Superfluid neutron matter is a key ingredient in the composition of neutron stars. The physics of the inner crust is largely dependent on that of its $S$-wave neutron superfluid which has made its presence known through pulsar glitches and modifications on the 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. \textit{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 $^1S_0$ pairing gap using the model-independent odd-even staggering in the context of the particle-conserving, projected 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 it is 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 $N\gtrapprox 50$ within a $2\%$ error margin from the infinite system. This can significantly reduce extrapolation-related errors in the extraction of superfluid neutron matter quantities.
We investigate effects of thermal and quantum fluctuations of the superfluid order parameter in $^1S_{0}$ superfluids in neutron stars. We construct a separable potential to reproduce the $^1S_{0}$ phase shift reconstructed by using the partial wave analysis from nucleon scattering data. We include superfluid fluctuations within a strong-coupling approximation developed by Nozières and Schmitt-Rink and determine self-consistently the superfluid order parameter as well as the chemical potential. We show that the quantum depletion, which gives a fraction of noncondensed neutrons at zero temperat…
We clarify a relation between the Gross-Pitaevskii energy functional for spin-2 spinor Bose-Einstein condensates and the Ginzburg-Landau theory for neutron $^3P_2$ superfluidis (spin-triplet $P$-wave pairing with total angular momentum two). We then classify all uniform states with nontrivial unbroken symmetries, with the help of geometric invariant theory.
We study the superfluid dynamics of the outer core of neutron stars by means of a hydrodynamic model made of a neutronic superfluid and a protonic superconductor, coupled by both the dynamic entrainment and the Skyrme SLy4 nucleon-nucleon interactions. The resulting nonlinear equations of motion are probed in the search for dynamical instabilities triggered by the relative motion of the superfluids that could be related to observed timing anomalies in pulsars. Through linear analysis, the origin and expected growth of the instabilities is explored for varying nuclear-matter density. Differentl…
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 differ…
Calculations of the effects of band structure on the neutron superfluid density in the crust of neutron stars made under the assumption that the effects of pairing are small [N. Chamel, Phys. Rev. C 85, 035801 (2012)] lead to moments of inertia of superfluid neutrons so small that the crust alone is insufficient to account for the magnitude of neutron star glitches. Inspired by earlier work on ultracold atomic gases in an optical lattice, we investigate fermions with attractive interactions in a periodic lattice in the mean-field approximation. The effects of band structure are suppressed when…
Several phenomena occurring in neutron stars are affected by the elementary excitations that characterize the stellar matter. In particular, low-energy excitations can play a major role in the emission and propagation of neutrinos, neutron star cooling and transport processes. In this paper, we consider the elementary modes in the star region where both proton and neutron components are superfluid. We study the overall spectral functions of protons, neutrons and electrons on the basis of the Coulomb and nuclear interactions. This study is performed in the framework of the Random Phase Approxim…
Nuclear matter and finite nuclei exhibit the property of superfluidity by forming Cooper pairs. We review the microscopic theories and methods that are being employed to understand the basic properties of superfluid nuclear systems, with emphasis on the spatially extended matter encountered in neutron stars, supernova envelopes, and nuclear collisions. Our survey of quantum many-body methods includes techniques that employ Green functions, correlated basis functions, and Monte Carlo sampling of quantum states. With respect to empirical realizations of nucleonic and hadronic superfluids, this r…
The neutron-star inner crust is assumed to be superfluid at relevant temperatures. The contribution of neutron quasiparticles to thermodynamic and transport properties of the crust is therefore strongly suppressed by the pairing gap. Nevertheless, the neutron gas still has low-energy excitations, namely long-wavelength collective modes. We summarize different approaches to describe the collective modes in the crystalline phases of the inner crust and present an improved model for the description of the collective modes in the pasta phases within superfluid hydrodynamics.
Superfluid extension of the self-consistent time-dependent band theory for neutron star matter: Anti-entrainment versus superfluid effects in the slab phase
We calculate the superfluid density of nucleons in disordered pasta phases in the inner crust of neutron stars using an effective medium approach which parallels that previously used for calculating the electrical conductivity of terrestrial matter. We allow for the effect of entrainment, the fact that the current density of one species of nucleon depends on the gradient of the phase not only of the same species but also of the other species. The superfluid density tensors for the perfectly ordered pasta phases are very anisotropic, and we derive expression for the effective superfluid densiti…
Axial anomalous contributions into neutrino PBF losses due to triplet pairing of neutrons are still ignored in modeling the evolution of neutron stars. In this paper, the influence of the anomalous axial contributions onto the rate of neutron stars cooling is estimated.
The superfluid pairing gap of neutron matter is calculated in the framework of Quark Compound Bag model with nucleon-nucleon interactions generated by the s-channel exchange of Jaffe-Low primitives (6-quark states).
We discuss collective excitations (both fundamental and solitonic excitations) of quantized superfluid vortices in neutron $^3P_2$ superfluids, which likely exist in high density neutron matter such as neutron stars. Besides the well-known Kelvin modes (translational zero modes), we find a gapfull mode whose low-energy description takes the simple form of a double sine-Gordon model. The associated kink solution and its effects on spontaneous magnetization inside the vortex core are analyzed in detail.
This review focuses on applications of the ideas of superfluidity and superconductivity in neutron stars in a broader context, ranging from the microphysics of pairing in nucleonic superfluids to macroscopic manifestations of superfluidity in pulsars. The exposition of the basics of pairing, vorticity and mutual friction can serve as an introduction to the subject. We also review some topics of recent interest, including the various types of pinning of vortices, glitches, and oscillations in neutron stars containing superfluid phases of baryonic matter.
A mixture of superconducting and superfluid nuclear liquids of protons coupled to the ultrarelativistic electron gas, and neutrons is considered. In the magnetohydrodynamic (MHD) approximation, the energy-momentum (stress) tensor is derived, and the entrainment contribution is found in the explicit form. It is shown that this contribution generates a force density, when a superfluid velocity lag and the magnetic field are simultaneously present. This force may be important in the nuclear "pasta" phase in neutron stars, if the proton and neutron Cooper pairing in the pasta phase is taken into a…
The interior of a neutron star is expected to be occupied by a neutron $^3P_2$ superfluid, which is the condensate of spin-triplet $p$-wave Cooper pairs of neutrons with total angular momentum $J=2$. Here we investigate the thermodynamic stability of $^3P_2$ superfluids in a neutron-star interior under a strong magnetic field. Using the theory incorporating the finite size correction of neutron Fermi surface, we show that the spin-polarized phases of $^3P_2$ superfluids, the magnetized biaxial nematic phase and the ferromagnetic phase, appear in high temperatures and high magnetic fields. Thes…
In a simple model it is demonstrated that the neutron star surface temperature evolution is sensitive to the phase state of the triplet superfluid condensate. A multicomponent triplet pairing of superfluid neutrons in the core of a neutron star with participation of several magnetic quantum numbers leads to neutrino energy losses exceeding the losses from the unicomponent pairing. A phase transition of the neutron condensate into the multicomponent state triggers more rapid cooling of superfluid core in neutron stars. This makes it possible to simulate an anomalously rapid cooling of neutron s…
We investigate the slowly rotating general relativistic superfluid neutron stars including the entrainment effect in a two-fluid model, where one fluid represents the superfluid neutrons and the other is the charge-neutral fluid called the proton fluid, made of protons and electrons. The equation of state and the entrainment effect between the superfluid neutrons and the proton fluid are computed using a relativistic mean field (RMF) model where baryon-baryon interaction is mediated by the exchange of $σ$, $ω$, and $ρ$ mesons and scalar self interactions are also included. The equations govern…
We constrain the parameters of neutron superfluidity in the cores of neutron stars making use of the recently proposed effect of resonance stabilization of $r$-modes. To this end, we, for the first time, calculate the finite-temperature $r$-mode spectra for realistic models of rotating superfluid neutron stars, accounting for both muons and neutron-proton entrainment in their interiors. We find that the ordinary (normal) $r$-mode exhibits avoided crossings with superfluid $r$-modes at certain stellar temperatures and spin frequencies. Near the avoided crossings, the normal $r$-mode dissipates …
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, $ρ_s/ρ$, at densities above that of neutron drip, $ρ_d \approx 4\times 10^{11}\,g/cm^3$. For an amorphous solid crust the suppression of $ρ_s$ 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 fo…
In the Ginzburg-Landau limit, a possible texture without singular cores in a rotating neutron spin-triplet superfluid is studied. It is constructed the lattice of non-singular vortices with a vorticity diffusely distributed over the entire unit cell. The upper limit of the free energy associated with this structure is estimated, and the result shows that non-singular vortices are more preferable in the core of rotating neutron stars than ordinary linear singular vortices. The order parameter of the studied neutron system belongs to the unitary class. This implies that the superfluid under cons…
Superfluidity of $Σ^-$ hyperons in $β$-stable neutron star matter
本文计算了$β$稳定中子星物质中$Σ^-$超子的$^1S_0$能隙.我们解决BCS间隙方程的有效$Σ^-Σ^-$配对相互作用来自最新的参数化的超子-超子相互作用的Nijmegen组。我们发现在密度区$\sim 0.27-0.7$ fm $^{-3}$中，$Σ^-$超子处于$^1S_0$超流态，在总重子数密度为$\sim 0.37$ fm $^{-3}$时，最大能隙为8 MeV，其中$Σ^-$的分数约为8%.我们研究了中子星冷却的影响。
