Elastic Stars in General Relativity: II. Radial perturbations

We study radial perturbations of general relativistic stars with elastic matter sources. We find that these perturbations are governed by a second order differential equation which, along with the boundary conditions, defines a Sturm-Liouville type problem that determines the eigenfrequencies. Although some complications arise compared to the perfect fluid case, leading us to consider a generalisation of the standard form of the Sturm-Liouville equation, the main results of Sturm-Liouville theory remain unaltered. As an important consequence we conclude that the mass-radius curve for a one-parameter sequence of regular equilibrium models belonging to some particular equation of state can be used in the same well-known way as in the perfect fluid case, at least if the energy density and the tangential pressure of the background solutions are continuous. In particular we find that the fundamental mode frequency has a zero for the maximum mass stars of the models with solid crusts considered in Paper I of this series.Comment: 22 pages, no figures, final version accepted for publication in Class. Quantum Grav. The treatment of the junction conditions has been improve

Relativistic mechanics of neutron superfluid in (magneto) elastic star crust

At densities below the neutron drip threshold, a purely elastic solid model (including, if necessary, a frozen-in magnetic field) can provide an adequate description of a neutron star crust, but at higher densities it will be necessary to allow for the penetration of the solid lattice by an independently moving current of superfluid neutrons. In order to do this, the previously available category of relativistic elasticity models is combined here with a separately developed category of relativistic superfluidity models in a unified treatment based on the use of an appropriate Lagrangian master function. As well as models of the purely variational kind, in which the vortices flow freely with the fluid, such a master function also provides a corresponding category of non-dissipative models in which the vortices are pinned to the solid structure

Axial quasi-normal modes of neutron stars: accounting for the superfluid in the crust

We present the results of the first study of global oscillations of relativistic stars with both elastic crusts and interpenetrating superfluid components. For simplicity, we focus on the axial quasi-normal modes. Our results demonstrate that the torsional crust modes are essentially unaffected by the coupling to the gravitational field. This is as expected since these oscillations are known to be weak gravitational-wave sources. In contrast, the presence of a loosely coupled superfluid neutron component in the crust can have a significant effect on the oscillation spectrum. We show that the entrainment between the superfluid and the crust nuclei is a key parameter in the problem. Our analysis highlights the need for a more detailed understanding of the coupled crust-superfluid at the microphysical level. Our numerical results have, even though we have not considered magnetized stars, some relevance for efforts to carry out seismology based on quasi-periodic oscillations observed in the tails of magnetar flares. In particular, we argue that the sensitive dependence on the entrainment may have to be accounted for in attempts to match theoretical models to observational data.<br/