High-energy spectral cutoffs in the prompt emission of Fermi gamma-ray bursts: bulk Lorentz factors, emission radii, and a cutoff-peak energy relation

The high-energy end of the gamma-ray burst (GRB) prompt spectrum carries information on the physical conditions of the relativistic outflow, but the number of well-characterized spectral cutoffs is small. We present a systematic search for high-energy spectral cutoffs in the time-integrated prompt spectra of 139 GRBs observed by Fermi between 2008 July and 2025 December, selected to have broadband coverage either through a LAT detection or through bright BGO emission. Joint GBM, LLE, and LAT spectra over T 90 are fitted with four empirical models and compared using the Bayesian information criterion, yielding 106 bursts with well-constrained cutoff energies E c. An empirical two-component Gaussian mixture model applied to 10(E c/MeV) separates a low- E c group from the main distribution at E c=2.12 MeV; the 77 bursts lying firmly above this boundary are interpreted within the internal γγ pair-opacity framework. Combining E c with wavelet-based minimum variability timescales (median 0.119 s), we infer bulk Lorentz factors of 11.7 to 2.78 times10 cubed (median 145) and emission radii of about10 13 to 10 15, cm. Neither the Γ - L iso nor the Γ - E iso relation is statistically significant for the full sample, whereas the 27 bursts with measured redshifts show a moderate Γ - L iso correlation with a slope of 0.36-0.23+0.22. We further find a strong rest-frame correlation between the cutoff and peak energies, E c,z proportional to E p,z 2.15-0.97+0.96, for the 26 bursts with measured redshifts, which persists after controlling for redshift.