We have collected the parameter of 38 neutron stars (NSs) in binary systems with spin periods and measured masses. By adopting the Boot-strap method, we reproduced the procedure of mass calculated for each system separately, to determine the truly ma
ss distribution of the NS that obtained from observation. We also applied the Monte-Carlo simulation and introduce the characteristic spin period 20 ms, in order to distinguish between millisecond pulsars (MSPs) and less recycled pulsars. The mass distributions of MSPs and the less recycled pulsars could be fitted by a Gaussian function as $rm 1.45pm0.42 M_{odot}$ and $rm 1.31pm0.17 M_{odot} (rm with ~ 1sigma)$ respectively. As such, the MSP masses are heavier than those in less recycled systems by factor of $rm sim 0.13M_{odot}$, since the accretion effect during the recycling process.
{We investigate the coherence of the twin kilohertz quasi-periodic oscillations (kHz QPOs) in the low-mass X-ray binary (LMXB) theoretically. The profile of upper kHz QPO, interpreted as Keplerian frequency, is ascribed to the radial extent of the kH
z QPO emission region, associated with the transitional layer at the magnetosphere-disk boundary, which corresponds to the coherence of upper kHz QPO. The theoretical model for Q-factor of upper kHz QPO is applied to the observational data of five Atoll and five Z sources, and the consistence is implied.
We investigate the spin-period evolutions of recycled pulsars in binary accreting systems. Taking both the accretion induced field decay and spin-up into consideration, we calculate their spin-period evolutions influenced by the initial magnetic-fiel
d strengths, initial spin-periods and accretion rates, respectively. The results indicate that the minimum spin-period (or maximum spin frequency) of millisecond pulsar (MSP) is independent of the initial conditions and accretion rate when the neutron star (NS) accretes $sim> 0.2ms$. The accretion torque with the fastness parameter and gravitational wave (GW) radiation torque may be responsible for the formation of the minimum spin-period (maximum spin frequency). The fastest spin frequency (716 Hz) of MSP can be inferred to associate with a critical fastness parameter about $omega_{c}=0.55$. Furthermore, the comparisons with the observational data are presented in the field-period ($B-P$) diagram.
We study the statistics of 61 measured masses of neutron stars (NSs) in binary pulsar systems, including 18 double NS (DNS) systems, 26 radio pulsars (10 in our Galaxy) with white dwarf (WD) companions, 3 NSs with main-sequence companions, 13 NSs in
X-ray binaries, and one undetermined system. We derive a mean value of M = 1.46 +/- 0.30 solar masses. When the 46 NSs with measured spin periods are divided into two groups at 20 milliseconds, i.e., the millisecond pulsar (MSP) group and others, we find that their mass averages are, respectively, M=1.57 +/- 0.35 solar masses and M=1.37+/- 0.23 solar masses. In the framework of the pulsar recycling hypothesis, this suggests that an accretion of approximately 0.2 solar mass is sufficient to spin up a neutron star and place it in the millisecond pulsar group. An empirical relation between the accreting mass and MSP spin period is Delta M=0.43 (solar mass)(P/1 ms)^{-2/3}. UNlike the standard recycling process, if a MSP is formed by the accretion induced collapse (AIC) of a white dwarf with a mass less than Chandrasekha limit, e.g. 1.35 solar mass, then the binary MSPs involved in AICs is not be higher than 20%, which imposes a constraint on the AIC origin of MSPs.
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.
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.
