On the maximum energy of protons in the hotspots of AGN jets

Radiogalaxies are the subclass of active galactic nuclei (AGN) where prominent jets are detected at radio frequencies. We study particle acceleration and magnetic field amplification in the termination shocks (hotspots) of radio-galaxy jets. The cut-off of the synchrotron spectrum in the hotspots of powerful radiogalaxies is typically observed between infrared and optical frequencies, indicating that the maximum energy of non-thermal electrons accelerated at the jet termination shock is about 1 TeV for a canonical magnetic field of 100 μG. Based on theoretical considerations and observational data we show that the maximum energy of electrons cannot be constrained by synchrotron losses as usually assumed, unless the jet density is unreasonable large and most of the jet kinetic energy goes to non-thermal electrons. The maximum energy is ultimately determined by the ability to scatter particles back and forth the shock, and this limit applies to both electrons and protons. Therefore, the maximum energy of protons is also about 1 TeV when radiative cooling is not efficient. We show that non-resonant hybrid (Bell) instabilities generated by the streaming of cosmic rays can grow fast enough to amplify the jet magnetic field up to 100 μG and accelerate particles up to the maximum energies observed in the hotspots of radiogalaxies