Internal Shock with a Background Magnetic Field for the Prompt Emission of Gamma-Ray Bursts-A Case Study of GRB 211211A

It is proposed that the synchrotron emission from an internal shock with a decaying shock-generated magnetic field can account for the prompt emission of gamma-ray bursts (GRBs). Generally, a jet from the central engine of a GRB is launched with a significant magnetization, and thus there would be a background magnetic field, rather than only the shock-generated magnetic field, in the emission region. In this paper, we study the synchrotron emission of internal shocks with both a decaying shock-generated magnetic field and a nondecaying background magnetic field. It is found that a shoulder with spectral index -1/2 appears in the low-energy regime of the radiation spectrum. The shoulder becomes dominant by increasing the ratio of the background magnetic field energy to the initial value of the shock-generated magnetic field energy f B. Correspondingly, a radiation spectrum with two bumps or a plateau around the peak of the nu F nu -nu spectrum may appear. Owing to the decay of the shock-generated magnetic field, the radiation spectral morphology in the high-energy regime is not a power-law function even though a power-law distribution of electrons is injected. We apply our model to GRB 211211A, of which the hard main emission is suggested to originate from the synchrotron emission. Compared with the spectral fitting results with a Band function and the synchrotron emission from the standard straightforward internal shocks, our model presents a perfect fitting to the observations. The fitting results show that f B is around 0.41-0.99 for the hard main emission of this burst.