A population synthesis study of low-mass X-ray binary systems

The origin of low-mass X-ray binary systems from the helium star-main-sequence binary remnants of a common-envelope phase is studied. Using a statistical Monte Carlo approach, the evolution of an initial distribution of zero-age binaries is followed from the main sequence through a phase of common-envelope evolution and subsequent supernova explosion of the helium star. The resultant population of low-mass main-sequence stars (≾3 M⊙) with a neutron star companion is studied as a function of the kick velocity associated with the possible asymmetry of the supernova explosion, the efficiency of mass ejection during the common-envelope phase, the minimum mass for evolution to a neutron star and the mass distribution of the secondary components in the system. A comparison of the results with the observed low-mass X-ray binary system population suggests that kick velocities are required. For an average kick velocity of ∼450 km s−1, as inferred from the radio pulsar distribution, birth rates in the range ∼3 × 10−6-10−5 yr−1 are indicated for efficiencies of the mass ejection process during the common-envelope phase of 0.25–1. The implications of the results for the general population of low-mass X-ray binaries, and for the formation of Her X-l type systems and long-period detached systems similar to PSR 1820 —11, are briefly discussed.