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Possible existence of extragalactic ultra-high energy cosmic ray sourcesgiving a very small particle flux on the Earth is considered. Accretion discsaround supermassive black holes where particles are accelerated in electricfields are discussed as an illustration of such sources. Due to accelerationmechanism particle injection spectra are assumed to be hard. In this caseparticle flux on the Earth is too low for detection. But particles produce inspace a noticeable flux of diffuse gamma-ray emission via electromagneticcascades. It should be accounted for when analyzing other source models anddark matter models. Also neutrinos are produced in cascades, and at energies E>10^19 eV cascade neutrino spectra depends on injection spectra. Therefore itis proposed to study cosmic ray sources under consideration using data ongamma-ray and neutrino emission.

Extragalactic cosmic ray sources with very small contribution in the particle flux on the Earth and their study