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Ultra-High-Energy Cosmic Ray Contribution from the Spin-Down Power of Black Holes

We investigate the production of ultra-high-energy cosmic ray (UHECR) in jets from low-luminosity active galactic nuclei (LLAGN). We propose a model for the UHECR contribution from the spin-down power of black holes (BHs) in LLAGN, which present a jet power $P_{\mathrm{j}} \leqslant 10^{46}$ erg s$^{-1}$. This is in contrast to the opinion that only high-luminosity AGN can accelerate particles to energies $ \geqslant 50$ EeV. We rewrite the equations which describe the synchrotron self-absorbed emission of a non-thermal particle distribution to obtain the observed radio flux density from flat-spectrum core sources and its relationship to the jet power. In general, the jet power provides the UHECR luminosity and so, its relationship to the observed radio flux density. We found that the UHECR luminosity is dependent on the observed radio flux density, the distance to the AGN, and the BH mass, where the particle acceleration regions can be sustained by the magnetic energy extraction from spinning BHs and where the strength of the magnetic field at the sites of particle acceleration scales with the maximum value of the BH magnetic field, which is $\sim 10^4$ gauss for a BH of $10^9 M_{\odot}$. We apply the model to M87 and Cen A, two possible sources of UHECRs, whose jet parameters can be inferred from observational data. Next, we use a complete sample of 29 steep spectrum radio sources with a total flux density greater than 0.5 Jy at 5 GHz to make predictions for the maximum particle energy, luminosity, and flux of the UHECRs from nearby AGN. Using our proposed model, it is possible to show that LLAGN can be sites of the origin of UHECRs. In additional, the scenario in which the contribution to the UHECR flux from many weak radio galaxies would dominate over that from a few strong radio galaxies, or vice-versa, should be substantiated with further statistics.