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Other parameters of the evolutionary scenario

We consider stars with a constant (solar) chemical composition. The process of mass transfer between the binary components is treated, when appropriate, as a conservative one, i.e. the total angular momentum of the binary system is considered to be constant. The non-conservativeness of the mass transfer is treated via ``isotropic re-emission" mode (Bhattacharya & van den Heuvel 1991). If the rate of accretion from one star to another is sufficiently high (e.g., the mass transfer occurs on a timescale a few times shorter than the thermal Kelvin-Helmholz time for the normal companion) or the compact object is engulfed by a giant companion, the common envelope (CE) stage of the binary evolution can set in (see Paczynski 1976; van den Heuvel 1983).

During the CE stage, an effective spiral-in of the binary components occurs. This complicated process is not fully understood as yet, so we use the conventional energy consideration to find the binary system characteristics after the CE stage by introducing a parameter that measures what fraction of the system's orbital energy goes, between the beginning and the end of the spiralling-in process, into the binding energy (gravitational minus thermal) of the ejected common envelope. Thus,

where is the mass of the core of the mass losing star of initial mass and radius (which is simply a function of the initial separation and the initial mass ratio ), and no substantial mass growth for the accretor is assumed (see, however, Chevalier 1993). The less , the closer becomes binary after the CE stage. In the present calculations we take .

Other cases of non-conservative evolution (e.g., evolutionary stages with a strong stellar wind or those where the loss of the binary angular momentum occurs due to gravitational radiation or magnetic stellar wind) are treated using the well known prescriptions (see e.g. Verbunt & Zwaan 1981; Rappaport et al. 1982; Lipunov & Postnov 1987).