On the synchrotron spectrum of GRB prompt emission

Understand

The prompt emission spectrum of Gamma-ray bursts (GRB) is characterized by a smoothly joint broken power-law spectrum known as the Band function.

• The typical low-energy photon index is $\sim -1$, which poses challenge to the 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 $-1$.