Resonant excitation of disk oscillations in deformed disks II: A model of high-frequency QPOs

The amplification of disk oscillations resulting from nonlinear resonant couplings between the oscillations and a disk deformation is examined. The disk is geometrically thin and general relativistic with a non-rotating central source. A Lagrangian formulation is adopted. The author examined the same problem a few years ago, but here we derive a general stability criterion in a more perspective way. Another distinct point from the previous work is that in addition to the case where the deformation is a warp, the case where the deformation is a one-armed pattern symmetric with respect to the equatorial plane is considered. The results obtained show that in addition to the previous results that the inertial-acoustic mode and g-mode oscillations are amplified by horizontal resonance in warped disks, they also amplified by horizontal resonance in disks deformed by one-armed pattern symmetric with respect to the equatorial plane. If we consider local oscillations that are localized around boundaries of their propagation region, the resonance occurs at 4r(g), where r(g) is the Schwarzschild radius. If nonlocal oscillations are considered, frequency ranges of oscillations where oscillations are resonantly amplified are specified.