Constraining the Bulk Lorentz Factor of GRB Outflow in the Magnetic-dominated Jet Model

TL;DR

This paper models the time delay of GeV photons in GRBs within a magnetic-dominated jet framework, estimating Lorentz factors that are lower than previous estimates and analyzing emission phases for different burst types.

Contribution

It provides a detailed calculation of photon delay in magnetic-dominated jets, offering revised Lorentz factor estimates for GRBs based on this model.

Findings

Lorentz factors are significantly lower than single-zone estimates.

Long GRBs emit GeV photons after saturation of the Lorentz factor.

Short GRBs emit MeV and GeV photons simultaneously.

Abstract

Recent observations by the Fermi-LAT showed that there are delayed arrivals of GeV photons relative to the onset of MeV photons in some GRBs. In order to avoid a large optical depth, the minimal value of the Lorentz factor has been estimated to be higher than 1000 in some brightest bursts. In this paper, we present a detailed calculation of the time delay between the MeV and GeV photons in the framework of the magnetic-dominated jet model. We find that the time delay strongly depends on the saturated bulk Lorentz factor of the jet. Inspired by this fact, we use this model to calculate the Lorentz factors of the four brightest Fermi bursts. The results indicate that the Lorentz factors are much smaller than that obtained from the "single-zone" scenario. The short GRB 090510 has a minimal Lorentz factor 385, while the three long bursts GRB 080916c, GRB090902b and GRB 090926 have almost the same Lorentz factors, with an average value near 260. Another interesting result is that, for long bursts, GeV photons are emitted after the bulk Lorentz factor saturates. For the short GRB, however, MeV and GeV photons are emitted at the same phase, i.e., either at the expansion phase or at the coast phase.