Abstract
Context.
The origin of prompt emission in gamma-ray bursts (GRBs) remains a fundamental open question. The internal shock (IS) model is a leading mechanism proposed to explain the dissipation of kinetic energy from relativistic ejecta into gamma rays. However, the model parameters have yet to be fully optimised to reproduce the diverse morphological properties observed in real GRB light curves (LCs).
Aims.
Utilising a machine-learning framework, we evaluated the IS model through parameter optimisation, comparing the statistical properties of simulated LCs against those of observed data.
Methods.
Our dataset consists of three GRB catalogues (
Swift
/BAT,
Fermi
/GBM, and
CGRO
/BATSE). By adopting a model for the GRB formation rate as a function of redshift, we employed a genetic algorithm to optimise the IS model parameters. The algorithm minimises a total loss function based on six independent metrics, representing both the average properties and the statistical distributions of real LCs.
Results.
The calibrated IS model successfully reproduces the average post-peak GRB temporal profile, together with the corresponding root-mean-square and third-moment temporal profiles, as well as the average autocorrelation function. Furthermore, it recovers the observed distributions of duration, signal-to-noise ratio, peak count per burst, peak flux, and fluence. We find that a generalised Zipf distribution governs the number of shells emitted per GRB, while rest-frame emission times follow a negative exponential distribution.
Conclusions.
The optimised formulation of the IS model reproduces a wide range of observed GRB LC properties, despite its simplified treatment of radiation physics. Moreover, it provides two key insights into the central engine’s activity: (i) the emission times suggest a stochastic process where all shells within a given burst have an identical, independent, and constant probability of ejection per unit time; and (ii) the heavy-tailed distribution of the number of shells per GRB mirrors the frequency-magnitude distribution of earthquakes, known as the Gutenberg-Richter law. Finally, this optimised model serves as a predictive tool for the GRB populations expected to be detected by future missions.