We consider the situation where a spin-induced wavy perturbation is present on disks of neutron-star low-mass X-ray binaries. By non-linearly coupling with the perturbation, some modes of disk oscillations resonantly interact with the disks. We examine the resonant conditions under the assumption that the disks are vertically isothermal. The results show that when the spin frequency has some particular values, resonant coupling occurs at some radii. The modes and frequencies of these resonant oscillations are summarized. Some of these resonant oscillations seem to explain the frequencies of the observed kHz QPOs in objects of which the spin frequency is known.1 In a series of papers (Kato 2003(Kato , 2004a(Kato ,b, 2005a, we proposed the idea that the cause of kHz QPOs are related to disk deformation by a warp. In this model, the presence of disk deformation by a warp is the cause of kHz QPOs, leading to resonant interactions between disk oscillations and the deformed disks at some particular radii. The resonance conditions due to these resonant processes are examined in detail (Kato 2004a(Kato , 2005a. Whether the oscillations are really spontaneously excited by the resonances is also examined (Kato 2004b). Based on these studies, we proposed a unified model of QPOs (Kato 2005a,b). That is, kHz QPOs in neutron-star X-ray binaries and high-frequency QPOs in black-hole X-ray binaries come from the same mechanism and are explained as resonant oscillations in warped disks.In the above-mentioned resonance model in warped disks, the spin of the central neutron star has no part. In real disks, however, the presence of spin-induced perturbations is expected on disks in addition to warps. A disk deformed by a spin-induced perturbation is similar to the disk deformed by a warp in our present problem. Hence, we can expect resonant interactions between disk oscillations and spin-induced deformed disks by the same mechanism as in the case of warped disks. In this paper, we examine this issue. The main interest is to derive relations between the frequencies of the resonant oscillations and the spin frequency, and examine whether there are cases where the frequency difference of the resonant oscillations is close to the spin frequency, or half of it. Finally, by applying our present model, we estimate the masses of X-ray sources whose spins as well as QPOs are known.
Spin-Induced Oscillations by the Star-Disk InteractionLet us assume a non-axisymmetric perturbation (such as a burst) on the surface of a spinning neutron-star. Since the central star and the surrounding disk are dynamically coupled by a magnetic field, or radiative processes, a perturbation rotating with the same spin frequency as the central star, say ω s , is imposed on the disk with various azimuthal wavenumber, m s , and vertical wavenumber, n s . Except for the inner transition zone of the disk, and except for the initial epoch of the perturbations, eigen-mode oscillations with (ω s , m s , n s ) remain on the disk. Without loss of any generality, we hereaf...