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Collective Properties of X-ray Binary Populations of Galaxies. I. Luminosity and Orbital Period Distributions of High-Mass X-ray Binaries

We introduce a method for obtaining the X-ray luminosity function (XLF) and the binary-period distribution of populations of high-mass X-ray binaries (HMXBs) in the stellar fields (i.e. outside globular clusters) of normal galaxies. We start from standard distributions of the parameters of those primordial binaries which are the progenitors of HMXBs, and follow the transformation of these ditributions with the aid of a Jacobian formalism as the former evolve into the latter through the processes of the first mass transfer and the supernova (SN) that follows. We discuss the distributions of the post-SN binaries and the HMXBs. We show that our calculated model XLF has a differential slope $\approx -1.6$ with a flattening at low luminosities, in excellent agreement with observations. The calculated binary-period distribution, which basically has a slightly sloping plateau-like character at intermediate periods, with a rise to this plateau at shorter periods and fall-off from it at longer periods, is in agreement with the observed distribution within observational uncertainties. We discuss the physical origin of these distributions. We demonstrate that, while the effects of both (a) the distribution of the properties of the massive companion in the HMXBs, and (b) the primordial orbital distribution and the SN dynamics are important, the former appear to be dominant in determining the XLF, and the latter in determining the HMXB binary-period distribution. We discuss the possible roles of stellar-mass black holes and ultra-luminous X-ray sources (ULX) in the observed "universal" XLF of HMXBs.