2023MNRAS.520.1339W

We employ the bimodal luminosity components, i.e. the disc luminosity L_d and non-disc luminosity L_r, to interpret the parallel track phenomena in the relation between the kilohertz quasi-periodic oscillation (kHz QPO) frequency ν and X-ray luminosity L_X observed in the neutron star low-mass X-ray binaries: For an individual source with a constant non-disc luminosity L_r, the increase of its disc accretion rate $\dot{M}_{\rm d}$ can arise the shrink of neutron star magnetosphere-disc radius that results in the increase of the kHz QPO frequency. Then, with the enhancements of both the kHz QPO frequency and total X-ray luminosity, L_X = L_d + L_r, the source will trace out an oblique track in ν-L_X relation. Furthermore, for the different sources with various constant non-disc luminosities, they trace out series of parallel tracks in ν-L_X relation. Our model presents an approximate power-law relation between the upper kHz QPO frequency ν₂ and L_X (i.e. $\nu _2\sim L_{\rm X}^k$), where the power-law index k decreases with the ratio parameter of $\mathcal {R}\equiv L_{\rm d}/L_{\rm r}$. Moreover, the fittings of $\nu _2{\!-\!}L_{\rm X}^k$ relation with the observation data indicate a range of ∼0.1-2.7 for the k values, which is basically compatible with the model prediction. In addition, we discussed the physical factors that affect the validity of the model.