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Lower limits on ultrahigh-energy cosmic ray and jet powers of TeV blazars

Lower limits on the power emitted in ultrahigh-energy cosmic rays (UHECRs), which are assumed to be protons with energy 1e17-1e20 eV, are derived for TeV blazars with the assumption that the observed TeV gamma rays are generated due to interactions of these protons with cosmic microwave photons. The limits depend on the spectrum of the injected UHECR protons. While for a -2.2 injection spectrum, the lower limits on the powers emitted in UHECRs by 1ES 0229+200, 1ES 1101-232 and 1ES 0347-121 are lower than their respective synchrotron luminosities (1e46 erg/s); in the case of 1ES 1426+428 it exceeds the corresponding synchrotron luminosity by up to an order of magnitude. The proposed Auger North Observatory should be able to detect 4e19 eV cosmic ray protons from 1ES 1426+428 within a few years of operation and test the TeV gamma-ray production model by UHECR energy losses while propagating along the line-of-sight, or constrain the intergalactic magnetic field to be larger than 1e-16 G in case of no detection. The lower limits on the apparent-isotropic jet power from accelerated 1e10-1e20 eV proton spectra in the blazar jet is of the order of the Eddington luminosity of a 1e9 solar mass black hole for a cosmic-ray injection spectrum -2.2 or harder for all blazars considered except for 1ES 1426+428. In the case of the latter the apparent-isotropic jet power exceeds the Eddington luminosity by an order of magnitude. For an injection spectrum softer than -2.2, as is required to fit the observed cosmic-ray data above 1e17-1e18 eV, the Eddington luminosity is exceeded by the lower limits on the jet power for all blazars considered.