Cosmological gamma-ray bursts and evolution of galaxies

Evolution of the rate density of cosmological gamma-ray bursts (GRBs) is calculated and compared to the BATSE brightness distribution in the context of binary neutron star mergers as the source of GRBs, taking account of the realistic star formation history in the universe and evolution of compact binary systems. We tried two models of the evolution of cosmic star formation rate (SFR): one is based on recent observations of SFRs at high redshifts, while the other is based on a galaxy evolution model of stellar population synthesis that reproduces the present-day colors of galaxies. It is shown that the binary merger scenario of GRBs naturally results in the rate evolution of proportional to(1 + z)(2-25) up to z similar to 1, which has been suggested independently from the compatibility between the number-brightness distribution and duration-brightness correlation. If the cosmic SFR has its peak at z similar to 1-2 as suggested by recent observations, then the effective power index of the GRB photon spectrum, alpha greater than or similar to 1.5, is favored, which is softer than the recent observational determination of alpha = 1.1 +/- 0.3. However, high-redshift starbursts (z greater than or similar to 5) in elliptical galaxies, which have not yet been detected, can alleviate this discrepancy. The redshift of GRB 970508 is likely about 2, just below the upper limit that is recently determined, and the absorption system at z = 0.835 seems not to be the site of the GRB.