Kinematic Arguments Against Single Relativistic Shell Models for Gamma-Ray Bursts

Abstract

Two main types of models have been suggested to explain the long durations and multiple peaks of Gamma-Ray Bursts (GRBs). In one, there is a very quick release of energy at a central site resulting in a single relativistic shell that produces peaks in the time history through its interactions with the ambient material. In the other, the central site sporadically releases energy over hundreds of seconds forming a peak with each burst of energy. We present three kinematic arguments against a single relativistic shell. These arguments are based only on symmetry. We show that the average envelope of emission of GRBs is a linear function rather than the power law expected for a single relativistic shell. We show that presence of gaps in GRBs is the strongest argument against a single relativistic shell. We estimate that the fraction of a single shell that can produce gamma-rays in a GRB with multiple peaks is about 0.001, implying that single relativistic shells require 1000 times more energy than previously thought. We conclude that either the central site of a GRB must produce 10^{51} erg/s for hundreds of seconds, or the relativistic shell must have structure on a scales the order of sqrt(epsilon)/Gamma, where Gamma is the bulk Lorentz factor and epsilon is the efficiency.