Abstract
The possibility of measuring the intergalactic magnetic field between an extragalactic ultra-high-energy (UHE) γ-ray source and our Galaxy is studied. The absorption of UHE γ-rays in the 3 K microwave background changes its character at a magnetic field strength of 10^-12^ G. In stronger magnetic fields, UHE γ-rays with E<SUB>gamma</SUB>_ ~ 10^15^ eV are effectively absorbed. But for weaker field strengths, UHE γ-rays are converted to lower energy γ-rays by the cascading of UHE γ-rays and electrons in the 3 K microwave background. These effects make the UHE γ-ray energy spectrum at energies E<SUB>gamma</SUB>_ >= 10^14^ eV very different for B > 10^-12^ and B <= 10^-12^ G fields. From observations of an extragalactic UHE γ-ray source, the upper or lower bound of the magnetic field strength can be obtained.
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