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(e), s(mu), and s(str). The approximation s(e) = s(mu) = s(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 Lambda, Xi(-), and 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 npe mu Lambda 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 nu of the superfluid g-modes can be exceptionally large (up to nu approximate to 742 Hz for a considered stellar model).