Hurst Index of Gamma-Ray Burst Light Curves and Its Statistical Study

TL;DR

This study applies monofractal detrended fluctuation analysis to 163 BATSE long GRB light curves to extract the Hurst index $H$ as a measure of long-range temporal correlations. By regressing $H$ against 12 GRB observables, the authors find a robust anti-correlation between $H$ and duration metrics $T_{50}$ and $T_{90}$, and moderate positive correlations with peak flux proxies $P_{pk1-3}$, while spectral parameters show only weak associations. The results imply that longer bursts exhibit weaker persistence in their prompt variability, whereas bursts with stronger peak emission tend to display stronger scaling behavior; however, substantial scatter and high reduced chi-square values suggest intrinsic dispersion and potential multi-component variability. The work highlights a quantitative link between prompt-emission temporal structure and key observables, motivating time-resolved DFA and cross-instrument comparisons to better understand GRB jet physics and central-engine processes.

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 (T50, T90), and moderate positive correlations with peak photon flux proxies (P_{pk1}--P_{pk3}). In contrast, correlations between the Hurst index and standard spectral parameters (including the low-energy index α) are weak 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.

Figures (14)

• Figure 1: Light curve of GRB 920110A as an example, the energy channel is 1-4 ($>20$ keV).
• Figure 2: $\ln F(s)-\ln s$ Scaling Relation and the OLS fit for GRB 920110A
• Figure 3: Scatter plot for $\alpha$ and Hurst index. The solid line is our fit result. The relation for the solid line is $\alpha=(-0.48\pm0.05)\times H +(1.83\pm0.06)$. The description of each parameter is in Section \ref{['subsec:phys_para']}.
• Figure 4: Scatter plot for $\beta$ and Hurst index. The solid line is our fit result. The relation for the solid line is $\beta=(0.12\pm0.03)\times H +(2.23\pm0.06)$. The description of each parameter is in Section \ref{['subsec:phys_para']}.
• Figure 5: Scatter plot for $\log{E_{peak}}$ and Hurst index. The solid line is our fit result. The relation for the solid line is $\log{E_{peak}}=(0.35\pm0.04)\times H +(1.83\pm0.06)$. The description of each parameter is in Section \ref{['subsec:phys_para']}.