One Fits All: A Unified Synchrotron Model Explains GRBs with FRED-Shaped Pulses

Abstract

The analysis of gamma-ray burst (GRB) spectra often relies on empirical models like the Band function, which lacks a distinct physical explanation. Previous attempts to couple physical models with observed data have been confined to individual burst studies, where the model is fitted to segmented spectra with independent physical parameters. These approaches frequently fail to explain the spectral evolution, which should be governed by a consistent set of physical conditions. In this study, we propose a novel approach by incorporating the synchrotron radiation model to provide a self-consistent explanation for a selection of single-pulse GRBs. Our sample is carefully chosen to minimize contamination from overlapping pulses, allowing for a comprehensive test of the synchrotron model under a unified physical condition, such as a single injection event of electrons. By tracing the evolution of cooling electrons in a decaying magnetic field, our model predicts a series of time-dependent observed spectra that align well with the observed data. Remarkably, using a single set of physical parameters, our model successfully fits all time-resolved spectra within each burst. Additionally, our model accurately predicts the evolution of some key features of GRBs such as the spectral peak $E_{\rm p}$ and light curve shapes, all of which are consistent with observations. Our findings strongly support the notion that the spectral and temporal evolution in GRB pulses originates from the expansion of the GRB emission region with an initial radius of approximately $10^{15}$ cm, with synchrotron radiation being the underlying emission mechanism.Comment: 25 pages, 18 figures, 4 table