On the redshift distribution of gamma-ray bursts in the Swift era

A simple physical model for long-duration gamma-ray bursts (GRBs) is used to fit the redshift (z) and the jet opening angle distributions measured with earlier GRB missions and with Swift. The effect of different sensitivities for GRB triggering is sufficient to explain the difference in the z distributions of the pre-Swift and Swift samples, with mean redshifts of < z > congruent to 1.5 and < z > congruent to 2.7, respectively. Assuming that the emission properties of GRBs do not change with time, we find that the data can only be fitted if the comoving rate density of GRB sources exhibits positive evolution to z greater than or similar to 3-5. The mean intrinsic beaming factor of GRBs is found to range from approximate to 34 to 42, with the Swift average opening half-angle <theta(j)> similar to 10 degrees, compared to the pre-Swift average of <theta(j)> similar to 7 degrees. Within the uniform jet model, the GRB luminosity function is proportional to L-*(-3.25) , as inferred from our best fit to the opening angle distribution. Because of the unlikely detection of several GRBs with z less than or similar to 0.25, our analysis indicates that low-redshift GRBs represent a different population of GRBs than those detected at higher redshifts. Neglecting possible metallicity effects on GRB host galaxies, we find that approximate to 1 GRB occurs every 600,000 yr in a local L-* spiral galaxy like the Milky Way. The fraction of high-redshift GRBs is estimated at 8%-12% and 2.5%-6% at z >= 5 and z >= 7, respectively, assuming continued positive evolution of the GRB rate density to high redshifts.