Oscillations of relativistic axisymmetric tori and implications for modelling kHz-QPOs in neutron star X-ray binaries

We perform a global linear perturbative analysis and investigate oscillation properties of relativistic, non-self-gravitating tori orbiting around neutron stars in the slow rotation limit approximation. Extending the work done in Schwarzschild and Kerr backgrounds, we consider the axisymmetric oscillations of vertically integrated tori in the Hartle-Thorne space-time. The equilibrium models are constructed by selecting a number of different non-Keplerian distributions of specific angular momentum, allowing for disc sizes L˜ 0.5-600 gravitational radii. Our results, obtained after solving a global eigenvalue problem to compute the axisymmetric p-modes, indicate that such oscillation modes could account for most observed lower (νL) and upper (νU) high-frequency quasi-periodic oscillations for Sco X-1, and for some Z and Atoll sources with νL≳ 500 Hz. However, when νL≲ 500 Hz, p-mode oscillations do not account for the linear relation νU=AνL+B, B≠ 0, between the upper and lower high-frequency quasi-periodic oscillations that are observed in neutron star low-mass X-ray binaries.