Time stretching of the GeV emission of GRBs: Fermi-LAT data vs geometrical model

Abstract

It is known that the high energy $(> 100\,\text{MeV})$ emission of gamma-ray bursts is delayed with respect to the low energy emission. However, the dependence of light curves on energy has not been studied for the high energy bands. In this paper we consider the bursts observed by Fermi LAT from 2008 August 4 to 2011 August 1, for which at least $10$ photons were observed with the energy greater than $1\,\text{GeV}$. These include $4$ bursts: GRB 080916C, GRB 090510, GRB 090902B, and GRB 090926A. We use the Kolmogorov-Smirnov test to compare the light curves in the two bands, $100\,\text{MeV} < E < 1\,\text{GeV}$ and $E > 1\,\text{GeV}$. For GRB 080916C and GRB 090510 the light curves in the two bands are statistically compatible. However, for GRB 090926A, the higher-energy light curve is stretched compared to the lower-energy one with a statistical significance of $3.3 \sigma$ and, for GRB 090902B, on the contrary, the lower-energy curve is stretched with $2.3 \sigma$ significance. We argue that the observed diversity of stretching factors may be explained in a simple geometrical model. The model assumes that the jet opening angle depends on the emission energy in a way that the most energetic photons are radiated near the axis of the jet. All the bursts are considered equivalent in their rest frames and the observed light curves differ only due to different redshifts and view directions. The model conforms to the total burst energy constraint and matches the Fermi LAT observations of the fraction of GRBs visible in $100\,\text{MeV} < E < 1\,\text{GeV}$ band, which may be observed at higher energies. The model predicts the distribution of observable stretching factors, which may be tested in the future data. Finally, we propose a method to estimate observer's off-axis angle based on the stretching factor and the fraction of the high-energy photons.