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 comoving rate-density evolution of \propto ( 1 + z ) ^ { 2 - 2.5 } up to z \sim 1 , that 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 \sim 1–2 as suggested by recent observations , the effective power-index of GRB photon spectrum , \alpha~ { } \raisebox { -4.3 pt } { $ \stackrel { \textstyle > } { \sim } $ } ~ { } 1.5 is favored , that is softer than the recent observational determination of \alpha = 1.1 \pm 0.3 .
However , high redshift starbursts ( z~ { } \raisebox { -4.3 pt } { $ \stackrel { \textstyle > } { \sim } $ } ~ { } 5 ) in elliptical galaxies , that have not yet been detected , can alleviate this discrepancy .
The redshift of GRB970508 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 .