The structure of a vortex in the inner crust of neutron stars is calculated within the framework of quantum mean field theory taking into account the interaction with the nuclei composing the Coulomb lattice. Making use of the results obtained with different nuclear interactions, the pinning energy, relevant in the study of glitches, is worked out. Quantal size and density dependent effects are found to be important.
We study, within a quantum mechanical framework based on self-consistent mean field theory, the interaction between a vortex and a nucleus immersed in a sea of free neutrons, a scenario representative of the inner crust of neutron stars. Quantal finite size effects force the vortex core outside the nucleus, influencing vortex pinning in an important way.
The rotating neutron superfluid in the inner crust of a neutron star is threaded by quantized vortex lines. The pinning force from lattice nuclei and the Magnus force from neutron superfluid act onto a vortex line that has a finite tension. The configuration of a vortex line in equilibrium comprises a number of pinned straight lengths separated by unpinned kinks when the rotation axis is slightly inclined to the major axis of a crystal lattice and the Magnus force is not so strong. Energy of $\sim 4 {MeV}$ is required to form a kink at densities of $\sim 3.4 \times 10^{13}{g cm}^{-3}$. Magnus …
The rotating neutron superfluid in the inner crust of a neutron star is threaded by quantized vortex lines. The pinning force from lattice nuclei and the Magnus force from neutron superfluid act onto a vortex line that has a finite tension. The configuration of a vortex line in equilibrium comprises a number of pinned straight lengths separated by unpinned kinks when the rotation axis is slightly inclined to the major axis of a crystal lattice and the Magnus force is not so strong. Energy of ~ 4 MeV is required to form a kink at densities of ~ 3.4 x 10^13 g cm^-3. Magnus force makes the vortex…
We show that the crust-core interface in neutron stars acts as a potential barrier to the peripheral neutron vortices approaching the interface in the model in which these are coupled to the proton vortex clusters. This elementary barrier because of the interaction of vortex magnetic flux with the Meissner currents set up by the crustal magnetic field at the interface. The dominant part of the force is derived from to the cluster-interface interaction. As a result of the stopping of the continuous neutron vortex current through the interface, angular momentum is stored in the superfluid layers…
To account for pulsar frequency glitches, it is necessary to use a neutron star crust model allowing not only for neutron superfluidity but also for elastic solidity. These features have been treated separarately in previous treatments of crust matter, but are combined here in a unified treatment that is based on the use of a Lagrangian master functon, so that the coherence the system is ensured by the relevant Noether identities. As well as the model obtained directly from the variation principle, the same master function can provide other conservative alternatives, allowing in particular for…
The neutron vortices thought to exist in the inner crust of a neutron star interact with nuclei and are expected to pin to the nuclear lattice. Evidence for long-period precession in pulsars, however, requires that pinning be negligible. We estimate the strength of vortex pinning and show that hydrodynamic forces present in a precessing star are likely sufficient to unpin all of the vortices of the inner crust. In the absence of precession, however, vortices could pin to the lattice with sufficient strength to explain the giant glitches observed in many radio pulsars.
The microscopic structure of an isolated vortex line in superfluid neutron star matter is studied by solving the Bogoliubov-de Gennes equations. Our calculation, which is the starting point for a microscopic calculation of pinning forces in neutron stars, shows that the size of the vortex core varies differently with density, and is in general smaller than assumed in some earlier calculations of vortex pinning in neutron star crusts. The implications of this result are discussed
We investigate the global transition from a turbulent state of superfluid vorticity to a laminar state, and vice versa, in the outer core of a neutron star. By solving numerically the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov equations for a rotating superfluid in a differentially rotating spherical shell, we find that the meridional counterflow driven by Ekman pumping exceeds the Donnelly-Glaberson threshold throughout most of the outer core, exciting unstable Kelvin waves which disrupt the rectilinear vortex array, creating a vortex tangle. In the turbulent state, the torque exerted on …
We calculate the force that pins vortices in the neutron superfluid to nuclei in the inner crust of rotating neutron stars, relying on a detailed microscopic description of both the vortex radial profile and the inner crust nuclear structure. The contribution to the pinning energy from pair condensation is estimated in the local density approximation with realistic nucleon-nucleon interactions. The kinetic contribution, not consistently included in previous approaches, is evaluated in the same approximation, and found to be relevant. The vortex-nucleus interaction turns out to be attractive fo…
The frequent glitches (sudden increases of the apparent angular velocity) observed in certain pulsars are generally believed to be attributable to discontinuous angular momentum transfer to the outer neutron star crust from a differentially rotating superfluid layer, but the precise mechanism is not quite elucidated. Most explanations invoke vortex pinning as the essential mechanism responsible for the build up of strain in the crust that is relaxed, either by fracture of the solid structure or by discontinous unpinning, during the glitch. It is shown here that there is another mechanism that …
A microscopic, quantum mechanical model for neutron vortices in the crust of a neutron star is presented. After a brief introduction to the Bogoliubov- de Gennes equations, which form the basis for our calculations, we present results for density distributions, vortex core sizes and vortex energies, both for an isolated neutron vortex and for the case when the vortex core overlaps with a cylindrical nucleus. Earlier results on the vortex core size are confirmed, indicating a much less dramatic variation of the vortex core size with density than predicted by the BCS formula.
The nuclear pasta -- a novel state of matter having nucleons arranged in a variety of complex shapes -- is expected to be found in the crust of neutron stars and in core-collapse supernovae at subnuclear densities of about $10^{14}$ g/cm$^3$. Due to frustration, a phenomenon that emerges from the competition between short-range nuclear attraction and long-range Coulomb repulsion, the nuclear pasta displays a preponderance of unique low-energy excitations. These excitations could have a strong impact on many transport properties, such as neutrino propagation through stellar environments. The ex…
We investigate when the energy that pins a superfluid vortex to the lattice of nuclei in the inner crust of neutron stars can be approximated by the energy that binds the vortex to a single nucleus. Indeed, although the pinning energy is the quantity relevant to the theory of pulsar glitches, so far full quantum calculations have been possible only for the binding energy. Physically, the presence of nearby nuclei can be neglected if the lattice is dilute, namely with nuclei sufficiently distant from each other. We find that the dilute limit is reached only for quite large Wigner-Seitz cells, w…
We show that the neutron star's crust-core interface acts as a potential barrier on the peripheral neutron vortices approaching this interface and thus prevents their continuous decay on it in the course of equilibrium state deceleration. The barrier arises due to the interaction of vortex magnetic flux with the Meissner currents set up by the crustal magnetic field at the interface. When the non-balanced part of the Magnus force reaches the value at which the vortices are able to annihilate at the interface, the rapid transfer of angular momentum from the superfluid spins-up the observable cr…
Aims: To determine whether ``vortex creep'' in neutron stars, the slow motion of neutron vortices with respect to pinning sites in the core or inner crust, is consistent with observations of long-period precession. Methods: Using the concept of vortex drag, I discuss the precession dynamics of a star with imperfectly-pinned (i.e., "creeping'') vortices. Results: The precession frequency is far too high to be consistent with observations, indicating that the standard picture of the outer core (superfluid neutrons in co-existence with type II, superconducting protons) should be reconsidered. The…
We calculate the electron shear viscosity (determined by Coulomb electron collisions) for a dense matter in a wide range of parameters typical for white dwarf cores and neutron star crusts. In the density range from ~10^3 g cm^-3 to 10^7-10^10 g cm^-3 we consider the matter composed of widely abundant astrophysical elements, from H to Fe. For higher densities, 10^10-10^14 g cm^-3, we employ the ground-state nuclear composition, taking into account finite sizes of atomic nuclei and the distribution of proton charge over the nucleus. Numerical values of the viscosity are approximated by an analy…
Making use of the possibility that gluon condensate can be formed in neutron star core, we study the vortex pinning force between the crust and the interior of the neutron star. Our estimations indicate an increase in pinning strength with the age of the neutron star. This helps in explaining observed pulsar glitches and removes some difficulties faced by vortex creep model.
Neutron stars are supposed to be mainly formed by a neutron superfluid. The angular momentum is given by the vortex array within the fluid, and a good account of the observable effects is determined by its coupling with the crust. In this article we show that the gravitational field introduces important modifications in the vortex distribution and shape. The inertial frame dragging on the quantum fluid produces a decrease in the vortex density, which for realistic models is in the order of 15%. This effect is relevant for neutron star rotation models and can provide a good framework for checki…
Many radio pulsars exhibit glitches wherein the star's spin rate increases fractionally by $\sim 10^{-10} - 10^{-6}$. Glitches are ascribed to variable coupling between the neutron star crust and its superfluid interior. With the aim of distinguishing among different theoretical explanations for the glitch phenomenon, we study the response of a neutron star to two types of perturbations to the vortex array that exists in the superfluid interior: 1) thermal motion of vortices pinned to inner crust nuclei, initiated by sudden heating of the crust, (e.g., a starquake), and 2) mechanical motion of…
We consider a model in which the soft gamma-ray repeaters (SGRs) result from young, magnetized strange stars with superconducting cores. As such a strange star spins down, the quantized vortex lines move outward and drag the magnetic field tubes because of the strong coupling between them. Since the terminations of the tubes interact with the stellar crust, the dragged tubes can produce sufficient tension to crack the crust. Part of the broken platelet will be dragged into the quark core, which is only $10^4$ cm from the surface, leading to the deconfinement of crustal matter into strange quar…
I study the dynamics of a superfluid vortex in a random potential, as in the inner crust of a neutron star. Below a critical flow velocity of the ambient superfluid, a vortex is effectively immobilized by lattice forces even in the limit of zero dissipation. Low-velocity, translatory motion is not dynamically possible, a result with important implications for understanding neutron star precession and the dynamical properties of superfluid nuclear matter.
We find a new mechanism of neutron star radiation wherein radiation is produced by the stellar interior. The source of radiation is oscillating neutron vortices in the superfluid core of a rotating neutron star. Thermally excited helical waves of vortices generate fast magnetosonic waves at the stellar crust. Near the crust bottom such waves reduce to a collisionless zero sound in an electron liquid, while near the stellar surface they behave as electromagnetic waves in a medium. The magnetosonic waves propagate across the crust and transform into electromagnetic radiation at the surface. The …
The recent temperature measurements of the two older isolated neutron stars PSR 1929+10 and PSR 0950+08 (ages of $3\times 10^6$ and $2\times 10^7$ yr, respectively) indicate that these objects are heated. A promising candidate heat source is friction between the neutron star crust and the superfluid it is thought to contain. We study the effects of superfluid friction on the long-term thermal and rotational evolution of a neutron star. Differential rotation velocities between the superfluid and the crust (averaged over the inner crust moment of inertia) of $\barω\sim 0.6$ rad s$^{-1}$ for PSR …
MHD equations are presented for the mixture of superfluid neutrons, superconducting protons, and normal electrons believed to exist in the outer cores of neutron stars. The dissipative effects of electron viscosity and mutual friction due to electron-vortex scattering are also included. It is shown that Alfven waves are replaced by cyclotron- vortex waves that have not been previously derived from MHD theory. The cyclotron- vortex waves are analogous to Alfven waves with the tension due to the magnetic energy density replaced by the vortex energy density. The equations are then put into a simp…
It is shown how to set up a mathematically elegant and fully relativistic superfluid model that can provide a realistic approximation (neglecting small anisotropies due to crust solidity, magnetic fields, et cetera, but allowing for the regions with vortex pinning) of the global structure of a rotating neutron star, in terms of just two independently moving constituents, one of which represents the differentially rotating neutron superfluid, while the other part represents the combination of all the other ingredients, including the degenerate electrons, the superfluid protons in the core, and …
We study relationships between the neutron-rich skin of a heavy nucleus and the properties of neutron-star crusts. Relativistic effective field theories with a thicker neutron skin in $^{208}$Pb have a larger electron fraction and a lower liquid-to-solid transition density for neutron-rich matter. These properties are determined by the density dependence of the symmetry energy which we vary by adding nonlinear couplings between isoscalar and isovector mesons. An accurate measurement of the neutron radius in $^{208}$Pb---via parity violating electron scattering---may have important implications…
Thermal and electric conductivities are calculated for degenerate electrons scattered by phonons in a crystal made of atomic nuclei. The exact phonon spectrum and the Debye--Waller factor are taken into account. Monte Carlo calculations are performed for body-centered cubic (bcc) crystals made of C, O, Ne, Mg, Si, S, Ca, and Fe nuclei in the density range from $10^3$ to $10^{11}$ g cm$^{-3}$ at temperatures lower than the melting temperature but higher than the temperature at which the Umklapp processes begin to be "frozen out". A simplified method of calculation is proposed, which makes it po…
Nonuniform neutron-rich matter present in both core-collapse supernovae and neutron-star crusts is described in terms of a semiclassical model that reproduces nuclear-matter properties and includes long-range Coulomb interactions. The neutron-neutron correlation function and the corresponding static structure factor are calculated from molecular dynamics simulations involving 40,000 to 100,000 nucleons. The static structure factor describes coherent neutrino scattering which is expected to dominate the neutrino opacity. At low momentum transfers the static structure factor is found to be small…
We consider the physical implications of the rapid spindown of Soft Gamma Repeater 1900+14, and of the apparent "braking glitch", ΔP/P = l x 10^-4, that was concurrent with the Aug. 27th giant flare. A radiation-hydrodynamical outflow associated with the flare could impart the required torque, but only if the dipole magnetic field is stronger than ~ 10^14 G and the outflow lasts longer and/or is more energetic than the observed X-ray flare. A positive period increment is also a natural consequence of a gradual, plastic deformation of the neutron star crust by an intense magnetic field, which f…
It is generally agreed on that the tremendous densities reached in the centers of neutron stars provide a high-pressure environment in which numerous novel particles processes are likely to compete with each other. These processes range from the generation of hyperons to quark deconfinement to the formation of kaon condensates and H-matter. There are theoretical suggestions of even more exotic processes inside neutron stars, such as the formation of absolutely stable strange quark matter, a configuration of matter even more stable than the most stable atomic nucleus, iron. In the latter event,…
We consider the precession of isolated neutron stars in which superfluid is not pinned to the stellar crust perfectly. In the case of perfect pinning, Shaham (1977) showed that there are no slowly oscillatory, long-lived modes. When the assumption of perfect pinning is relaxed, new modes are found that can be long-lived, but are expected to be damped rather than oscillatory, unless the drag force on moving superfluid vortex lines has a substantial component perpendicular to the direction of relative motion. The response of a neutron star to external torques, such as the spindown torque, is als…
We find that neutron star interior is transparent for collisionless electron sound, the same way as it is transparent for neutrinos. In the presence of magnetic field the electron sound is coupled with electromagnetic radiation and form the fast magnetosonic wave. We find that electron sound is generated by superfluid vortices in the stellar core. Thermally excited helical vortex waves produce fast magnetosonic waves in the stellar crust which propagate toward the surface and transform into outgoing electromagnetic radiation. The vortex radiation has the spectral index -0.45 and can explain no…
Differential rotation between the neutron star crust and a more rapidly rotating interior superfluid leads to frictional heating that affects the star's long-term thermal evolution and resulting surface emission. Here we present the results of thermal evolution simulations based on two models of the vortex pinning forces that bracket a range of plausible pinning strengths. We include the effects of superfluidity, magnetic fields, and temperature gradients. As representative standard and accelerated neutrino emission processes taking place in the core, we consider the modified Urca process in n…
After some post-natal cooling, a spinning, magnetized, canonical neutron-star (NS) has a core of superconducting protons, superfluid neutrons, and degenerate extreme relativistic electrons, all surrounded by a thin highly conducting solid crust. The quantum fluids are threaded by a dense array of quantized vortex-lines which can interact strongly with a denser and much less uniform one of quantizedmagnetic flux-tubes. The physics of such a core predicts the evolution of a NS'ssurface magnetic field and related phenomena as the star's spin changes. Predictions include changes in NS magnetic dip…
Gravity compresses the matter in the cores of neutron stars to densities which are significantly higher than the density of ordinary atomic nuclei, thus providing a high-pressure environment in which numerous particle processes - from the generation of new baryonic particles to quark deconfinement to the formation of Boson condensates and H-matter - may compete with each other. There are theoretical suggestions of even more `exotic' processes inside pulsars, such as the formation of absolutely stable strange quark matter, a configuration of matter even more stable than the most stable atomic n…
We explore the dynamics of the r-modes in accreting neutron stars in two ways. First, we explore how dissipation in the magneto-viscous boundary layer (MVBL) at the crust-core interface governs the damping of r-mode perturbations in the fluid interior. Two models are considered: one assuming an ordinary-fluid interior, the other taking the core to consist of superfluid neutrons, type II superconducting protons, and normal electrons. We show, within our approximations, that no solution to the magnetohydrodynamic equations exists in the superfluid model when both the neutron and proton vortices …
