Cross-correlation of the extragalactic gamma-ray background with the thermal Sunyaev-Zel'dovich effect in the cosmic microwave background

Cosmic rays in galaxy clusters are unique probes of energetic processes operating with large-scale structures in the Universe. Precise measurements of cosmic rays in galaxy clusters are essential for improving our understanding of nonthermal components in the intracluster medium (ICM) as well as the accuracy of cluster mass estimates in cosmological analyses. In this paper, we perform a cross-correlation analysis with the extragalactic gamma-ray background and the thermal Sunyaev-Zeldovich (tSZ) effect in the cosmic microwave background. The expected cross-correlation signal would contain rich information about the cosmic-ray-induced gamma-ray emission in the most massive galaxy clusters at z ∼ 0.1-0.2. We analyze the gamma-ray background map with 8 years of data taken by the Large Area Telescope onboard Fermi satellite and the publicly available tSZ map by Planck. We confirm that the measured cross-correlation is consistent with a null detection, and thus it enables us to put the tightest constraint on the acceleration efficiency of cosmic-ray protons at shocks in and around galaxy clusters. We find the acceleration efficiency must be below 5% with a 2σ confidence level when the hydrostatic mass bias of clusters is assumed to be 30%, and our result is not significantly affected by the assumed value of the hydrostatic mass bias. Our constraint implies that the nonthermal cosmic-ray pressure in the ICM can introduce only a ≲ 3% level of the hydrostatic mass bias, highlighting that cosmic rays alone do not account for the mass bias inferred by the Planck analyses. Finally, we discuss future detectability prospects of cosmic-ray-induced gamma rays from the Perseus cluster for the Cherenkov Telescope Array.