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We have calculated the binary coalescence rate with time using the ``Scenario Machine'' code, which allows us to simulate evolution of large ensembles of binary stars in an artificial galaxy using a Monte Carlo method (see Lipunov 1992, Lipunov et al 1994, 1995 and references therein).
It is reasonable to expect a priori that the evolution of events
is strongly time dependent, so the star formation history
in a galaxy is another important parameter. Therefore,
by calculating the evolution of events after a 
-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
( 
) 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
, so we neglect them in this context.
The source evolution in a galaxy with given star formation rate
is thus calculated as 
, where 
is the redshift at the turn-on of star
formation, which is the second important parameter of
the model. Assuming to the zero approximation 
, 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 with
the initial star formation during first 500 million years. The
mean number of galaxies each of 
was taken 
per cubic megaparsec (this roughly corresponds to
a density of baryonic matter in galaxies without hidden
mass of 
).
We assumed an initial distributions of binary stars similar to
those presently observed in our Galaxy (a Salpeter function for
mass 
of the primary component, 
and a flat distribution of the initial binary
separations A: f(log A) = const). Based on findings by the
``Scenario Machine'' analysis of the evolutionary scenario by
Lipunov et al. (1995), we take the initial mass ratio
distribution in a power-law form 
and the
efficiency coefficient of angular momentum removal at the common
envelope stage 
(as defined by van den Heuvel
1994).