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Next: Calculation
of Binary Neutron Up: No
Title Previous: Results
and Discussion
The observed isotropy on the sky and non-uniform spatial distribution
of gamma-ray bursts (GRB) revealed by the BATSE
device onboard the Compton Gamma-Ray Observatory (e.g. Meegan et al.,
1992)[138] lend support to the
idea of a cosmological origin of GRB (Prilutski and Usov, 1975;[165]
Usov and Chibisov, 1975)[199]
for which the best candidates could be merging binary NS+NS
or NS+BH at high redshifts (z 
1
-2), (Blinnikov et al., 1984;[19]
Paczynski, 1991[152], 1992).[153]
Narayan et al. (1992)[145]
argued that the rate of double NS coalescence as a
result of orbital shrinking induced by gravitational waves is far from
being sufficient to explain the observed properties of cosmic GRB and their
rate ( 
0.8 bursts
per day). Wickramasinghe et al. (1993)[213]
showed the consistency of standard cosmology and the BATSE
GRB 
- 
distribution.
The cosmological models for GRB have not yet been proven; moreover, they are associated with severe problems (such as no-host-galaxy limits, baryon contamination degradation of the high energy photons, efficiency problems in transferring the NS binding energy out of the BH into gamma-rays etc.), which we do not address here.
However, the cosmological models involving binary NS or NS+BH coalescences
must have clear observational consequences in showing the effects of binary
coalescence rate evolution on the observed
- distribution
and 
. Attempts
to take the intrinsic evolution of the sources into account have been carried
out in a number of papers (see e.g. Piran, 1992;[162]
Yi, 1994;[215] Cohen and Piran, 1995),[35]
but all of them used simple ad hoc assumptions for the source evolution.
Both the parameters of the cosmological model and source evolution are known to influence the shape of the integral statistical distributions of sources (e.g. Weinberg, 1972),[211] and it has until now been very difficult or even impossible to separate these effects from each other. This is similar to the failure of to check the cosmological models using counts of radio sources, as the evolution of number per comoving frame, spectral shape, luminosity etc. is very complicated and poorly understood as yet.
In contrast, the evolution of binary systems being based on and confirmed
by a large number of observations at different wavelengths is much better
understood. The analysis of the evolutionary scenario of binary systems
by Lipunov et al. (1995d)[128]
showed that a few key parameters largely define the overall binary evolution.
These parameters are the spectrum f(q)
of the initial binary mass ratio 
and the efficiency 
of binary orbital momentum transfer into a common envelope.
These parameters can be constrained by comparing the numbers of binaries
in different stages of evolution in the Galaxy predicted by the scenario
with the observed numbers (Lipunov et al., 1995d).[128]
In this Section, we compute the cumulative statistical distribution,
-
and test for binary
NS and NS+BH coalescence taking into account the temporal
change of their rates found by Monte-Carlo modelling
of the modern scenario of binary star evolution (the Scenario Machine method).
A comparison of the computed distribution with that of the second BATSE
GRB catalogue (Meegan et al., 1994)[139]
is also made.
-
distribution and
-test