An advanced pulse-avalanche stochastic model of long gamma-ray burst light curves

TL;DR

The paper addresses the diversity of long GRB light curves by modeling the inner-engine variability as a stochastic pulse avalanche operating near a critical regime ($\mu \approx 1$). It introduces an enhanced model that constrains individual-pulse peak fluxes with a broken power-law distribution and validates performance across BATSE, Swift-BAT, and Fermi-GBM using a genetic algorithm for parameter optimization. The study reports improved agreement with real LGC statistics, including a new $S/N$-based metric, and finds consistent near-critical behavior across instruments, suggesting a universal stochastic dissipation mechanism. By providing a robust light-curve generator tailored to instrument characteristics, the work supports realistic simulations for future missions and deepens understanding of GRB prompt-emission variability.

Abstract

A unified explanation of the variety of long-duration gamma-ray burst (GRB) light curves (LCs) is essential for identifying the dissipation mechanism and possibly the nature of their central engines. In the past, a model was proposed to describe GRB LCs as the outcome of a stochastic pulse avalanche process, possibly originating from a turbulent regime, and it was tested by comparing average temporal properties of simulated and real LCs. Recently, we revived this model and optimised its parameters using a genetic algorithm (GA), a machine-learning-based approach. Our findings suggested that GRB inner engines may operate near a critical regime. Here we present an advanced version of the model, which allows us to constrain the peak flux distribution of individual pulses, and evaluate its performance on a new dataset of GRBs observed by the Fermi Gamma-ray Burst Monitor (GBM). After introducing new model parameters and a further comparison metric, that is the observed signal-to-noise (S/N) distribution, we test the new model on three complementary datasets: CGRO/BATSE, Swift/BAT, and Fermi/GBM. As in our previous work, the model parameters are optimised using a GA. The updated sets of parameters achieve a further reduction in loss compared to both the original model and our earlier optimisation. The different values of the parameters across the datasets are shown to originate from the different energy passbands, effective areas, trigger algorithms, and, ultimately, different GRB populations of the three experiments. Our results further underpin the stochastic and avalanche character of the dissipation process behind long GRB prompt emission, with an emphasis on the near-critical behaviour, and establish this new model as a reliable tool for generating realistic GRB LCs as they would be seen with future experiments.

Figures (5)

• Figure 1: Distributions of the logarithmic peak-flux-to-count-rate conversion factors $k$ for CGRO/BATSE, Swift/BAT, and Fermi/GBM.
• Figure 2: Distributions of the five metrics for real BATSE light curves (blue) and simulated profiles (red) obtained using the latest optimised parameter set (see Table \ref{['table::parameterresults']}). Top left: average peak-aligned post-peak normalised time profile and root mean square (r.m.s.) deviation of the individual peak-aligned profiles, $F_{\mathrm{rms}} \equiv[\langle(F / F_p)^2\rangle-\langle F / F_p\rangle^2]^{1/2}$. Top middle: average peak-aligned third moment profiles. Top left: average autocorrelation function of the GRBs. Bottom left: distribution of the $T_{20\%}$ duration. Bottom right: S/N distribution of the GRBs. Like in Bazzanini24, the curves in the top left and top middle panels were smoothed using a Savitzky-Golay filter to reduce the effects of Poisson noise, while the distributions in the bottom left panel were smoothed with a Gaussian kernel convolution.
• Figure 3: Comparison between the simulated peak flux distributions of the BATSE, Swift, and Fermi samples. Values were rescaled in the BATSE energy passband (25--2000 keV). The sharp drop in the low-tail distribution of BATSE simply reflects the optimal value of the minimum peak flux $F_{min}$ obtained with the GA, whereas the same drop for the other two sets was smeared out by the rescaling in the BATSE passband.
• Figure 4: Comparison between the real Swift/BAT dataset and the corresponding simulated dataset on the same metrics defined for the BATSE dataset, as in Fig. \ref{['fig::5observables_batse']}.
• Figure 5: Comparison between the real Fermi/GBM dataset and the corresponding simulated dataset on the same metrics defined for the BATSE dataset, as in Fig. \ref{['fig::5observables_batse']}.