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.