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Parameters of binary compact star evolution


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 [16].

Figure: Massive binary evolutionary track.

An example of the evolutionary track leading to BH+BH binary system formation is shown in Fig.gif. 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 [17].

We have approximated this 3-dimensional distribution as


where tex2html_wrap_inline908 and the characteristic velocity tex2html_wrap_inline910 is a parameter in our calculations. The observed pulsar transverse velocity distribution corresponds to tex2html_wrap_inline912  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 tex2html_wrap_inline914 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 [18] tex2html_wrap_inline916 -80M tex2html_wrap_inline874 ; Tsujimoto et al. [19] give 40-60M tex2html_wrap_inline874 ; Portegies Zwart et al. [20] derive >20M tex2html_wrap_inline874 .

The second parameter is the fraction of the presupernova mass, tex2html_wrap_inline926 , 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 tex2html_wrap_inline930 M tex2html_wrap_inline874 is the maximal NS mass (Oppenheimer-Volkoff limit). When BH mass is close to tex2html_wrap_inline934 , velocities of BH and NS are assumed to be almost the same, whereas at tex2html_wrap_inline936 BH kick velocity is assumed to vanish. (Of course, other dependences tex2html_wrap_inline938 are possible, but their specific shape weakly affects the results).

next up previous
Next: Detection rate of binary Up: BH+BH merging Previous: BH+BH merging

Lipunov V.M.
Fri Nov 28 17:12:56 MSK 1997