Timing spectroscopy of quasi-periodic oscillations in the low-mass X-ray neutron star binaries

Precise simultaneous measurements of the frequencies of the two kilohertz q uasi-periodic oscillations (referred in the literature as upper and lower k Hz QPOs) cast doubts on the validity of the simple beat-frequency interpret ation and some of the modifications introduced to explain the results of th e varying frequency difference. A new model explains the variation of the f requency difference, suggesting that the upper Wt QPO, namely v(h), is an u pper hybrid frequency of the Keplerian oscillator under the influence of th e Coriolis force and the lower kHz QPO is the Keplerian frequency v(K). Suc h an oscillator has two branches characterized by a high frequency v(h) (si milar to 1 kHz) and by a low frequency v(L) (similar to 50 Hz). The frequen cy v(L) depends strongly on the angle delta between the normal to the neutr on star disk and Omega-the angular velocity of the magnetosphere surroundin g the neutron star In the lower part of the QPO spectrum (similar to 10 Hz) , this model identifies the frequency of radial viscous oscillations v(V) ( previously called ''extra noise component") and the break frequency v(b), w hich is associated with the diffusive process in the transition region (the innermost part of the disk). According to this model, all frequencies (nam ely v(h), y(L), y(b), and v(V)) have specific dependences on v,. This Lette r focuses on the verification of the predicted relations. For the source 4U 1728-34, the best theoretical fit is obtained for delta = 8 degrees.3 +/- 1 degrees.0, which is slightly larger than the value of delta = 5 degrees.5 +/- 0 degrees.5 previously found for Scorpius X-1. In addition, we show th at the theoretically derived power-law relation v(b) proportional to v(V)(1 .61) is consistent with the recent observations of other atoll and Z-source s.