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

We analyze in detail the hydrodynamics and afterglow emission of an ultrarelativistic blast wave when it expands in a density-jump medium. Such a medium is likely to appear in the vicinity of gamma-ray bursts (GRBs) associated with massive stars. The interaction of the blast wave with this medium is described through a reverse shock and a forward shock. We show that the 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 also calculate light curves of the afterglow emission during the interaction and find that the optical flux density initially decays abruptly, then rises rapidly, and finally fades down based on a power-law, which could be followed by an abrupt decay when the reverse shock has just crossed the originally swept-up matter. Therefore, one property of an afterglow occurring in a density-jump medium is an abrupt drop followed by a bump in the light curve and thus provides a probing of circumburst environments. In addition, this property could not only account for the optical afterglows of GRB 970508 and GRB 000301C but also explain the X-ray afterglow of GRB 981226.