Can we probe the Lorentz factor of gamma-ray bursts from GeV-TeV spectra integrated over internal shocks?

TL;DR

This paper investigates how the high-energy spectral cutoff in gamma-ray bursts, caused by pair creation, is affected by internal shock emissions, revealing that the Lorentz factor estimates are often underestimated due to spectral smearing.

Contribution

The study introduces a new analytical and numerical framework to account for spectral smearing, refining Lorentz factor estimates from GRB spectra, especially for integrated emissions from multiple shocks.

Findings

Spectral cutoff appears as a shallower broken power-law due to shock integration.

The Lorentz factor for GRB 080916C is estimated to be around 600, lower than previous estimates.

Future observations of the pair-break energy can better diagnose the Lorentz factor and emission site.

Abstract

We revisit the high-energy spectral cutoff originating from the electron-positron pair creation in the prompt phase of gamma-ray bursts (GRBs) with numerical and analytical calculations. We show that the conventional exponential and/or broken power law cutoff should be drastically modified to a shallower broken power-law in practical observations that integrate emissions from different internal shocks. Since the steepening is tiny for observations, this "smearing" effect can generally reduce the previous estimates of the Lorentz factor of the GRB outflows. We apply our formulation to GRB 080916C, recently detected by the Large Area Telescope detector on the Fermi satellite, and find that the minimum Lorentz factor can be ~600 (or even smaller values), which is below but consistent with the previous result of ~900. Observing the steepening energy (so-called "pair-break energy") is crucial to diagnose the Lorentz factor and/or the emission site in the future observations, especially current and future Cherenkov telescopes such as MAGIC, VERITAS, and CTA.