The reduction of distant blazars' inverse Compton cascade emission by plasma instability induced beam plateauing

The attenuation of TeV gamma-rays from distant blazars by the extragalactic background light produces collimated relativistic electron-positron pair beams. The pair beams traversing the intergalactic medium are unstable to linear two-stream instabilities of both electrostatic and electromagnetic nature. We investigate the case of weak blazars where the back reaction of generated electrostatic turbulence leads to a parallel plateauing of the electron energy spectrum. We determine the inverse Compton cascade flux reduction above a certain normalized energy x(l) resulting from the incorporation of plasma effects on the beam particles distribution functions. A rational function R-S(x(l)) is presented, which gives the exact reduction factor in the steady-state case as well a good approximation in the flaring case. For a typical blazar scenario, the cascade flux reduction factor above 10 GeV is similar to 0.1. Application of our findings to the spectrum of 1ES 0229+200 shows that the incorporation of plasma effects leads to a natural explanation of the reduced observed GeV flux. Claims on the lower bound of the intergalactic magnetic field strengths, made by several authors to explain the flux reduction while neglecting plasma effects, are thus put into question.