We collect the data of twin kilohertz quasi-periodic oscillations (kHz QPOs) published before 2012 from 26 neutron star (NS) low-mass X-ray binary (LMXB) sources, then we analyze the centroid frequency (ν) distribution of twin kHz QPOs (lower frequency ν1 and upper frequency ν2) both for Atoll and Z sources. For the data without shift-and-add, we find that Atoll and Z sources show the different distributions of ν1, ν2 and ν2/ν1, but the same distribution of ∆ν (difference of twin kHz QPOs), which indicates that twin kHz QPOs may share the common properties of LXMBs and have the same physical origins. The distribution of ∆ν is quite different from constant value, so is ν2/ν1 from constant ratio. The weighted mean values and maxima of ν1 and ν2 in Atoll sources are slightly higher than those in Z sources. We also find that shift-and-add technique can reconstruct the distribution of ν1 and ∆ν. The K-S test results of ν1 and ∆ν between Atoll and Z sources from data with shift-and-add are quite different from those without it, and we think that this may be caused by the selection biases of the sample. We also study the properties of the quality factor (Q) and the root-mean-squared (rms) amplitude of 4U 0614+09 with the data from the two observational methods, but the errors are too big to make a robust conclusion. The NS spin frequency (νs) distribution of 28 NS-LMXBs show a bigger mean value (∼ 408 Hz) than that (∼ 281 Hz) of the radio binary millisecond pulsars (MSPs), which may be due to the lack of the spin detections from Z sources (systematically lower than 281 Hz). Furthermore, on the relations between the kHz QPOs and NS spin frequency νs, we find the approximate correlations of the mean values of ∆ν with NS spin and its half, respectively.

We test the relativistic precession model (RPM) and the MHD Alfvén wave oscillation model (AWOM) for the kHz QPOs by the sources with measured NS masses and twin kHz QPO frequencies. For RPM, the derived NS mass of Cyg X-2 (SAX J1808.4-3658 and 4U 1820-30) is 1.96 ± 0.10 M ⊙ (2.83 ± 0.04 M ⊙ and 1.85 ± 0.02 M ⊙ ), which is ∼ 30% (100% and 40%) higher than the measured result 1.5 ± 0.3 M ⊙ (< 1.4 M ⊙ and 1.29 +0.19 −0.07 M ⊙ ). For AWOM, where the free parameter of model is the density of star, we infer the NS radii to be around 10 ∼ 20 km for the above three sources, based on which we can infer the matter compositions inside NSs with the help of the equations of state (EOSs). In particular, for SAX J1808.4-3658, AWOM shows a lower mass density of its NS than those of the other known kHz QPO sources, with the radius range of 17 − 20 km, which excludes the strange quark matter inside its star.

No abstract