Study on Correlations between the Twin Kilohertz Quasi-periodic Oscillations in Low-mass X-ray Binaries

The recently updated data of the twin kilohertz quasi-periodic oscillations (kHz QPOs) in the neutron star low-mass X-ray binaries are analyzed. The power-law fitting $ u_{1}=a( u_{2}/1000)^{b}$ and linear fitting $ u_{2}=A u_{1}+B$ are applied, individually, to the data points of four Z sources (GX 17+2, GX 340+0, GX 5-1 and Sco X-1) and four Atoll sources (4U 0614+09, 4U 1608-52, 4U 1636-53 and 4U 1728-34). The $chi^{2}$-tests show that the power-law correlation and linear correlation both can fit data well. Moreover, the comparisons between the data and the theoretical models for kHz QPOs are discussed.