BL Lacertae objects (BLLs) constitute a class of active galactic nuclei (AGNs) with extreme observational features explained by non-thermal radiation from a relativistic jet nearly pointed along the observer’s line-of-sight. Their spectral energy distribution (SED), extending over 17-19 orders of the frequency, is of non-thermal origin and shows a typical two-humped structure. The lower-energy component, ranging from the radio to X-rays, is explained via synchrotron radiation emitted by ultra-relativistic electrons/positrons/protons, to be initially accelerated via the Blandford-Znajek mechanism or magneto-hydrodynamic processes in the vicinity of a central supermassive black hole. Afterwards, the particles should undergo further acceleration to ultra-relativistic energies by means of different mechanisms (first and second-order Fermi processes, relativistic magnetic reconnection, shear acceleration, jet-star interaction etc.) locally, in the jet emission zone. Our intensive X-ray spectral study of TeV-detected, high-energy-peaked BLLs (HBLs) often show the signatures of an effective second-order Fermi (stochastic) acceleration close to the shock front, while the processes related to the first-order Fermi acceleration are relatively rarely presented. The TeV-undetected HBLs and low-energy-peaked BLLs (LBLs) mostly do not show the signatures of efficient stochastic acceleration in their jets. Concerning the higher-energy component, the most frequently considered scenario incorporates an inverse Compton (IC) scattering of synchrotron photons by their ”parent” electron-positron population (synchrotron self-Compton model, SSC). However, this simple scenario sometimes is challenged by uncorrelated X-ray and TeV variability, more easily explained by multizone SSC, external Compton (EC) and hadronic scenarios.
Simulations of second-order Fermi acceleration of electrons: solving the injection problem