High precision spectro-temporal analysis of ultra-fast radio bursts using per-channel arrival times

Fast radio bursts (FRBs), especially those from repeating sources, exhibit a rich variety of morphologies in their dynamic spectra (or waterfalls). Characterizing these morphologies and spectro-temporal properties is a key strategy in investigating the underlying unknown emission mechanism of FRBs. This type of analysis has been typically accomplished using two-dimensional Gaussian techniques and the autocorrelation function (ACF) of the waterfall. These techniques suffer from high uncertainties when applied to recently observed ultra-FRBs: FRBs that are only a few microseconds long. We present a technique that involves the tagging of per-channel arrival times of an FRB to perform sub-burst slope measurements. This technique leverages the number of frequency channels and can increase the precision of sub-burst slope measurements by several orders of magnitude, allowing it to be easily applied to ultra-FRBs and microshot forests. While scattering and dispersion remain important and often dominating sources of uncertainty in measurements, this technique provides an adaptable and firm foundation for obtaining spectro-temporal properties from all kinds of FRB morphologies. We present measurements using this technique of several hundred bursts across 12 repeating sources, including over 400 bursts from the repeating sources FRB 20121102A, FRB 20220912A, and FRB 20200120E, all of which exhibit microsecond-long FRBs, as well as 136 drift rates. In addition to retrieving the known relationship between sub-burst slope and duration, we explore other correlations between burst properties. We find that ultra-FRBs obey the sub-burst slope law along with longer duration bursts, and appear to form a distinct population in the duration-frequency relation.