Building mountains on neutron stars

The first detection of gravitational waves in 2015, along with the many subsequent detections, has provided profound insights into theories of gravity and the nature of compact objects such as black holes and neutron stars. The signals detected so far have been transient, originating from events like binary mergers. However, we also expect quasi-monochromatic signals, known as continuous gravitational waves, to be emitted by rapidly rotating neutron stars with non-axisymmetric quadrupole moments, for instance, neutron stars with a ``mountain.'' Such continuous signals will offer an independent probe of neutron star physics, complementing electromagnetic and neutrino observations. In this thesis, we investigate elastic mountains, in which the non-zero quadrupole ellipticity is supported by the elastic properties of the crust, under two distinct models: the starquake model and the superfluid vortex pinning model. In the starquake model, originally developed to explain pulsar glitches, we extend the symmetric analysis of Baym and Pines (1971) to the general case of both symmetric and asymmetric crust breaking, where the latter gives rise to a mountain. We apply this framework to the spin-up of an initially non-rotating star and estimate the maximum mountain that can be formed, subject only to energy and angular momentum conservation. We find that the creation of a mountain in this scenario necessarily requires a simultaneous change in the axisymmetric shape too. In the latter half of the thesis, we investigate the formation of a ``Magnus mountain,'' arising from the non-axisymmetric Magnus force acting on the elastic crust through pinned superfluid vortices. We numerically solve the coupled perturbed equations of motion for the elastic and fluid components of the star, and compute the associated displacement field corresponding to a non-axisymmetric shape change. We begin with the simplified case of an infinitely long cylindrical star, with the aim of extending the model to a more realistic spherical configuration in future work.