The maximum energy and spectra of cosmic rays accelerated in active galactic nuclei

Abstract

We computed the energy spectra of the incident (on an air shower array) ultrahigh-energy (E>4×10¹⁹eV) cosmic rays (CRs) that were accelerated in nearby Seyfert nuclei at redshifts z≤0.0092 and in BL Lac objects. These were identified as possible CR sources in our previous works. For our calculations, we took the distribution of these sources over the sky from catalogs of active galactic nuclei. In accordance with the possible particle acceleration mechanisms, the initial CR spectrum was assumed to be monoenergetic for BL Lac objects and a power law for Seyfert nuclei. The CR energy losses in intergalactic space were computed by the Monte Carlo method. We considered the losses through photopion reactions with background radiation and the adiabatic losses. The artificial proton statistic was 10⁵ for each case considered. The maximum energy of the CRs incident on an air shower array was found to be 10²¹ eV, irrespective of where they were accelerated. The computed spectra of the particles incident on an air shower array agree with the measurements, which indirectly confirms the adopted acceleration models. At energies E≥5×10¹⁹eV, the spectrum of the protons from nearby Seyfert nuclei that reached an air shower array closely matches the spectrum of the particles from BL Lac objects. BL Lac objects are, on average, several hundred Mpc away. Therefore, it is hard to tell whether a blackbody cutoff exists by analyzing the shape of the measured spectrum at E≥5×10¹⁹eV.