Resonant Excitation of Disk Oscillations by Warps: A Model of kHz QPOs

Abstract

The amplification of disk oscillations resulting from non-linear resonant couplings between the oscillations and a warp is examined. The disks are geometrically thin and general relativistic with non-rotating central objects. By using a Lagrangian formulation, a general stability criterion is derived. The criterion is applied to horizontal and vertical resonances of g-mode oscillations and to horizontal resonances of p-mode oscillations. The results of analyses show that g-mode oscillations (including p-mode oscillations of n = 0) are amplified by horizontal resonances with the warp. Other modes of oscillations with other resonances are all damped by resonances. The amplified g-mode oscillations are located around the radius 4r g , the radius of the epicyclic frequency being maximum, i.e., κ max . The frequencies of amplified oscillations are harmonics of κ max , and well explain the 2 : 3 pairs of observed QPOs for reasonable masses (and spins) of the central objects.

Quasi periodic oscillations in black hole binaries

“…Stuchlik and collaborators proposed a further version of the relativistic precession model, that has been studied in many papers by this group. Here the model is related to the warped-disk oscillations discussed by Kato, 2004a (see below). -The the warped disc model proposed by Kato, 2004a, Kato, 2004b, states that the HFQPOs are resonantly excited by specific disc deformations warps.…”

“…Here the model is related to the warped-disk oscillations discussed by Kato, 2004a (see below). -The the warped disc model proposed by Kato, 2004a, Kato, 2004b, states that the HFQPOs are resonantly excited by specific disc deformations warps. The model was generalized to include precession of the warped disk in Kato, 2005 and spin-induced perturbations were included in Kato, 2005.…”

Models of quasi-periodic oscillations related to mass and spin of the GRO J1655-40 black hole

“…We study the RP model along with its variants and the epicyclic resonance (ER) model and its variants. We extend this selection for the tidal disruption model where the twin HF QPOs are created by inhomogeneities deformed to a ring by tidal forces of the black hole (Čadež et al 2008;Kostić et al 2009), and by the model of warped thin disc oscillations (Kato 2004(Kato , 2008. Frequencies of the twin oscillatory modes used in the twin HF QPO models are given in Table 1. Contrary to the Monte Carlo technique applied in Motta et al (2014a), here we use the frequency ratio technique inspired by the resonance conditions relating the dimensionless black hole spin a to the common dimensionless radius x in the resonance models of the twin HF QPOs (Stuchlík et al , 2013.…”

Weak nonlinear coupling between epicyclic modes in slender tori

“…In the context of QPOs, the resonance effects in thin accretion disk were already studied by Kato (2003Kato ( , 2004Kato ( , 2008. In these models, QPOs are identified with waves (corresponding to either g-mode or p-mode oscillations), parametrically excited by the deformation of the disk (warp or precession).…”