Oscillations of thick accretion discs around black holes -- II

Abstract

We present a numerical study of the global modes of oscillation of thick accretion discs around black holes. We have previously studied the case of constant distributions of specific angular momentum. In this second paper, we investigate (i) how the size of the disc affects the oscillation eigenfrequencies, and (ii) the effect of power‐law distributions of angular momentum on the oscillations. In particular, we compare the oscillations of the disc with the epicyclic eigenfrequencies of a test particle with different angular momentum distributions orbiting around the central object. We find that there is a frequency shift away from the epicyclic eigenfrequency of the test particle to lower values as the size of the tori is increased. We have also studied the response of a thick accretion disc to a localized external perturbation using non‐constant specific angular momentum distributions within the disc. We find that in this case it is also possible (as reported previously for constant angular momentum distributions) to efficiently excite internal modes of oscillation. In fact, we show here that the local perturbations excite global oscillations (acoustic p modes) closely related to the epicyclic oscillations of test particles. Our results are particularly relevant in the context of low‐mass X‐ray binaries and microquasars, and the high‐frequency quasi‐periodic oscillations observed in them. Our computations make use of a smoothed particle hydrodynamics code in azimuthal symmetry, and use a gravitational potential that mimics the effects of strong gravity.

Oscillations of tori in the pseudo-Newtonian potential

“…8. A similar trend was reported by Rubio-Herrera & Lee (2005b), and Blaes et al (2006b), where it has been explored analytically for slightly non-slender Newtonian tori. It is worth mentioning that even when we excite both the epicyclic modes, we do not see any exchange of energy between them (see Fig.…”

Oscillation modes of relativistic slender tori

“…We have presented a rather complete discussion of the oscillation modes of non‐self‐gravitating, relativistic, polytropic tori in an arbitrary axisymmetric space–time with reflection symmetry, in the limit where the tori are very slender. Non‐slender torus oscillation modes can be explored numerically, and some work on this has already been done by Zanotti et al (2005) and Rubio‐Herrera & Lee (2005b). It would also be possible to examine the behavior of modes for thicker tori analytically using perturbative methods, generalizing the technique employed by Blaes (1985).…”

“…For example, Zanotti et al (2005) tried initial radial velocity perturbations, initial density perturbations and perturbations based on the eigenfunctions of the modes of vertically integrated tori. Lee et al (2004) and Rubio‐Herrera & Lee (2005a,b) have also tried periodic external forcing of the inner regions of the torus at a specific frequency.…”

Epicyclic Oscillations of Fluid Bodies: Newtonian Nonslender Torus

“…One possibility is that radial pressure gradients set up fluid tori in the accretion flow which can support discrete, trapped hydrodynamic modes. That oscillations of such tori might be an interesting model for QPOs was first recognized by Rezzolla and his collaborators Rezzolla et al 2003; see also Lee et al 2004;Rubio-Herrera & Lee 2005;Blaes et al 2006). It is not yet clear whether such tori provide a realistic model for the accretion flow in the steep power-law state , where high-frequency QPOs are observed.…”

“…0 z are the radial and vertical epicyclic frequencies for particles, c s0 is the sound speed at the torus center, and the coefficients A r and A z are (not exactly specified) functions of the equation of state and the background gravitational potential. Numerical work by Rubio-Herrera & Lee (2005) revealed that A r > 0 and A z > 0. In this paper we analytically calculate explicit forms of A r and A z .…”