A possible explanation of the parallel tracks in kilohertz quasi-periodic oscillations from low-mass-X-ray binaries

We recalculate the modes of the magnetohydrodynamics (MHD) waves in the MHD model (Shi, Zhang & Li 2014) of the kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low mass X-ray binaries (NS-LMXBs), in which the compressed magnetosphere is considered. A method on pointby- point scanning for every parameter of a normal LMXBs is proposed to determine the wave number in a NS-LMXB. The dependence of the twin kHz QPO frequencies on accretion rates ( DOt(M) ) is obtained with the wave number and magnetic field (B?) determined by our method. Based on the MHD model, a new explanation of the parallel tracks, i.e. the slowly varying effective magnetic field leads to the shift of parallel tracks in a source, is presented. In this study, we obtain a simple power-law relation between the kHz QPO frequencies and Dot(M) /B^2 ? in those sources. Finally, we study the dependence of kHz quasi-periodic oscillation frequencies on the spin, mass and radius of a neutron star. We find that the effective magnetic field, the spin, mass and radius of a neutron star lead to the parallel tracks in different sources.