A Monte Carlo Study of the Average Power Spectra of Gamma-Ray Bursts

Based on the results of several articles devoted to the study of the average power spectra (<PDS>) of γ-ray bursts (GRBs), a list of <PDS> features has been compiled that need to be explained. Using the possibility, proven in a number of publications, of decomposing the time profile of each γ-ray burst into the sum of several two-sided pulses, GRB modeling is performed in the time domain and the study of the average power spectra of models is carried out in the frequency domain. Brief reviews of the results of a number of theoretical works are made. A Monte Carlo simulation of time series consisting of a set of two-sided pulses with a Poisson distribution of the position of the pulses on the time scale, with different pulse shapes and distributions of amplitude and pulse duration, was carried out. All the basic properties of the average power spectrum in the form of a quasi-Lorentzian theoretically derived in various published studies have been confirmed. <PDS> of superposition of two-sided pulses randomly distributed over time are not described by a single power law. In general, the <PDS> shape consists of three quasi-power sections separated by two breaks. The position of the two breaks in the <PDS> is determined by the parameters of asymmetry and the effective pulse duration. The pulse-duration distribution and their shape affect the shape of the <PDS>, and the pulse amplitude distribution has practically no such effect. The amount of intermittency (at large values of γ ≥ 1) affects the shape of the <PDS>. Based on previous theoretical work and the Monte Carlo simulations carried out in this study, it can be argued that all the features of the average power spectra of GRBs are explained using a simple light curve model in the form of a superposition of uncorrelated random two-sided pulses. The main features of the <PDS> of GRBs are determined only by such pulse characteristics as the asymmetry parameter, the duration distribution, and the shape of the pulses.