Afterglows from precursors in Gamma Ray Bursts. Application to the optical afterglow of GRB 091024

About 15% of Gamma Ray Bursts have precursors, i.e. emission episodes preceding the main event, whose spectral and temporal properties are similar to the main emission. We propose that precursors have their own fireball, producing afterglow emission due to the dissipation of the kinetic energy via external shock. In the time lapse between the precursor and the main event, we assume that the central engine is not completely turned off, but it continues to eject relativistic material at a smaller rate, whose emission is below the background level. The precursor fireball generates a first afterglow by the interaction with the external circumburst medium. Matter injected by the central engine during the "quasi-quiescent" phase replenishes the external medium with material in relativistic motion. The fireball corresponding to the main prompt emission episode crashes with this moving material, producing a second afterglow, and finally catches up and merges with the first precursor fireball. We apply this new model to GRB 091024, an event with a precursor in the prompt light curve and two well defined bumps in the optical afterglow, obtaining an excellent agreement with the existing data.