Gamma-Ray Burst Spectrum with a Time-dependent Injection Rate of High-energy Electrons

Abstract

Abstract Although the physical origin of prompt emission in gamma-ray bursts (GRBs) remains inconclusive, previous studies have considered the synchrotron radiation of relativistic electrons as a promising mechanism. These works usually adopted an invariable injection rate of electrons (Q) which may be discordant with that in a Poynting-flux-dominated jet. In a Poynting-flux-dominated jet (e.g., internal-collision-induced magnetic reconnection and turbulence model), the number of magnetic reconnections occurring simultaneously may grow rapidly with time and result in an increase of Q with time. This paper is dedicated to studying the synchrotron radiation spectrum in this scenario. It is found that the radiation spectrum would obviously get harder if an increasing Q is adopted and a Band-like radiation spectrum can be obtained if the increase of Q is fast enough. The latter is related to the fact that a bump shape rather than a power-law spectrum appears in the low-energy regime of the obtained electron spectrum. This effect can strongly harden the low-energy radiation spectrum. It indicates that an increasing Q can help to alleviate the “fast-cooling problem” of synchrotron radiation for GRBs. Our studies also reveal that a Poynting-flux dominated jet with a large emission radius, a short magnetic reconnection region length, or an injected electron with low minimum energy would prefer to form a Band-like radiation spectrum. We suggest that the Band spectrum found in GRBs may be the synchrotron emission of the electrons with a bump-shape distribution in its low-energy regime.