Towards a model of population of astrophysical sources of ultrahigh-energy cosmic rays

We construct and discuss a toy model of the population of numerous nonidentical extragalactic sources of ultrahigh-energy cosmic rays. In the model, cosmic-ray particles are accelerated in magnetospheres of supermassive black holes in galactic nuclei, the key parameter of acceleration being the black-hole mass. We use astrophysical data on the redshift-dependent black-hole mass function to describe the population of these cosmic-ray accelerators, from weak to powerful, and confront the model with cosmic-ray data.

Figure 1

Dependence of the normalized maximal energy $\xi$ from the angular momentum $a$ of the black hole with mass $M$ for different values of the vacuum-gap size $H$ (curves labeled by values of $H/M$; see the text for definitions of parameters).

Figure 2

The cosmic-ray flux predicted by the model for three different assumptions about the SMBH magnetic field, see labels on the plot and explanations in the text, versus the Auger experimental data [40].

Figure 3

Dependence of the coefficient ${\kappa }^{1/4}$ from the angular momentum $a$ of the black hole with mass $M$ for different values of the vacuum-gap size $H$ (curves labeled by values of $H/M$; see the text for definitions of parameters).

Figure 4

Gamma-ray fluxes predicted by the same models as shown in Fig. 2.