Constraining Intergalactic Magnetic Field with Fermi-LAT Observation of Cascade Radiation for TeV Blazars

Abstract

The problem concerning the origin of the Intergalactic Magnetic Field (IGMF) is one of the long-standing problems of astrophysics and cosmology, and direct measurements are difficult. TeV photons emitted by TeV blazars produce electron-positron pairs because of interactions with the extragalactic background light (EBL). These pairs emit secondary cascade gamma-rays via Inverse Compton scattering of the cosmic microwave background (CMB) photons. In this process, the trajectories of the pairs are deviated by the IGMF, and the cascade gamma-ray emission appears as extended emission around TeV source. We used the EBL, synchrotron self-Compton (SSC) model and the observed limits on Lorentz factor of electron-positron pairs to calculate the cascade-radiation spectrum, and then to fit the observed GeV to TeV and multi-waveband spectra of TeV blazars to constrain the IGMF. We obtained the GeV energy spectra of three TeV blazars by analyzing the Fermi-LAT data of the past $ \sim$ 3 yr. The flux upper limits of Fermi-LAT in the 90% significant level of 1ES 0229$ +$ 200 suggests that the IGMF is stronger than 2 $ \times$ 10$ ^{-18}$ G for an engine time of TeV activity with three years. The relationships between the deduced lower limits of IGMF and various engine times for 1ES 0229$ +$ 200 and 1ES 0347$-$ 121 are presented by us.