Oscillations of dissipative superfluid neutron stars

We investigate the oscillations of slowly rotating superfluid stars, taking into account the vortex-mediated mutual friction force that is expected to be the main damping mechanism in mature neutron star cores. Working to linear order in the rotation of the star, we consider both the fundamental f-modes and the inertial r-modes. In the case of the (polar) f-modes, we work out an analytic approximation of the mode which allows us to write down a closed expression for the mutual friction damping time scale. The analytic result is in good agreement with previous numerical results obtained using an energy integral argument. We extend previous work by considering the full range of permissible values for the vortex drag, e.g. the friction between each individual vortex and the electron fluid. This leads to the first ever results for the f-mode in the strong drag regime. Our estimates provide useful insight into the dependence on, and relevance of, various equation of state parameters. In the case of the (axial) r-modes, we confirm the existence of two classes of modes. However, we demonstrate that only one of these sets remains purely axial in more realistic neutron star models. Our analysis lays the foundation for companion studies of the mutual friction damping of the r-modes at second order in the slow-rotation approximation, the first time evolutions for superfluid neutron star perturbations and also the first detailed attempt at studying the dynamics of superfluid neutron stars with both a relative rotation between the components and mutual friction.