Measuring the bulk Lorentz factors of gamma-ray bursts with Fermi

Gamma-ray bursts (GRBs) are powered by ultra-relativistic jets. Usually a minimum value of the Lorentz factor of the relativistic bulk motion is obtained based on the argument that the observed high energy photons ($\gg {\rm MeV}$) can escape without suffering from absorption due to pair production. The exact value, rather than a lower limit, of the Lorentz factor can be obtained if the spectral cutoff due to such absorption is detected. With the good spectral coverage of the Large Area Telescope (LAT) on \textsl{Fermi}, measurements of such cutoff become possible, and two cases (GRB~090926A and GRB~100724B) have been reported to have high-energy cutoffs or breaks. We systematically search for such high energy spectral cutoffs/breaks from the LAT and the Gamma-ray burst monitor (GBM) observations of the prompt emission of GRBs detected since August 2011. Six more GRBs are found to have cutoff-like spectral feature at energies of $\sim10-500$~MeV. Assuming that these cutoffs are caused by pair-production absorption within the source, the bulk Lorentz factors of these GRBs are obtained. We further find that the Lorentz factors are correlated with the isotropic gamma-ray luminosity of the bursts, indicating that more powerful GRB jets move faster.