Effects of non-continuous inverse Compton cooling in blazars

Context. Blazar flares provide a window into the extreme physical processes occurring in relativistic outflows. Most numerical codes used for modeling blazar emission during flares utilize a simplified continuous-loss description of particle cooling due to the inverse Compton (IC) process, neglecting non-continuous (discrete) effects that arise in the Klein-Nishina (KN) regime. The significance of such effects has not been explored in detail yet. Aims. In this study, we investigate the importance of non-continuous Compton cooling losses and their impact on the electron spectrum and spectral energy distribution (SED) of blazars during high flux states (flares), as well as in the low state. Methods. We solve numerically the full transport equation accounting for large relative jumps in energy, by extending our existing blazar flare modeling code EMBLEM. We perform a detailed physical modeling of the brightest gamma-ray flare of the archetypal Flat Spectrum Radio Quasar (FSRQ) 3C 279 detected in June 2015. We then compare results obtained using the full cooling term and using the continuous-loss approximation. Results. We show that during flaring states of FSRQs characterized by high Compton dominance, the non-continuous cooling can lead to a significant modification of the electron spectrum, introducing a range of distinct features, such as low-energy tails, hardening/softening, narrow and extended particle excesses, and shifts in the cooling break position. Such distortion translates to differences in the associated SED up to 50%. This highlights the importance of non-continuous effects and the need to consider them in blazar emission models, particularly applied to extreme gamma-ray flares.