Constraints on the AGN flares as sources of ultra-high energy cosmic rays from the Fermi-LAT observations

Abstract

It is well known that if the most energetic cosmic rays ($E>10^{20}$ eV) were protons then their acceleration sites should possess some extreme properties, including gigantic luminosity. As no stationary sources with such properties are known in the local ($D<200$ Mpc) neighborhood of the Milky Way, it is highly likely that the UHECR acceleration takes place in some transient events. In this paper we investigate scenario where the UHECRs are produced in strong AGN flares. Using more than 7 years of the Fermi-LAT observations we select candidate flares and, using correlation between jet kinetic luminosity and its bolometric luminosity, estimate local kinetic emissivity of giant AGN flares: $\mathcal{L}\sim3.7\times10^{44}\mathrm{erg~Mpc^{-3}~{yr^{-1}}}$. This value is about an order of magnitude larger than the emissivity in the CRs with $E>10^{20}$ eV, thus making this scenario feasible, if the UHECR escape spectrum is rather hard and/or narrow. This shape of spectrum is predicted in a number of present models of strong relativistic collisionless shocks. Also the scenario of acceleration in AGN flares can accommodate constraints coming from the observed arrival distribution of UHECRs. Finally, we demonstrate that in case of heavier UHECR composition all the constraints are greatly relaxed.