Kilohertz Quasi-periodic Oscillations in Neutron Star Binaries Modeled as Keplerian Oscillations in a Rotating Frame of Reference

Since the discovery of kHz quasi-periodic oscillations (QPOs) in neutron star binaries, the difference between peak frequencies of two modes in the upper part of the spectrum, i.e., Deltaomega=omega_h-omega_K has been studied extensively. The idea that Deltaomega is constant and (as a beat frequency) is related to the rotational frequency of the neutron star has been tested previously. The observed decrease of Deltaomega when omega_h and omega_K increase has weakened the beat frequency interpretation. We put forward a different paradigm: a Keplerian oscillator under the influence of the Coriolis force. For such an oscillator, omega_h and the assumed Keplerian frequency omega_K hold an upper hybrid frequency relation: omega^2_h-omega^2_K=4Omega^2, where Omega is the rotational frequency of the star's magnetosphere near the equatorial plane. For three sources (Sco X-1, 4U 1608-52, and 4U 1702-429), we demonstrate that the solid-body rotation Omega=Omega_0=const. is a good first order approximation. Within the second-order approximation, the slow variation of Omega as a function of omega_K reveals the structure of the magnetospheric differential rotation. For Sco X-1, the QPOs have frequencies ~45 and 90 Hz which we interpret as the first and second harmonics of the lower branch of the Keplerian oscillations for the rotator with Omega not aligned with the normal of the disk: omega_L/2pi=(Omega/pi)(omega_K/omega_h)sindelta, where delta is the angle between Omega and the vector normal to the disk.