Gamma-ray Burst High-latitude Emission: Simulating the Propagation Effect

Relativistic outflows in Gamma-ray Bursts (GRBs) are collimated into jets with narrow angles due to the beaming effect. In simple kinetic models, these jets are composed of relativistic, emitting shells with spherical geometry causing a propagation effect: emission that abruptly stops results in the observed flux decaying with time, rather than immediately ceasing. We study the propagation effect in isolation by generating random, uniform emission from the surface of a static shell. We consider two types of emission profiles: a single pulse of emission and emission that varies sinusoidally with time. The observed profile is seen to be delayed by a time scale that is consistent with the angular spreading time scale found in literature. In particular, we find that the presence of flux variations in the observed profile depends on the size of the emission region relative to the time scale of pulses in the emission profile.