Long pulse by short central engine: Prompt emission from expanding dissipation rings in the jet front of gamma-ray bursts

Recent observations have challenged the long-held opinion that the duration of gamma-ray burst (GRB) prompt emission is determined by the activity epochs of the central engine. Specifically, the observations of GRB 230307A have revealed a different scenario in which the duration of the prompt emission is predominantly governed by the energy dissipation process following a brief initial energy injection from the central engine. In this paper, we explore a mechanism where the energy injection from the central engine initially causes turbulence in a small region and radiates locally. This turbulence then propagates to more distant regions and radiates. Consequently, the emission regions form concentric rings that extend outward. Using an idealized toy model, we show that such a mechanism, initiated by a pulsed energy injection, can produce a prompt emission light curve resembling a single broad pulse exhibiting the typical softer-wider/softer-later feature. Under some parameters, the main characteristics of the GRB 230307A spectra and light curves can be reproduced by the toy model.