Formation of Low-Mass X-Ray Binaries

Abstract

A quantitative study of the origin and properties of low-mass X-ray binaries (compact objects with Roche-lobe filling low-mass companions) by means of population syntheses is presented. A semi-analytical synthesis method that offers major advantages in terms of statistical accuracy and computational efficiency is developed. The effects of asymmetric supernova (SN) explosions on orbital dynamics are studied in detail and analytical expressions for the distributions of binaries over post-SN characteristics are derived. As a necessary ingredient of the population models, the binary properties of nascent LMXBs are investigated and found to be determined by mass-transfer stability and system-age constraints only. It is further shown that super-Eddington mass transfer accompanied by mass loss is crucial for the formation of LMXBs with evolved donors; also systems with ultra-short periods must have survived such a super-critical phase. LMXBs are formed only if their progenitors satisfy a set of structural and evolutionary constraints, the study of which shows that (i) the progenitor orbital separations are restricted to a narrow range, and (ii) supernova kicks are necessary for the formation of short-period LMXBs. Population synthesis models are calculated for a wide range of model parameters with special focus on the dependence of the results on them. It is found that the predicted birth rates essentially reflect the choice of the--mostly unknown--characteristics of the primordial binary population. The distribution of nascent LMXBs over their allowed parameter space is primarily set by the efficiency of angular momentum losses, while SN kicks weaken its dependence on pre-SN evolution and hamper the distinction between formation paths that involve a common-envelope phase. Finally, a new LMXB formation channel, the direct-supernova mechanism, is proposed; the required small post-SN orbits are achieved because of a favorable supernova kick, instead of a common-envelope phase. Depending on the average kick magnitude, this mechanism can account for one third of the LMXB population, and more importantly it naturally leads to the formation of the binary millisecond pulsars in very-long-period orbits.