The intergalactic magnetic field constrained by Fermi/Large Area Telescope observations of the TeV blazar 1ES 0229+200

TeV photons from blazars at relatively large distances, interacting with the optical-IR cosmic background, are efficiently converted into electron-positron pairs. The produced pairs are extremely relativistic (Lorentz factors of the order of 1e6 1e7 and promptly loose their energy through inverse Compton scatterings with the photons of the microwave cosmic background, producing emission in the GeV band. The spectrum and the flux level of this reprocessed emission is critically dependent on the intensity of the intergalactic magnetic field, B, that can deflect the pairs diluting the intrinsic emission over a large solid angle. We derive a simple relation for the reprocessed spectrum expected from a steady source. We apply this treatment to the blazar 1ES 0229+200, whose intrinsic very hard TeV spectrum is expected to be approximately steady. Comparing the predicted reprocessed emission with the upper limits measured by the Fermi/Large Area Telescope, we constrain the value of the intergalactic magnetic field to be larger than $B \simeq 5\times 10^{-15}$ Gauss, depending on the model of extragalactic background light.