A Practical Framework for Estimating the Repetition Likelihood of Fast Radio Bursts from Spectral Morphology

Abstract

The repeating behavior of fast radio bursts (FRBs) is regarded as a key clue to understanding their physical origin, yet reliably distinguishing repeaters from apparent non-repeaters with current observations remains challenging. Here we propose a physically interpretable and practically quantifiable classification framework based on spectral morphology. Using dimensionality reduction, clustering, and feature-importance analysis, we identify the spectral running $r$ and spectral index $\gamma$ as the most critical parameters for distinguishing repeaters from apparent non-repeaters in the CHIME/FRB sample. In the $\gamma$-$r$ space, repeaters preferentially occupy regions with steeper, narrower-band spectra, whereas non-repeaters cluster in flatter, broader-band regions, resulting in a clear density separation. We further construct an empirical probability map in the $\gamma$-$r$ space, showing a clear gradient of repetition likelihood, from $\sim 65\%$ in the high-repetition region to $\sim 5\%$ in the low-repetition region. Combining this with Gaussian Mixture Model posterior analysis, we identify several apparent non-repeaters with high inferred repetition probability, recommending them as priority targets for future monitoring. This framework provides a simple and generalizable tool for assessing repeatability in the CHIME/FRB sample and highlights the diagnostic power of spectral morphology in unveiling FRB origins.