Abstract
A toy model of the population of numerous non-identical extragalactic sources of ultra-high-energy cosmic rays is presented. In the model, the acceleration of cosmic-ray particles is direct (not diffusive) and takes place in magnetospheres of supermassive black holes in galactic nuclei, the key parameter of acceleration being the black-hole mass. We use astrophysical data to describe the population of these cosmic-ray accelerators and confront the model with cosmic-ray and gamma-ray data.
Highlights
There are numerous hints which might help to constrain possible models of presently unknown sources of ultra-high-energy (UHE) cosmic rays (CRs)
The observation [1,2,3] of the spectrum steepening consistent with the Greisen–Zatsepin–Kuzmin [4, 5] (GZK) cutoff, together with the global isotropy of the arrival directions and the fact that the UHE particles are not expected to be confined by the MilkyWay magnetic field suggest that the bulk of cosmic rays at energies 1019 eV come from outside of the Galaxy
A toy model of particle acceleration in the black-hole magnetosphere was proposed by Neronov et al [13, 14], where the reader may find its detailed description
Summary
There are numerous hints which might help to constrain possible models of presently unknown sources of ultra-high-energy (UHE) cosmic rays (CRs). For numerous sources, the assumption of equal fluxes is well justifiable (in the sense that only the mean flux of a large sample of sources is important and this mean flux does not vary significantly from one region in the Universe to another) and the injection spectrum is often fixed by the acceleration model, the maximal energies are expected to vary significantly, having a serious impact on the observed spectrum [12] We discuss a toy model of numerous and different sources of UHECRs and, within certain assumptions, confront it with the experimental data
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