LAUSR

Parallel tracks in the relation between the lower kilohertz quasi-periodic oscillation (kHz QPO) frequency ν1 and the X-ray intensity I have been observed in the neutron star low-mass X-ray binary (NS-LMXB) 4U 1728−34, and we try to ascribe these phenomena to the bimodal accretion modes, i.e. the disc accretion and radial accretion. For the source with one constant radial accretion rate $\dot{M}_{\rm r}$, as the increase of the disc accretion rate $\dot{M}_{\rm d}$, the NS magnetosphere-disc radius can shrink from ∼18 to ∼16 km, while ν1 increases from ∼670 to ∼870 Hz. Then, due to the increase of the kHz QPO frequency and total X-ray intensity Itot, the source will trace out an oblique track in ν1–I relation. While, if the source enters another constant radial accretion rate due to the variation of the accretion environment, the increase of the disc accretion rate can arise another parallel track in ν1–I relation. Finally, the reliability of the theoretical assumptions, the variability of the accretion radius and accretion rate, as well as the dependence of the two accretion modes, are also investigated and discussed.