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We recalculate the modes of the magnetohydrodynamics (MHD) waves in the MHDmodel (Shi, Zhang & Li 2014) of the kilohertz quasi-periodic oscillations (kHzQPOs) in neutron star low mass X-ray binaries (NS-LMXBs), in which thecompressed magnetosphere is considered. A method on pointby- point scanning forevery parameter of a normal LMXBs is proposed to determine the wave number in aNS-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 byour 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 paralleltracks in a source, is presented. In this study, we obtain a simple power-lawrelation between the kHz QPO frequencies and Dot(M) /B^2 ? in those sources.Finally, we study the dependence of kHz quasi-periodic oscillation frequencieson the spin, mass and radius of a neutron star. We find that the effectivemagnetic field, the spin, mass and radius of a neutron star lead to theparallel tracks in different sources.

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