ar X iv : a st ro - p h / 97 12 30 3 v 1 2 3 D ec 1 99 7 Kinematic Arguments Against Single Relativistic Shell Models for GRBs

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 show that the average envelope of emission and the presence of gaps in GRBs are inconsistent with a single relativistic shell. We estimate that the maximum fraction of a single shell that can produce gamma-rays in a GRB with multiple peaks is 10, implying that single relativistic shells require 10 times more energy than previously thought. We conclude that either the central site of a GRB must produce ∼ 10 erg s for hundreds of seconds, or the relativistic shell must have structure on a scales the order of √ ǫΓ, where Γ is the bulk Lorentz factor (∼ 10 to 10) and ǫ is the efficiency.