantizing magnetic fields might be the progenitors of overluminous type Ia supernovae like SN 2006gz and SN 2009dc. In this work, we show that the onset of electron captures and pycnonuclear reactions in these putative super-Chandrasekhar white dwarfs may severely limit their stability., Comment: 5 pages, revised version

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., Comment: Proceedings of IAUS 291 "Neutron Stars and Pulsars: Challenges and Opportunities after 80 years", J. van Leeuwen (ed.); 3 pages, 1 figure

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., Comment: Proceedings of IAUS 291 "Neutron Stars and Pulsars: Challenges and Opportunities after 80 years", J. van Leeuwen (ed.); 3 pages

The neutron superfluid permeating the inner crust of mature neutron stars is expected to play a key role in various astrophysical phenomena like pulsar glitches. Despite the absence of viscous drag, the neutron superfluid can still be coupled to the solid crust due to non-dissipative entrainment effects. Entrainment challenges the interpretation of pulsar glitches and suggests that a revision of the interpretation of other observed neutron-star phenomena might be necessary., Comment: Proceedings of IAUS 291 "Neutron Stars and Pulsars: Challenges and Opportunities after 80 years", J. van Leeuwen (ed.); 4 pages, 1 figure

Large pulsar frequency glitches are generally interpreted as sudden transfers of angular momentum between the neutron superfluid permeating the inner crust and the rest of the star. Despite the absence of viscous drag, the neutron superfluid is strongly coupled to the crust due to non-dissipative entrainment effects. These effects are shown to severely limit the maximum amount of angular momentum that can possibly be transferred during glitches. In particular, it is found that the glitches observed in the Vela pulsar require an additional reservoir of angular momentum., Comment: 5 pages, 3 figures, revised version

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., Comment: 25 pages, 5 figures, revised version

We study the low-energy collective excitations of the neutron star inner crust, where a neutron superfluid coexists with a Coulomb lattice of nuclei. The dispersion relation of the modes is calculated systematically from a microscopic theory including neutron band structure effects. These effects are shown to lead to a strong mixing between the Bogoliubov-Anderson bosons of the neutron superfluid and the longitudinal crystal lattice phonons. In addition, the speed of the transverse shear mode is greatly reduced as a large fraction of superfluid neutrons are entrained by nuclei. Not only does the much smaller velocity of the transverse mode increase the specific heat of the inner crust, but it also decreases its electron thermal conductivity. These results may impact our interpretation of the thermal relaxation in accreting neutron stars. Due to strong mixing, the mean free path of the superfluid mode is found to be greatly reduced. Our results for the collective mode dispersion relations and their damping may also have implications for neutron star seismology., Comment: 25 pages, 8 figures, revised version

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., Comment: 2 pages, to appear in the proceedings of the ERPM conference, Zielona Gora, Poland, April 2012

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., Comment: 4 pages, to appear in the proceedings of the ERPM conference, Zielona Gora, Poland, April 2012

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., Comment: 4 pages, to appear in the proceedings of the ERPM conference, Zielona Gora, Poland, April 2012

The equation of state and composition of the inner crust of neutron stars at zero temperature are calculated, using the T = 0 version of the TETFSI (temperature-dependent extended Thomas-Fermi plus Strutinsky integral) method, for each of a family of three functionals based on Skyrme-type forces BSk19, BSk20 and BSk21, which are characterized by different degrees of symmetry-energy stiffness, and also for the SLy4 functional. We also solve the Tolman-Oppenheimer-Volkoff equations to calculate the distribution of mass within the inner crust. Qualitatively similar results are found for all four functionals, and in particular the number of protons per Wigner-Seitz cell is in all cases equal to 40 throughout the inner crust., Comment: 35 pages, 13 figures, accepted for publication in Physical Review C

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., Comment: 9 pages, 8 figures

Nuclear pairing is studied both in atomic nuclei and in neutron-star crusts in the unified framework of the energy-density functional theory using generalized Skyrme functionals complemented with a local pairing functional obtained from many-body calculations in homogeneous nuclear matter using realistic forces., Comment: 16 pages, 3 figures. Contribution for the book "50 years of nuclear BCS", edited by R.A. Broglia and V. Zelevinsky

We calculate the maximum mass of neutron stars for three different equations of state (EOS) based on generalized Skyrme functionals that are simultaneously fitted to essentially all the 2003 nuclear mass data (the rms deviation is 0.58 MeV in all three cases) and to one or other of three different equations of state of pure neutron matter, each determined by a different many-body calculation using realistic two- and three-body interactions but leading to significantly different degrees of stiffness at the high densities prevailing in neutron-star interiors. The observation of a neutron star with mass 1.97 $\pm$ 0.04 $\mathcal{M}_{\odot}$ eliminates the softest of our models (BSk19), but does not discriminate between BSk20 and BSk21. However, nuclear-mass measurements that have been made since our models were constructed strongly favor BSk21, our stiffest functional., Comment: 11 pages, 4 figures; Physical Review C in press

The rapid neutron-capture process, or r-process, is known to be fundamental for explaining the origin of approximately half of the A>60 stable nuclei observed in nature. In recent years nuclear astrophysicists have developed more and more sophisticated r-process models, by adding new astrophysical or nuclear physics ingredients to explain the solar system composition in a satisfactory way. Despite these efforts, the astrophysical site of the r-process remains unidentified. The composition of the neutron star outer crust material is investigated after the decompression that follows its possible ejection. The composition of the outer crust of a neutron star is estimated before and after decompression. Two different possible initial conditions are considered, namely an idealized crust composed of cold catalyzed matter and a crust initially in nuclear statistical equilibrium at temperatures around 10 GK. We show that in this second case before decompression and at temperatures typically corresponding to 8 GK, the Coulomb effect due to the high densities in the crust leads to an overall composition of the outer crust in neutron-rich nuclei with a mass distribution close to the solar system r-abundance distribution. Such distributions differ, however, from the solar one due to a systematic shift in the second peak to lower values. After decompression, the capture of the few neutrons per seed nucleus available in the hot outer crust leads to a final distribution of stable neutron-rich nuclei with a mass distribution of 80 < A < 140 nuclei in excellent agreement with the solar distribution, provided the outer crust is initially at temperatures around 8 GK and all layers of the outer crust are ejected. The decompression of the neutron star matter from the outer crust provides suitable conditions for a robust r-processing of the light species, i.e., r-nuclei with A < 140., Comment: 11 pages, 16 figures; Accepted in A&A main Journal

When applied to a single nucleon, nuclear energy density functionals may yield a non-vanishing internal energy thus implying that the nucleon is interacting with itself. It is shown how to avoid this unphysical feature for semi-local phenomenological functionals containing all possible bilinear combinations of local densities and currents up to second order in the derivatives. The method outlined in this Rapid Communication could be easily extended to functionals containing higher order terms, and could serve as a guide for constraining the time-odd part of the functional.

Self-consistent mean field methods based on phenomenological Skyrme effective interactions are known to exhibit spurious spin and spin-isospin instabilities both at zero and finite temperatures when applied to homogeneous nuclear matter at the densities encountered in neutron stars and in supernova cores. The origin of these instabilities is revisited in the framework of the nuclear energy density functional theory and a simple prescription is proposed to remove them. The stability of several Skyrme parametrizations is reexamined., Comment: 28 pages, 2 figures

Mature neutron stars are expected to contain various kinds of superfluids in their interiors. Modeling such stars requires the knowledge of the mutual entrainment couplings between the different condensates. We present a unified equation of state describing the different regions of a neutron star with superfluid neutrons and superconducting protons in its core., Comment: 6 pages, 4 figures, conference "Astrophysics of Neutron Stars - 2010" in honor of M. Ali Alpar, Izmir, Turkey

We construct three new Hartree-Fock-Bogoliubov (HFB) mass models, labeled HFB-19, HFB-20, and HFB-21, with unconventional Skyrme forces containing $t_4$ and $t_5$ terms, i.e., density-dependent generalizations of the usual $t_1$ and $t_2$ terms, respectively. The new forces underlying these models are fitted respectively to three different realistic equations of state of neutron matter for which the density dependence of the symmetry energy ranges from the very soft to the very stiff, reflecting thereby our present lack of complete knowledge of the high-density behavior of nuclear matter. All unphysical instabilities of nuclear matter, including the transition to a polarized state in neutron-star matter, are eliminated with the new forces. At the same time the new models fit essentially all the available mass data with rms deviations of 0.58 MeV and give the same high quality fits to measured charge radii that we obtained in earlier models with conventional Skyrme forces. Being constrained by neutron matter, these new mass models, which all give similar extrapolations out to the neutron drip line, are highly appropriate for studies of the $r$-process and the outer crust of neutron stars. Moreover, the underlying forces, labeled BSk19, BSk20 and BSk21, respectively, are well adapted to the study of the inner crust and core of neutron stars. The new family of Skyrme forces thus opens the way to a unified description of all regions of neutron stars., Comment: 45 pages, 16 figures, accepted for publication in Physical Review C

T. Li {\it et al.}[Phys. Rev. C {\bf 81}, 034309 (2010)] have analyzed their measured breathing-mode energies of some tin isotopes in terms of a first-order leptodermous expansion, and find for the symmetry-incompressibility coefficient $K_{\tau}$ the value of -550 $\pm$ 100 MeV. Removing an approximation that they made, we find that the first-order estimate of $K_{\tau}$ shifts to -661 $\pm$ 144 MeV. However, taking into account higher-order terms in the leptodermous expansion shows that the data are compatible with the significantly lower magnitudes indicated by both another experiment and some theoretical estimates., Comment: 6 pages, 1 figure

A simple description of superfluid hydrodynamics in the inner crust of a neutron star is given. Particular attention is paid to the effect of the lattice of nuclei on the properties of the superfluid neutrons, and the effects of entrainment, the fact that some fraction of the neutrons are locked to the motion of the protons in nuclei.

The neutron superfluidity in the inner crust of a neutron star has been traditionally studied considering either homogeneous neutron matter or only a small number of nucleons confined inside the spherical Wigner-Seitz cell. Drawing analogies with the recently discovered multi-band superconductors, we have solved the anisotropic multi-band BCS gap equations with Bloch boundary conditions, thus providing a unified description taking consistently into account both the free neutrons and the nuclear clusters. Calculations have been carried out using the effective interaction underlying our recent Hartree-Fock-Bogoliubov nuclear mass model HFB-16. We have found that even though the presence of inhomogeneities lowers the neutron pairing gaps, the reduction is much less than that predicted by previous calculations using the Wigner-Seitz approximation. We have studied the disappearance of superfluidity with increasing temperature. As an application we have calculated the neutron specific heat, which is an important ingredient for modeling the thermal evolution of newly-born neutron stars. This work provides a new scheme for realistic calculations of superfluidity in neutron-star crusts., Comment: 15 pages, 31 figures, accepted for publication in Physical Review C