Optical and gamma-ray emissions from internal forward-reverse shocks: application to GRB 080319B?

In the popular internal shock model for the prompt emission of gamma-ray bursts (GRBs), collisions between a series of relativistic shells generate lots of paired forward and reverse shocks. We show that the synchrotron emission produced by the forward and reverse shocks respectively could peak at two quite different energy bands if the Lorentz factors of these two types of shocks are significantly different with each other (e.g., one shock is relativistic and the other is Newtonian). We then investigate whether this scenario is applicable to the case of GRB 080319B and find that a bimodal distribution of the shell Lorentz factors, peaking at $\sim400$ and $\sim10^5$, is required. In addition, this scenario predicts an accompanying inverse-Compton (IC) GeV emission with a luminosity comparable to (not much higher than) that of the synchrotron MeV emission, which can be tested with future \textit{Fermi} observations.