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 10 ^ { 6 } – 10 ^ { 7 } ) 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 .