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Universe
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Superfluidity and Superconductivity in Neutron Stars
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Superfluidity and Superconductivity in Neutron Stars

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Compact Objects".

Deadline for manuscript submissions: closed (15 February 2022) | Viewed by 36869

Special Issue Editor

Prof. Dr. Nicolas Chamel

E-Mail Website
Guest Editor
Institut d’Astronomie et d’Astrophysique, CP-226, Université Libre de Bruxelles, B-1050 Brussels, Belgium
Interests: neutron stars; pulsars; dense matter; quantum condensates; gravitation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Formed in the aftermath of gravitational core-collapse supernova explosions, neutron stars contain matter crushed at densities exceeding that found inside the heaviest atomic nuclei and are, therefore, unique laboratories for exploring novel phases of matter under conditions so extreme that they cannot be reproduced on Earth. In particular, neutron stars are the only celestial bodies that are expected to be superfluids and superconducting. Although quantum condensates have been extensively studied in the laboratory, the properties of their stellar counterpart remain largely unknown. This stems from the tremendous gravitational pressure that matter is subjected to in a neutron star. According to theoretical calculations, various kinds of superfluid and superconducting phases may exist in different regions of the star. One of the difficulties in modeling the global dynamics of a neutron star lies in the widely different scales involved: a neutron star (whose radius is about 10 kilometers) is thought to be threaded by quantized vortices with tiny cores of about 10–100 fermis. To add to the challenge, a neutron star is so compact (having a mass between once and twice that of the Sun) that it must be ultimately described by Einstein’s theory of general relativity. On the other hand, astrophysical observations can shed light on superfluidity and superconductivity in neutron stars through remarkable phenomena, such as pulsar frequency glitches. In addition to electromagnetic observations, the advent of gravitational-wave astronomy provides another way to probe the interior of a neutron star. The main goal of this Special Issue is to review recent progress in the field, from both theoretical and observational points of view.

You can now listen to some of the author discussion from the Universe webinar “Superfluidity and Superconductivity in Neutron Stars” here: https://universe-5.sciforum.net/. This webinar provided an overview of our current understanding of superfluidity and superconductivity in neutron stars and considered what can be learned from astrophysical observations by focusing on neutron star cooling, pulsar glitches, and neutron star asteroseismology.

Prof. Dr. Nicolas Chamel
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Neutron stars
  • pulsars
  • quantum condensates
  • superfluidity
  • superconductivity
  • hydrodynamics
  • vortices
  • general relativity
  • gravitation
  • gravitational waves

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Published Papers (14 papers)

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Editorial

Jump to: Research, Review

4 pages, 171 KiB  
Editorial
Superfluidity and Superconductivity in Neutron Stars
by Nicolas Chamel
Universe 2024, 10(3), 104; https://doi.org/10.3390/universe10030104 - 22 Feb 2024
Viewed by 1283
Abstract
By compressing matter to densities up to several times the density of atomic nuclei, the catastrophic gravitational collapse of the core of stars with a mass M≳8M⊙ during supernova explosions and the neutron star left behind (see, e [...] Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)

Research

Jump to: Editorial, Review

18 pages, 1022 KiB  
Article
Oscillating Magnetized Color Superconducting Quark Stars
by Marcos Osvaldo Celi, Mauro Mariani, Milva Gabriela Orsaria and Lucas Tonetto
Universe 2022, 8(5), 272; https://doi.org/10.3390/universe8050272 - 6 May 2022
Cited by 3 | Viewed by 2003
Abstract
The main objective of this work is to study the structure, composition, and oscillation modes of color superconducting quark stars with intense magnetic fields. We adopted the MIT bag model within the color superconductivity CFL framework, and we included the effects of strong [...] Read more.
The main objective of this work is to study the structure, composition, and oscillation modes of color superconducting quark stars with intense magnetic fields. We adopted the MIT bag model within the color superconductivity CFL framework, and we included the effects of strong magnetic fields to construct the equation of state of stable quark matter. We calculated observable quantities, such as the mass, radius, frequency, and damping time of the oscillation fundamental f mode of quark stars, taking into account current astrophysical constraints. The results obtained show that color superconducting magnetized quark stars satisfy the constraints imposed by the observations of massive pulsars and gravitational wave events. Furthermore, the quantities associated with the oscillation f mode of these objects fit the universal relationships for compact objects. In the context of the new multi-messenger gravitational wave astronomy era and the future asteroseismology of neutron stars, we hope that our results contribute to the understanding of the behavior of dense matter and compact objects. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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32 pages, 4087 KiB  
Article
Superconducting Phases in Neutron Star Cores
by Toby S. Wood and Vanessa Graber
Universe 2022, 8(4), 228; https://doi.org/10.3390/universe8040228 - 8 Apr 2022
Cited by 17 | Viewed by 2314
Abstract
Using a phenomenological Ginzburg–Landau model that includes entrainment, we identify the possible ground states for the neutron and proton condensates in the core of a neutron star, as a function of magnetic field strength. Combining analytical and numerical techniques, we find that much [...] Read more.
Using a phenomenological Ginzburg–Landau model that includes entrainment, we identify the possible ground states for the neutron and proton condensates in the core of a neutron star, as a function of magnetic field strength. Combining analytical and numerical techniques, we find that much of the outer core is likely to be a “type-1.5” superconductor (instead of a type-II superconductor as often assumed), in which magnetic flux is distributed inhomogeneously, with bundles of magnetic fluxtubes separated by flux-free Meissner regions. We provide an approximate criterion to determine the transition between this type-1.5 phase and the type-I region in the inner core. We also show that bundles of fluxtubes can coexist with non-superconducting regions, but only in a small part of the parameter space. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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34 pages, 915 KiB  
Article
1S0 Pairing Gaps, Chemical Potentials and Entrainment Matrix in Superfluid Neutron-Star Cores for the Brussels–Montreal Functionals
by Valentin Allard and Nicolas Chamel
Universe 2021, 7(12), 470; https://doi.org/10.3390/universe7120470 - 30 Nov 2021
Cited by 12 | Viewed by 2745
Abstract
Temperature and velocity-dependent 1S0 pairing gaps, chemical potentials and entrainment matrix in dense homogeneous neutron–proton superfluid mixtures constituting the outer core of neutron stars, are determined fully self-consistently by solving numerically the time-dependent Hartree–Fock–Bogoliubov equations over the whole range of temperatures [...] Read more.
Temperature and velocity-dependent 1S0 pairing gaps, chemical potentials and entrainment matrix in dense homogeneous neutron–proton superfluid mixtures constituting the outer core of neutron stars, are determined fully self-consistently by solving numerically the time-dependent Hartree–Fock–Bogoliubov equations over the whole range of temperatures and flow velocities for which superfluidity can exist. Calculations have been made for npeμ in beta-equilibrium using the Brussels–Montreal functional BSk24. The accuracy of various approximations is assessed and the physical meaning of the different velocities and momentum densities appearing in the theory is clarified. Together with the unified equation of state published earlier, the present results provide consistent microscopic inputs for modeling superfluid neutron-star cores. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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19 pages, 2245 KiB  
Article
The I-Love-Q Relations for Superfluid Neutron Stars
by Cheung-Hei Yeung, Lap-Ming Lin, Nils Andersson and Greg Comer
Universe 2021, 7(4), 111; https://doi.org/10.3390/universe7040111 - 20 Apr 2021
Cited by 21 | Viewed by 2212
Abstract
The I-Love-Q relations are approximate equation-of-state independent relations that connect the moment of inertia, the spin-induced quadrupole moment, and the tidal deformability of neutron stars. In this paper, we study the I-Love-Q relations for superfluid neutron stars for a general relativistic two-fluid model: [...] Read more.
The I-Love-Q relations are approximate equation-of-state independent relations that connect the moment of inertia, the spin-induced quadrupole moment, and the tidal deformability of neutron stars. In this paper, we study the I-Love-Q relations for superfluid neutron stars for a general relativistic two-fluid model: one fluid being the neutron superfluid and the other a conglomerate of all charged components. We study to what extent the two-fluid dynamics might affect the robustness of the I-Love-Q relations by using a simple two-component polytropic model and a relativistic mean field model with entrainment for the equation-of-state. Our results depend crucially on the spin ratio Ωn/Ωp between the angular velocities of the neutron superfluid and the normal component. We find that the I-Love-Q relations can still be satisfied to high accuracy for superfluid neutron stars as long as the two fluids are nearly co-rotating Ωn/Ωp≈1. However, the deviations from the I-Love-Q relations increase as the spin ratio deviates from unity. In particular, the deviation of the Q-Love relation can be as large as O(10%) if Ωn/Ωp differ from unity by a few tens of percent. As Ωn/Ωp≈1 is expected for realistic neutron stars, our results suggest that the two-fluid dynamics should not affect the accuracy of any gravitational waveform models for neutron star binaries that employ the relation to connect the spin-induced quadrupole moment and the tidal deformability. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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35 pages, 534 KiB  
Article
Superfluid Dynamics in Neutron Star Crusts: The Iordanskii Force and Chemical Gauge Covariance
by Lorenzo Gavassino, Marco Antonelli and Brynmor Haskell
Universe 2021, 7(2), 28; https://doi.org/10.3390/universe7020028 - 29 Jan 2021
Cited by 11 | Viewed by 2609
Abstract
We present a geometrical derivation of the relativistic dynamics of the superfluid inner crust of a neutron star. The resulting model is analogous to the Hall-Vinen-Bekarevich-Khalatnikov hydrodynamics for a single-component superfluid at finite temperature, but particular attention should be paid to the fact [...] Read more.
We present a geometrical derivation of the relativistic dynamics of the superfluid inner crust of a neutron star. The resulting model is analogous to the Hall-Vinen-Bekarevich-Khalatnikov hydrodynamics for a single-component superfluid at finite temperature, but particular attention should be paid to the fact that some fraction of the neutrons is locked to the motion of the protons in nuclei. This gives rise to an ambiguity in the definition of the two currents (the normal and the superfluid one) on which the model is built, a problem that manifests itself as a chemical gauge freedom of the theory. To ensure chemical gauge covariance of the hydrodynamic model, the phenomenological equation of motion for a quantized vortex should contain an extra transverse force, that is the relativistic version of the Iordanskii force discussed in the context of superfluid Helium. Hence, we extend the mutual friction model of Langlois et al. (1998) to account for the possible presence of this Iordanskii-like force. Furthermore, we propose that a better understanding of the (still not completely settled) controversy around the presence of the Iordanskii force in superfluid Helium, as well as in neutron stars, may be achieved by considering that the different incompatible results present in the literature pertain to two, opposite, dynamical regimes of the fluid system. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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23 pages, 545 KiB  
Article
Superfluid Neutron Matter with a Twist
by Georgios Palkanoglou and Alexandros Gezerlis
Universe 2021, 7(2), 24; https://doi.org/10.3390/universe7020024 - 26 Jan 2021
Cited by 4 | Viewed by 3121
Abstract
Superfluid neutron matter is a key ingredient in the composition of neutron stars. The physics of the inner crust are largely dependent on those of its S-wave neutron superfluid, which has made its presence known through pulsar glitches and modifications in neutron [...] Read more.
Superfluid neutron matter is a key ingredient in the composition of neutron stars. The physics of the inner crust are largely dependent on those of its S-wave neutron superfluid, which has made its presence known through pulsar glitches and modifications in neutron star cooling. Moreover, with recent gravitational-wave observations of neutron star mergers, the need for an equation of state for the matter of these compact stars is further accentuated and a model-independent treatment of neutron superfluidity is important. Ab initio techniques developed for finite systems can be guided to perform extrapolations to the thermodynamic limit and attain this model-independent extraction of various quantities of infinite superfluid neutron matter. To inform such an extrapolation scheme, we performed calculations of the neutron 1S0 pairing gap using model-independent odd–even staggering in the context of the particle-conserving, projected Bardeen–Cooper–Schrieffer (BCS) theory under twisted boundary conditions. While the practice of twisted boundary conditions is standard in solid-state physics and has been used repeatedly in the past to reduce finite-size effects, this is the first time that it has been employed in the context of pairing. We find that a twist-averaging approach results in a substantial reduction of the finite-size effects, bringing systems with N⪆50 within a 2% error margin from the infinite system. This can significantly reduce extrapolation-related errors in the extraction of superfluid neutron matter quantities. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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Graphical abstract

18 pages, 456 KiB  
Article
Statistical Estimates of the Pulsar Glitch Activity
by Alessandro Montoli, Marco Antonelli, Brynmor Haskell and Pierre Pizzochero
Universe 2021, 7(1), 8; https://doi.org/10.3390/universe7010008 - 5 Jan 2021
Cited by 9 | Viewed by 2654
Abstract
A common way to calculate the glitch activity of a pulsar is an ordinary linear regression of the observed cumulative glitch history. This method however is likely to underestimate the errors on the activity, as it implicitly assumes a (long-term) linear dependence between [...] Read more.
A common way to calculate the glitch activity of a pulsar is an ordinary linear regression of the observed cumulative glitch history. This method however is likely to underestimate the errors on the activity, as it implicitly assumes a (long-term) linear dependence between glitch sizes and waiting times, as well as equal variance, i.e., homoscedasticity, in the fit residuals, both assumptions that are not well justified from pulsar data. In this paper, we review the extrapolation of the glitch activity parameter and explore two alternatives: the relaxation of the homoscedasticity hypothesis in the linear fit and the use of the bootstrap technique. We find a larger uncertainty in the activity with respect to that obtained by ordinary linear regression, especially for those objects in which it can be significantly affected by a single glitch. We discuss how this affects the theoretical upper bound on the moment of inertia associated with the region of a neutron star containing the superfluid reservoir of angular momentum released in a stationary sequence of glitches. We find that this upper bound is less tight if one considers the uncertainty on the activity estimated with the bootstrap method and allows for models in which the superfluid reservoir is entirely in the crust. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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20 pages, 579 KiB  
Article
BCS-BEC Crossover Effects and Pseudogap in Neutron Matter
by David Durel and Michael Urban
Universe 2020, 6(11), 208; https://doi.org/10.3390/universe6110208 - 13 Nov 2020
Cited by 7 | Viewed by 2096
Abstract
Due to the large neutron–neutron scattering length, dilute neutron matter resembles the unitary Fermi gas, which lies half-way in the crossover from the BCS phase of weakly coupled Cooper pairs to the Bose–Einstein condensate of dimers. We discuss crossover effects in analogy with [...] Read more.
Due to the large neutron–neutron scattering length, dilute neutron matter resembles the unitary Fermi gas, which lies half-way in the crossover from the BCS phase of weakly coupled Cooper pairs to the Bose–Einstein condensate of dimers. We discuss crossover effects in analogy with the T-matrix theory used in the physics of ultracold atoms, which we generalize to the case of a non-separable finite-range interaction. A problem of the standard Nozières–Schmitt-Rink approach and different ways to solve it are discussed. It is shown that in the strong-coupling regime, the spectral function exhibits a pseudo-gap at temperatures above the critical temperature Tc. The effect of the correlated density on the density dependence of Tc is found to be rather weak, but a possibly important effect due to the reduced quasiparticle weight is identified. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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17 pages, 754 KiB  
Article
Comparison between the Thomas–Fermi and Hartree–Fock–Bogoliubov Methods in the Inner Crust of a Neutron Star: The Role of Pairing Correlations
by Matthew Shelley and Alessandro Pastore
Universe 2020, 6(11), 206; https://doi.org/10.3390/universe6110206 - 11 Nov 2020
Cited by 14 | Viewed by 2364
Abstract
We investigated the role of a pairing correlation in the chemical composition of the inner crust of a neutron star with the extended Thomas–Fermi method, using the Strutinsky integral correction. We compare our results with the fully self-consistent Hartree–Fock–Bogoliubov approach, showing that the [...] Read more.
We investigated the role of a pairing correlation in the chemical composition of the inner crust of a neutron star with the extended Thomas–Fermi method, using the Strutinsky integral correction. We compare our results with the fully self-consistent Hartree–Fock–Bogoliubov approach, showing that the resulting discrepancy, apart from the very low density region, is compatible with the typical accuracy we can achieve with standard mean-field methods. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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16 pages, 812 KiB  
Article
Nuclear Pairing Gaps and Neutron Star Cooling
by Jin-Biao Wei, Fiorella Burgio and Hans-Josef Schulze
Universe 2020, 6(8), 115; https://doi.org/10.3390/universe6080115 - 8 Aug 2020
Cited by 6 | Viewed by 2920
Abstract
We study the cooling of isolated neutron stars with particular regard to the importance of nuclear pairing gaps. A microscopic nuclear equation of state derived in the Brueckner-Hartree-Fock approach is used together with compatible neutron and proton pairing gaps. We then study the [...] Read more.
We study the cooling of isolated neutron stars with particular regard to the importance of nuclear pairing gaps. A microscopic nuclear equation of state derived in the Brueckner-Hartree-Fock approach is used together with compatible neutron and proton pairing gaps. We then study the effect of modifying the gaps on the final deduced neutron star mass distributions. We find that a consistent description of all current cooling data can be achieved and a reasonable neutron star mass distribution can be predicted employing the (slightly reduced by about 40%) proton 1S0 Bardeen-Cooper-Schrieffer (BCS) gaps and no neutron 3P2 pairing. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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Review

Jump to: Editorial, Research

22 pages, 1225 KiB  
Review
Transport Properties of Superfluid Phonons in Neutron Stars
by Cristina Manuel and Laura Tolos
Universe 2021, 7(3), 59; https://doi.org/10.3390/universe7030059 - 5 Mar 2021
Cited by 6 | Viewed by 1858
Abstract
We review the effective field theory associated with the superfluid phonons that we use for the study of transport properties in the core of superfluid neutrons stars in their low temperature regime. We then discuss the shear and bulk viscosities together with the [...] Read more.
We review the effective field theory associated with the superfluid phonons that we use for the study of transport properties in the core of superfluid neutrons stars in their low temperature regime. We then discuss the shear and bulk viscosities together with the thermal conductivity coming from the collisions of superfluid phonons in neutron stars. With regard to shear, bulk, and thermal transport coefficients, the phonon collisional processes are obtained in terms of the equation of state and the superfluid gap. We compare the shear coefficient due to the interaction among superfluid phonons with other dominant processes in neutron stars, such as electron collisions. We also analyze the possible consequences for the r-mode instability in neutron stars. As for the bulk viscosities, we determine that phonon collisions contribute decisively to the bulk viscosities inside neutron stars. For the thermal conductivity resulting from phonon collisions, we find that it is temperature independent well below the transition temperature. We also obtain that the thermal conductivity due to superfluid phonons dominates over the one resulting from electron-muon interactions once phonons are in the hydrodynamic regime. As the phonons couple to the Z electroweak gauge boson, we estimate the associated neutrino emissivity. We also briefly comment on how the superfluid phonon interactions are modified in the presence of a gravitational field or in a moving background. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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23 pages, 1406 KiB  
Review
A Superfluid Perspective on Neutron Star Dynamics
by Nils Andersson
Universe 2021, 7(1), 17; https://doi.org/10.3390/universe7010017 - 15 Jan 2021
Cited by 24 | Viewed by 4246
Abstract
As mature neutron stars are cold (on the relevant temperature scale), one has to carefully consider the state of matter in their interior. The outer kilometre or so is expected to freeze to form an elastic crust of increasingly neutron-rich nuclei, coexisting with [...] Read more.
As mature neutron stars are cold (on the relevant temperature scale), one has to carefully consider the state of matter in their interior. The outer kilometre or so is expected to freeze to form an elastic crust of increasingly neutron-rich nuclei, coexisting with a superfluid neutron component, while the star’s fluid core contains a mixed superfluid/superconductor. The dynamics of the star depend heavily on the parameters associated with the different phases. The presence of superfluidity brings new degrees of freedom—in essence we are dealing with a complex multi-fluid system—and additional features: bulk rotation is supported by a dense array of quantised vortices, which introduce dissipation via mutual friction, and the motion of the superfluid is affected by the so-called entrainment effect. This brief survey provides an introduction to—along with a commentary on our current understanding of—these dynamical aspects, paying particular attention to the role of entrainment, and outlines the impact of superfluidity on neutron-star seismology. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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18 pages, 675 KiB  
Review
Superfluid Phonons in Neutron Star Core
by Marcello Baldo
Universe 2021, 7(1), 16; https://doi.org/10.3390/universe7010016 - 14 Jan 2021
Cited by 1 | Viewed by 1925
Abstract
In neutron stars the nuclear asymmetric matter is expected to undergo phase transitions to a superfluid state. According to simple estimates, neutron matter in the inner crust and just below should be in the s-wave superfluid phase, corresponding to the neutron-neutron [...] Read more.
In neutron stars the nuclear asymmetric matter is expected to undergo phase transitions to a superfluid state. According to simple estimates, neutron matter in the inner crust and just below should be in the s-wave superfluid phase, corresponding to the neutron-neutron 1S0 channel. At higher density in the core also the proton component should be superfluid, while in the inner core the neutron matter can be in the 3P2 superfluid phase. Superluidity is believed to be at the basis of the glitches phenomenon and to play a decisive influence on many processes like transport, neutrino emission and cooling, and so on. One of the peculiarity of the superfluid phase is the presence of characteristic collective excitation, the so called ’phonons’, that correspond to smooth modulations of the order parameter and display a linear spectrum at low enough momentum. This paper is a brief review of the different phonons that can appear in Neutron Star superfuid matter and their role in several dynamical processes. Particular emphasis is put on the spectral functions of the different components, that is neutron, protons and electrons, which reveal their mutual influence. The open problems are discussed and indications on the work that remain to be done are given. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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