Hurst index of gamma-ray burst light curves and its statistical study

Abstract

Gamma-ray bursts (GRBs) rank among the most powerful astrophysical phenomena, characterized by complex and highly variable prompt emission light curves that reflect the dynamics of their central engines. In this work, we analyze a sample of 163 long-duration GRBs detected by the Burst and Transient Source Experiment (BATSE), applying detrended fluctuation analysis (DFA) to derive the Hurst index as a quantitative descriptor of temporal correlations in the light curves. We further explore statistical correlations between the Hurst index and 12 other observational parameters through regression and correlation analyses. Our results reveal anti-correlations between the Hurst index and the burst durations ($T_{50}$, $T_{90}$), and moderate positive correlations with peak photon flux proxies ($P_{pk1}$--$P_{pk3}$). By contrast, the standard spectral parameters (including the low-energy index $\alpha$) show no evidence for a linear dependence on the Hurst index in our sample. We do not find a clear monotonic weakening of the correlation strength from 64 ms to 1024 ms peak-flux measures; rather, the correlation coefficients for $P_{pk1}$--$P_{pk3}$ are comparable within uncertainties. The results offer new perspectives on the temporal structure of the GRB emission and its potential link to the underlying physical mechanisms driving these bursts.

arXiv comment34 pages, 14 figures, accepted by Journal of High Energy Astrophysics (JHEAP)

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