We test the relativistic precession model (RPM) and the MHD Alfven 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 18
20-30) is 1.96 +/- 0.10 solar masses (2.83 +/- 0.04 solar masses and 1.85 +/- 0.02 solar masses), which is 30% (100% and 40%) higher than the measured result 1.5 +/- 0.3 solar masses (< 1.4 solar masses and 1.29 + 0.19 / - 0.07 solar masses). 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.
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 ( u) distribution of twin kHz QPOs (lower freque
ncy u_1 and upper frequency u_2) 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 u_1, u_2 and u_2/ u_1, but the same distribution of Delta u (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 Delta u is quite different from constant value, so is u_2/ u_1 from constant ratio. The weighted mean values and maxima of u_1 and u_2 in Atoll sources are slightly higher than those in Z sources. We also find that shift-and-add technique can reconstruct the distribution of u_1 and Delta u. The K-S test results of u_1 and Delta u 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 ( u_s) distribution of 28 NS-LMXBs show a bigger mean value (about 408Hz) than that (about 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 u_s, we find the approximate correlations of the mean values of Delta u with NS spin and its half, respectively.
{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.
Based the Alfven wave oscillation model (AWOM) and relativistic precession model (RPM) for twin kHz QPOs, we estimate the emission positions of most detected kHz QPOs to be at r=18+-3 km (R/15km) except Cir X-1 at r = 30+-5 km (R/15km). For the propo
sed Keplerian frequency as an upper limit to kHz QPO, the spin effects in Kerr Spacetime are discussed, which have about a 5% (2%) modification for that of the Schwarzchild case for the spin frequency of 1000 (400) Hz.The application to the four typical QPO sources, Cir X-1, Sco X-1, SAX J1808.4-3658 and XTE 1807-294, is mentioned.
The evolution of the magnetic field of an accreting magnetic white dwarf with an initially dipolar field at the surface has been studied for non-spherical accretion under simplifying assumptions. Accretion on to the polar regions tends to advect the
field toward the stellar equator which is then buried. This tendency is countered by Ohmic diffusion and magneto-hydrodynamic instabilities. It is argued that if matter is accreted at a rate of $dot{M}_{rm crit} sim 10^{16}$ g s$^{-1}$ and the total mass accreted exceeds a critical value $Delta M_{rm crit} sim 0.1-0.2ms$, the field may be expected to be restructured, and the polar field to be reduced} reaching a minimum value of $sim 10^3$ G (the bottom field) independently of the initial field strength. Below this critical accretion rate, the field diffuses faster than it can be advected, and accretion has little effect on field strength and structure.
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.
