On the relationship between the duration and energy of non-repeating fast radio bursts: census with the CHIME data

Abstract

A correlation between the intrinsic energy and the burst duration of non-repeating fast radio bursts (FRBs) has been reported. If it exists, the correlation could be used to estimate the intrinsic energy from the duration, and thus could provide a new distance measure for cosmology. However, the correlation arose from small-number statistics (68 FRBs) and was not free from contamination by latent repeating populations, which might not have such a correlation. Finding a way to separate/exclude the repeating bursts from the mixture of all different types of FRBs is essential for investigating this property. Using a much larger sample from the new FRB catalogue (containing 536 FRBs) recently released by the CHIME (Canadian Hydrogen Intensity Mapping Experiment)/FRB Project, combined with a new classification method developed based on unsupervised machine learning, we carried out further scrutiny of the relationship. We found that there is a weak correlation between the intrinsic energy and duration for non-repeating FRBs at z < 0.3, with a Kendall τ correlation coefficient of 0.239 and a significance of 0.001 (statistically significant), whose slope looks similar to that of gamma-ray bursts. This correlation becomes weaker and insignificant at higher redshifts (z > 0.3), possibly owing to the lack of faint FRBs at high z and/or the redshift evolution of the correlation. The 'scattering time' in the CHIME/FRB catalogue shows an intriguing trend: it varies along the line obtained from a linear fit on the energy versus duration plane between these two parameters. A possible cosmological application of the relationship must wait for more observations of faint FRBs at high z.