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 ∼10% if the sensitivity of the gamma-ray or neutrino telescope is ∼10−12 erg cm−2 s−1 and the source number density is ∼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.

Searching for UHECR-associated gamma-ray sources with LHAASO-WCDA

“…In ref [6] we had calculated the probability to detect gamma-ray sources in the directions of observed UHECRs as function of source number density, assuming a common origin of UHECRs and TeV diffuse neutrinos. UHECRs may escape quickly from their source environment, e.g., the host galaxy, due to their high rigidity, while lower energy CRs propagate in the host galaxy for longer time, and all of their energy is depleted in 𝑝 𝑝 interactions with interstellar medium (ISM).…”

“…We have considered the spatial and temporal associations between UHECRs and gamma-ray or neutrino sources in [6]. For UHECR protons with energy 𝐸 ∼ 100 EeV, the deflection by magnetic field during propagation is smaller than 𝜃 ∼ 2 • for sources within 𝑑 ∼ 100 Mpc.…”

“…A single source should be luminous or close enough to be detected in gamma-rays. As in [6], for telescopes of certain sensitivity we can consider an "horizon" of cosmological redshift 𝑧 max , within which gamma-ray sources can be detected. Tacking into account the detector sensitivity and gamma-ray absorption by extra-galactic background light (EBL) 𝑧 max is determined by…”

“…where 𝑄(𝐸, 𝑧) is the specific production rate density of UHECRs, d𝑉/dΩd𝑧 is the comoving volume per unit redshift and per unit solid angle. 𝜏 GZK accounts for the GZK effect, and details can be found in [6]. The probability of finding a gamma-ray source associated with a certain detected UHECR is…”