The bulk Lorentz factors of Fermi-LAT GRBs

TL;DR

This paper revisits the constraints on gamma-ray burst Lorentz factors using Fermi-LAT data, considering multi-zone emission models and self-consistent optical depth calculations, suggesting lower Lorentz factors than previously thought.

Contribution

It introduces a two-zone emission model and self-consistent optical depth calculations to refine Lorentz factor estimates for GRBs, challenging the high values previously inferred.

Findings

A bulk Lorentz factor of about 600 is consistent with observations in the two-zone model.

Multi-zone emission models can lead to lower Lorentz factor estimates.

Spectral steepening rather than exponential cutoff indicates less severe gamma-ray attenuation.

Abstract

The Lorentz factor (LF) of gamma-ray burst (GRB) ejecta may be constrained by observations of high-energy (HE) spectral attenuation. The recent Fermi-LAT observations of prompt GeV emission from several bright GRBs have leaded to conclusions of unexpectedly large LFs, $\Gamma>10^3$. Here we revisit this problem with two main concerns. (1) With one-zone assumption where all photons are assumed to be generated in the same region (radius) and time, we {\em self-consistently} calculate the $\gamma\gamma$ optical depth by adopting a target photon spectrum with HE cutoff. We find that this might be important when the GRB LF is below a few hundreds. (2) Recent Fermi-LAT observations suggest that the bulk MeV-range and HE ($\ga100$ MeV) emission may arise from different regions. We then consider a two-zone case where HE emission is generated in much larger radii than that of the MeV-range emission. We find that the HE emission may be mainly attenuated by MeV-range emission and that the attenuated HE spectrum does not show an exponential spectral cutoff but a slight steepening. This suggests that there may be no abrupt cutoff due to $\gamma\gamma$ attenuation if relaxing the one-zone assumption. By studying the spectra of three bright Fermi-LAT GRBs 080916C, 090510 and 090902B, we show that a bulk LF of\textbf{ $\Gamma\sim600$ }can be consistent with observations in the two-zone case. Even lower LFs can be obtained in the multi-zone case.