An Observational Limit on the Earliest GRBs

We predict the redshift of the first observable (i.e., in our past light cone) Gamma Ray Burst (GRB) and calculate the GRB-rate redshift distribution of the Population III stars at very early times (z=20-60). Using the last 2 years of data from Swift we place an upper limit on the efficiency (\eta_{GRB}) of GRB production per solar mass from the first generation of stars. We find that the first observable GRB is most likely to have formed at redshift 60. The observed rate of extremely high redshift GRBs (XRGs) is a subset of a group of 15 long GRBs per year, with no associated redshift and no optical afterglow counterparts, detected by Swift. Taking this maximal rate we get that \eta_{GRB}<1.1~10^{-4} GRBs per solar mass in stars. A more realistic evaluation, e.g., taking a subgroup of 5% of the total sample of Swift gives an upper limit of \eta_{GRB}<3.2~10^{-5} GRBs per solar mass.