Galaxy Clusters as Reservoirs of Heavy Dark Matter and High-Energy Cosmic Rays: Constraints from Neutrino Observations

Galaxy Clusters (GCs) are the largest reservoirs of both dark matter and cosmic rays (CRs). Dark matter self-annihilation can lead to a high luminosity in gamma rays and neutrinos, enhanced by a strong degree of clustering in dark matter substructures. Hadronic CR interactions can also lead to a high luminosity in gamma rays and neutrinos, enhanced by the confinement of CRs from cluster accretion/merger shocks and active galactic nuclei. We show that IceCube/KM3Net observations of high-energy neutrinos can probe the nature of GCs and the separate dark matter and CR emission processes, taking into account how the results depend on the still-substantial uncertainties. Neutrino observations are relevant at high energies, especially at >10 TeV. Our results should be useful for improving experimental searches for high-energy neutrino emission. Neutrino telescopes are sensitive to extended sources formed by dark matter substructures and CRs distributed over large scales. Recent observations by Fermi and imaging atmospheric Cherenkov telescopes have placed interesting constraints on the gamma-ray emission from GCs. We also provide calculations of the gamma-ray fluxes, taking into account electromagnetic cascades inside GCs, which can be important for injections at sufficiently high energies. This also allows us to extend previous gamma-ray constraints to very high dark matter masses and significant CR injections at very high energies. Using both neutrinos and gamma rays, which can lead to comparable constraints, will allow more complete understandings of GCs. Neutrinos are essential for some dark matter annihilation channels, and for hadronic instead of electronic CRs. Our results suggest that the multi-messenger observations of GCs will be able to give useful constraints on specific models of dark matter and CRs. [Abstract abridged.]