Applying the starquake model to study the formation of elastic mountains on spinning neutron stars

When a neutron star is spun-up or spun-down, the changing strains in its solid elastic crust can give rise to sudden fractures known as starquakes. Early interest in starquakes focused on their possible connection to pulsar glitches. While modern glitch models rely on pinned superfluid vorticity rather than crustal fracture, starquakes may nevertheless play a role in the glitch mechanism. Recently, there has been interest in the issue of starquakes resulting in non-axisymmetric shape changes, potentially linking the quake phenomenon to the building of neutron star mountains, which would then produce continuous gravitational waves. Motivated by this issue, we present a simple model that extends the energy minimisation-based calculations, originally developed to model axisymmetric glitches, to also include non-axisymmetric shape changes. We show that the creation of a mountain in a quake necessarily requires a change in the axisymmetric shape too. We apply our model to the specific problem of the spin-up of an initially non-rotating star, and estimate the maximum mountain that can be built in such a process, subject only to the constraints of energy and angular momentum conservation.