Power Density Spectra of Gamma-Ray Bursts in the Internal Shock Model

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Abstract
We simulate gamma-ray bursts arising from internal shocks in relativistic winds, calculate their power density spectrum (PDS), and identify the factors to which the PDS is most sensitive: the wind ejection features, which determine the wind dynamics and its optical thickness, and the energy release parameters, which give the pulse 50-300 keV radiative efficiency. We found that the upper limit on the efficiency of conversion of wind kinetic energy into 50-300 keV photons is ~1%. Winds with a modulated Lorentz factor distribution of the ejecta yield PDSs that exhibit a -5/3 power law up to ~1 Hz and have efficiencies ~10-3, while winds with a random, uniform Lorentz factor ejection must be optically thick to the short-duration pulses to yield the same PDS features and have an overall efficiency around 10-4.
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