Numerical models for stationary superfluid neutron stars in general relativity with realistic equations of state

We present a numerical model for uniformly rotating superfluid neutron stars, for the first time with realistic microphysics including entrainment, in a fully general relativistic framework. We compute stationary and axisymmetric configurations of neutron stars composed of two fluids, namely superfluid neutrons and charged particles (protons and electrons), rotating with different rates around a common axis. Both fluids are coupled by entrainment, a non-dissipative interaction which in case of a non-vanishing relative velocity between the fluids, causes the fluid momenta being not aligned with the respective fluid velocities. We extend the formalism by Comer and Joynt (2003) in order to calculate the equation of state (EoS) and entrainment parameters for an arbitrary relative velocity. The resulting entrainment matrix fulfills all necessary sum rules and in the limit of small relative velocity our results agree with Fermi liquid theory ones, derived to lowest order in the velocity. This formalism is applied to two new nuclear equations of state which are implemented in the numerical model. We are able to obtain precise equilibrium configurations. Resulting density profiles and moments of inertia are discussed employing both EoSs, showing the impact of entrainment and the dependence on the EoS.Comment: 18 pages, 10 figures, minor changes to match published version in PRD, a typo present in Eq.A1 in the published version has been correcte

Global numerical simulations of the rise of vortex-mediated pulsar glitches in full general relativity

In this paper, we study in detail the role of general relativity on the global dynamics of giant pulsar glitches as exemplified by Vela. For this purpose, we carry out numerical simulations of the spin up triggered by the sudden unpinning of superfluid vortices. In particular, we compute the exchange of angular momentum between the core neutron superfluid and the rest of the star within a two-fluid model including both (non-dissipative) entrainment effects and (dissipative) mutual friction forces. Our simulations are based on a quasi-stationary approach using realistic equations of state (EoSs). We show that the evolution of the angular velocities of both fluids can be accurately described by an exponential law. The associated characteristic rise time $\tau_{\text{r}}$, which can be precisely computed from stationary configurations only, has a form similar to that obtained in the Newtonian limit. However, general relativity changes the structure of the star and leads to additional couplings between the fluids due to frame-dragging effects. As a consequence, general relativity can have a large impact on the actual value of $\tau_{\text{r}}$: the errors incurred by using Newtonian gravity are thus found to be as large as $\sim 40 \%$ for the models considered. Values of the rise time are calculated for Vela and compared with current observational limits. Finally, we study the amount of gravitational waves emitted during a glitch. Simple expressions are obtained for the corresponding characteristic amplitudes and frequencies. The detectability of glitches through gravitational wave observatories is briefly discussed.Comment: 19 pages, 12 figures, minor changes to match version to be published in MNRA

General relativistic models of superfluid neutron stars : applications to pulsars dynamics

L'objectif de cette thèse est d'étudier différents aspects microscopiques et macroscopiques liés à la présence de superfluidité dans les étoiles à neutrons. Dans un premier temps, nous avons calculé des configurations stationnaires d'étoiles à neutrons superfluides en rotation, en relativité générale, basées sur l'utilisation d'équations d'état réalistes. A l'aide de ces configurations d'équilibre, nous avons ensuite développé un modèle simple de glitch, en relativité générale, vu comme un transfert de moment cinétique entre les neutrons superfluides et les particules chargées constituant l'étoile. Cela nous a permis d'obtenir des temps caractéristiques de montée qui pourront être comparés à de futures observations précises de glitches afin d'apporter de meilleures contraintes sur l'intérieur de ces étoiles. Enfin, nous nous sommes également intéressés à la dynamique des vortex superfluides, en présence de tubes de flux, dans le cas où les protons dans le coeur des étoiles formeraient un supraconducteur de type II.The aim of this thesis is to study different aspects, both microscopic and macroscopic, associated with the presence of a large amount of superfluid matter inside neutron stars. First, we computed stationary configurations of rotating superfluid neutron stars, in general relativity, using realistic equations of state. Based on these equilibrium configurations, we then developed a simple model of pulsar glitches, in general relativity, seen as angular momentum transfers between the superfluid neutrons and the charged particles composing the star. This enables us to infer spin-up time scales that could be compared with future accurate glitch observations, in order to get some constraints on the interior of neutron stars. Finally, we also focused on the dynamics of superfluid vortex lines, accounting for the presence of fluxtubes, if the protons are forming a type II superconductor in the core of neutron stars

Modèles superfluides d’étoiles à neutrons en relativité générale – applications à la dynamique des pulsars

The long-term braking of pulsars is sometimes accompanied with tiny irregularities, during which the neutron star suddenly spins up, before slowly relaxing. These “glitches” are commonly interpreted as angular momentum transfers occurring between two fluids present in the stellar interior, triggered by the rapid motion of superfluid vortex lines at large scales. Considering for the first time all general relativistic effects in a numerical model for glitches, this work is a major step towards the full understanding of this phenomenon. A first part is dedicated to the numerical calculation of stationary configurations of neutron stars composed of a neutron superfluid and a fluid made of charged particles, spinning with different rotation rates. These general relativistic calculations are based on realistic equations of state accounting for entrainment effects between the fluids. These configurations are then used to build a numerical model for pulsar glitches in full general relativity. In particular, we study in details the characteristic time scale associated with the spin-up stage, during which the stellar dynamics are governed by a mutual friction force arising from the interactions between the superfluid vortices and the surrounding fluids. Taking general relativity into account leads to an additional coupling between the fluids through frame-dragging effects and is shown to affect significantly the actual value of the spin-up time scale. Finally, the expression of the mutual friction force is derived assuming that the superfluid vortex lines are pinned to the magnetic flux tubes present in the core of neutron stars. The different time scales associated with the spin-up stage and the subsequent relaxation period may be explained by a variation of the number of flux tubes pinned to each vortex line during the glitch event.Le ralentissement de certains pulsars s’accompagne de petites irrégularités, caractérisées par une soudaine accélération, suivie d’une lente phase de relaxation. Ces « glitches » sont couramment interprétés comme de brusques transferts de moment cinétique entre deux fluides présents dans l’étoile à neutrons, rendus possibles par un mouvement rapide de tourbillons superfluides à grande échelle. Incluant pour la première fois tous les effets de la relativité générale dans un modèle numérique de glitch, le travail présenté ici constitue une étape essentielle vers la compréhension de ce phénomène. Une première partie se concentre sur le calcul numérique de configurations stationnaires d’étoiles à neutrons formées par un superfluide de neutrons et un fluide de particules chargées tournant à des vitesses différentes. Ces calculs de structure, réalisés en relativité générale, reposent sur des équations d’état réalistes tenant compte des effets d’entraînement mutuel entre les fluides. Nous présentons ensuite un modèle numérique de glitch faisant appel à ces configurations. En particulier, nous étudions en détails le temps caractéristique associé à la phase de montée du glitch, au cours de laquelle la dynamique de l’étoile est gouvernée par une force de friction mutuelle liée à l’interaction des tourbillons superfluides avec les fluides environnants. La prise en compte de la relativité générale, qui conduit notamment à l’apparition d’un nouveau couplage entre les fluides par effet d’entraînement des référentiels inertiels, a un impact significatif sur la valeur de ce temps de montée. Nous établissons enfin l’expression de la force de friction mutuelle dans le cas où les tourbillons superfluides sont ancrés aux tubes de flux magnétiques présents dans le cœur des étoiles à neutrons. Une variation du nombre de tubes de flux ancrés à chaque tourbillon lors du glitch permet alors de rendre compte des échelles de temps très différentes associées aux phases de montée et de relaxation

Generalization of the Kutta-Joukowski theorem for the hydrodynamic forces acting on a quantized vortex

International audienceThe hydrodynamic forces acting on a quantized vortex in a superfluid have long been a highly controversial issue. A new approach, originally developed in the astrophysical context of compact stars, is presented to determine these forces by considering small perturbations of the asymptotically uniform flows in the region far from the vortex in the framework of Landau-Khalatnikov two-fluid model. Focusing on the irrotational part of the flows in the Helmholtz decomposition, the classical Kutta-Joukowski theorem from ordinary hydrodynamics is thus generalized to superfluid systems. The same method is applied to predict the hydrodynamic forces acting on vortices in cold atomic condensates and superfluid mixtures

Force on a neutron quantized vortex pinned to proton fluxoids in the superfluid core of cold neutron stars

International audienceThe superfluid and superconducting core of a cold rotating neutron star (NS) is expected to be threaded by a tremendous number of neutron quantized vortices and proton fluxoids. Their interactions are unavoidable and may have important astrophysical implications. In this paper, the various contributions to the force acting on a single vortex to which fluxoids are pinned are clarified. The general expression of the force is derived by applying the variational multifluid formalism developed by Carter and collaborators. Pinning to fluxoids leads to an additional Magnus type force due to proton circulation around the vortex. Pinning in the core of an NS may thus have a dramatic impact on the vortex dynamics, and therefore on the magnetorotational evolution of the star

Vortex pinning in the superfluid core of neutron stars and the rise of pulsar glitches

International audienceTiming of the Crab and Vela pulsars has recently revealed very peculiar evolutions of their spin frequency during the early stage of a glitch. We show that these differences can be interpreted from the interactions between neutron superfluid vortices and proton fluxoids in the core of these neutron stars. In particular, pinning of individual vortices to fluxoids is found to have a dramatic impact on the mutual friction between the neutron superfluid and the rest of the star. The number of fluxoids attached to vortices turns out to be a key parameter governing the global dynamics of the star. These results may have implications for the interpretation of other astrophysical phenomena such as pulsar-free precession or the r-mode instability

Evolution of our galaxy and others with the high-resolution version of the code Pégase

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Role of the crust in the tidal deformability of a neutron star within a unified treatment of dense matter

International audienceThe role of the crust on the tidal deformability of a cold nonaccreted neutron star is studied using the recent unified equation of state BSk24. This equation of state, which is based on the nuclear energy-density-functional theory, provides a thermodynamically consistent description of all stellar regions. Results obtained with this equation of state are compared to those calculated for a putative neutron star made entirely of homogeneous matter. The presence of the crustal layers is thus found to significantly reduce the Love number k2, especially for low-mass stars. However, this reduction mainly arises from the increase in the stellar radius almost independently of the equation of state. This allows for a simple analytic estimate of k2 for realistic neutron stars using the equation of state of homogeneous matter only

Numerical models for superfluid neutron stars and application to pulsar glitches

International audienceWe describe recent progress in the modelling of realistic equilibrium configurations of rotating superfluid neutron stars, in a fully general relativistic framework. We compute stationary and axisymmetric configurations of neutron stars composed of two interpenetrating and interacting fluids, namely superfluid neutrons and charged particles (protons and electrons), rotating with different rotation rates around a common axis. Two different realistic equations of state are considered. As a first application, we propose a simple bulk model for pulsar glitches, seen as angular momentum transfers between the two fluids through mutual friction force. From a series of equilibrium states, we compute the evolution in time of the properties of a neutron star during the rise period of a glitch. This enables us to infer characteristic features relative to glitches, such as spin-up timescales, that could be compared with future accurate observations in order to put some constraints on the interior of neutron stars