Spectral evolution in gamma-ray bursts: Predictions of the internal shock model and comparison to observations

Context. Several trends have been identified in the prompt gamma-ray burst (GRB) emission: e. g. hard-to-soft evolution, pulse width evolution with energy, time lags, and hardness-intensity and hardness-fluence correlations. Recently, Fermi has significantly extended the spectral coverage of GRB observations and improved the characterization of this spectral evolution. Aims. We want to study how internal shocks can reproduce these observations. In this model the emission comes from the synchrotron radiation of shock accelerated electrons, and the spectral evolution is governed by the evolution of the physical conditions in the shocked regions. Methods. We present a comprehensive set of simulations of a single pulse and investigate the impact of the model parameters, related to the shock microphysics and to the initial conditions in the ejecta. Results. We find general qualitative agreement between the model and the various observations used for the comparison. All these properties or relations are governed by the evolution of the peak energy and photon indices of the spectrum. In addition, we identify the conditions for quantitative agreement. We find that the best agreement is obtained for (i) steep electron slopes (p greater than or similar to 2.7); (ii) microphysics parameters varying with shock conditions so that more electrons are accelerated in stronger shocks; and (iii) steep variations in the initial Lorentz factor in the ejecta. When simulating short GRBs by contracting all timescales, all other parameters being unchanged, we show that the hardness-duration correlation is reproduced, as well as the evolution with duration of the pulse properties. Finally, we investigate the signature at high energy of these different scenarios and find distinct properties - delayed onset, longer emission, and flat spectrum in some cases - suggesting that internal shocks could have a significant contribution to the prompt LAT emission. Conclusions. Spectral evolution is an important property of GRBs that is not easily reproduced in most models for the prompt emission. We find that the main observed features can be accounted for in a quantitative way within the internal shock model. However, the current uncertainties on shock acceleration in the mildly relativistic regime and relativistic ejection by compact sources prevent us from deciding if one or several of the proposed scenario are viable. By combining observations over the whole spectral range of Fermi, it may be possible in the future to identify specific signatures imprinted by this uncertain underlying physics.