Variability in Shell Models of Gamma-Ray Bursts

Many cosmological models of gamma-ray bursts (GRBs) assume that a single relativistic shell carries kinetic energy away from the source and later converts it into gamma rays, perhaps by interactions with the interstellar medium or by shocks within the shell. We investigate methods of achieving the observed variability using symmetry. Since our model emphasizes geometric and statistical considerations, rather than the detailed physics of the shell, it is applicable to any theory that relies on relativistic shells. In order to achieve the observed variability in GRBs using a single-shell model, we have found that the gamma-ray emission must occur from small patches on the shell (entities). We have derived two significant characteristics of the time histories expected from such a model. First, the average number of entities contributing to the signal remains constant throughout much of the time history, although the overall photon flux decreases due to relativistic effects. Second, the "peaks" in a time history can be ascribed to Poisson variations in the actual number of entities contributing to the signal at any given time. Taken together, these properties imply that the relative variations in a GRB (i.e. the heights of the peaks relative to the average envelope of the signal) should remain constant throughout a time history.