Lower limit on the strength and filling factor of extragalactic magnetic
  fields
  High energy photons from blazars can initiate electromagnetic pair cascades
interacting with the extragalactic photon background. The charged component of
such cascades is deflected and delayed by extragalactic magnetic fields (EGMF),
reducing thereby the observed point-like flux and leading potentially to multi
degree images in the GeV energy range. We calculate the fluence of 1ES 0229+200
as seen by Fermi-LAT for different EGMF profiles using a Monte Carlo simulation
for the cascade development. The non-observation of 1ES 0229+200 by Fermi-LAT
suggests that the EGMF fills at least 60% of space with fields stronger than
{\cal O}(10^{-16}-10^{-15})G for life times of TeV activity of {\cal
O}(10^2-10^4)yr. Thus the (non-) observation of GeV extensions around TeV
blazars probes the EGMF in voids and puts strong constraints on the origin of
EGMFs: Either EGMFs were generated in a space filling manner (e.g.
primordially) or EGMFs produced locally (e.g. by galaxies) have to be
efficiently transported to fill a significant volume fraction, as e.g. by
galactic outflows.
