A Comprehensive Review of Low-Luminosity Gamma-Ray Burst Afterglow Modelling in the Synchrotron External Shock Scenario with Bayesian Population Analysis
This paper presents a comprehensive review of the broadband afterglow modelling of low-luminosity gamma-ray bursts (LLGRBs) within the standard synchrotron external forward-shock framework. We synthesize two decades of theoretical developments and observational findings, providing a unified picture of LLGRB afterglow properties from radio to gamma-ray frequencies. Using a sample of eight confirmed LLGRBs (GRB 980425, 031203, 060218, 100316D, 171205A, 111005A, 120422A, and 161219B), we complement this review with an original Bayesian population inference on their redshift, isotropic-equivalent energy, and luminosity distributions. Our analysis demonstrates that LLGRBs form a coherent, nearby population that extends the classical Amati and Yonetoku relations toward lower energies. The review synthesizes current knowledge on: i) the dynamical evolution of the forward shock in LLGRB environments; ii) the spectral regimes and closure relations characteristic of slow-cooling synchrotron emission; iii) the diversity of observed multi-wavelength light curves; and iv) the implications for LLGRB progenitor models and their connection to the broader GRB population. We also discuss current challenges, including selection biases, the small number of confirmed events, and the role of numerical codes such as afterglowpy in future analyses. This review provides a foundation for interpreting current and future LLGRB observations and highlights the value of Bayesian methods in extracting population-level inferences from sparse datasets.
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