Constraints on the internal shock model from the temporal analysis of GRBs

Abstract

We analyze the power density spectrum (PDS) of Gamma Ray Bursts arising from multiple shocks in a relativistic wind. The factors to which the PDS is most sensitive are: the wind ejection features, which determinate the wind dynamics and its optical thickness, and the energy release parameters, which give the pulse 50–300 keV radiative efficiency. The model takes into account the photons down-scattering on cold electrons in the wind. For an almost optically thick wind we identify a combination of ejection features and wind parameters that yield bursts with an average power spectrum in agreement with the observations, and with an efficiency of converting the wind kinetic energy in 50–300 keV emission of order of 1%. The interval between peaks and pulse fluences have distributions consistent with the log-normal distribution observed in real bursts.