TeV gamma rays from BL Lac objects due to synchrotron radiation of extremely high energy protons

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 γ-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 ¹⁵-10 ¹⁶ cm and Doppler factor δ_j≃10-30. It is shown that if protons are accelerated at the maximum possible rate, i.e. t_acc= η( r_g/ c) with so-called gyro-factor η∼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 γ-ray extinction) to the γ-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 γ-radiation in the observer's frame is determined essentially by the self-regulated "synchrotron cutoff" at ɛ ₀≃0.3 δ _jη ^-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 γ-ray emitting region exceeds the kinetic energy of accelerated protons.