Excitation of Trapped g-Mode Oscillations in Warped Disks around Black Holes

Abstract

In order to study the origin of high-frequency quasi-periodic oscillations observed in X-ray binaries, Kato (2004) suggested a resonant excitation mechanism of disk oscillations in deformed disks. In this paper, we investigate numerically, following his formulation, whether trapped g-mode oscillations in a warped disk, where the warp amplitude varies with radius, can be excited by this mechanism. For simplicity, we adopt Newtonian hydrodynamic equations with relativistic expressions for the characteristic frequencies of disks. We also assume that the accretion disk is isothermal. We find that the fundamental modes of trapped g-mode oscillations with eigenfrequencies close to the maximum of epycyclic frequency are excited. The intermediate oscillations found are isolated in a narrow region around the resonance radius. After varying some parameters, we find that the growth rate increases as the warp amplitude or the black hole spin parameter increases, while it decreases as the sound speed increases.

HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. I. Hydrodynamic simulations

“…1) might avoid this damping, but would then have frequencies too high to explain HFQPOs in systems containing black holes with any non-negligible spin angular momentum (Wagoner 2012). On the other hand, lower frequency nonaxisymmetric r-modes lying within their corotation radius do play an ancillary role in the excitation mechanism for m = 0 r-modes considered in this paper (Kato 2004(Kato , 2008Ferreira & Ogilvie 2008;Oktariani et al 2010).…”

Resonant Excitation of Disk Oscillations in Deformed Disks. V. Effects of Dissipative Process

“…Related to this subject, Kato (2004Kato ( , 2008a suggested that a pair of positive-and negative-energy oscillations can be excited in deformed (warped or eccentric) disks by their resonant interaction through disk deformation. The presence of this excitation mechanism seems to be confirmed by numerical calculations (Ferreira and Ogilvie 2008;Oktariani et al 2010) and by analytical examinations (Kato et al 2011) made by a different method from Kato's original one.…”

Resonant Excitation of Disk Oscillations in Deformed Disks IV: A New Formulation Studying Stability

“…Finally, as an application of the present resonant excitation process of oscillations, we briefly note Kato's model of high-frequency twin QPOs (e.g., Kato and Fukue 2006). In this model the lower-frequency QPO of the twin is related to the set of g-mode and p-mode os-cillations considered numerically by Ferreira and Ogilvie (2008) and Oktariani et al (2010). The higher-frequency QPO of the twin is considered to be the set of one-armed g-mode and two-armed p-mode oscillations [see for details figures 1 to 3 of Kato (2008a)].…”

“…First, let us describe, in terms of the present formulation, the g-and p-modes resonant instability that was numerically studied by Ferreira and Ogilvie (2008) and Oktariani et al (2010). They considered the resonant interaction, through a standing warp (ω D = 0), between i) the axisymmetric g-mode oscillation whose ξ r has one node in the vertical direction and ii) the one-armed p-mode oscillation whose ξ r has no node in the vertical direction.…”