arXiv subjects

Bennett Link

Publications and source records attributed to Bennett Link.

At least 19 recordsLinked to original sources

arXiv2026

Superfluidity and Vortex Dynamics in Neutron Stars

Neutron stars contain several forms of quantum condensed matter whose microscopic properties control macroscopic rotational dynamics and magnetic behavior of these fascinating objects. This review surveys superfluidity and superconductivity in compact stars, with emphasis on phenomena associated with quantized vorticity and magnetic-flux structures, and the possible connections to observed phenomena. We first summarize the microphysics of nucleonic pairing, including spin-singlet $^1S_0$ neutron pairing in the inner crust, proton superconductivity in the outer core, and spin-triplet $^3P_2$--$^3F_2$ neutron pairing at higher densities, together with the principal many-body uncertainties affecting the corresponding pairing gaps. We then discuss the dynamics of neutron vortices, including pinning, vortex creep, and dissipative motion, and the role of vortex dynamics in angular-momentum exchange between the superfluid and the observable crustal component. We give special attention to proton flux tubes in type-II superconducting cores, the possible realization of type-I superconductivity, and vortex--flux-tube interactions. We also review collective rotational phenomena, including Tkachenko oscillations of the vortex lattice and free precession, and their possible relation to long-term variability in pulsar timing. Finally, we discuss the possible deconfinement of hadronic matter into quark matter, the formation of color-superconducting phases, and the topological defects associated with these phases, together with their possible observational consequences. Throughout the review, we identify key open questions connecting microscopic pairing, mesoscopic defect dynamics, and observable neutron-star phenomena.

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arXiv2025

Vortex Dynamics in the Neutron Star Inner Crust

We study the superfluid vortex motion in the neutron star inner crust through direct three-dimensional simulations of the coupled dynamics of the vortex and the nuclear lattice. We demonstrate the pinning of an initially moving vortex to the lattice through excitation of lattice vibrations, and show that the efficiency of this process is higher for attractive than for repulsive nucleus-vortex interactions. We explore the unpinning of a vortex under the action of the applied Magnus force, and find that it is influenced by multiple parameters, including the sign of the pinning force, the lattice orientation, composition, temperature, and the energy of pinning to individual nucleus. In lattices with multiple grains, the unpinning transition is triggered inside the grains with weaker pinning, propagates along the vortex (mediated by the excited Kelvin waves) and crosses into grains with stronger pinning. This is likely to effectively decrease the critical force at which vortices unpin and to produce extended regions of unpinned vorticity. Shearing of the crust lattice (e.g., by a starquake) initiates the unpinning of the vortices that are crossing the slip plane. A close encounter of an unpinned vortex with a pinned vortex would cause the latter to unpin, perhaps initiating an unpinning avalanche of many vortices.

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arXiv2023

Superfluid Rivers in Spinning-down Neutron Stars

We study the motion of neutron superfluid vortices in a spinning-down neutron star, assuming axisymmetry of the flow and ignoring motion of vortices about the rotation axis. We find that the vortex array, if initially rectilinear, is soon substantially deformed as the star spins down; vortices are swept outward by the Magnus force, accumulating in regions of the inner crust where they pin, accompanied by significant bending of the vortex array. As the star spins down to below a spin rate of ~20 Hz (twice the spin rate of the Vela pulsar), the Magnus and pinning forces gradually compress the vortex array into dense sheets that follow spherical shells. In some cases, the vortex array bends on itself and reconnects, forming one or more tori of vortex rings that contain superfluid ``rivers" with significant angular momentum. Vortex sheets are likely to form near the base of the inner crust, in the regime of nuclear pasta.

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arXiv2022

Vortex Pinning in Neutron Stars, Slip-stick Dynamics, and the Origin of Spin Glitches

We study pinning and unpinning of superfluid vortices in the inner crust of a neutron star using 3-dimensional dynamical simulations. Strong pinning occurs for certain lattice orientations of an idealized, body-centered cubic lattice, and occurs generally in an amorphous or impure nuclear lattice. The pinning force per unit length is $\sim 10^{16}$ dyn cm$^{-1}$ for a vortex-nucleus interaction that is repulsive, and $\sim 10^{17}$ dyn cm$^{-1}$ for an attractive interaction. The pinning force is strong enough to account for observed spin jumps (glitches). Vortices forced through the lattice move with a slip-stick character; for a range of superfluid velocities, the vortex can be in either a cold, pinned state or a hot unpinned state, with strong excitation of Kelvin waves on the vortex. This two-state nature of vortex motion sets the stage for large-scale vortex movement that creates an observable spin glitch. We argue that the vortex array is likely to become tangled as a result of repeated unpinnings and repinnings. We conjecture that during a glitch, the Kelvin-wave excitation spreads rapidly along the direction of the mean superfluid vorticity and slower in the direction perpendicular to it, akin to an anisotropic deflagration.

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arXiv2022

Tangled magnetic field model of QPOs

The highly tangled magnetic field of a magnetar supports shear waves similar to Alfv\'en waves in an ordered magnetic field. Here we explore if torsional modes excited in the stellar interior and magnetosphere can explain the quasi-periodic oscillations (QPOs) observed in the tail of the giant flare of SGR 1900+14. We solve the initial value problem for a tangled magnetic field that couples interior shear waves to relativistic Alfv\'en shear waves in the magnetosphere. Assuming stellar oscillations arise from the sudden release of magnetic energy, we obtain constraints on the energetics and geometry of the process. If the flare energy is deposited initially inside the star, the wave energy propagates relatively slowly to the magnetosphere which is at odds with the observed rise time of the radiative event of $\lesssim 10$ ms. Nor can the flare energy be deposited entirely outside the star, as most of the energy reflects off the stellar surface, giving surface oscillations of insufficient magnitude to produce detectable modulations of magnetospheric currents. Energy deposition in a volume that straddles the stellar surface gives agreement with the observed rise time and excites a range of modes with substantial amplitude at observed QPO frequencies. In general, localized energy deposition excites a broad range of modes that encompasses the observed QPOs, though many more modes are excited than the number of observed QPOs. If the flare energy is deposited axisymmetrically, as is possible for a certain class of MHD instabilities, the number of modes that is excited is considerably reduced.

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arXiv2018

Hydrodynamic Stability Analysis of the Neutron Star Core

Hydrodynamic instabilities and turbulence in neutron stars have been suggested to be related to observable spin variations in pulsars, such as spin glitches, timing noise, and precession (nutation). Accounting for the stabilizing effects of the stellar magnetic field, we revisit the issue of whether the inertial modes of a neutron star can become unstable when the neutron and proton condensates flow with respect to one another. The neutron and proton condensates are coupled through the motion of imperfectly pinned vorticity (vortex slippage) and vortex-mediated scattering (mutual friction). Two-stream instabilities that occur when the two condensates rotate with respect to one another in the outer core are stabilized by the toroidal component of the magnetic field. This stabilization occurs when the Alfv\'en speed of the toroidal component of the magnetic field becomes larger than the relative rotational velocity of the condensates, corresponding to toroidal field strengths in excess of $\simeq 10^{10}\,{\rm G}$. In contrast with previous studies, we find that spin down of a neutron star under a steady torque is stable. The Donnelly--Glaberson instability is not stabilized by the magnetic field, and could play an important role if neutron stars undergo precession.

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arXiv2016

Torsional Oscillations of a Magnetar with a Tangled Magnetic Field

Motivated by stability considerations and observational evidence, we argue that magnetars possess highly-tangled internal magnetic fields. We propose that the quasi-periodic oscillations (QPOs) seen to accompany giant flares can be explained as torsional modes supported by a tangled magnetic field, and we present a simple model that supports this hypothesis for SGR 1900+14. Taking the strength of the tangle as a free parameter, we find that the magnetic energy in the tangle must dominate that in the dipolar component by a factor of $\sim 14$ to accommodate the observed 28 Hz QPO. Our simple model provides useful scaling relations for how the QPO spectrum depends on the bulk properties of the neutron star and the tangle strength. The energy density in the tangled field inferred for SGR 1900+14 renders the crust nearly dynamically irrelevant, a significant simplification for study of the QPO problem. The predicted spectrum is about three times denser than observed, which could be explained by preferential mode excitation or beamed emission. We emphasize that field tangling is needed to stabilize the magnetic field, so should not be ignored in treatment of the QPO problem.

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arXiv2015

Torsional oscillations of a magnetar with a tangled magnetic field

We propose a scenario for the quasi-periodic oscillations observed in magnetar flares wherein a tangled component of the stellar magnetic field introduces nearly isotropic stress that gives the fluid core of the star an effective shear modulus. In a simple, illustrative model of constant density, the tangled field eliminates the problematic Alfv\'en continuum that would exist in the stellar core for an organized field. For a tangled field energy density comparable to that inferred from the measured dipole fields of $\sim 10^{15}$ G in SGRs 1806-20 and 1900+14, torsional modes exist with fundamental frequencies of about 20 Hz, and mode spacings of $\sim 10$ Hz. For fixed stellar mass and radius, the model has only one free parameter, and can account for {\em every} observed QPO under 160 Hz to within 3 Hz for both SGRs 1806-20 and 1900+14. The combined effects of stratification and crust stresses generally decrease the frequencies of torsional oscillations by $<10$% for overtones and increase the lowest-frequency fundamentals by up to 50%, and so the star can be treated as having constant density to a generally good first approximation. We address the issue of mode excitation by sudden readjustment of the stellar magnetosphere. While the total energy in excited modes is well within the energy budget of giant flares, the surface amplitude is $< 10^{-3}$ of the stellar radius for global oscillations, and decreases strongly with mode frequency. The 626 Hz QPO reported for SGR 1806-20 is particularly problematic to excite beyond a surface amplitude of $10^{-6}$ of the stellar radius.

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arXiv2013

Constraining the Origin of Magnetar Flares

Sudden relaxation of the magnetic field in the core of a magnetar produces mechanical energy primarily in the form of shear waves which propagate to the surface and enter the magnetosphere as relativistic Alfv\'en waves. Due to a strong impedance mismatch, shear waves excited in the star suffer many reflections before exiting the star. If mechanical energy is deposited in the core and is converted {\em directly} to radiation upon propagation to the surface, the rise time of the emission is at least seconds to minutes, and probably minutes to hours for a realistic magnetic field geometry, at odds with observed rise times of $\lap 10$ ms for both and giant flares. Mechanisms for both small and giant flares that rely on the sudden relaxation of the magnetic field of the core are rendered unviable by the impedance mismatch, requiring the energy that drives these events to be stored in the magnetosphere just before the flare. ends, unless the waves are quickly damped.

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arXiv2013

Thermally-Activated Post-Glitch Response of the Neutron Star Inner Crust and Core. I: Theory

Pinning of superfluid vortices is predicted to prevail throughout much of a neutron star. Based on the idea of Alpar et al., I develop a description of the coupling between the solid and liquid components of a neutron star through {\em thermally-activated vortex slippage}, and calculate the the response to a spin glitch. The treatment begins with a derivation of the vortex velocity from the vorticity equations of motion. The activation energy for vortex slippage is obtained from a detailed study of the mechanics and energetics of vortex motion. I show that the "linear creep" regime introduced by Alpar et al. and invoked in fits to post-glitch response is not realized for physically reasonable parameters, a conclusion that strongly constrains the physics of post-glitch response through thermal activation. Moreover, a regime of "superweak pinning", crucial to the theory of Alpar et al. and its extensions, is probably precluded by thermal fluctuations. The theory given here has a robust conclusion that can be tested by observations: {\em for a glitch in spin rate of magnitude $\Delta\nu$, pinning introduces a delay in the post-glitch response time}. The delay time is $t_d=7 (t_{sd}/10^4\mbox{yr})((\Delta\nu/\nu)/10^{-6})$ d where $t_{sd}$ is the spin-down age; $t_d$ is typically weeks for the Vela pulsar and months in older pulsars, and is independent of the details of vortex pinning. Post-glitch response through thermal activation cannot occur more quickly than this timescale. Quicker components of post-glitch response as have been observed in some pulsars, notably, the Vela pulsar, cannot be due to thermally-activated vortex motion but must represent a different process, such as drag on vortices in regions where there is no pinning. I also derive the mutual friction force for a pinned superfluid at finite temperature for use in other studies of neutron star hydrodynamics.

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arXiv2013

Pulsar timing noise from superfluid turbulence

Shear-driven turbulence in the superfluid interior of a neutron star exerts a fluctuating torque on the rigid crust, causing the rotational phase to walk randomly. The phase fluctuation spectrum is calculated analytically for incompressible Kolmogorov turbulence and is found to be red; the half-power point is set by the observed spin-down rate, the crust-superfluid lag, and the dynamical response time of the superfluid. Preliminary limits are placed on the latter quantities using selected time- and frequency-domain data. It is found that measurements of the normalization and slope of the power spectrum are reproduced for reasonable choices of the turbulence parameters. The results point preferentially to the neutron star interior containing a turbulent superfluid rather than a turbulent Navier-Stokes fluid. The implications for gravitational wave detection by pulsar timing arrays are discussed briefly.

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arXiv2012

Observable core response in neutron star spin glitches

The superfluid core of a neutron star is usually assumed to corotate with the crust over timescales longer than minutes. I show that the interaction between the neutron superfluid and the type II superconductor of the outer core increases the coupling time to weeks or longer. I suggest that observed post-glitch response over timescales of weeks to years represents recovery of the outer core. Spin glitches could originate in either the inner crust or the outer core.

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arXiv2012

Time-Correlated Structure in Spin Fluctuations in Pulsars

We study statistical properties of stochastic variations in pulse arrival times, timing noise, in radio pulsars using a new analysis method applied in the time domain. The method proceeds in two steps. First, we subtract low-frequency wander using a high-pass filter. Second, we calculate the discrete correlation function of the filtered data. As a complementary method for measuring correlations, we introduce a statistic that measures the dispersion of the data with respect to the data translated in time. The analysis methods presented here are robust and of general usefulness for studying arrival time variations over timescales approaching the average sampling interval. We apply these methods to timing data for 32 pulsars. In two radio pulsars, PSRs B1133+16 and B1933+16, we find that fluctuations in arrival times are correlated over timescales of 10 - 20 d with the distinct signature of a relaxation process. Though this relaxation response could be magnetospheric in origin, we argue that damping between the neutron star crust and interior liquid is a more likely explanation. Under this interpretation, our results provide the first evidence independent from pulsar spin glitches of differential rotation in neutron stars. PSR B0950+08, shows evidence for quasi-periodic oscillations that could be related to mode switching.

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arXiv2011

Instability of Superfluid Flow in the Neutron Star Core

Pinning of superfluid vortices to magnetic flux tubes in the outer core of a neutron star supports a velocity difference of $\sim 10^5$ \cms\ between the neutron superfluid and the proton-electron fluid as the star spins down. Under the Magnus force that arises on the vortex array, vortices undergo {\em vortex creep} through thermal activation or quantum tunneling. We examine the hydrodynamic stability of this situation. Vortex creep introduces two low-frequency modes, one of which is unstable above a critical wavenumber for any non-zero flow velocity of the neutron superfluid with respect to the charged fluid. For typical pinning parameters of the outer core, the superfluid flow is unstable over wavelengths $\lambda\lap 10$ m and over timescales of $\sim (\lambda/{1 m})^{1/2}$ yr down to $\sim 1$ d. The vortex lattice could degenerate into a tangle, and the superfluid flow would become turbulent. We suggest that superfluid turbulence could be responsible for the red timing noise seen in many neutron stars, and find a predicted spectrum that is generally consistent with observations.

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arXiv2011

Thermo-Resistive Instability in Magnetar Crusts

We investigate a thermo-resistive instability in the outer crusts of magnetars wherein a perturbation in temperature increases ohmic heating. We show that magnetars of characteristic age {\tau}_{age} ~ 10^4 yr are unstable over timescales as short as days if strong current sheets are present in the outer crust. This instability could play an important role in the thermal and magnetic field evolution of magnetars, and may be related to bursting activity in magnetars.

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arXiv2011

Instability of Superfluid Flow in the Neutron Star Inner Crust

Pinning of superfluid vortices to the nuclear lattice of the inner crust of a neutron star supports a velocity difference between the superfluid and the solid as the star spins down. Under the Magnus force that arises on the vortex lattice, vortices undergo {\em vortex creep} through thermal activation or quantum tunneling. We examine the hydrodynamic stability of this situation. Vortex creep introduces two low-frequency modes, one of which is unstable above a critical wavenumber for any non-zero flow velocity of the superfluid with respect to the solid. For typical pinning parameters of the inner crust, the superfluid flow is unstable over length scales $\lap 10$ m and over timescales as fast as months. The vortex lattice could degenerate into a tangle, and the superfluid flow could become turbulent. Unexpectedly large dissipation would suppress this instability.

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arXiv2009

Dynamics of Quantum Vorticity in a Random Potential

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.

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arXiv2006

Incompatibility of long-period neutron star precession with creeping neutron vortices

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. There is a slow precession mode, but it is highly over-damped and cannot complete even a single cycle. Moreover, the vortices of the inner crust must be able to move with little dissipation with respect to the solid.

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