The existence of extragalactic ultrahigh-energy cosmic ray sources giving a very small particle flux on the Earth is considered. While the majority of cosmic rays is emitted by a source class providing the flux observed on the Earth, this small part of the particle flux is assumed to be accelerated in an additional subclass of sources of cosmic rays. As an illustration of this subclass of sources, we discuss accretion disks around supermassive black holes where particles are accelerated by electric fields. Because of acceleration mechanism, particle injection spectra are assumed to be hard. In this case cosmic ray flux on the Earth is too low for detection. But propagating particles produce in space a noticeable flux of diffuse gamma ray emission and neutrinos. It should be accounted for when analyzing other source models and dark matter models. At energies $E>{10}^{19}\mathrm{eV}$ cascade neutrino spectra depends on cosmic ray injection spectra. It is proposed to study cosmic ray sources under consideration using data on gamma ray and neutrino emission along with cosmic ray data.

• Received 8 May 2019

DOI:https://doi.org/10.1103/PhysRevD.100.083019