2023ApJ...957..101S

Active galactic nuclei (AGNs) are widely believed to be one of the promising acceleration sites of ultrahigh-energy cosmic rays (CRs). Essentially, AGNs are powered by the gravitational energy of matter falling into supermassive black holes. However, the conversion efficiency of gravitational to kinetic energy of CRs in AGNs, which is defined as the baryon loading factor η_p, is not well known yet. After being accelerated, high-energy CRs could escape the host galaxy and enter the intracluster medium (ICM). These CRs can be confined within the galaxy cluster and produce γ-rays and neutrinos through proton-proton collisions with the ICM. In this paper, we study the diffusion of CRs in galaxy clusters and calculate the diffuse neutrino flux from the galaxy cluster population. Using the latest upper limits on the cumulative unresolved TeV-PeV neutrino flux from galaxy clusters posed by the IceCube Neutrino Observatory, we derive the upper limit of the average baryon loading factor as η_p,grav ≲ 2 × 10^–3 - 0.1 for the population of galaxy clusters. This constraint is more stringent than the one obtained from γ-ray observation on the Coma cluster.