[Formula Presented]-modes in relativistic superfluid stars

We discuss the modal properties of the r modes of relativistic superfluid neutron stars, taking account of the entrainment effects between superfluids. In this paper, the neutron stars are assumed to be filled with neutron and proton superfluids and the strength of the entrainment effects between the superfluids are represented by a single parameter [Formula Presented] We find that the basic properties of the r modes in a relativistic superfluid star are very similar to those found for a Newtonian superfluid star. The r modes of a relativistic superfluid star are split into two families: ordinary fluid-like r modes [Formula Presented] mode) and superfluid-like r modes [Formula Presented] mode). The two superfluids counter-move for the [Formula Presented] modes, while they co-move for the [Formula Presented] modes. For the [Formula Presented] modes, the quantity [Formula Presented] is almost independent of the entrainment parameter [Formula Presented] where m and [Formula Presented] are the azimuthal wave number and the oscillation frequency observed by an inertial observer at spatial infinity, respectively. For the [Formula Presented] modes, on the other hand, [Formula Presented] almost linearly increases with increasing [Formula Presented] It is also found that the radiation driven instability due to the [Formula Presented] modes is much weaker than that of the [Formula Presented] modes because the matter current associated with the axial parity perturbations almost completely vanishes.