Prompt γ-ray and early X-ray afterglow emissions in gamma-ray bursts (GRBs) are characterized by a bursty behavior and are often interspersed with long quiescent times. There is compelling evidence that X-ray flares are linked to prompt γ-rays. However, the physical mechanism that leads to the complex temporal distribution of gamma-ray pulses and X-ray flares is not understood. Here we show that the waiting time distribution (WTD) of pulses and flares exhibits a power-law tail extending over four decades with an index of about two and can be the manifestation of a common time-dependent Poisson process. This result is robust and is obtained on different catalogs. Surprisingly, GRBs with many (⩾8) gamma-ray pulses are very unlikely to be accompanied by X-ray flares after the end of the prompt emission (3.1σ Gaussian confidence). These results are consistent with a simple interpretation: a hyperaccreting disk breaks up into one or a few groups of fragments, each of which is independently accreted with the same probability per unit time. Prompt gamma-rays and late X-ray flares are nothing but different fragments being accreted at the beginning and at the end, respectively, following the very same stochastic process and likely the same mechanism.
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