Flaring of blazars from an analytical, time-dependent model for combined synchrotron and synchrotron self-Compton radiative losses of multiple ultrarelativistic electron populations

We present a fully analytical, time-dependent leptonic one-zone model that describes a simplified radiation process of multiple interacting ultrarelativistic electron populations and accounts for the flaring of GeV blazars. In this model, several mono-energetic, ultrarelativistic electron populations are successively and instantaneously injected into the emission region, that is, a magnetized plasmoid propagating along the blazar jet, and subjected to linear, time-independent synchrotron radiative losses, which are caused by a constant magnetic field, and nonlinear, time-dependent synchrotron self-Compton radiative losses in the Thomson limit. Considering a general (time-dependent) multiple-injection scenario is, from a physical point of view, more realistic than the usual (time-independent) single-injection scenario invoked in common blazar models, as blazar jets may extend over tens of kiloparsecs and thus most likely pick up several particle populations from intermediate clouds. We analytically compute the electron number density by solving a kinetic equation using Laplace transformations and the method of matched asymptotic expansions. Moreover, we explicitly calculate the optically thin synchrotron intensity, the synchrotron self-Compton intensity in the Thomson limit, as well as the associated total fluences. In order to mimic injections of finite duration times and radiative transport, we model flares by sequences of these instantaneous injections, suitably distributed over the entire emission region. Finally, we present a parameter study for the total synchrotron and synchrotron self-Compton fluence spectral energy distributions for a generic three-injection scenario, varying the magnetic field strength, the Doppler factor, and the initial electron energy of the first injection in realistic parameter domains, demonstrating that our model can reproduce the typical broadband behavior seen in observational data