2010A&A...511A..26E

An analytical model is presented which describes the intrinsic synchrotron intensity emitted by a spherical plasmoid volume of radius R in the jet of an active galactic nucleus (AGN). Analytical results for the emergent synchrotron intensity could be achieved by using a monochromatic approximation for the synchrotron power. The synchrotron intensity is given by an infinite sum, reflecting the spatial eigenfunction distribution of the radiating electrons over the emission knot. The radiative transport of the generated synchrotron photons is simplified by the use of the escape probability concept which approximates the spatial photon diffusion caused by multiple Compton scatterings off thermal electrons in the knot. With these assumptions conclusions on the total duration of the synchrotron flare, its starting time and the cause for even shorter time variabilities are derived. The total flare duration at all photon energies ε equals the light travel time 2R/c. Shorter photon energy-dependent synchrotron intensity time variations are possible, which reflect the influence of the photon retardation and escape as well as the temporal and spatial dependences of the relativistic electron density distribution. The starting time of the synchrotron flare is delayed with respect to the injection time of ultrarelativistic electrons t₀ by a photon energy dependent time scale ∝ε^–1/2, reflecting the necessary cooling time which relativistic electrons need in order to radiate at photon energies below the initial characteristic synchrotron photon energy E₀.