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 e
xplored 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.
The current-quadrupole gravitational-wave signal emitted during the spin-up phase of a pulsar glitch is calculated from first principles by modeling the vortex dynamics observed in recent Gross-Pitaevskii simulations of pinned, decelerating quantum c
ondensates. Homogeneous and inhomogeneous unpinning geometries, representing creep- and avalanche-like glitches, provide lower and upper bounds on the gravitational wave signal strength respectively. The signal arising from homogeneous glitches is found to scale with the square root of glitch size, whereas the signal from inhomogeneous glitches scales proportional to glitch size. The signal is also computed as a function of vortex travel distance and stellar angular velocity. Convenient amplitude scalings are derived as functions of these parameters. For the typical astrophysical situation, where the glitch duration (in units of the spin period) is large compared to the vortex travel distance (in units of the stellar radius), an individual glitch from an object $1,rm{kpc}$ from Earth generates a wave strain of $10^{-24} [(Deltaomega/omega) / 10^{-7}] (omega/10^2 rm{rad s}^{-1})^3 (Delta r / 10^{-2} rm{m})^{-1}$, where $Delta r$ is the average distance travelled by a vortex during a glitch, $Deltaomega/omega$ is the fractional glitch size, and $omega$ is the pulsar angular velocity. The non-detection of a signal from the 2006 Vela glitch in data from the fifth science run conducted by the Laser Interferometer Gravitational-Wave Observatory implies that the glitch duration exceeds $sim 10^{-4},rm{ms}$. This represents the first observational lower bound on glitch duration to be obtained.
The radio polarization characteristics of millisecond pulsars (MSPs) differ significantly from those of non-recycled pulsars. In particular, the position angle (PA) swings of many MSPs deviate from the S-shape predicted by the rotating vector model,
even after relativistic aberration is accounted for, indicating that they have non-dipolar magnetic geometries, likely due to a history of accretion. Stokes tomography uses phase portraits of the Stokes parameters as a diagnostic tool to infer a pulsars magnetic geometry and orientation. This paper applies Stokes tomography to MSPs, generalizing the technique to handle interpulse emission. We present an atlas of look-up tables for the Stokes phase portraits and PA swings of MSPs with current-modified dipole fields, filled core and hollow cone beams, and two empirical linear polarization models. We compare our look-up tables to data from 15 MSPs and find that the Stokes phase portraits for a current-modified dipole approximately match several MSPs whose PA swings are flat or irregular and cannot be reconciled with the standard axisymmetric rotating vector model. PSR J1939+2134 and PSR J0437$-$4715 are modelled in detail. The data from PSR J1939+2134 at 0.61,GHz can be fitted well with a current-modified dipole at $(alpha, i) = (22 pm 2^circ, 80 pm 1^circ)$ and emission altitude 0.4 $r_text{LC}$. The fit is less accurate for PSR J1939+2134 at 1.414,GHz, and for PSR J0437$-$4715 at 1.44,GHz, indicating that these objects may have a more complicated magnetic field geometry, such as a localized surface anomaly or a polar magnetic mountain.
Precession in an accretion-powered pulsar is expected to produce characteristic variations in the pulse properties. Assuming surface intensity maps with one and two hotspots, we compute theoretically the periodic modulation of the mean flux, pulse-ph
ase residuals and fractional amplitudes of the first and second harmonic of the pulse profiles. These quantities are characterised in terms of their relative precession phase offsets. We then search for these signatures in 37 days of X-ray timing data from the accreting millisecond pulsar XTE J1814-338. We analyse a 12.2-d modulation observed previously and show that it is consistent with a freely precessing neutron star only if the inclination angle is < 0.1 degrees, an a priori unlikely orientation. We conclude that if the observed flux variations are due to precession, our model incompletely describes the relative precession phase offsets (e.g. the surface intensity map is over-simplified). We are still able to place an upper limit on epsilon of 3.0 x 10^{-9} independently of our model, and estimate the phase-independent tilt angle theta; to lie roughly between 5 and 10 degrees. On the other hand, if the observed flux variations are not due to precession, the detected signal serves as a firm upper limit for any underlying precession signal. We then place an upper limit on the product epsilon cos(theta) of leq 9.9 x 10^{-10}. The first scenario translates into a maximum gravitational wave strain of 10^{-27} from XTE J1814-338 (assuming a distance of 8 kpc), and a corresponding signal-to-noise ratio of leq 10^{-3} (for a 120 day integration time) for the advanced LIGO ground-based gravitational wave detector.
We investigate the time taken for global collapse by a dipolar Bose-Einstein condensate. Two semi-analytical approaches and exact numerical integration of the mean-field dynamics are considered. The semi-analytical approaches are based on a Gaussian
ansatz and a Thomas-Fermi solution for the shape of the condensate. The regimes of validity for these two approaches are determined, and their predictions for the collapse time revealed and compared with numerical simulations. The dipolar interactions introduce anisotropy into the collapse dynamics and predominantly lead to collapse in the plane perpendicular to the axis of polarization.
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 citep{Melatos07a}, 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 paramters used. The fitted power law exponents for the glitch sizes ($a$) and durations ($b$) decreases 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 $-4.3leq a leq -2.0$ and $-5.5leq bleq -2.2$, and mean glitching rates in the range $0.0023leqlambdaleq0.13$ in units of inverse time.
