Hydrodynamics of Relativistic Blast Waves in a Density-Jump Medium and Their Emission Signature

We analyze in detail the hydrodynamics and afterglow emission of anultrarelativistic blast wave when it expands in a density-jump medium. Such amedium is likely to appear in the vicinity of gamma-ray bursts (GRBs)associated with massive stars. The interaction of the blast wave with thismedium is described through a reverse shock and a forward shock. We show thatthe reverse shock is initially relativistic if the factor of a density jump($\alpha$) is much larger than 21, and Newtonian if $1<\alpha\ll 21$. We alsocalculate light curves of the afterglow emission during the interaction if thereverse shock is relativistic, and find that the optical flux density initiallydecays abruptly, then rises rapidly, and finally fades based on a power-law,which could be followed by an abrupt decay when the reverse shock has justcrossed the originally swept-up matter. Therefore, one property of an afterglowoccurring in a large-density-jump medium is an abrupt drop followed by a bumpin the light curve and thus provides a probe of circumburst environments. Inaddition, this property could not only account for the optical afterglows ofGRB 970508 and GRB 000301C but also explain the X-ray afterglow of GRB 981226.Comment: minor changes, accepted for publication in ApJ Letter