2018ApJ...853...43X

The prompt emission spectrum of gamma-ray bursts is characterized by a smoothly joint broken power-law spectrum known as the Band function. The typical low-energy photon index is ∼-1, which poses a challenge to standard synchrotron radiation models. We investigate the electron energy spectrum as a result of the interplay among adiabatic stochastic acceleration (ASA), particle injection, and synchrotron cooling. In the ASA-dominated low-energy range, ASA enables an efficient hardening of the injected energy spectrum to approach a spectral index -1. In the synchrotron cooling-dominated high-energy range, the injected high-energy electrons undergo fast synchrotron cooling and have a softer photon spectrum. With the energy range of the injected electrons broadly covering both the ASA- and synchrotron cooling-dominated ranges, the resulting photon number spectrum has low- and high-energy indices of α_s∼-1 and β_s∼-p/2-1, respectively. The break energy is of the order of ∼100 keV, depending on the turbulence properties.