Abstract 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 ~ 5000–10 000 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.

Keywords binaries: close — stars: neutron — X-rays: binaries

null