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By statistically analyzing the masses of twelve double neutron star (DNS) systems, it is concluded that the weighted mean value of DNS masses is (1.339±0.042) M⊙, where the weighted mean masses of the primary and companion stars are respectively (1.439±0.036) M⊙ and (1.239±0.020) M⊙. The mean value of the masses of primary stars is higher than that of companion stars, which indicates that the primary star may increase its mass by accretion, or the mass of its progenitor star is higher. Therefore, the physical process of supernova explosion through which the high-mass stars become NSs can be investigated hereby. Also it is found that the total masses of the DNSs span a narrow range of 2.5∼2.8 M⊙, implying that the companion stars might impact on the mass formation of DNSs. Moreover, the mass ratios of the DNSs (primaries to companions) approximate 1 (slightly larger than 1), indicating that the masses of the progenitors of primary stars are approximately equal to the masses of the progenitors of companion stars. By analyzing the distribution of the 12 DNSs in the surface magnetic field strength versus spin period (B-Ps) diagram, it is found that the surface magnetic field strength in the primary stars of the DNSs is ∼ 1010 Gs, and the spin period is ∼ 50 ms; while the two pulsars, i.e. PSR J1906+0746 and PSR J0737-3039B, are located in the region of normal pulsars in the B-Ps diagram, their surface magnetic field strength is ∼ 1012 Gs, suggesting that they might not be accelerated through accretion.

Pulsars posses extremely strong magnetic fields, and their magnetic axis does not coincide with their rotation axis, this causes the pulsars to emit electromagnetic radiations. Pulsars rely on their rotational energy to compensate for the energy loss caused by the electromagnetic radiation, which leads to the gradually decelerated spin of pulsars. According to the theoretical deduction, we have calculated the initial period of the Crab Nebula pulsar, and derived the period evolution of the pulsar at any time in the future under the effect of the electromagnetic radiation. Considered the possible existence of quadrupole moment in the mass distribution of a pulsar, the gravitational wave radiation will also make the pulsar spin down, hence the variation of spin period of the Crab pulsar under the effect of gravitational wave radiation is further analyzed. Finally, combining the two kinds of radiation mechanisms, the evolution of spin period of the Crab pulsar under the joint action of these two kinds of radiation mechanisms is analyzed.

By reviewing the methods of mass measurements of neutron stars in four different kinds of systems, i.e., the high-mass X-ray binaries (HMXBs), low-mass X-ray binaries (LMXBs), double neutron star systems (DNSs) and neutron star-white dwarf (NS-WD) binary systems, we have collected the orbital parameters of 40 systems. By using the boot-strap method and the Monte-Carlo method, we have rebuilt the likelihood probability curves of the measured masses of 46 neutron stars. The statistical analysis of the simulation results shows that the masses of neutron stars in the X-ray neutron star systems and those in the radio pulsar systems exhibit different distributions. Besides, the Bayes statistics of these four different kind systems yields the most-probable probability density distributions of these four kind systems to be (1.340 ± 0.230)M8, (1, 505 ± 0.125)M8,(1.335 ± 0.055)M8 and (1.495 ± 0.225)M8, respectively. It is noteworthy that the masses of neutron stars in the HMXB and DNS systems are smaller than those in the other two kind systems by approximately 0.16M8. This result is consistent with the theoretical model of the pulsar to be accelerated to the millisecond order of magnitude via accretion of approximately 0.2M8. If the HMXBs and LMXBs are respectively taken to be the precursors of the BNS and NS-WD systems, then the influence of the accretion effect on the masses of neutron stars in the HMXB systems should be exceedingly small. Their mass distributions should be very close to the initial one during the formation of neutron stars. As for the LMXB and NS-WD systems, they should have already under- gone the process of suffcient accretion, hence there arises rather large deviation from the initial mass distribution.

We analyzed 186 binary pulsars (BPSRs) in the magnetic field versus spin period (B-P) diagram, where their relations to the millisecond pulsars (MSPs) can be clearly shown. Generally, both BPSRs and MSPs are believed to be recycled and spun-up in binary accreting phases, and evolved below the spin-up line setting by the Eddington accretion rate ($\dot{M}{\bf \simeq}10^{18} g/s$). It is noticed that most BPSRs are distributed around the spin-up line with mass accretion rate $\dot{M}=10^{16} g/s$ and almost all MSP samples lie above the spin-up line with $\dot{M}\sim10^{15} g/s$. Thus, we calculate that a minimum accretion rate ($\dot{M}\sim 10^{15} g/s$) is required for the MSP formation, and physical reasons for this are proposed. In the B-P diagram, the positions of BPSRs and their relations to the binary parameters, such as the companion mass, orbital period and eccentricity, are illustrated and discussed. In addition, for the seven BPSRs located above the limit spin-up line, possible causes are suggested., Comment: 8 pages,6figures, 1 table; accepted for publication in Astrophysics and Space Science