GRB prompt emission from the synchrotron radiation of relativistic electrons in a decaying magnetic field

The origin of the prompt gamma-ray burst (GRB) emission is still highly debated. The observed spectra provide key constraints: the low energy slope of the photon spectrum α, which is commonly determined in energy range of ∼ 10 keV up to ∼ a few MeV, shows a mean values α ∼ –1 above the expected value −3/2 for the synchrotron fast cooling regime, and even values above −2/3, the synchrotron slow cooling limit. We studied the effect of a decaying magnetic field in the emission region on the synchrotron spectrum of relativistic electrons. An important parameter is the timescale for the decay of the magnetic field compared to two other relevant timescales: the dynamical timescale (adiabatic cooling) and the radiative timescale of electrons responsible of the peak of the spectrum. If the magnetic field decay timescale is between these two timescales, our simulation show that the marginally fast cooling regime can be naturally achieved, leading to photon index up to -2/3.