Mechanisms for high-frequency quasi-periodic oscillations in neutron star and black hole binaries

We explain the millisecond variability detected by Rossi X-Ray Timing Explorer (RXTE) in the X-ray emission from a number of low-mass X-ray binary systems (Sco X-1, 4U 1728-34, 4U 1608-522, 4U 1636-536, 4U 0614+091, 4U 1735-44, 4U 1820-30, GX 5-1) in terms of dynamics of the centrifugal barrier, a hot boundary region surrounding a neutron star (NS). We demonstrate that this region may experience the relaxation oscillations and that the displacements of a gas element both in radial and vertical directions occur at the same main frequency, of order of the local Keplerian frequency. We show the importance of the effect of a splitting of the main frequency produced by the Coriolis force in a rotating disk for the interpretation of a spacing between the quasi-periodic oscillation (QPO) peaks. We estimate a magnitude of the splitting effect and present a simple formula for the whole spectrum of the split frequencies. It is interesting that the first three lowest order overtones (corresponding to the azimuthal numbers m = 0, -1, and -2) fall in the range of 200-1200 Hz and match the kHz QPO frequencies observed by RXTE. Similar phenomena should also occur in black hole (BH) systems, but, since the QPO frequency is inversely proportional to the mass of a compact object, the frequency of the centrifugal-barrier oscillations in the BH systems should be a factor of 5-10 lower than that for the NS systems. The X-ray spectrum formed in this region is a result of upscattering of a soft radiation (from a disk and an NS surface) off relatively hot electrons in the boundary layer. The typical size of the emission region should be 1-3 km, which is consistent with the time-lag measurements. We also briefly discuss some alternative QPO models, including the possibility of acoustic oscillations in the boundary layer, the proper stellar rotation, and g-mode disk oscillations.