Galaxy clusters exhibit remarkable self-similar behavior which allows us to establish simple scaling relationships between observable quantities and cluster masses, making galaxy clusters useful cosmological probes. Recent X-ray observations suggested that self-similarity may be broken in the outskirts of galaxy clusters. In this work, we analyze a mass-limited sample of massive galaxy clusters from the Omega500 cosmological hydrodynamic simulation to investigate the self-similarity of the diffuse X-ray emitting intracluster medium (ICM) in the outskirts of galaxy clusters. We find that the self-similarity of the outer ICM profiles is better preserved if they are normalized with respect to the mean density of the universe, while the inner profiles are more self-similar when normalized using the critical density. However, the outer ICM profiles as well as the location of accretion shock around clusters are sensitive to their mass accretion rate, which causes the apparent breaking of self-similarity in cluster outskirts. We also find that the collisional gas does not follow the distribution of collisionless dark matter (DM) perfectly in the infall regions of galaxy clusters, leading to 10% departures in the gas-to-DM density ratio from the cosmic mean value. Our results have a number implications for interpreting observations of galaxy clusters in X-ray and through the Sunyaev-Zel'dovich effect, and their applications to cosmology.
