Power density spectra of gamma-ray burst light curves: Implications on theory and observation

We investigate statistical properties of gamma-ray burst (GRB) light curves by comparing the reported characteristics in the power density spectra (PDSs) of the observed GRBs with those that we model and discuss implications on interpretations of the PDS analysis results. Results of PDS analysis of observed GRBs suggest that the averaged PDS of GRBs follows a power law over about two decades of frequency with the power-law index, -5/3, and the distribution of individual power follows an exponential distribution. Although an attempt to identify the most sensitive physical parameter has been made on the basis of the internal shock model, we demonstrate that conclusions of this kind of approach should be derived with due care. We show that the reported slope and the distribution can be reproduced by adjusting the sampling interval in the time domain for a given decaying timescale of individual pulse in a specific form of GRB light curve. In particular, given that the temporal feature is modeled by a two-sided exponential function, the power-law behavior with the index of -5/3 and the exponential distribution of the observed PDS is recovered at the 64 ms trigger timescale when the decaying timescale of individual pulses is ∼1 s, provided that the pulse sharply rises. Another way of using the PDS analysis is an application of the same method to individual long bursts in order to examine a possible evolution of the decaying timescale in a single burst.