The dynamics of differentially rotating neutron stars
This thesis investigates the effect of rapid accretion and differential rotation on neutron star oscillations. The research is motivated by the fact that vibrating neutron stars are a promising source of gravitational waves. The first part of the thesis is a study of a nascent neutron star accreting supernova remnant material. We model an unstable r-mode oscillation that leads to the emission of gravitational waves, and the torques and heating associated with rapid accretion onto a star with a magnetic field. We consider the consequences for both gravitational wave emission and the rotation rate of the star. The main part of the thesis addresses differential rotation. This is likely to arise at times, such as the immediate aftermath of the supernova, when we expect strong vibrations. We focus on two factors unique to differentially rotating systems; dynamical shear instabilities, and the existence of a corotation band (a frequency band in which mode pattern speed matches the local angular velocity). Using a simple model, we find dynamical shear instabilities that arise where modes cross into the corotation band, if the degree of differential rotation exceeds a certain threshold. Recently, several authors have reported the discovery of dynamical instabilities in differentially rotating stars at low values of the ratio of kinetic to potential energy. We demonstrate that our instability mechanism explains all of the reported features of these instabilities. We also investigate the nature of oscillations within the corotation band. The band gives rise to a continuous spectrum whose collective physical perturbation exhibits complicated temporal behaviour. We also report the existence of modes within the continuous spectrum that appear physically indistinguishable from the discrete modes outside the band, despite the singular nature of their eigenfunctions.