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External Compton emission in blazars of non-linear SSC cooled electrons

The origin of the high-energy component in spectral energy distributions (SED) of blazars is still a bit of a mystery. While BL Lac objects can be rather successfully modelled within the one-zone synchrotron self-Compton (SSC) scenario, the SED of low peaked Flat Spectrum Radio Quasars (FSRQ) is more difficult to reproduce. Their high-energy component needs the abundance of strong external photon sources, giving rise to stronger cooling via the inverse Compton channel, and thusly to a powerful component in the SED. Recently, we were able to show that such a powerful inverse Compton component can also be achieved within the SSC framework. This, however, is only possible if the electrons cool by SSC, which results in a non-linear process, since the cooling depends on an energy integral over the electrons. In this paper we aim to compare the non-linear SSC framework with the external Compton (EC) output by calculating analytically the external Compton component with the underlying electron distribution being either linearly or non-linearly cooled. Due to the additional linear cooling of the electrons with the external photons, higher number densities of electrons are required to achieve non-linear cooling, resulting in more powerful inverse Compton components. If the electrons initially cool non-linearly, the resulting SED can exhibit a dominating SSC over the EC component. However, this dominance depends strongly on the input parameters. We conclude that with the correct time-dependent treatment the SSC component should be taken into account to model blazar flares.