We take the recently published data of twin kHz quasi-period oscillations (QPOs) in neutron star (NS) lowmass X-ray binaries (LMXBs) as the samples, and investigate the morphology of the samples, which focuses on the quality factor, peak frequency of
kHz QPOs, and try to infer their physical mechanism. We notice that: (1) The quality factors of upper kHz QPOs are low (2 ~ 20 in general) and increase with the kHz QPO peak frequencies for both Z and Atoll sources. (2) The distribution of quality factor versus frequency for the lower kHz QPOs are quite different between Z and Atoll sources. For most Z source samples, the quality factors of lower kHz QPOs are low (usually lower than 15) and rise steadily with the peak frequencies except for Sco X-1, which drop abruptly at the frequency of about 750 Hz. While for most Atoll sources, the quality factors of lower kHz QPOs are very high (from 2 to 200) and usually have a rising part, a maximum and an abrupt drop. (3) There are three Atoll sources (4U 1728-34, 4U 1636-53 and 4U 1608-52) of displaying very high quality factors for lower kHz QPOs. These three sources have been detected with the spin frequencies and sidebands, in which the source with higher spin frequency presents higher quality factor of lower kHz QPOs and lower difference between sideband frequency and lower kHz QPO frequency.
With the possible detection of the fastest spinning nuclear-powered pulsar XTE J1739-285 of frequency 1122 Hz (0.8913 ms), it arouses us to constrain the mass and radius of its central compact object and to imply the stellar matter compositions: neut
rons or quarks. Spun-up by the accreting materials to such a high rotating speed, the compact star should have either a small radius or short innermost stable circular orbit. By the empirical relation between the upper kHz quasi-periodic oscillation frequency and star spin frequency, a strong constraint on mass and radius is obtained as 1.51 solar masses and 10.9 km, which excludes most equations of states (EOSs) of normal neutrons and strongly hints the star promisingly to be a strange quark star. Furthermore, the star magnetic field is estimated to be about $4times10^{7} (G) < B < 10^{9} (G) $, which reconciles with those of millisecond radio pulsars, revealing the clues of the evolution linkage of two types of astrophysical objects.
