Population synthesis of ultra-compact X-ray binaries

Ultra-compact X-ray binaries (UCXBs) are very interesting and important objects. By taking the population synthesis approach to the evolution of binaries, we carry out a detailed study of UCXBs. We estimate that there are ∼ 5000–10000 UCXBs in the Galaxy, and their birthrates are ∼ 2.6–7.5 × 10 −4 yr −1 . Most UCXBs are transient X-ray sources, but their X-ray luminosities are much lower than those of persistent sources. Therefore, the majority of observed UCXBs should be persistent sources. About 40%–70% of neutron stars (NSs) in UCXBs form via an accretion-induced collapse from an accreting ONe white dwarf (WD), 1%–10% of NSs in UCXBs form via core-collapse supernovae and others form via the evolution-induced collapse of a naked helium star. About 50%–80% of UCXBs have naked helium star donors, 5%–10% of UCXBs have HeWD donors, 15%–40% of UCXBs have COWD donors and UCXBs with ONeWD donors are negligible. Our investigation indicates that the uncertainty mainly comes from evolution of the common-envelope which develops in these systems.