Entropy at the Outskirts of Galaxy Clusters as Implications for
  Cosmological Cosmic-Ray Acceleration
  Recently, gas entropy at the outskirts of galaxy clusters attracts much
attention. We propose that the entropy profiles could be used to study
cosmic-ray (CR) acceleration around the clusters. If the CRs are effectively
accelerated at the formation of clusters, the kinetic energy of infalling gas
is consumed by the acceleration and the gas entropy should decrease. As a
result, the entropy profiles become flat at the outskirts. If the acceleration
is not efficient, the entropy should continue to increase outwards. By
comparing model predictions with X-ray observations with Suzaku, which show
flat entropy profiles, we find that the CRs have carried ~<7% of the kinetic
energy of the gas away from the clusters. Moreover, the CR pressure at the
outskirts can be ~<40% of the total pressure. On the other hand, if the entropy
profiles are not flat at the outskirts as indicated by combined Plank and ROSAT
observations, the carried energy and the CR pressure should be much smaller
than the above estimations.
