On the Efficiency of Internal Shocks in Gamma-Ray Bursts

The fraction of a fireball kinetic kinetic energy that can be radiated away by internal shocks is sensitive to the amplitude of initial fluctuations in the fireball. We give a simple analytical description for dissipation of modest-amplitude fluctuations and confirm it with direct numerical simulations. At high amplitudes, the dissipation occurs in a non-linear regime with efficiency approaching 100 %. Most of the explosion energy is then radiated away by the prompt GRB and only a fraction remains to be radiated by the afterglow.