Radiation mechanism of gamma-ray burst prompt emission

Synchrotron radiation of relativistic electrons is an important radiation mechanism in many astrophysical sources. In the sources where the synchrotron cooling timescale is shorter than the dynamical timescale, electrons are cooled down below the minimum injection energy. It has been believed that such fast-cooling electrons have a power-law distribution in energy with an index -2, and their synchrotron radiation has a photon spectral index -1.5. On the other hand, in a transient expanding astrophysical source, such as a gamma-ray burst (GRB), the magnetic field strength in the emission region continuously decreases with radius. Here we study such a system, and find that in a certain parameter regime, the fast-cooling electrons can have a harder energy spectrum. We apply this new physical regime to GRBs, and suggest that the GRB prompt emission spectra whose low-energy photon spectral index has a typical value -1 could be due to synchrotron radiation in this moderately fast-cooling regime.