Search for extended $\gamma$-ray emission around AGN with H.E.S.S. and Fermi-LAT

Context. Very-high-energy (VHE; E > 100 GeV) $\gamma$-ray emission from blazars inevitably gives rise to electron-positron pair production through the interaction of these γ-rays with the extragalactic background light (EBL). Depending on the magnetic fields in the proximity of the source, the cascade initiated from pair production can result in either an isotropic halo around an initially beamed source or a magnetically broadened cascade flux. Aims. Both extended pair-halo (PH) and magnetically broadened cascade (MBC) emission from regions surrounding the blazars 1ES 1101-232, 1ES 0229+200, and PKS 2155-304 were searched for using VHE $\gamma$-ray data taken with the High Energy Stereoscopic System (H.E.S.S.) and high-energy (HE; 100 MeV < E < 100 GeV) $\gamma$-ray data with the Fermi Large Area Telescope (LAT). Methods. By comparing the angular distributions of the reconstructed $\gamma$-ray events to the angular profiles calculated from detailed theoretical models, the presence of PH and MBC was investigated. Results. Upper limits on the extended emission around 1ES 1101-232, 1ES 0229+200, and PKS 2155-304 are found to be at a level of a few per cent of the Crab nebula flux above 1 TeV, depending on the assumed photon index of the cascade emission. Assuming strong extra-Galactic magnetic field (EGMF) values,  >10^{-12} G, this limits the production of pair haloes developing from electromagnetic cascades. For weaker magnetic fields, in which electromagnetic cascades would result in MBCs, EGMF strengths in the range (0.3−3)× 10^{-15}G were excluded for PKS 2155-304 at the 99% confidence level, under the assumption of a 1 Mpc coherence length.