Semi-Analytic Model for Intergalactic Gamma-Ray Cascades in
  Extragalactic Magnetic Fields
  Primary gamma rays emitted by extragalactic sources, such as blazars, will
generate electromagnetic cascades in intergalactic space. These cascades
proceed via electron-positron pair production and inverse Compton scattering on
cosmic background radiation, mainly the cosmic microwave background (CMB) and
extragalactic background light (EBL) fields. The existence of an extragalactic
magnetic field (EGMF) could deflect electron-positron pair trajectories and
scatter the cascade photons, possibly creating a halo around the source while
suppressing the cascade flux collected by a detector. We develop a
semi-analytic model for the cascade process and apply it to combine GeV-TeV
data on high-frequency-peaked Bl Lacertae objects (HBLs) from the Fermi Large
Area Telescope (LAT) and ground-based Cherenkov telescopes, comparing
observation results with model predictions using a robust statistical
framework. Lower limits with different confidence levels on the field strength
of the EGMF derived from this procedure are discussed under various assumptions
about the source livetime.
