Constraining the Cosmic-Ray Energy Based on Observations of Nearby Galaxy Clusters by LHAASO

Galaxy clusters act as reservoirs of high-energy cosmic rays (CRs). As CRs propagate through the intracluster medium, they generate diffuse γ-rays detectable by arrays such as LHAASO. These γ-rays result from proton-proton (pp) collisions of very high-energy cosmic rays or inverse Compton (IC) scattering of positron-electron pairs created by pγ interactions of ultra-high-energy cosmic rays (UHECRs). We analyzed diffuse γ-ray emission from the Coma, Perseus, and Virgo clusters using LHAASO data. Diffuse emission was modeled as a disk of radius R₅₀₀ for each cluster while accounting for point sources. No significant diffuse emission was detected, yielding 95% confidence level (C.L.) upper limits on the γ-ray flux: for WCDA (1-25 TeV) and KM2A (>25 TeV), less than (49.4, 13.7, 54.0) and (1.34, 1.14, 0.40) × 10⁻¹⁴ ph cm⁻² s⁻¹ for Coma, Perseus, and Virgo, respectively. The γ-ray upper limits can be used to derive model-independent constraints on the integral energy of cosmic ray protons above 10 TeV (corresponding to the LHAASO observational range >1 TeV under the pp scenario) to be less than (1.96, 0.59, 0.08) × 10⁶¹ erg. The absence of detectable annuli/ring-like structures, indicative of cluster accretion or merging shocks, imposes further constraints on models in which the UHECRs are accelerated in the merging shocks of galaxy clusters.