C. Peralta

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%.

GRAVITATIONAL RADIATION FROM HYDRODYNAMIC TURBULENCE IN A DIFFERENTIALLY ROTATING NEUTRON STAR

The mean-square current quadrupole moment associated with vorticity fluctuations in high-Reynolds-number turbulence in a differentially rotating neutron star is calculated analytically, as are the amplitude and decoherence time of the resulting, stochastic gravitational wave signal. The calculation resolves the subtle question of whether the signal is dominated by the smallest or largest turbulent eddies: for the Kolmogorov-like power spectrum observed in superfluid spherical Couette simulations, the wave strain is controlled by the largest eddies, and the decoherence time approximately equals the maximum eddy turnover time. For a neutron star with spin frequency νs and Rossby number Ro, at a distance d from Earth, the root mean square wave strain reaches hrms ≈ 3 × 10 −24 Ro 3 (νs/30 Hz) 3 (d/1 kpc) −1 . Ordinary rotation-powered pulsars (νs 30 Hz, Ro 10 −4 ) are too dim to be detected by the current generation of long-baseline interferometers. Millisecond pulsars are brighter; for example, an object born recently in a Galactic supernova or accreting near the Eddington rate can have νs ∼ 1k Hz, Ro 0.2, and hence hrms ∼ 10 −21 . A cross-correlation search can detect such a source in principle, because the signal decoheres over the timescale τc ≈ 1 × 10 −3 Ro −1 (νs/30 Hz) −1 s, which is adequately sampled by existing long-baseline interferometers. Hence, hydrodynamic turbulence imposes a fundamental noise floor on gravitational wave observations of neutron stars, although its polluting effect may be muted by partial decoherence in the hectohertz band, where current continuous-wave searches are concentrated, for the highest frequency (and hence most powerful) sources. This outcome is contingent on the exact shape of the turbulent power spectrum, which is modified by buoyancy and anisotropic global structures, such as stratified boundary layers, in a way that is understood incompletely even in laboratory situations.

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 (E 10–3, Ro 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 E 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.

Superfluid spherical Couette flow

We solve numerically the two-fluid, Hall-Vinen-Bekarevich-Khalatnikov equations for a He-II-like superfluid contained in a differentially rotating, spherical shell, generalizing previous simulations of viscous spherical Couette flow (SCF) and superfluid Taylor-Couette flow. The system tends towards a stationary but unsteady state, where the torque oscillates persistently, with amplitude and period determined by dimensionless gap width δ and rotational shear ΔΩ. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as the Reynolds number Re increases. In nonaxisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants. We find that the mutual friction is patchy; that is, it takes different forms in different parts of the vessel, a surprising new result.