BL Lacertae objects constitute a rare class of active galactic nuclei with extreme observational features attributed to the Doppler-boosted emission from a relativistic jet, closely aligned to our line-of-sight. Their spectral energy distribution, extending over 17–19 orders of frequency from radio to the TeV energy range, is of non-thermal origin and shows a typical two-component structure. The lower-energy component, ranging from the radio to X-rays in the high-energy peaked BL Lacertae sources, is widely accepted to be a synchrotron radiation emitted by ultra-relativistic charged particles, to be initially accelerated via the Blandford–Znajek mechanism or magneto-hydrodynamic processes in the vicinity of the central super-massive black hole. However, the accelerated particles should lose the energy, sufficient for the emission of the keV-GeV photons, very quickly and the source can maintain its flaring state on the daily-weekly timescales only if some additional acceleration mechanisms are continuously at work. According to different studies and simulations,the particles can gain tremendous energies due to the propagation of relativistic shocks through the jet: By means of first-order Fermi mechanism at the shock front, or they undergo an efficient stochastic (second-order Fermi) acceleration close to the shock front, in the turbulent jet medium. Our intensive X-ray spectral study of TeV-detected, bright BL Lacertae objects (Mrk 421, 1ES 1959+650, Mrk 501) often show the signatures of the stochastic acceleration, while those related to the first-order Fermi process arefound relatively rarely. The TeV-undetected sources (1H 1516+660, BZB J1341+3959, BZB J1237+6258) mostly do not show the signatures of the efficient stochastic acceleration in their jets.
BL Lacertae Objects: A Short Review