School of Physics - Theses
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ItemCollective superfluid vortex dynamics and pulsar glitches( 2011)Pulsar glitches offer a way of studying the dynamics of cold, ultradense matter in systems of stellar dimensions, under extremes of density, temperature and magnetisation unattainable on Earth. This thesis aims to build a robust model of pulsar glitches, based on the superfluid vortex unpinning paradigm, which relates the physical parameters of the pulsar interior to the observed distribution of glitch sizes and waiting times (power laws and exponentials respectively). Our modelling efforts draw together knowledge about superfluid vortex dynamics and pinning, garnered from condensed matter and nuclear physics, the observational facts gathered by pulsar astronomers, and the theoretical framework of non-equilibrium stochastic systems, such as those exhibiting self-organised criticality. In each case, we emphasise the necessity of collective mechanisms in triggering avalanche-like vortex unpinning events. We begin by studying the dynamics of superfluid vortices from first principles, using numerical solutions of the Gross-Pitaevskii equation (GPE). We solve the GPE in the presence of a lattice of pinning sites, in a container that is decelerated at a constant rate, mimicking the electromagnetic spin-down torque on a pulsar. The superfluid spins down spasmodically, as vortices unpin and hop between pinning sites when the Magnus force, due to the lag between the superfluid and vortex line velocities, exceeds a threshold. Torque feedback between the superfluid and its container regulates the lag between the superfluid and crust, resulting in abrupt increases in the container angular velocity. We study how the statistics of the sizes and waiting times between spin-up events change with the mean and dispersion of pinning strengths, the electromagnetic spin-down torque, the relative number of vortices compared to pinning sites, and the ratio of the crust and superfluid moment of inertia - all parameters of interest in neutron stars. We find that mean glitch size increases with mean pinning strength and the ratio of the moments of inertia. It is independent of the relative number of pinning sites and vortices, suggesting that vortices move a characteristic distance before repinning, rather than repinning at the next available site. The mean waiting time decreases with the number of pinning sites and vortices, the ratio of the moments of inertia and the spin-down torque, and it increases with the width of the pinning strength distribution. In order to explain the broad range of observed glitch sizes using the vortex unpinning paradigm, a collective unpinning mechanism is required. Using numerical solutions of the GPE, we study how the unpinning of one vortex can cause other vortices to unpin. We identify two knock-on triggers: acoustic pulses emitted as a vortex repins, and the increased repulsive force between vortices locally, when an unpinned vortex approaches its nearest neighbours. In the second half of the thesis, we construct a suite of three large-scale stochastic models of glitches. We are inspired to prosecute this program by similarities between the statistics of archetypal self-organised critical systems, such as earthquakes and sand piles, and those of pulsar glitches. The essential features of the vortex dynamics observed in the GPE simulations are abstracted and condensed into a set of iterative rules that form the basis of automata and analytic glitch models. A cellular automaton model, in which vortices interact with nearest neighbours via the Magnus force, reveals that when all pinning sites are of the same strength, large-scale inhomogeneities in the pinned vortex distribution are necessary to produce a broad range of glitch sizes. In this case, glitch sizes and durations are power-law-distributed, and waiting times obey an exponential distribution. We find no evidence of history-dependent glitch sizes or aftershocks. A coherent noise model, based on a similar model developed to study atom hopping in glasses, in which pinning strength varies from site to site, but the pinned vortex distribution is assumed to be spatially homogeneous, exhibits power-law-distributed glitch sizes. Exponential waiting times are put in by hand, by assuming that the stress released in a glitch accumulates over exponentially-distributed time intervals. A wide range of pinning strengths is needed to find agreement with radio timing data. Mean pinning strength is found to decrease with increasing characteristic pulsar age. Finally, we construct a statistical model that tracks the vortex unpinning rate as a function of the stochastically fluctuating global lag between the superfluid and container. Monte-Carlo simulations and a jump-diffusion master equation reveal that a knock-on mechanism that is finely tuned with respect to the pinning strength, is essential to producing a broad range of glitch sizes. Estimates of the power dissipated in acoustic waves during repinning, and of the strength of the proximity effect, do not meet the fine-tuning criteria. We propose to extend this promising model to include nearest-neighbour interactions in the future, in the hope that this may lessen the need for fine tuning. The non-axisymmetric rearrangement of the superfluid velocity field during a vortex-avalanche-driven glitch is a source of gravitational radiation. We calculate the gravitational wave strain using the characteristic vortex motion observed in the GPE simulations. We set an upper bound on the wave strain of h ~ 10-23 for a glitch resulting from an unpinning avalanche of the maximum observed size. We also estimate the contribution to the stochastic gravitational wave background from the superposition of many glitches from a Galactic neutron star population. We place an upper bound on the signal-to-noise ratio of the background of ~ 10-5 for the Advanced LIGO (Laser Interferometer Gravitational-wave Observatory) detector. Detection of a gravitational wave signal from glitches can teach us about the physics of matter at nuclear densities, from the equation of state to transport coefficients like viscosity.