CONTRIBUTIONS TO THE COSMIC-RAY FLUX ABOVE THE ANKLE - CLUSTERS OF GALAXIES

Motivated by the suggestion of Kang, Ryu & Jones that particles can be accelerated to high energies via diffusive shock acceleration process es at the accretion shocks formed by the infalling flow toward cluster s of galaxies, we have calculated the expected particle flux from a co smological ensemble of clusters. We use the observed temperature distr ibution of local clusters and assume a simple power-law evolutionary m odel for the comoving density of the clusters. The shock parameters, s uch as the shock radius and velocity, are deduced from the intracluste r medium (ICM) temperature using the self-similar solutions for second ary infall on to the clusters. The magnetic field strength is assumed to be in equipartition with the postshock thermal energy behind the ac cretion shock. We also assume that the injected energy spectrum is a p ower law with the exponential cut-off at the maximum energy which is c alculated from the condition that the energy gain rate for diffusive s hock acceleration is balanced by the loss rate due to the interactions with the cosmic background radiation. In contrast to the earlier pape r, we have adopted here the description of the cosmic ray diffusion by Jokipii which leads to considerably higher particle energies. Finally , the injected particle spectrum at the clusters is integrated over th e cosmological distance to Earth by considering the energy loss due to the interactions with the cosmic background radiation. Our calculatio ns show that the expected spectrum of high-energy protons from the cos mological ensemble of the cluster accretion shocks could match well th e observed cosmic ray spectrum near 10(19) eV with reasonable paramete rs and models if about 10(-4) of the infalling kinetic energy can be i njected into the intergalactic space as high-energy particles.