Correlation between X-ray and gamma data of Swift measurements

Several studies over the last two decades have used canonical correlation analysis (CCA) to study the relationships between main γ-ray (e.g. fluence, peak flux, and duration) and main X-ray (flux, decay and spectral index, and hydrogen column density) data from gamma-ray bursts (GRBs). In this paper, we revisit this approach using a much larger dataset to identify potential new insights into these relationships. We used CCA to investigate the interrelationship of the aforementioned gamma-ray and X-ray parameters. Using the derived canonical variables, we calculated their correlations (canonical loadings) with the original data. Consistently with previous research, the analysis revealed that gamma-ray fluence and X-ray flux have the strongest correlation, while the X-ray decay index and spectral index have a lower contribution. Interestingly, our analysis of a much larger dataset reveals that the HI column density makes a significant contribution to the overall correlation. This finding, in the context of the collapsar model for long GRBs, could be interpreted as an indication that the progenitor star ejected an HI envelope during the GRB.