Oscillations of superfluid hyperon stars: decoupling scheme and g-modes

We analyse the oscillations of general relativistic superfluid hyperon stars, following the approach suggested by Gusakov & Kantor and Gusakov et al. and generalizing it to the nucleon-hyperon matter. We show that the equations governing the oscillations can be split into two weakly coupled systems with the coupling parameters $s_{rm e}$, $s_{rm mu}$, and $s_{rm str}$. The approximation $s_{rm e} = s_{rm mu} = s_{rm str} = 0$ (decoupling approximation) allows one to drastically simplify the calculations of stellar oscillation spectra. An efficiency of the presented scheme is illustrated by the calculation of sound speeds in the nucleon-hyperon matter composed of neutrons (n), protons (p), electrons (e), muons ($mu$), as well as $rm Lambda$, ${rm Xi}^-$, and ${rm Xi}^0$-hyperons. However, the gravity oscillation modes (g-modes) cannot be treated within this approach, and we discuss them separately. For the first time we study the composition g-modes in superfluid hyperon stars with the $rm npemuLambda$ core and show that there are two types of g-modes (`muonic and `$Lambda$--hyperonic) in such stars. We also calculate the g-mode spectrum and find out that the eigenfrequencies $ u$ of the superfluid g-modes can be exceptionally large (up to $ u approx 742~{rm Hz}$ for a considered stellar model).