Constraints on the bulk Lorentz factor of Gamma-Ray Burst jets from Fermi/LAT upper limits
Abstract
It is largely recognized that Gamma-Ray Burst (GRB) jets involve ultra-relativistic motion. However, the value of the Lorentz factor Gamma0 is still not clear and only lower limits are known for most bursts. We suggest here a new method to obtain upper limits on Gamma0. The early high-energy synchrotron afterglow flux depends strongly on Gamma0. Upper limits on GeV emission therefore provide uppers limit on Gamma0. Applying this method to 190 Fermi GRBs that have not been detected by the Fermi-LAT we place upper limits on the high-energy afterglow flux, and in turn on Gamma0. For bursts at a typical redshift z=2, we find values of the order of 200 (and above) for a homogeneous density medium, and in the range 100-400 for a wind-like medium. These upper limits are consistent with (and are very close to) lower limits and direct estimates inferred using other methods, suggesting that the typical Lorentz factors of GRB jets are of order a few hundred.