2000NewA....5..377A

One of remarkable features of the gamma-ray blazar Markarian 501 is the reported shape of the TeV spectrum which during strong flares of the source remains essentially stable despite dramatic variations of the absolute gamma-ray flux. I argue that this unusual behavior of the source could be explained assuming that the TeV emission is a result of synchrotron radiation of extremely high energy (E ≥ 10^19 eV) protons in highly magnetized (B ∼ 30-100 G) compact regions of the jet with typical size R ∼ 10^15–1016 cm and Doppler factor delta_j ~= 10-30. It is shown that if protons are accelerated at the maximum possible rate i.e. t_acc=eta(rg/c) with so-called gyro-factor eta ∼ 1 the synchrotron cooling of protons could not only dominate over other radiative and non-radiative losses but could also provide good fits (within uncertainties introduced by extragalactic gamma-ray extinction) to the gamma-radiation of two firmly established TeV blazars - Markarian 501 and Markarian 421. Remarkably if the proton acceleration takes place in the regime dominated by synchrotron losses the spectral shape of the Doppler-boosted gamma-radiation in the observer's frame is determined essentially by the self-regulated "synchrotron cutoff" at epsi_0 ~= 0.3 delta_j eta^ - 1 TeV. The hypothesis of the proton-synchrotron origin of TeV flares of BL Lac objects inevitably implies that the energy contained in the form of magnetic field in the gamma-ray emitting region exceeds the kinetic energy of accelerated protons.