The GRB luminosity function: Prediction of the internal shock model and comparison to observations

We compute the expected GRB luminosity function in the internal shock model. We find that if the population of GRB central engines produces all kind of relativistic outflows, from very smooth to highly variable, the luminosity function has to branchs: at low luminosity, the distribution is dominated by low efficiency GRBs and is close to a power law of slope-0.5, whereas at high luminosity, the luminosity function follows the distribution of injected kinetic power. Using Monte Carlo simulations and several observational constrains (BATSE logN-logP diagram, peak energy distribution of bright BATSE bursts, fraction of XRFs in the HETE2 sample), we show that it is currently impossible to distinguish between a single power law or a broken power law luminosity function. However, when the second case is considered, the low-luminosity slope is found to be-0.6±0.2, which is compatible with the prediction of the internal shock model.