SSC radiation in BL Lacertae sources, the end of the tether

Context. The synchrotron-self Compton (SSC) radiation process is widely held to provide a close representation of the double peaked spectral energy distributions from BL Lac Objects (BL Lacs). This subclass of Active Galactic Nuclei is marked by non-thermal beamed radiations, highly variable on timescales of days or less. Their outbursts in the γ rays relative to the optical/X rays might be surmised to be enhanced in BL Lacs as these photons are upscattered via the inverse Compton (IC) process. Aims. From the observed correlations among the spectral parameters (peak frequencies, fluxes and curvature) during optical/X-ray variations we aim at predicting corresponding correlations in the γ-ray band, and the actual relations between the γ-ray and the X-ray variability consistent with the SSC emission process. Methods. We start from the homogeneous single-zone SSC source model, with log-parabolic energies distributions of emitting electron as required by the X-ray data of many sources. We find relations among spectral parameters of the IC radiation in both the Thomson (for Low energy BL Lacs) and the Klein-Nishina regimes (mainly for High energy BL Lacs); whence we compute how variability is driven by a smooth increase of key source parameters, primarily the root mean square electron energy. Results. In the Klein-Nishina regime the model predicts for HBLs lower inverse Compton fluxes relative to synchrotron, and milder γ-ray relative to X-ray variations. Stronger γ-ray flares observed in some HBLs like Mrk 501 are understood in terms of additional, smooth increases also of the emitting electron density. However, episodes of rapid flares as recently reported at TeV energies are beyond the reach of the single component SSC model with one dominant varying parameter. Furthermore, spectral correlations at variance with our predictions, as well as TeV emissions in LBL objects (like BL Lacertae itself) cannot be explained in terms of the simple HSZ SSC model, and in these cases the source may require additional electron populations in more elaborate structures like decelerated relativistic outflows or sub-jet scenarios. Conclusions. We provide a comprehensive benchmark to straightforwardly gauge the capabilities and effectiveness of the SSC radiation process. The single component SSC source model in the Thomson regime turns out to be adequate for many LBL sources. In the mild Klein-Nishina regime it covers HBL sources undergoing variations driven by smooth increase of a number of source parameters. However, the simple model meets its limits with the fast/strong flares recently reported for a few sources in the TeV range; these clearly require sudden accelerations of emitting electrons in a second source component.