Inertial modes of non-stratified superfluid neutron stars

Description/Abstract

We present results concerning adiabatic inertial-mode oscillations of non-stratified superfluid neutron stars in Newtonian gravity, using the anelastic and slow-rotation approximations. We consider a simple two-fluid model of a superfluid neutron star, where one fluid consists of the superfluid neutrons and the second fluid contains all the comoving constituents (protons, electrons). The two fluids are assumed to be 'free' in the sense that vortex-mediated forces such as mutual friction or pinning are absent, but they can be coupled by the equation of state, in particular by entrainment. The stationary background consists of the two fluids rotating uniformly around the same axis with potentially different rotation rates. We study the special cases of corotating backgrounds, vanishing entrainment, and the purely toroidal r modes analytically. We calculate numerically the eigenfunctions and frequencies of inertial modes in the general case of non-corotating backgrounds, and study their dependence on the relative rotation rate and entrainment. In these non-stratified models, we find avoided crossings only between associated mode pairs, e.g. an 'ordinary' mode and its 'superfluid' counterpart, while other mode frequencies generally cross as the background parameters are varied. We confirm (for the first time in a mode calculation) the onset of a 'two-stream instability' at a critical relative background rotation rate, and we study some of the properties of this instability for the inertial modes.