Evolution of the double neutron star merging rate and the cosmological origin of gamma-ray burst sources

Evolution of the coalescence rate of double neutron stars (NS) and neutron star -- black hole (BH) binaries are computed for model galaxies with different star formation rates. Assuming gamma-ray bursts (GRB) to originate from NS+NS or NS+BH merging in distant galaxies, theoretical logN--logS distributions and <V/V_max> tests of gamma-ray bursts (GRB) are calculated for the first time taking the computed merging rates into account. We use a flat cosmological model (Omega=1) with different values of the cosmological constant Lambda and under various assumptions about the star formation history in galaxies. The calculated source evolution predicts a 5-10 times increase of the source statistics at count rates 3-10 times lower than the exising BATSE sensitivity limit. The most important parameter in fitting the 2nd BATSE catalogue is the initial redshift of star formation, which is found to be z_*=2-5 depending on a poorly determined average spectral index of GRB.