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Population Synthesis of Millisecond X-ray Pulsars

As the evolutionary link between the radio millisecond pulsars (MSPs) and the low mass X-ray binaries or intermediate mass X-ray binaries, the millisecond X-ray pulsars (MSXPs) are important objects in testing theories of pulsar formation and evolution. In general, neutron stars in MSXPs can form via core collapse supernova (CC channel) of massive stars or accretion induced collapse (AIC channel) of an accreting ONeMg WD whose mass reaches the Chandrasekhar limit. Here, in addition to CC and AIC channels we also consider another channel, i.e., evolution induced collapse (EIC channel) of a helium star with mass between $1.4$ and $2.5 M_{\odot}$. Using a population synthesis code, we have studied MSXPs arising from three different evolutionary channels. We find that the Galactic birthrates of transient MSXPs and persistent MSXPs are about 0.7---$1.4\times 10^{-4}$ yr$^{-1}$. Our population synthesis calculations have shown that about 50\%---90\% of the MSXPs have undergone CC channel, about 10\%---40\% of them have undergone EIC channel, and the MSXPs via AIC channel are the least.