Extragalactic electromagnetic cascades in various magnetic fields

Herein discussed is the magnetic field influence on diffuse gamma-ray emission that is generated by electromagnetic cascades which are initiated by ultra-high energy cosmic rays in extragalactic space. In space the magnetic field strength varies considerably. It is of 10 −12 G and lower in voids, of ~10 −6 G inside galaxies, galactic clusters and groups, and of ~10 −7 G around them. In filaments the field varies from ~10 −8 to ~10 −9 G. Structures, where fields are higher than in voids, occupy a relatively tiny part of the Universe, and their effect on cascade emission is weak. However, the knowledge of that influence may still come relevant to investigation of the large-scale component of the extragalactic magnetic field, and also to the search for exotic particles, because in the latter case all the diffuse emission components should be known, one of which is cascade emission. We study magnetic field effect in the simple case of homogeneous magnetic field and simulate particle propagation in field of ~10 −6 , 10 −9 , and 10 −12 G and lower strength. It turns out that at energies E ≤ 10 17 eV the calculated spectra of cascade gamma-rays are equal to each other in the fields of ~10 −9 G and lower strength. So, it can be concluded that possibly no particular models of extragalactic magnetic field are required to investigate the contribution of cascade emission in the extragalactic gamma-ray background at E ≤ 10 17 eV. The magnetic field being of 10 −6 G, which seems highly improbable, such conclusion is valid in the energy range E~(10 7 − ~10 9 ) eV.