ar X iv : a st ro - p h / 98 02 20 0 v 1 1 4 Fe b 19 98 Submitted to ApJ Gamma - Ray Bursts and Relativistic Shells : The Surface Filling Factor

The variability observed in many complex gamma-ray bursts (GRBs) is inconsistent with causally connected variations in a single, symmetric, relativistic shell interacting with the ambient material (" external shocks "). Rather, either the central site must produce ∼ 10 50 erg s −1 for hundreds of seconds (" internal shocks ") or the symmetry of the shell must be broken on an angular scale much smaller than Γ −1 where Γ is the bulk Lorentz factor for the shell. The observed variability in the external shock models arises from the number of causally connected regions that (randomly) become active. We define the " surface filling factor " to be the ratio of the area of causally connected regions that become active to the observable area of the shell. From the observed variability in 52 BATSE bursts, we estimate the surface filling factor to be typically ∼ 5 × 10 −3 although some values are near unity. We find that the surface filling factor is ∼ 0.1∆T /T in both the constant Γ phase (which probably produces the GRB) and the deaccelerating phase (which probably produces the x-ray afterglows). Here, ∆T is a typical time scale of variability and T is the time since the initial signal. We analyze the 2 hr flare seen by ASCA 36 hr after the GRB and conclude that the surface filling factor must be small (10 −3) in the x-ray afterglow phase as well. Explanations for low surface filling factor can either require more or less energy compared to that expected for a symmetric shell.