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 M . 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 M and M = 1.37 ± 0.23 M . In the framework of the pulsar recycling hypothesis, this suggests that an accretion of approximately ∼0.2 M is sufficient to spin up a neutron star and place it in the millisecond pulsar group. Based on these estimates, an approximate empirical relation between the accreting mass (ΔM) of recycled pulsar and its spin period is proposed as ΔM = 0.43 (M )(P/1 ms) −2/3 . If we focus only on the DNS, the mass average of all 18 DNSs is 1.32 ± 0.14 M , and the mass averages of the recycled DNSs and the non-recycled NS companions are, respectively, 1.38 ± 0.12 M and 1.25 ± 0.13 M . This is consistent with the hypothesis that the masses of both NSs in DNS system have been affected by accretion. The mass average of MSPs is higher than the Chandrasekhar limit 1.44 M , which may imply that most of binary MSPs form via the standard scenario by accretion recycling. If we were to assume that the mass of a MSP formed by the accretion induced collapse (AIC) of a white dwarf must be less than 1.35 M , then the portion of the binary MSPs involved in the AICs would not be higher than 20%, which imposes a constraint on the AIC origin of MSPs. With accreting mass from the companion, the nuclear matter composition of MSP may experience a transition from the "soft" equation of state (EOS) to a "stiff" EOS or even neutron to quark matter.

We analyzed the recently published kHz quasi‐period oscillaiton (QPO) data in the neutron star low‐mass X‐ray binaries (LMXBs), in order to investigate the different correlations of the twin‐peak kHz QPOs in bright Z sources and in the less luminous Atoll sources. We find a power‐law relation ν1∼νb2 between the upper and the lower kHz QPOs with different indices: b≃ 1.5 for the Atoll source 4U 1728‐34 and b≃ 1.9 for the Z source Sco X‐1. The implications of our results for the theoretical models for kHz QPOs are discussed.

Aims. We studied the correlations between spin frequencies and kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low-mass X-ray binaries. Methods. The updated data on kHz QPOs and spin frequencies are statistically analyzed. Results. We find that when two simultaneous kHz QPOs are present in the power spectrum, the minimum frequency of upper kHz QPO is at least 1.3 times higher than the spin frequency, i.e. ν s < ν 2 min /1.3. We also find that the average kHz QPO peak separation in 6 Atoll sources anti-correlates with the spin frequency in the form ∆ν = −(0.19 ± 0.05)ν s + (389.40 ± 21.67)Hz. If we shift this correlation in the direction of the peak separation by a factor of 1.5, this correlation matches the data points of the two accretionpowered millisecond X-ray pulsars, SAX J1808.4-3658 and XTE J1807-294.