FORMATION OF LOW-MASS X-RAY BINARIES - II - COMMON ENVELOPE EVOLUTIONOF PRIMORDIAL BINARIES WITH EXTREME MASS RATIOS

We study the formation of low-mass X-ray binaries (LMXBs) through heli um star supernovae in binary systems that have each emerged from a com mon envelope phase. LMXB progenitors must satisfy a large number of ev olutionary and structural constraints, including survival through comm on envelope evolution, through the post-common envelope phase, where t he precursor of the neutron star becomes a Wolf-Rayet star, and surviv al through the supernova event. Furthermore, the binaries that survive the explosion must reach interaction within a Hubble time and must sa tisfy stability criteria for mass transfer. These constraints, imposed under the assumption of a symmetric supernova explosion, prohibit the formation of short-period LMXBs transferring mass at sub-Eddington ra tes through any channel in which the intermediate progenitor of the ne utron star is not completely degenerate. Barring accretion-induced col lapse, the existence of such systems therefore requires that natal kic ks be imparted to neutron stars. We use an analytical method to synthe size the distribution of nascent LMXBs over donor masses and orbital p eriods and evaluate their birthrate and systemic velocity dispersion. Within the limitations imposed by observational incompleteness and sel ection effects, and our neglect of secular evolution in the LMXB state , we compare our results with observations. However, our principal obj ective is to evaluate how basic model parameters (common envelope ejec tion efficiency, rms kick velocity, primordial mass ratio distribution ) influence these results. We conclude that the characteristics of new born LMXBs are primarily determined by age and stability constraints a nd the efficiency of magnetic braking and are largely independent of t he primordial binary population and the evolutionary history of LMXB p rogenitors (except for extreme values of the average kick magnitude or of the common envelope ejection efficiency). Theoretical estimates of total LMXB birthrates are not credible, since they strongly depend on the observationally indeterminate frequency of primordial binaries wi th extreme mass ratios in long-period orbits.