Validating the Sub-Burst Slope Law: A Comprehensive Multi-Source Spectro-Temporal Analysis of Repeating Fast Radio Bursts

We conduct a comprehensive spectro-temporal analysis of repeating Fast Radio Bursts (FRBs) utilizing nine distinct sources, the largest sample to date. Our data set includes 175 sub-bursts and 31 multi-component bursts from 11 data sets, with centre frequencies ranging from 149--7144 MHz and durations spanning from 73 $\mu$s--13 ms. Our findings are consistent with the predictions of the Triggered Relativistic Dynamical Model (TRDM) of FRB emission. We affirm the predicted quadratic relationship between sub-burst slope and central frequency, as well as a linear dependence of the sub-burst bandwidth on central frequency that is consistent with mildly-relativistic Doppler broadening of narrow-band emission. Most importantly, we confirm the sub-burst slope law, a predicted inverse relationship between sub-burst slope and duration, to hold consistently across different sources. Remarkably, we also discover that the drift rates of multi-component bursts follow the same law as the sub-burst slopes, an unexplained result that warrants further investigation. These findings not only support the TRDM as a viable framework for explaining several aspects of FRB emission, but also provide new insights into the complex spectro-temporal properties of FRBs.