Gamma-ray bursts from internal shocks in a relativistic wind: temporal and spectral properties

We construct models for gamma-ray bursts where the emission comes from internal shocks in a relativistic wind with a highly non uniform distribution of the Lorentz factor. We follow the evolution of the wind using a very simplified approach where a large number of layers interact by direct collisions but where all pressure waves have been suppressed. We suppose that the magnetic field and the electron Lorentz factor reach large equipartition values in the shocks. Synchrotron photons emitted by the relativistic electrons have a typical energy in the gamma-ray range in the observer frame. Synthetic bursts are constructed as the sum of the contributions from all the internal elementary shocks and their temporal and spectral properties are compared to the observations. We reproduce the diversity of burst profiles, the ``FRED'' shape of individual pulses and the short time scale variability. Synthetic bursts also satisfy the duration-hardness relation and individual pulses are found to be narrower at high energy, in agreement with the observations. These results suggest that internal shocks in a relativistic wind may indeed be at the origin of gamma-ray bursts. A potential problem is however the relatively low efficiency of the dissipation process. If the relativistic wind is powered by accretion from a disc to a stellar mass black hole it implies that a substantial fraction of the available energy is injected into the wind.