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We study the formation of low-mass X-ray binaries (LMXBs) through helium star supernovae in binary systems that have each emerged from a common-envelope phase. LMXB progenitors must satisfy a large number of evolutionary and structural constraints, which imposed under the assumption of a symmetric supernova explosion, prohibit the formation of short-period LMXBs transferring mass at sub-Eddington rates through any channel in which the intermediate progenitor of the neutron star is not completely degenerate. Barring accretion-induced collapse, the existence of such systems therefore requires that natal kicks be imparted to neutron stars. We use an analytical method to synthesize the distribution of nascent LMXBs over donor masses and orbital periods, and evaluate their birth rate and systemic velocity dispersion. Within the limitations imposed by observational incompleteness and selection effects, and our neglect of secular evolution in the LMXB state, we compare our results with observations. However, our principal objective is to evaluate how basic model parameters influence these results. We conclude that the characteristics of newborn LMXBs are primarily determined by age and stability constraints and the efficiency of magnetic braking, and are largely independent of the primordial binary population and the evolutionary history of LMXB progenitors (except for extreme values of the average kick magnitude or of the common-envelope ejection efficiency). Theoretical estimates of total LMXB birth rates are not credible, since they strongly depend on the observationally indeterminate frequency of primordial binaries with extreme mass ratios in long-period orbits.
Kalogera et al. (Tue,) studied this question.