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Calculation of Binary Neutron Star Coalescence Rates

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Calculation of Binary Neutron Star Coalescence Rates

It is reasonable to expect a priori that the evolution of events is strongly time dependent, so the star formation history tex2html_wrap_inline11899 in a galaxy is another important parameter. Therefore, by calculating the evolution of events after a tex2html_wrap_inline9046 -function like star formation burst,  one gets a Green function for any arbitrary star formation history.

At the one extreme we assume instantaneous star formation at a particular redshift resulting in a stellar system which we call ``elliptical''  since stars in elliptical galaxies to a good approximation can be assumed to be old and little if any additional star formation is occuring today. Thus the event rates in ``ellipticals'' can be described by the computed Green function. At the other extreme, constant star formation ( tex2html_wrap_inline11899 = const) would result in ``spiral''-like stellar systems.  Irregular galaxies have probably also an irregular star formation history, but their contribution to the overall event rate hardly exceeds their fraction among all galaxies, that is 5-7 percent, so we neglect them in this context.

The source evolution in a galaxy with given star formation rate tex2html_wrap_inline11899 is thus calculated as

where tex2html_wrap_inline9017 is the redshift at the turn-on of star formation, which is the second important parameter of the model. Assuming to the zero approximation  = const, we get

We parametrize the star formation history in the Universe by the fractional part of the luminous baryonic matter entering into elliptical galaxies,  , where E and S refer to ``elliptical'' galaxies (i.e. without additional star formation) and ``spiral'' galaxies  (with a constant star formation rate). In fact, this parameter must be higher than the presently observed fraction of elliptical galaxies, as any galaxy must have had more violent star formation at earlier time. The galaxies are supposed to be formed at the moment tex2html_wrap_inline9017 with the initial star formation during first 500 Myr. The mean number of galaxies each of tex2html_wrap_inline8891 was taken  Mpc tex2html_wrap_inline11748 (this roughly corresponds to a density of baryonic matter in galaxies without hidden mass of ).

We make usual assumptions about initial distributions of binary stars (see Section 6) similar to those presently observed in our Galaxy (a Salpeter function for mass tex2html_wrap_inline10264 of the primary component,  and a flat distribution of the initial binary separations A: ). Based on findings by the Scenario Machine analysis of the evolutionary scenario by Lipunov et al. (1995b)[128] (Section 7), we take the initial mass ratio distribution in a power-law form tex2html_wrap_inline11989 and the efficiency coefficient of angular momentum removal at the common envelope  stage tex2html_wrap_inline10630 (as defined by van den Heuvel 1994[205]).


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Next: Effect of sources evolution Up: Evolution of the Double Previous: Evolution of the Double

Mike E. Prokhorov
Sat Feb 22 18:38:13 MSK 1997