Kilohertz quasi-periodic oscillations as probes of the X-ray color-color diagram and neutron star accretion-disk structure for Z sources

Based on the detected kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low-mass X-ray binaries (NS-LMXBs), we investigate the evolution of the NS magnetosphere-disk structure along the Z track in the X-ray color-color diagram (CCD) for luminous Z sources, such as Cyg X-2, GX 5-1, GX 17+2, and Sco X-1. We find that the magnetosphere-disk radius r inferred by kHz QPOs for all the sources shows a monotonically decreasing trend along the Z track from the horizontal branch (HB) to the normal branch (NB), implying that the dominated radiation components may dramatically change as the accretion disk moves toward the NS surface. In addition, the specific radius that corresponds to the HB/NB vertex is found to be around r  ∼ 20 km, implying a potential characteristic position of transiting for the X-ray radiation mode. Furthermore, we find that the NBs that occur near the NS surface have a radius of r  ∼ 16−20 km, which is systematically smaller than those of HBs that have radii of r  ∼ 20−29 km. To interpret the relation between the CCD properties and the special magnetosphere-disk radii of Z sources, we suggest that the magnetic field lines corresponding to NB are “frozen-in” to the plasma, and move further inward with the shrinking of the NS magnetosphere-disk radius and pile up near the NS surface. They then form a strong magnetic field region around r  ∼ 16−20 km, where the high magnetic energy density and high plasma mass density may dominate the radiation process in NB.