Exploring the evolution of the particle distribution and the cascade in a moving, expanding emission region in blazar jets

Aims. Models built to explain blazar flares display a broad variety of results. In this work, we study the flare profile induced by a moving and expanding blob, with a special emphasis on gamma - gamma pair production.Methods. We first developed a simple semi-analytical model to study the evolution of the particle distribution in the expanding blob and show the influence of the pair production. In a second step, we produced a realistic simulation using the OneHaLe code based upon the parameters of PKS 1510-089.Results. The applied semi-analytical model shows that the pair production significantly influences the flare evolution, while the opening angle and the expansion can prolong flares considerably. The simulation based on PKS 1510-089 indicates that flares of a moving, expanding blob result in strongly wavelength-dependent light curves that may include delayed, secondary flares.Conclusions. A moving, expanding blob can cause significant flaring events, with a broad variety in terms of the light curve profiles. High-cadence multiwavelength observations are necessary for deriving the details behind the cause of the flare. Extended observations beyond the initial burst may provide important information on the opening angle and the particle content attributed to delayed secondary flares in some energy bands.