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Next: Concluding
Remarks and Future Up: Evolution
of the Double Previous: Effect
of sources evolution
Our calculations show that if GRB indeed are due to binary neutron star
coalescence, they can potentially constrain the cosmological
parameters as well as the early star formation history. Even for the simplest
models we used, late epochs of galaxy formation ( 
) do not seem to be consistent with the observed BATSE
- 
distribution. The best-fit model we obtained by fitting to the 411 GRB
available from the second BATSE catalogue (Meegan et
al., 1994)[139] corresponds
to 
, 
and 
, with a 
95 percent agreement according to 
-test (we also used a Kolmogorov-Smirnov test; both criteria give qualitatively
similar results but we present results for the
-test as it gives a more smooth likelihood function). According to the
best-fit, the most distant BATSE GRB come from 
(compared to Cohen and Piran (1995)[35]
who obtained 
;
however, we made no data selection). The results are also sensitive to
the accepted mean spectral index of the GRB (s=1.5
in our case) and favours earlier star formation 
for flatter spectra (s=1). We also note that
the earlier epochs of the primordial star formation are not favored by
other cosmological grounds (see calculations by Cen et al. (1994)).[28]
One may also wonder how the assumption about the total 
change the results. Obviously, we can fit the observations for a wide range
of
by varying other parameters ( 
, s, 
etc.). The dependence of
- curves on
was found to be rather small (Yi, 1994),[215]
and our main conclusion still holds --
- should show a
dramatic turn-up at low count rates due to early evolutionary effects.
The total merging event rate predicted by our evolutionary
model is 
per yr per 
, that is 
events per year for the entire Universe, implying a factor of 
overproduction relative to the presently observed BATSE
GRB rate of 0.8 events per day. This could be explained, for example, by
a relativistic beaming in GRB sources (Paczynski, 1994).[154]
The corresponding angle required to explain the GRB anisotropy that high
is about (Mao and Yi, 1994).[134]
Taking this factor into account yields the expected total GRB rate 5000
events per year for a limiting sensitivity lower by a factor of 3-10 than
the presently exisitng BATSE limit. We note that use
of another mean galactic density 
in the Universe would accordingly change the overall GRB rate in the Universe,
but does not change the
- curve shape:
taking it to be less than 0.08 Mpc
would somewhat decrease the anisotropy required ( 
R^-1/2).
We conclude that the crucial test of the cosmological origin of GRB
would be observing the predicted increase of the
- slope at smaller
fluxes, inevitable due to early evolutionary effects. If the cosmological
origin of GRB is confirmed, the
- and 
test could be used independently to estimating the cosmological parameters
and tracing star formation history in galaxies.