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

Abstract: We perform a global linear perturbative analysis, and investigate the oscillation properties of relativistic, non-selfgravitating 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 spacetime. The equilibrium models are constructed by selecting a number of different non-Keplerian distributions of specific angular momentum, allowing for disc sizes $L \sim 0.5 - 600$ gravitational radii. Our results, obtained after solving a global eigenvalue problem to compute the xisymmetric $p$-modes, indicate that such oscillation modes could account with most observed lower ($\nu_L$) and upper ($\nu_U$) high frequency quasi-periodic oscillations for Sco X-1, and for some Z sources and Atoll sources with $\nu_L\ gtrsim 500$ Hz. However, when $\nu_L \lesssim 500$ Hz, $p$-modes oscillations do not account for the linear relation $\nu_U = A \nu_L + B$, $B \neq 0$ between the upper and the lower high frequency quasi-periodic oscillations that are observed in neutron star low-mass X-ray binaries.