We investigate the modal properties of inertial modes of rotating neutron stars with the core filled with neutron and proton superfluids , taking account of entrainment effects between the superfluids .
In this paper , the entrainment effects are modeled by introducing a parameter \eta so that no entrainment state is realized at \eta = 0 .
We find that inertial modes of rotating neutron stars with the superfluid core are split into two families , which we call ordinary fluid inertial modes ( i ^ { o } -mode ) and superfluid inertial modes ( i ^ { s } -mode ) .
The two superfluids in the core counter-move for the i ^ { s } -modes .
For the i ^ { o } -modes , \kappa _ { 0 } = \lim _ { \Omega \rightarrow 0 } \omega / \Omega is only weakly dependent on the entrainment parameter \eta , where \Omega and \omega are the angular frequency of rotation and the oscillation frequency observed in the corotating frame of the star , respectively .
For the i ^ { s } -modes , on the other hand , | \kappa _ { 0 } | almost linearly increases as \eta increases .
Avoided crossings as functions of \eta are therefore quite common between i ^ { o } - and i ^ { s } -modes .
We find that some of the i ^ { s } -modes that are unstable against the gravitational radiation reaction at \eta = 0 become stable when \eta is larger than \eta _ { crit } , the value of which depends on the mode .
Since the radiation driven instability associated with the current multipole radiation is quite weak for the inertial modes and the mutual friction damping in the superfluid core is strong , the instability caused by the inertial modes will be easily suppressed unless the entrainment parameter \eta is extremely small and the mutual friction damping is sufficiently weak .