Rotational glitches in radio pulsars and magnetars

Neutron stars are the most compact known stars; their cores are of higher density than an atomic nucleus. Their rotation rates are generally very predictable, with a slow decrease over time. This spin-down is occasionally interrupted, however, by abrupt 'glitches' when the rotation rate increases slightly. Glitches are attributed to a sudden coupling between a neutron star's crust and an interior superfluid component - and therefore the nature and frequency of glitches encodes important information about physics at densities which cannot be attained in terrestrial laboratories.
This thesis contains analysis of both observational and theoretical aspects of the physics of neutron-star glitches. It describes glitch detectability limits and a search algorithm, which together allow for a more systematic analysis of glitch data than was previously possible. These are applied to one of the most closely-observed neutron stars, the Crab pulsar, finding it has an unexpected deficit of small glitches. Next, a multifluid model of the neutron-star interior is used to simulate glitches; it is shown that different kinds of glitch and post-glitch behaviour can be explained within this theoretical approach. One highly-magnetised neutron star with particularly notable glitch properties is PSR J1119-6127. This thesis presents a detailed observational study of its glitches and discusses their implications for theoretical models of the dynamics of the neutron star's crust and exterior magnetic field. Finally, the aftermath of a large glitch from the Vela pulsar is analysed, and the potential to use this data to constrain models of the interior superfluid is discussed.