R modes and mutual friction in rapidly rotating superfluid neutron stars

Abstract

We develop a new perturbative framework for studying the r-modes of rotating superfluid neutron stars. Our analysis accounts for the centrifugal deformation of the star, and considers the two-fluid dynamics at linear order in the perturbed velocities. Our main focus is on a simple model system where the total density profile is that of an $n=1$ polytrope. We derive a partially analytic solution for the superfluid analogue of the classical r-mode. This solution is used to analyse the relevance of the vortex mediated mutual friction damping, confirming that this dissipation mechanism is unlikely to suppress the gravitational-wave driven instability in rapidly spinning superfluid neutron stars. Our calculation of the superfluid r-modes is significantly simpler than previous approaches, because it decouples the r-mode from all other inertial modes of the system. This leads to the results being clearer, but it also means that we cannot comment on the relevance of potential avoided crossings (and associated "resonances") that may occur for particular parameter values. Our analysis of the mutual friction damping differs from previous studies in two important ways. Firstly, we incorporate realistic pairing gaps which means that the regions of superfluidity in the star's core vary with temperature. Secondly, we allow the mutual friction parameters to take the whole range of permissible values rather than focussing on a particular mechanism. Thus, we consider not only the weak drag regime, but also the strong drag regime where the fluid dynamics is significantly different.