We studied the correlations between spin frequencies and kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low mass X-ray binaries. The updated data of kHz QPOs and spin frequencies are statistically analyzed. We found that when two si
multaneous kHz QPOs are present in the power spectrum, the minimum frequency of upper kHz QPO is at least 1.3 times larger than the spin frequency, i.e. u_{s}< u_{2min}/1.3. We also found that the average kHz QPO peak separation in 6 Atoll sources anti-correlates with the spin frequency in the form landnran = -(0.19pm0.05) s+(389.40pm21.67)Hz. If we shifted this correlation in the direction of the peak separation by a factor of 1.5, this correlation matches the data points of the two accretion powered millisecond X-ray pulsars, SAX J1808.4-3658 and XTE J1807-294.
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, indi
vidually, 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.
