Excitation of g-Mode Oscillations on Relativistic Disks by Parametric Resonances with a Warp

Excitations by parametric resonances of axisymmetric ($m=0$) and one-armed ($m=1$) $g$-mode oscillations on the innermost region of geometrically thin, relativistic disks are examined. As a deformation of the unperturbed disks from an axisymmetric steady state, which is necessary for the operation of parametric resonances, we assume a long-living warp. Analyses are made under the approximations that the oscillations are local in the radial direction in the sense that their radial wavelength is short compared with a radial characteristic length of the disk, but long compared with the disk thickness. The results show that $g$-mode oscillations are amplified by coupling with the warp through an intermediate state, which is higher harmonics in the vertical direction. The oscillations amplified have some particular frequencies. The frequency ratio of two typical oscillations is $\sim \sqrt{2}$, which is close to $3:2$ observed as twin kHz quasi-periodic oscillations in some X-ray binaries.