ORBITAL CHARACTERISTICS OF BINARY-SYSTEMS AFTER ASYMMETRIC SUPERNOVA EXPLOSIONS

We present an analytical method for studying the changes of the orbita l characteristics of binary systems with circular orbits due to a kick velocity imparted to the newborn neutron star during a supernova (SN) explosion. Assuming a Maxwellian distribution of kick velocities we d erive analytical expressions for the distribution functions of orbital separations and eccentricities immediately after the explosion, of or bital separations after circularization of the post-SN orbits, and of systemic velocities of binaries that remain bound after the explosion. These distributions of binary characteristics can be used to perform analytical population synthesis calculations of various types of binar ies, the formation of which involves a supernova explosion. We study i n detail the dependence of the derived distributions on the kick veloc ity and the pre-SN characteristics, we identify all the limits imposed on the post-SN orbital characteristics, and we discuss their implicat ions for the population of X-ray binaries and double neutron star syst ems. We show that large kick velocities do not necessarily result in l arge systemic velocities; for typical X-ray binary progenitors the max imum post-SN systemic velocity is comparable to the relative orbital v elocity prior to the explosion. We also find that, unless accretion-in duced collapse is a viable formation channel, X-ray binaries in globul ar clusters have most probably been formed by stellar dynamical intera ctions only and not directly from primordial binaries.