Memory in the Burst Occurrence of Repeating FRBs

Understanding the nature of repeating FRBs is crucial to probe the physics of FRBs. In this work, we analyze the statistics of waiting time between bursts of three repeating FRBs from four data sets. We find a universally pronounced dependency of the waiting times on the previous time interval (denoted as $\lambda_0$). We observe a temporal clustering where short waiting times tend to be followed by short ones, and long by long. This memory dependency is manifested in the conditional mean waiting time as well as in the conditional mean residual time to the next burst, both of which increase in direct proportion to $\lambda_0$. Consequently, the likelihood of experiencing a subsequent FRB burst within a given time window after the preceding burst is significantly influenced by the burst history. We reveal that, for the first time, these memory effects are present in the scale-invariant preconditioned waiting time distribution. We show that the memory effect provides a unified description of waiting times which may account for both the repeating FRBs and the apparent non-repeating FRBs (i.e. only observed one time). These results shed new light on the mechanism of FRBs.