A Model for Diffusive Shock Acceleration of Protons in Intracluster Shocks and Gamma-ray and Neutrino Emissions from Clusters of Galaxies

During the formation of large-scale structures in the universe, shocks with the sonic Mach number Ms <~ 5 are naturally induced by supersonic flow motions of baryonic matter in the intracluster medium (ICM). Cosmic rays (CRs) are expected to be accelerated via diffusive shock acceleration (DSA) at these ICM shocks, although the existence of CR protons in the ICM remains to be confirmed through gamma-ray observations. Based on the results obtained from kinetic plasma simulations, we build an analytic DSA model for weak, quasi-parallel shocks in the test-particle regime. With our DSA model, the CR acceleration efficiency ranges ~ 0.001 - 0.02 in supercritical quasi-parallel shocks with sonic Mach number Ms ~ 2.25 - 5, and the acceleration would be negligible in subcritical shocks wth Ms <~ 2.25. Adopting our DSA model, we estimate gamma-ray and neutrino emissions from clusters of galaxies by performing cosmological hydrodynamic simulations. The estimated gamma-ray flux is below the Fermi-LAT upper limit. In addition, the possible neutrino emission due to the decay of charged pions in galaxy clusters would be about <~ 1% of the atmospheric neutrino intensity in the energy range of <~ 100 GeV. In this talk, we will discuss the implication of our results.