## Abstract

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 that the r-modes in the superfluid core are split into ordinary r-modes and superfluid r-modes, which we call, respectively, r^{0}- and r^{s}-modes. The two superfluids in the core flow together for the r^{0}-modes, while they countermove for the r^{s}-modes. For the r^{0}-modes, the coefficient κ_{0} ≡ lim_{Ω→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 is 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^{s}-modes, on the other hand, κ_{0} is equal to 2m/[l′ (l′ + 1)] at η = 0 (noentrainment), and it almost linearly increases as η is increased from η = 0. The r^{0}-modes, for which w′ ≡ v′_{p} - v′_{n} ∝ Ω^{3}, correspond to the r-modes discussed by L. Lindblom & G. Mendell, where v′_{n} 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^{0}-mode except in a few narrow regions of η. The r-mode instability caused by the r^{s}-modes, on the other hand, is extremely weak and easily damped by dissipative processes in the star.

Original language | English |
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Pages (from-to) | 403-418 |

Number of pages | 16 |

Journal | Astrophysical Journal |

Volume | 586 |

Issue number | 1 I |

DOIs | |

Publication status | Published - 2003 Mar 20 |

## Keywords

- Instabilities
- Stars: neutron
- Stars: oscillations
- Stars: rotation