COLLECTIVE PROPERTIES OF NEUTRON-STAR X-RAY BINARY POPULATIONS OF GALAXIES. II. PRE-LOW-MASS X-RAY BINARY PROPERTIES, FORMATION RATES, AND CONSTRAINTS

We continue our exploration of the collective properties of neutron-star X-ray binaries in the stellar fields (i.e., outside globular clusters) of normal galaxies. In Paper I of this series, we considered high-mass X-ray binaries (HMXBs). In this paper (Paper II), we consider low-mass X-ray binaries (LMXBs), whose evolutionary scenario is very different from that of HMXBs. We consider the evolution of primordial binaries up to the stage where the neutron star just formed in the supernova explosion of the primary is in a binary with its low-mass, unevolved companion, and this binary has circularized tidally, producing what we call a pre-low-mass X-ray binary (pre-LMXB). We study the constraints on the formation of such pre-LMXBs in detail (since these are low-probability events), and calculate their collective properties and formation rates. To this end, we first consider the changes in the binary parameters in the various steps involved, viz., the common-envelope phase, the supernova, and the tidal evolution. This naturally leads to a clarification of the constraints. We then describe our calculation of the evolution of the distributions of primordial binary parameters into those of pre-LMXB parameters, following the standard evolutionary scenario for individual binaries. We display the latter as both bivariate and monovariate distributions, discuss their essential properties, and indicate the influences of some essential factors on these. Finally, we calculate the formation rate of these pre-LMXBs. The results of this paper will be used in a subsequent one to compute the expected X-ray luminosity function of LMXBs.