It is generally expected that in a deformed disk, disk oscillations can have a resonant coupling with the disk through non-linear interaction with the deformation,
when certain conditions are satisfied.
If the conditions are satisfied, the disk oscillations are amplified or dampened, depending on characteristics of
the non-linear interactions.
As disk deformation we consider a warp or an eccentric
deformation symmetric with respect to the equator.
There are two kinds of resonance.
One is resonance through horizontal motions (hereafter we call it horizontal resonance),
and the other is resonance through vertical motions (vertical resonance).
We derive conditions of resonance and of resonant excitation of oscillations in the case where the disks
are geometrically thin and relativistic.
The results show that inertial-acoustic oscillations
and g-mode oscillations are excited by the horizontal resonance.
Excited oscillations are described on the so-called propagation diagram of oscillations.
If oscillations are localized around the boundaries of the
propagation region (where the group velocity of oscillations vanishes and we can expect that oscillations
have large amplitude there),
the resonance occurs at 4r_g ( r_g being the Schwarzschild
radius), and the frequencies of resonant oscillations
are mΩ±κ at the resonant radius, where m (=1, 2, 3,…)
is the azimuthal wavenumber of excited oscillations.
Applications of the disk oscillation model to high frequency quasi-periodic oscillations (HF QPOs)
observed in low-mass X-ray binaries are discussed.
Comparison of observations and the disk oscillation model shows that some characteristics of observed QPOs can
be well described by the model by assuming that the
deformation has precession.
However, there are important characteristics that cannot be described yet by the model, e.g., correlations with
low frequency QPOs.
These problems will be also discussed in the workshop. |