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Monte-Carlo method for statistical simulation of binary evolution was originally proposed by Kornilov & Lipunov (1983a,b) for massive binaries and developed later by Lipunov & Postnov (1987) for low-massive binaries. Dewey & Cordes (1987) applied an analogous method for analysis of radio pulsar statistics, and de Kool (1992) investigated by the Monte-Carlo method the formation of the galactic cataclysmic variables. Recently Leitherer & Heckman (1995) have modelled star formation for elliptical and spiral galaxies, taking into consideration only the single stars.
Monte-Carlo simulations of binary star evolution allows one to investigate the evolution of a large ensemble of binaries and to estimate the number of binaries at different evolutionary stages. Inevitable simplifications in the analytical description of the binary evolution that we allow in our extensive numerical calculations, make those numbers approximate to a factor of 2-3. However, the inaccuracy of direct calculations giving the numbers of different binary types in the Galaxy (see e.g. Iben & Tutukov 1984, Meurs & van den Heuvel 1989, van den Heuvel 1994) seems to be comparable to what follows from the simplifications in the binary evolution treatment. Moreover, no rotational evolution of magnetized compact stars has been properly considered in those papers.
In our analysis of binary evolution, we use the `scenario machine', a computer code that incorporates all current scenarios of binary evolution (for a review, see van den Heuvel 1994) and takes into account the influence of magnetic field of compact objects on their observational appearance. A detailed description of the computational techniques and input assumptions is summarized elsewhere (Lipunov et al. 1995b), and here we list only principal parameters and initial distributions.
We trace the evolution of binary systems during the first 10 Myr after their formation in a star burst. Obviously, only massive enough stars (with masses ) can evolve off the main sequence during the time as short as this to yield compact remnants (NSs and BHs). Therefore we consider only massive binaries, i.e. those having the mass of the primary (more massive) component in the range of 10-120 .