To calculate binary evolution, we have used the population synthesis method (the Scenario Machine code), which is in fact a version of the Monte-Carlo calculations. Here we shall not enter into detail of the evolutionary scenario used. Much more detailed description of the method can be found in our review .
Figure: Massive binary evolutionary track.
An example of the evolutionary track leading to BH+BH binary system formation is shown in Fig.. A short glance to this track is sufficient to understand that there are a lot of evolutionary scenario parameters, which affect different stages of the binary evolution. Fortunately, a very limited number of parameters has effect on the compact binary merging rate.
The most important (and practically unique) parameter changing the galactic binary NS merging rate is the distribution of an additional (kick) velocity imparted to NS at birth. The kick velocity distribution widely accepted at present is derived from the analysis of spatial velocities of single radiopulsars .
We have approximated this 3-dimensional distribution as
where and the characteristic velocity is a parameter in our calculations. The observed pulsar transverse velocity distribution corresponds to km/s.
Critical Mass and Collapse Mass Fraction
In contrast, for BH two additional parameters appear. First of them is a threshold main sequence stellar mass for the star to collapse into a BH after its nuclear evolution has ended.
This parameter is still poorly determined and varies in a wide range: e.g., according to van den Heuvel and Habets  -80M ; Tsujimoto et al.  give 40-60M ; Portegies Zwart et al.  derive >20M .
The second parameter is the fraction of the presupernova mass, , collapsing into BH. This parameter is fully unknown, so we varied it from 0.1 to 1 in our calculations.
The third parameter, as for NS, is the kick velocity. Clearly, in the general case the more massive BH will acquire smaller velocities than NS. In our calculation we used the following ad hoc relationship
where M is the maximal NS mass (Oppenheimer-Volkoff limit). When BH mass is close to , velocities of BH and NS are assumed to be almost the same, whereas at BH kick velocity is assumed to vanish. (Of course, other dependences are possible, but their specific shape weakly affects the results).