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.
