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 \geq 10 ^ { 19 } eV ) protons in highly magnetized ( B \sim 30 - 100 G ) compact regions of the jet with typical size R \sim 10 ^ { 15 } -10 ^ { 16 } cm and Doppler factor \delta _ { j } \simeq 10 - 30 .
It is shown that if protons are accelerated at the maximum possible rate , i.e . t _ { acc } = \eta ( r _ { g } / c ) with so-called gyro-factor \eta \sim 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 \epsilon _ { 0 } \simeq 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 .