Oscillations of tori in the pseudo-Newtonian potential

TL;DR

This study investigates the oscillations of tori in a pseudo-Newtonian potential, finding no pressure coupling between epicyclic modes and suggesting other modes may explain high-frequency QPOs.

Contribution

The paper provides numerical evidence that axisymmetric tori do not exhibit coupling between radial and vertical epicyclic modes in a strong gravity approximation.

Findings

Epicyclic frequencies decrease with thicker tori.

No coupling found between radial and vertical epicyclic motions.

Other modes may be responsible for HF QPOs.

Abstract

Context. The high-frequency quasi-periodic oscillations (HF QPOs) in neutron star and stellar-mass black hole X-ray binaries may be the result of a resonance between the radial and vertical epicyclic oscillations in strong gravity. Aims. In this paper we investigate the resonant coupling between the epicyclic modes in a torus in a strong gravitational field. Methods. We perform numerical simulations of axisymmetric constant angular momentum tori in the pseudo-Newtonian potential. The epicyclic motion is excited by adding a constant radial velocity to the torus. Results. We verify that slender tori perform epicyclic motions at the frequencies of free particles, but the epicyclic frequencies decrease as the tori grow thicker. More importantly, and in contrast to previous numerical studies, we do not find a coupling between the radial and vertical epicyclic motions. The appearance of other modes than the radial epicyclic motion in our simulations is rather due to small numerical deviations from exact equilibrium in the initial state of our torus. Conclusions. We find that there is no pressure coupling between the two axisymmetric epicyclic modes as long as the torus is symmetric with respect to the equatorial plane. However we also find that there are other modes in the disc that may be more attractive for explaining the HF QPOs.