The effect of pair cascades on the high-energy spectral cut-off 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 Γ. GRBs with spectral cut-off due to pair production (γγ → e⁺e^-) at energies E_c ≳ 10MeV are extremely useful for inferring Γ. 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^±-pairs can shift the spectral cut-off energy well below the self-annihilation threshold, E_sa = Γ m_ec²/(1 + z). We treat this effect numerically and show that Γ obtained assuming E_c = E_sa can underpredict its true value by as much as an order of magnitude.