The signature of a wind reverse shock in Gamma-ray bursts afterglows
  Explosions of massive stars are believed to be the source of a significant fraction of gamma-ray bursts (GRBs). If this is indeed the case, then the explosion blast wave propagates into a complex density structure, composed of a stellar wind bounded by two shock waves - a wind reverse shock and a forward shock. As the explosion blast wave reaches R_0, the radius of the wind reverse shock, it splits into two shock waves - a reverse and a forward shock wave. We show that the reverse shock thus produced is not strong, therefore full analytical treatment is required in calculating its properties. We calculate the dynamics of the flow and the evolution of the blast waves in all of the different stages. We show that the fluid Lorentz factor at r>R_0 is equal to 0.725 times the blast wave Lorentz factor as it reaches R_0, and is time (and r) independent as long as the blast wave reverse shock exists. Following the calculation of the blast wave evolution, we calculate the radiation expected in different energy bands. We show that about a day after the main explosion, as the blast wave reaches R_0, the observed afterglow flux starts to rise. It rises by a factor of about 2 in a few hours, during which the blast wave reverse shock exists, and then declines. We show that the power law index describing light curve time evolution is different at early (before the rise) and late times, and is frequency dependent. We present light curves in the different energy bands for this scenario. 
Asaf Pe'er and Ralph A.M.J. Wijers