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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.