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Abstract

A self-similar _spherical collapse model predicts a dark matter (DM) _splashback and accretion shock in the outskirts of galaxy clusters while missing a key ingredient of structure formation – processes associated with mergers. To fill this gap, we perform simulations of merging self-similar clusters and investigate their DM and gas evolution in an idealized cosmological context. Our simulations show that the cluster rapidly contracts during the major merger and the _splashback radius r_sp decreases, approaching the _virial radius r_vir. While in the self-similar model r_sp depends on a smooth mass accretion rate parameter Γ_s, our simulations show that in the presence of mergers, r_sp re_sponds to the changes in the total mass accretion rate Γ_vir, which accounts for both mergers and smooth accretion. The scatter of the Γ_vir − r_sp/r_vir relation indicates a generally low Γ_s ∼ 1 in clusters in cosmological simulations. In contrast to the DM, the hot gaseous atmo_spheres significantly expand by the merger-accelerated (MA-) shocks formed when the runaway merger shocks overtake the outer accretion shock. After a major merger, the MA-shock radius is larger than r_sp by a factor of up to ∼1.7 for Γ_s ≲ 1 and is ∼r_sp for Γ_s ≳ 3. This implies that (1) mergers could easily generate the MA-shock-_splashback offset measured in cosmological simulations, and (2) the smooth mass accretion rate is small in regions away from filaments where MA-shocks reside. We further discuss the shapes of the DM haloes, various shocks, and contact discontinuities formed at different epochs of the merger, and the ram-pressure stripping in cluster outskirts.