Time Delay of Cascade Radiation for TeV Blazars and the Measurement of the Intergalactic Magnetic Field

Abstract: Recent claims that the strength B_IGMF of the intergalactic magnetic field (IGMF) is >~ 1e-15 G are based on upper limits to the expected cascade flux in the GeV band produced by blazar TeV photons absorbed by the extragalactic background light. This limit depends on an assumption that the mean blazar TeV flux remains constant on timescales >~2 (B_ IGMF/1e-18 G)^2 / (E/{10 GeV})^2 yr for an IGMF coherence length ~ 1 Mpc, where E is the measured photon energy. Restricting TeV activity of 1ES 0229+200 to ~3 -- 4 years during which the source has been observed leads to a more robust lower limit of B_IGMF >~ 1e-18 G, which can be larger by an order of magnitude if the intrinsic source flux above ~5 -- 10 TeV from 1ES 0229+200 is strong.