A. Melatos

Avalanche Dynamics of Radio Pulsar Glitches

We test statistically the hypothesis that radio pulsar glitches result from an avalanche process, in which angular momentum is transferred erratically from the flywheel-like superfluid in the star to the slowly decelerating, solid crust via spatially connected chains of local, impulsive, threshold-activated events, so that the system fluctuates around a self-organized critical state. Analysis of the glitch population (currently 285 events from 101 pulsars) demonstrates that the size distribution in individual pulsars is consistent with being scale invariant, as expected for an avalanche process. The measured power-law exponents fall in the range -->-0.13 ≤ a≤ 2.4, with -->a ≈ 1.2 for the youngest pulsars. The waiting-time distribution is consistent with being exponential in seven out of nine pulsars where it can be measured reliably, after adjusting for observational limits on the minimum waiting time, as for a constant-rate Poisson process. PSR J0537–6910 and PSR J0835–4510 are the exceptions; their waiting-time distributions show evidence of quasi-periodicity. In each object, stationarity requires that the rate λ equal −/Δν, where is the angular acceleration of the crust, --> Δ ν is the mean glitch size, and is the relative angular acceleration of the crust and superfluid. Measurements yield --> ≤ 7 × 10−5 for PSR J0358+5413 and --> ≤ 1 (trivially) for the other eight objects, which have -->a λ ≥ 0.25 yr−1, with --> λ = 1.3+ 0.7−0.6 yr−1. For -->λ λ > 0.25 yr−1 must exceed ~70%.

Burial of the polar magnetic field of an accreting neutron star – I. Self‐consistent analytic and numerical equilibria

The hydromagnetic structure of a neutron star accreting symmetrically at both magnetic poles is calculated as a function of accreted mass, M a , and polar cap radius, starting from a centred magnetic dipole and evolving through a quasi-static sequence of two-dimensional, Grad-Shafranov equilibria. The calculation is the first to track fully the growth of high-order magnetic multipoles, due to equatorward hydromagnetic spreading, while simultaneously preserving flux-freezing and a self-consistent mass-flux distribution. Equilibria are constructed numerically by an iterative scheme and analytically by Green functions. Two key results are obtained, with implications for recycled pulsars. (i) The mass required to reduce significantly the magnetic dipole moment, 10 -5 M ○. , greatly exceeds previous estimates (∼10 -10 M ○. ), which ignored the confining stress exerted by the compressed equatorial magnetic field. (ii) Magnetic bubbles, disconnected from the stellar surface, form in the later stages of accretion (M a ≥ 10 -4 M ○. ).

Gravitational Radiation from an Accreting Millisecond Pulsar with a Magnetically Confined Mountain

The amplitude of the gravitational radiation from an accreting neutron star undergoing polar magnetic burial is calculated. During accretion, the magnetic field of a neutron star is compressed into a narrow belt at the magnetic equator by material spreading equatorward from the polar cap. In turn, the compressed field confines the accreted material in a polar mountain, which is generally misaligned with the rotation axis, producing gravitational waves. The equilibrium hydromagnetic structure of the polar mountain, and its associated mass quadrupole moment, are computed as functions of the accreted mass Ma by solving a Grad-Shafranov boundary value problem. The orientation- and polarization-averaged gravitational wave strain at Earth is found to be hc = 6 × 10-24(Ma/Mc)(1 + Mab2/8Mc)-1(f/0.6 kHz)2(d/1 kpc)-1, where f is the wave frequency, d is the distance to the source, b is the ratio of the hemispheric to polar magnetic flux, and the cutoff mass Mc ~ 10-5 M☉ is a function of the natal magnetic field, temperature, and electrical conductivity of the crust. This value of hc exceeds previous estimates that failed to treat equatorward spreading and flux freezing self-consistently. It is concluded that an accreting millisecond pulsar emits a persistent, sinusoidal gravitational wave signal at levels detectable, in principle, by long-baseline interferometers after phase-coherent integration, provided that the polar mountain is hydromagnetically stable. Magnetic burial also reduces the magnetic dipole moment μ monotonically as μ ∝ (1 + 3Ma/4Mc)-1, implying a novel, observationally testable scaling hc(μ). The implications for the rotational evolution of (accreting) X-ray and (isolated) radio millisecond pulsars are explored.

Transitions between Turbulent and Laminar Superfluid Vorticity States in the Outer Core of a Neutron Star

We investigate the global transition from a turbulent state of superfluid vorticity (quasi-isotropic vortex tangle) to a laminar state (rectilinear vortex array), 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 that disrupt the rectilinear vortex array, creating a vortex tangle. In the turbulent state, the torque exerted on the crust oscillates, and the crust-core coupling is weaker than in the laminar state. This leads to a new scenario for the rotational glitches observed in radio pulsars: a vortex tangle is sustained in the differentially rotating outer core by the meridional counterflow, a sudden spin-up event (triggered by an unknown process) brings the crust and core into corotation, the vortex tangle relaxes back to a rectilinear vortex array (in 105 s), and then the crust spins down electromagnetically until enough meridional counterflow builds up (after 1 yr) to reform a vortex tangle. The turbulent-laminar transition can occur uniformly or in patches; the associated timescales are estimated from vortex filament theory. We calculate numerically the global structure of the flow with and without an inviscid superfluid component, for Hall-Vinen (laminar) and Gorter-Mellink (turbulent) forms of the mutual friction. We also calculate the postglitch evolution of the angular velocity of the crust and its time derivative and compare the results with radio pulse timing data, predicting a correlation between glitch activity and Reynolds number. Terrestrial laboratory experiments are proposed to test some of these ideas.

Global Three-dimensional Flow of a Neutron Superfluid in a Spherical Shell in a Neutron Star

We integrate for the first time the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov equations of motion of a 1S0-paired neutron superfluid in a rotating spherical shell, using a pseudo-spectral collocation algorithm coupled with a time-split fractional scheme. Numerical instabilities are smoothed by spectral filtering. Three numerical experiments are conducted, with the following results. (1) When the inner and outer spheres are put into steady differential rotation, the viscous torque exerted on the spheres oscillates quasi-periodically and persistently (after an initial transient). The fractional oscillation amplitude (~10-2) increases with the angular shear and decreases with the gap width. (2) When the outer sphere is accelerated impulsively after an interval of steady differential rotation, the torque increases suddenly, relaxes exponentially, then oscillates persistently as in (1). The relaxation timescale is determined principally by the angular velocity jump, whereas the oscillation amplitude is determined principally by the gap width. (3) When the mutual friction force changes suddenly from Hall-Vinen to Gorter-Mellink form, as happens when a rectilinear array of quantized Feynman-Onsager vortices is destabilized by a counterflow to form a reconnecting vortex tangle, the relaxation timescale is reduced by a factor of ~3 compared to (2), and the system reaches a stationary state in which the torque oscillates with fractional amplitude ~10-3 about a constant mean value. Preliminary scalings are computed for observable quantities such as angular velocity and acceleration as functions of the Reynolds number, angular shear, and gap width. The results are applied to the timing irregularities (e.g., glitches and timing noise) observed in radio pulsars.

Radiative precession of an isolated neutron star

Eulers equations of motion are derived exactly for a rigid, triaxial, internally frictionless neutron star spinning down electromagnetically in vacuo. It is shown that the star precesses, but not freely: its regular precession relative to the principal axes of inertia couples to the component of the radiation torque associated with the near-zone radiation fields and is modified into an anharmonic wobble. The wobble period τ1 typically satisfies τ1≲10^−2τ0, where τ0 is the braking time-scale; the wobble amplitude evolves towards a constant non-zero value, oscillates, or decreases to zero, depending on the degree of oblateness or prolateness of the star and its initial spin state; the (negative) angular frequency derivative ω˙ oscillates as well, exhibiting quasi-periodic spikes for triaxial stars of a particular figure. In light of these properties, a young, Crab-like pulsar ought to display fractional changes of order unity in the space of a few years in its pulse profile, magnetic inclination angle and ω˙. Such changes are not observed, implying that the wobble is damped rapidly by internal friction, if its amplitude is initially large upon crystallization of the stellar crust. If the friction is localized in the inner and outer crusts, the thermal luminosity of the neutron star increases by a minimum amount ΔL≈3×10^31(e/10^−12)(ω/10^3 rad s^−1)^2(τd/1 yr)^−1 erg s^−1, where e is the ellipticity, and τd is the damping time-scale, with the actual value of ΔL determined in part by the thermal conduction time τcond. The increased luminosity is potentially detectable as thermal X-rays lasting for a time ≈ max(τd,τcond) following crystallization of the crust.

Models of pulsar glitches

Radio pulsars provide us with some of the most stable clocks in the universe. Nevertheless several pulsars exhibit sudden spin-up events, known as glitches. More than forty years after their first discovery, the exact origin of these phenomena is still open to debate. It is generally thought that they an observational manifestation of a superfluid component in the stellar interior and provide an insight into the dynamics of matter at extreme densities. In recent years there have been several advances on both the theoretical and observational side, that have provided significant steps forward in our understanding of neutron star interior dynamics and possible glitch mechanisms. In this article we review the main glitch models that have been proposed and discuss our understanding, in the light of current observations.

Hydromagnetic Structure of a Neutron Star Accreting at Its Polar Caps

The hydromagnetic structure of a neutron star accreting symmetrically at both magnetic poles is calculated as a function of accreted mass, Ma, starting from a polytropic sphere plus central magnetic dipole (Ma =0) and evolving the configuration through a quasistatic sequence of twodimensional, Grad–Shafranov equilibria as Ma increases. It is found that the accreted material spreads equatorward under its own weight, compressing the magnetic field into a thin boundary layer and burying it everywhere except in a narrow, equatorial belt. The magnetic dipole moment of the star is given by =5.2×1024(B0/1012.5G)1.3( Ma/10-8M yr-1)0.18(Ma/M)-1.3Gcm3, and the fractional difference between its principal moments of inertia is given by =2.110-5 (B0/1012.5G)0.27 (Ma/10-8M yr-1)0.18(Ma/M)1.7, for Ma in the range 10-5 Ma/M 10-1,where B0 is the pre-accretion magnetic field strength, and Ma is the accretion rate.

A cellular automaton model of pulsar glitches

A cellular automaton model of pulsar glitches is described, based on the superfluid vortex unpinning paradigm. Recent analyses of pulsar glitch data suggest that glitches result from scale-invariant avalanches, which are consistent with a self-organized critical system (SOCS). A cellular automaton provides a computationally efficient means of modelling the collective behaviour of up to 10 16 vortices in the pulsar interior, whilst ensuring that the dominant aspects of the microphysics are not lost. The automaton generates avalanche distributions that are qualitatively consistent with a SOCS and with glitch data. The probability density functions of glitch sizes and durations are power laws, and the probability density function of waiting times between successive glitches is Poissonian, consistent with statistically independent events. The output of the model depends on the physical and computational parameters used. The fitted power-law exponents a and b (the size and duration distributions, respectively) decrease as the strength of the vortex pinning increases. Similarly, the exponents increase as the fraction of vortices that are pinned decreases. For the physical and computational parameters considered, one finds −4.3 ≤ a ≤− 2.0, −5.5 ≤ b ≤− 2.2, and mean glitching rates in the range 0.0023 ≤ λ ≤ 0.13 in units of inverse time.

Three‐dimensional hydrodynamic simulations of asymmetric pulsar wind bow shocks

We present three-dimensional, non-relativistic, hydrodynamic simulations of bow shocks in pulsar wind nebulae. The simulations are performed for a range of initial and boundary conditions to quantify the degree of asymmetry produced by latitudinal variations in the momentum flux of the pulsar wind, radiative cooling in the post-shock flow and density gradients in the interstellar medium (ISM). We find that the bow shock is stable even when travelling through a strong ISM gradient. We demonstrate how the shape of the bow shock changes when the pulsar encounters density variations in the ISM. We show that a density wall can account for the peculiar bow shock shapes of the nebulae around PSR J2124-3358 and PSR B0740-28. A wall produces kinks in the shock, whereas a smooth ISM density gradient tilts the shock. We conclude that the anisotropy of the wind momentum flux alone cannot explain the observed bow shock morphologies but it is instead necessary to take into account external effects. We show that the analytic (single layer, thin shell) solution is a good approximation when the momentum flux is anisotropic, fails for a steep ISM density gradient and approaches the numerical solution for efficient cooling. We provide analytic expressions for the latitudinal dependence of a vacuum-dipole wind and the associated shock shape, and compare the results to a split-monopole wind. We find that we are unable to distinguish between these two wind models purely from the bow shock morphology.