Polarization and light-curve variability: The "patchy-shell" model

Recent advances in early detection and detailed monitoring of gamma-ray burst (GRB) afterglows have revealed variability in some afterglow light curves. One of the leading models for this behavior is the patchy-shell model. This model attributes the variability to random angular fluctuations in the relativistic jet energy. These nonaxisymmetric fluctuations should also impose variations in the degree and angle of polarization that are correlated to the light-curve variability. In this Letter we present a solution of the light curve and polarization resulting from a given spectrum of energy fluctuations. We compare light curves produced using this solution with the variable light curve of GRB 021004, and we show that the main features in both the light curve and the polarization fluctuations are very well reproduced by this model. We use our results to draw constraints on the characteristics of the energy fluctuations that might have been present in GRB 021004.