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, 4U1728-34, 4U1608-522, 4U1636-536, 4U0614+091, 4U1735-44, 4U1820-30, GX5-1 and etc) 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 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 a 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 a possibility of acoustic oscillations in the boundary layer, the proper stellar rotation, and g-mode disk oscillations.

We present results of RXTE observations of the low-mass X-ray binary and atoll source 4U 1608−52 made over 9 days during the decline of an X-ray intensity outburst in March 1996. A fast-timing analysis shows a strong and narrow quasi periodic oscillation (QPO) peak at frequencies between 850 and 890 Hz on March 3 and 6, and a broad peak around 690 Hz on March 9.Observations on March 12 show no significant signal. On March 3, the X-ray spectrum of the QPO is quite hard; its strength increases steadily from 5 % at ∼2 to ∼20 % at ∼12 keV. The QPO frequency varies between 850 and 890 Hz on that day, and the peak widens and its rms decreases with centroid frequency in a way very similar to the well-known horizontal branch oscillations (HBO) in Z-sources. We apply the HBO beat frequency model to atoll sources, and suggest that, whereas the model could produce QPOs at the observed frequencies, the lack of correlation we observe between QPO properties and X-ray count rate is hard to reconcile with this model. Subject headings: stars: individual (4U 1608−52) -stars: neutron -accretion, accretion disks However, in spite of these arguments, the absence of a correlation between X-ray intensity on the one hand and QPO frequency and rms amplitude on the other hand poses a major problem for a beat frequency model interpretation. The QPO frequency remains constant near 850 Hz between 3 and 6 March while the count rate drops by more than a factor 4, from ∼3200 to ∼600 counts/sec (Sect. 2). The beat frequency model predicts that if the QPO frequency remains constant, the mass flow through the inner edge of the disk should remain constant as well. Our data therefore are inconsistent with a beat frequency model interpretation if all accretion takes place via the inner edge of the disk. We note that the presence of a hypothetical additional (non-disk) mass flow component contributing more than 75% of the total flux on March 3 and much weaker on March 6 can not easily resolve this discrepancy. The rms amplitude of the QPO only increases by a factor 2 from March 3 to 6 while the X-ray intensity drops by a factor of more than 4, whereas a similar fractional change would be predicted in this explanation. Only by invoking rather large and entirely ad-hoc changes in the beaming or bolometric correction could the model be maintained. The 150 Hz drop in QPO from March 6 to March 9 without a change in count rate presents similar difficulties. Further observations of 4U 1608−52 during other outbursts, and study of its X-ray bursts are required to shed further light on the relation of the 800 Hz QPO in 4U 1608−52 with those in 4U 1728−34, and with the QPO in Sco X-1. Sztajno M. 1985, Nature 316, 225 van der Klis M., 1989. NATO ASI C262: Timing Neutron Stars,Ögelman and van den Heuvel (eds.), Kluwer, p. 27. van der Klis M. 1995, in X-ray Binaries, Van Paradijs and Van den Heuvel (eds.), Cambridge University Press, p. 252.

We present a study of 581 Hz oscillations observed during a thermonuclear X-ray burst from the low mass X-ray binary (LMXB) 4U 1636-54 with the Rossi X-ray Timing Explorer (RXTE). This is the first X-ray burst to exhibit both millisecond oscillations during the rising phase as well as photospheric radius expansion. We measure an oscillation amplitude within 0.1 s of the onset of this burst of 75 ± 17%, that is, almost the entire thermal burst flux is modulated near onset. The spectral evolution during the rising phase of this burst suggests that the X-ray emitting area on the neutron star was increasing, similar to the behavior of bursts from 4U 1728-34 with 363 Hz oscillations reported recently. We argue that the combination of large pulsed amplitudes near burst onset and the spectral evidence for localized emission during the rise strongly supports rotational modulation as the mechanism for the oscillations. We discuss how theoretical interpretation of spin modulation amplitudes, pulse profiles and pulse phase spectroscopy can provide constraints on the masses and radii of neutron stars. We also discuss the implications of these findings for the beat frequency models of kHz X-ray variability in LMXB.

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