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

TL;DR

This paper investigates how pair cascades and Compton downscattering in gamma-ray burst outflows can significantly alter the observed spectral cutoff, leading to underestimation of the outflow's Lorentz factor if not properly accounted for.

Contribution

It introduces a numerical treatment of pair cascade effects on spectral cutoffs, revealing their impact on Lorentz factor estimates in GRBs.

Findings

Spectral cutoff can be shifted below the self-annihilation threshold due to pair cascades.

Lorentz factor estimates assuming cutoff at the self-annihilation energy can be underestimated by up to an order of magnitude.

High compactness in emission regions enhances the effect of Compton downscattering.

Abstract

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 $\Gamma$. GRBs with spectral cutoff due to pair production ($\gamma\gamma\to e^+e^-$) at energies $E_c\gtrsim10\;$MeV are extremely useful for inferring $\Gamma$. 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, $E_{\rm sa}=\Gamma m_ec^2/(1+z)$. We treat this effect numerically and show that $\Gamma$ obtained assuming $E_c=E_{\rm sa}$ can under-predict its true value by as much as an order of magnitude.