Formation of Low-Mass X-Ray Binaries

Low-mass X-ray binaries (LMXBs) are bright X-ray sources that consist of a compact object (neutron star or black hole) accreting from a low-mass companion that fills its Roche lobe and tidally loses mass. A study of the origin and properties of such systems formed in the Galactic disk is presented, involving the statistical modeling of the evolution of a primordial ensemble of binaries through evolutionary stages until the onset of the X-ray phase. For the completion of this study, understanding of the effects of supernova explosions on orbital dynamics, as well as knowledge of the binary characteristics of nascent LMXBs are required. Observational evidence exists in support of the idea that kicks are imparted to neutron stars at their birth. An analytical method is developed for studying the effect of supernova explosions on the orbital dynamics of a binary population with initially circular orbits. Expressions for the distribution of systems over post-SN orbital separations, eccentricities, and center-of-mass velocities are derived, and their dependence on the kick and binary characteristics is studied. This analysis is a necessary tool for population studies of binaries that experience supernova explosions (see Kalogera 1996). The binary properties of LMXBs at the onset of the X-ray phase are studied, and the donor masses and orbital separations are found to be constrained by the requirement that mass transfer be stable and the age of the systems be shorter than the age of the Galaxy. It is also shown that super-Eddington mass transfer allows relatively massive donors to remain in hydrostatic and thermal equilibrium, and that observed long-period LMXBs with evolved donors as well as ultra-short-period LMXBs with hydrogen deficient donors must have survived a phase of super-Eddington mass transfer (see Kalogera & Webbink 1996). Formation of LMXBs has been suggested to occur when primordial binaries with extreme mass ratios evolve through a common envelope phase and the exposed helium core subsequently explodes as a supernova. The complete set of structural and evolutionary constraints on the properties of LMXB progenitors is identified, and it is shown that (i) their orbital separations are restricted to a narrow range, and (ii) short-period LMXBs are formed only if kicks are imparted to neutron stars at birth. Population synthesis calculations are performed with the use of a semi-analytical method which offers major advantages in terms of statistical accuracy and computational efficiency. The results of an extensive parameter study indicate that the predicted birth rates essentially reflect the choice of the -- mostly unknown -- characteristics of the primordial binary population, while the properties of the nascent LMXBs are primarily determined by stability and age constraints and the efficiency of angular momentum losses. The random natal kicks imparted to neutron stars weaken the dependence of the results on pre-SN evolution and hamper the distinction between formation paths that involve a common-envelope phase (see Kalogera & Webbink 1997). In light of the importance of neutron stars kicks in LMXB formation, a new evolutionary path is proposed, the direct-supernova mechanism, which does not invoke common-envelope evolution. Instead, the required small post-SN binary orbits are achieved because of a kick velocity of appropriate magnitude and direction relative to the pre-SN orbital velocity. The efficiency of this new mechanism strongly depends on the average kick magnitude, and can account for one third of the LMXB population for kicks of ~ 100kms-1 . More importantly, the direct-supernova path provides the only natural way for the formation of binary millisecond pulsars in very-long-period orbits (see Kalogera 1997).