Abstract Primary gamma rays emitted from extragalactic very-high-energy (VHE) sources, such as blazars, will generate cascade radiation in intergalactic space with a scale of ∼100 Mpc, for z ∼ 0.1 and Eγ ∼ 1 TeV. These cascades proceed through electron-positron pair production and inverse Compton (IC) scattering in the cosmic background radiation fields, mainly cosmic microwave background (CMB) radiation and extragalactic background light in the voids of the universe. The existence of an intergalactic magnetic field (IGMF) would deflect paths of electron-positron pairs that scatter CMB photons, causing some observable effects, such as time delay, an extended halo, and a spectral change. Here we reanalyze the diffusion of an electron jet deflected by IGMF and propose a unified semi-analytical model. By using publicly available data from the Fermi/LAT detector and contemporaneous TeV observations, we find that the cascade photon flux is not significantly affected by the IGMF strength for non-variable blazars when the IGMF is weaker than ∼ 10−16 G. This result is clearly different from previous works that analyzed the extended halo and time delay separately for non-variable blazars and flaring blazars. By applying our model to two extreme blazars (1ES 0229+200 and 1ES 1218+304), we obtain the IGMF lower limit of order ≳10−13 ∼ 10−14 G in the non-variable case, which is a stronger constraint on the IGMF strength than previous works (≳10−16 ∼ 10−18 G), and ≳10−18 ∼ 10−19 G in the case of flaring blazars. Furthermore, we study the light curves and extended halo of the cascade photons by considering the effects of the IGMF.
Keywords gamma rays: general — galaxies: magnetic field — galaxies: individual (1ES 0229+200, 1ES 1218+304)
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