Fast fossil rotation of neutron star cores

It is argued that the superfluid core of a neutron star super-rotates relative to the crust, because stratification prevents the core from responding to the electromagnetic braking torque, until the relevant dissipative (viscous or Eddington-Sweet) time-scale, which can exceed ~ 10^3 yr and is much longer than the Ekman timescale, has elapsed. Hence, in some young pulsars, the rotation of the core today is a fossil record of its rotation at birth, provided that magnetic crust-core coupling is inhibited, e.g. by buoyancy, field-line topology, or the presence of uncondensed neutral components in the superfluid. Persistent core super-rotation alters our picture of neutron stars in several ways, allowing for magnetic field generation by ongoing dynamo action and enhanced gravitational wave emission from hydrodynamic instabilities.Comment: 20 pages, 1 figure, accepted by The Astrophysical Journa

Radiative Precession of an Isolated Neutron Star

Euler's 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 \tau_1 typically satisfies \tau_1 < 10^{-2}\tau_0, where \tau_0 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; and the (negative) angular frequency derivative d{\omega}/dt 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 d{\omega}/dt. 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 \Delta L = 3*10^{31} (\epsilon / 10^{-12}) (\omega / 10^3 rad s^{-1})^2 (\tau_d / 1 yr)^{-1} erg s^{-1}, where epsilon is the ellipticity and \tau_d is the damping time-scale, with the actual value of \Delta L determined in part by the thermal conduction time \tau_cond. The increased luminosity is potentially detectable as thermal X-rays lasting for a time max(tau_d,tau_cond) following crystallization of the crust.Comment: 28 pages, 5 figures, to appear in Monthly Notices of the Royal Astronomical Societ

An unstable superfluid Stewartson layer in a differentially rotating neutron star

Experimental and numerical evidence is reviewed for the existence of a Stewartson layer in spherical Couette flow at small Ekman and Rossby numbers (\Ek \lsim 10^{-3}, \Ro \lsim 10^{-2}), the relevant hydrodynamic regime in the superfluid outer core of a neutron star. Numerical simulations of a superfluid Stewartson layer are presented for the first time, showing how the layer is disrupted by nonaxisymmetric instabilities. The unstable ranges of \Ek and \Ro are compared with estimates of these quantities in radio pulsars that exhibit glitches. It is found that glitching pulsars lie on the stable side of the instability boundary, allowing differential rotation to build up before a glitch.Comment: 4 pages, 3 figures. Accepted for publication in ApJ Letter

Unpinning triggers for superfluid vortex avalanches

The pinning and collective unpinning of superfluid vortices in a decelerating container is a key element of the canonical model of neutron star glitches and laboratory spin-down experiments with helium II. Here the dynamics of vortex (un)pinning is explored using numerical Gross-Pitaevskii calculations, with a view to understanding the triggers for catastrophic unpinning events (vortex avalanches) that lead to rotational glitches. We explicitly identify three triggers: rotational shear between the bulk condensate and the pinned vortices, a vortex proximity effect driven by the repulsive vortex-vortex interaction, and sound waves emitted by moving and repinning vortices. So long as dissipation is low, sound waves emitted by a repinning vortex are found to be sufficiently strong to unpin a nearby vortex. For both ballistic and forced vortex motion, the maximum inter-vortex separation required to unpin scales inversely with pinning strength.Comment: 16 pages, 18 figure

Superfluid turbulence and pulsar glitch statistics

Experimental evidence is reviewed for the existence of superfluid turbulence in a differentially rotating, spherical shell at high Reynolds numbers (\Rey\gsim 10^3), such as the outer core of a neutron star. It is shown that torque variability increases with \Rey, suggesting that glitch activity in radio pulsars may be a function of \Rey as well. The \Rey distribution of the 67 glitching radio pulsars with characteristic ages $\tau_c \leq 10^6$ {\rm yr} is constructed from radio timing data and cooling curves and compared with the \Rey distribution of all 348 known pulsars with $\tau_c \leq 10^6$ {\rm yr}. The two distributions are different, with a Kolmogorov-Smirnov probability $\geq 1 - 3.9 \times 10^{-3}$. The conclusion holds for (modified) Urca and nonstandard cooling, and for Newtonian and superfluid viscosities