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〉 ∼= 1.5 and 〈z〉 ∼= 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 & 3 – 5. The mean intrinsic beaming factor of GRBs is found to range from ≈ 34 – 42, with the Swift average opening half-angle 〈θj〉 ∼ 10, compared to the pre-Swift average of 〈θj〉 ∼ 7. Within the uniform jet model, the GRB luminosity function is ∝ L ∗ , as inferred from our best fit to the opening angle distribution. Because of the unlikely detection of several GRBs with z . 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 ≈ 1 GRB occurs every 600,000 yrs 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. Subject headings: gamma-rays: bursts — cosmology: theory