Variability of gamma-ray burst afterglows due to interstellar turbulence

Gamma-ray burst (GRB) afterglows are commonly interpreted as synchrotron emission from a relativistic blast wave produced by a point explosion in an ambient medium, plausibly the interstellar medium of galaxies. We calculate the amplitude of flux fluctuations in the light curves of afterglows due to inhomogeneities in the surrounding medium. Such inhomogeneities are an inevitable consequence of interstellar turbulence but could also be generated by variability and anisotropy in a precursor wind from the GRB progenitor. Detection of their properties could provide important clues about the environments of GRB sources. We apply our calculations to GRB 990510, where an rms scatter of similar to 2% was observed for the optical flux fluctuations on the 0.1-2 hr timescale during the first day of the afterglow, consistent with it being due entirely to photometric noise. The resulting upper limits on the density fluctuations on scales of similar to 20-200 AU around the source of GRB 990510 are lower than the inferred fluctuation amplitude on similar scales in the Galactic interstellar medium. Hourly monitoring of future optical afterglows might therefore reveal fractional flux fluctuations at the level of a few percent.