Synchrotron X-ray and gamma-ray haloes of ultra-high-energy gamma-ray sources

Previous work on electron-photon cascades through the cosmic-microwave-background radiation initiated by primary γ-rays and electrons is extended to a three-dimensional calculation which includes synchrotron radiation. New functions which enable synchrotron photon spectra to be calculated more easily are described. These functions are used in a Monte Carlo cascade simulation to predict the size and intensity of synchrotron haloes surrounding sources of ultra-high-energy γ-rays. I conclude that these haloes may be observed with the next generation of X-ray and γ-ray telescopes. The observed hard X-ray spectrum of Cygnus X-3 at minimum flux in the 4.8-hr cycle is used, together with the present calculations, to obtain an upper limit to the time-averaged ultra-high-energy γ-ray flux from Cygnus X-3. (author)