2012ApJ...745..196R

Lower limits on the power emitted in ultrahigh-energy cosmic rays (UHECRs), which are assumed to be protons with energy ≳ 10¹⁷-10²⁰ eV, are derived for TeV blazars with the assumption that the observed TeV γ-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 (∼10⁴⁶ 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 4x10¹⁹ eV cosmic-ray (CR) protons from 1ES 1426+428 within a few years of operation and test the TeV γ-ray production model by UHECR energy losses while propagating along the line of sight or constrain the intergalactic magnetic field to be larger than ∼10^–16 G in case of no detection. The lower limits on the apparent-isotropic jet power from accelerated 10¹⁰-10²⁰ eV proton spectra in the blazar jet is of the order of the Eddington luminosity of a 10⁹ M_☉ black hole for a CR 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 CR data above ∼10¹⁷-10¹⁸ eV, the Eddington luminosity is exceeded by the lower limits on the jet power for all blazars considered.