A Revised Limit of the Lorentz Factors of GRBs with Two Emitting Regions

TL;DR

This paper proposes a two-zone model for gamma-ray bursts, showing that the Lorentz factor limits are significantly lower than previous one-zone estimates, suggesting more modest relativistic speeds.

Contribution

It introduces a two-zone emission model for GRBs, revising the Lorentz factor limits based on extended GeV emission observations.

Findings

Two-zone model yields lower Lorentz factor limits by a factor of five.

Modest Lorentz factors (~200-400) are plausible for both MeV and GeV emission regions.

Revises previous one-zone opacity limits based on Fermi observations.

Abstract

Fermi observations of GeV emission from GRBs have suggested that the Lorentz factor of some GRBs is around a thousand or even higher. At the same time the same Fermi observations have shown an extended GeV emission indicating that this higher energy emission might be a part of the afterglow and it does not come from the same region as the lower energy prompt emission. If this interpretation is correct than we should reconsider the opacity limits on the Loretnz factor of the emitting regions which are based on a one-zone model. We describe here a two-zone model in which the GeV photons are emitted in a larger radius than the MeV photons and we calculate the optical depth for pair creation of a GeV photon passing the lower energy photons shell. We find that, as expected, the new two-zone limits on the Lorentz factor are significantly lower. The corresponding limits for the Fermi bursts are lower by a factor of five compared to the one-zone model and it is possible that both the MeV and GeV regions have relatively modest Lorentz factors (~200 - 400).