Following the previous research on epicyclic oscillations of accretion disks around black holes (BHs) and neutron stars (NSs), a new model of high-frequency quasiperiodic oscillations (QPOs) has been proposed, so-called cusp torus (CT) model, which deals with oscillations of fluid in marginally overflowing accretion tori (i.e., tori terminated by cusps). According to preliminary investigations, the model provides better fits of the NS QPO data compared to the relativistic precession (RP) model. It also implies a significantly higher upper limit on the Galactic microquasar BH spins. A short analytic formula has been noticed to well reproduce the model’s predictions on the QPO frequencies in Schwarzschild spacetimes. Here we derive an extended version of this formula that applies to rotating compact objects. We start with the consideration of Kerr spacetimes and derive a formula that is not restricted to a particular specific angular momentum distribution of the inner accretion flow, such as a Keplerian or constant one. Finally, we consider Hartle–Thorne spacetimes and include corrections implied by the NS oblateness. For a particular choice of a single parameter, our relation provides frequencies predicted by the CT model. For another value, it provides frequencies predicted by the RP model. We conclude that the formula is well applicable to rotating oblate NSs and both models. We briefly illustrate the application of our simple formula on several NS sources and confirm the expectation that the CT model is compatible with realistic values of the NS mass and provides better fits of data than the RP model.

We examine the influence of quadrupole moment of a slowly rotating neutron star (NS) on the oscillations of a fluid accretion disk (torus) orbiting a compact object the spacetime around which is described by the Hartle-Thorne geometry.Explicit formulae for non-geodesic orbital epicyclic and precession frequencies, as well as their simplified practical versions that allow for an expeditious application of the universal relations determining the NS properties, are obtained and examined. We demonstrate that the difference in the accretion disk precession frequencies for NSs of the same mass and angular momentum, but different oblateness, can reach up to tens of percent. Even higher differences can arise MODEL OF AN OSCILLATING TORUSTo model the torus, we assume a stationary, purely azimuthal flow of perfect fluid with constant specific

We examine the influence of the quadrupole moment of a slowly rotating neutron star on the oscillations of non-slender accretion tori. We apply previously developed methods to perform analytical calculations of frequencies of the radial epicyclic mode of a torus in the specific case of the Hartle-Thorne geometry. We present here our preliminary results and provide a brief comparison between the calculated frequencies and the frequencies previously obtained assuming both standard and linearized Kerr geometry. Finally, we shortly discuss the consequences for models of high-frequency quasi-periodic oscillations observed in low-mass X-ray binaries.