Compton rockets and the minimum power of relativistic jets

The power of a relativistic jet depends on the number of leptons and protons carried by the jet itself. We have reason to believe that powerful gamma-ray flat spectrum radio sources emit most of their radiation where radiative cooling is severe. This helps us to find the minimum number of emitting leptons needed to explain the radiation we see. The number of protons is more uncertain. If there is one proton per electron, they dominate the jet power, but they could be unimportant if the emission is due to electron-positron pairs. In this case, the total jet power could be much smaller. However, if the gamma-ray flux is due to inverse Compton scattering with seed photons produced outside the jet, the radiation is anisotropic also in the comoving frame, making the jet recoil. This Compton rocket effect is strong for light, electron-positron jets, and negligible for heavy, proton-dominated jets. No significant deceleration, required by fast superluminal motion, requires a minimum number of protons per lepton, and thus a minimum jet power. We apply these ideas to the blazar 3C 454.3 to establish a robust lower limit to its total jet power: if the viewing angle theta(v) approximate to 1/Gamma, the jet power is larger than the accretion luminosity L(d) for any bulk Lorentz factor Gamma. For theta(v) = 0 degrees, instead, the minimum jet power can be smaller than L(d) for Gamma < 25. No more than similar to 10 pairs per proton are allowed.