ar X iv : a st ro - p h / 02 11 58 0 v 1 2 6 N ov 2 00 2 R - modes of neutron stars with the superfluid core

We investigate the modal properties of the r-modes of rotating neutron stars with the core filled with neutron and proton superfluids, taking account of entrainment effects between the superfluids. The stability of the r-modes against gravitational radiation reaction is also examined considering viscous dissipation due to shear and a damping mechanism called mutual friction between the superfluids in the core. We find the r-modes in the superfluid core are split into ordinary r-modes and superfluid r-modes, which we call, respectively, rand r-modes. The two superfluids in the core flow together for the r-modes, while they counter-move for the r-modes. For the r-modes, the coefficient κ0 ≡ limΩ→0 ω/Ω is equal to 2m/[l (l + 1)], almost independent of the parameter η that parameterizes the entrainment effects between the superfluids, where Ω is the angular frequency of rotation, ω the oscillation frequency observed in the corotating frame of the star, and l and m are the indices of the spherical harmonic function representing the angular dependence of the r-modes. For the r-modes, on the other hand, κ0 is equal to 2m/[l (l + 1)] at η = 0 (no entrainment), and it almost linearly increases as η is increased from η = 0. The r-modes, for which w ≡ vp − v ′ n ∝ Ω , correspond to the r-modes discussed by Lindblom & Mendell (2000), where vn and v ′ p are the Eulerian velocity perturbations of the neutron and proton superfluids, respectively. The mutual friction in the superfluid core is found ineffective to stabilize the r-mode instability caused by the r-mode except in a few narrow regions of η. The r-mode instability caused by the r-modes, on the other hand, is extremely weak and easily damped by dissipative processes in the star. Subject headings: instabilities — stars: neutron — stars: oscillations — stars : rotation