Observe Gamma-Rays and Neutrinos Associated with Ultra-High Energy Cosmic Rays

Abstract: IceCube measures a diffuse neutrino flux comparable to the Waxman-Bahcall bound, which suggests the possibility that the ultra-high energy cosmic rays (UHECRs) have a common origin with diffuse high energy neutrinos. We propose high energy gamma-ray and/or neutrino observations toward the arrival directions of UHECRs to search for the sources and test this possibility. We calculate the detection probability of gamma-ray/neutrino sources, and find that the average probability per UHECR of >10 EeV is $\sim$10% if the sensitivity of the gamma-ray or neutrino telescope is $\sim$10$^{-12}$ erg cm$^{-2}$s$^{-1}$ and the source number density is $\sim$10$^{-5}$ Mpc$^{-3}$. Future gamma-ray and neutrino observations toward UHECRs, e.g., by LHAASO-WCDA, CTA, IceCube/Gen2, are encouraged to constrain the density of UHECR sources or even identify the sources of UHECRs.