The Effect of Pair Cascades on the High-Energy Spectral Cutoff in Gamma-Ray Bursts

The highly luminous and variable prompt emission in Gamma-Ray Bursts (GRBs) arises in an ultra-relativistic outflow. The exact underlying radiative mechanism shaping its non-thermal spectrum is still uncertain, making it hard to determine the outflow’s bulk Lorentz factor $\mathrm{\Gamma }$. GRBs with spectral cutoff due to pair production ($\gamma \gamma \to e^{+}{e}^{-}$) at energies $E_c\gtrsim 10$MeV are extremely useful for inferring $\mathrm{\Gamma }$. We find that when the emission region has a high enough compactness, then as it becomes optically thick to scattering, Compton downscattering by non-relativistic $e^{\pm }$-pairs can shift the spectral cutoff energy well below the self-annihilation threshold, $E_{\mathrm{s}\mathrm{a}}=\mathrm{\Gamma }{m}_e{c}^2\mathrm{/}(1+z)$. We treat this effect numerically and show that $\mathrm{\Gamma }$ obtained assuming $E_c=E_{\mathrm{s}\mathrm{a}}$ can under-predict its true value by as much as an order of magnitude.