Gamma‐Ray Bursts and Relativistic Shells: The Surface Filling Factor

The variability observed in many complex gamma-ray bursts (GRBs) isinconsistent with causally connected variations in a single, symmetric,relativistic shell interacting with the ambient material ("external shocks").Rather, the symmetry of the shell must be broken on an angular scale muchsmaller than Gamma^{-1} where Gamma is the bulk Lorentz factor for the shell.The observed variability in the external shock models arises from the number ofcausally connected regions that (randomly) become active. We define the"surface filling factor" to be the ratio of the area of causally connectedregions that become active to the observable area of the shell. From theobserved variability in 52 BATSE bursts, we estimate the surface filling factorto be typically 0.005 although some values are near unity. We find that thesurface filling factor is about 0.1 Delta T/T in both the constant Gamma phase(which probably produces the GRB) and the deaccelerating phase (which probablyproduces the x-ray afterglows). Here, \Delta T is a typical time scale ofvariability and T is the time since the initial signal. We analyze the 2 hrflare seen by ASCA 36 hr after the GRB and conclude that the surface fillingfactor must be small (0.001) in the x-ray afterglow phase as well. Explanationsfor low surface filling factor can either require more or less energy (by afactor of about 1000) compared to that expected for a symmetric shell.Comment: 26 pages, 5 embedded figures, Latex, revised version as in press, ApJ, added figure to show the possible expanding shell geometries that can give low filling facto