R-modes of neutron stars with the superfluid core
Abstract
Description
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, $r^o$- and $r^s$-modes. The two superfluids in the core flow together for the $r^o$-modes, while they counter-move for the $r^s$-modes. For the $r^o$-modes, the coefficient $κ_0\equiv\lim_{Ω\to 0}ω/Ω$ is equal to $2m/[l^\prime(l^\prime+1)]$, 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 $l^\prime$ 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 $2m/[l^\prime(l^\prime+1)]$ at $η=0$ (no entrainment), and it almost linearly increases as $η$ is increased from $η=0$. The mutual friction in the superfluid core is found ineffective to stabilize the $r$-mode instability caused by the $r^o$-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.
22 pages, 22 figures, accepted for publication in the Astrophysical Journal
22 pages, 22 figures, accepted for publication in the Astrophysical Journal