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., Δω = ω_h - ω_K has been studied extensively. The idea that Δω 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 Δω when ω_h and ω_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, ω_h and the assumed Keplerian frequency ω_K hold an upper hybrid frequency relation: ω_h² - ω_K² = 4Ω², where Ω 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 Ω = Ω₀ = const. is a good first order approximation. Within the second-order approximation, the slow variation of Ω as a function of ω_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 Ω not aligned with the normal of the disk: ω_L/2π = (Ω/π)(ω_K/ω_h) sin δ, where δ is the angle between Ω and the vector normal to the disk.