Smooth Light Curves from a Bumpy Ride: Relativistic Blast Wave Encounters a Density Jump

Some GRB afterglow light curves show significant variability, which often includes episodes of rebrightening. This was attributed in several cases to large fluctuations in the external density. Here we examine the effect of a sharp increase in the external density on the light curve by considering, for the first time, a full treatment of both the hydrodynamic evolution and the radiation in this scenario. To this end we develop a semi-analytic model for the light curve and carry out several elaborate numerical simulations using a 1D hydrodynamic code together with a synchrotron radiation code.Two spherically symmetric cases are explored in detail: a density jump in a uniform external medium, and a wind termination shock. Contrary to previous works, we find that even a sharp (step function) and large (by a factor of $a>>1$) increase in the external density does not produce sharp features in the light curve, and cannot account for significant temporal variability. For a wind termination shock, the light curve smoothly transitions between the asymptotic power-laws over about one decade in time, and there is no rebrightening in the optical or X-rays to serve as a clear observational signature. For a sharp jump in a uniform density we find that the maximal deviation $\Delta\alpha_max$ of the temporal decay index $\alpha$ from its asymptotic value, is bounded (e.g., $\Delta\alpha_max <0.4$ for $a=10$); $\Delta\alpha_max$ slowly increases with $a$, converging to $\Delta\alpha_{max} \approx 1$ at very large $a$ values. Therefore, no optical rebrightening is expected here as well. In the X-rays, while the asymptotic flux is unaffected by the density jump, the fluctuations in $\alpha$ are found to be comparable to those in the optical. Finally, we discuss the implications of our results for the origin of the fluctuations in several afterglows.