Several types/classes of shocks naturally arise during formation and evolution of galaxy clusters. One such class is represented by accretion shocks, associated with deceleration of infalling baryons. Such shocks, characterized by a very high Mach number, are present even in 1D models of cluster evolution. Another class is composed of 'runaway merger shocks', which appear when a merger shock, driven by a sufficiently massive infalling subcluster, propagates away from the main-cluster centre. We argue that, when the merger shock overtakes the accretion shock, a new long-living shock is formed that propagates to large distances from the main cluster (well beyond its virial radius), affecting the cold gas around the cluster. We refer to these structures as Merger-accelerated Accretion shocks (MA-shocks) in this paper. We show examples of such MA-shocks in one-dimensioanal (1D) and three-dimensional (3D) simulations and discuss their characteristic properties. In particular, (1) MA-shocks shape the boundary separating the hot intracluster medium (ICM) from the unshocked gas, giving this boundary a 'flower-like' morphology. In 3D, MA-shocks occupy space between the dense accreting filaments. (2) Evolution of MA-shocks highly depends on the Mach number of the runaway merger shock and the mass accretion rate parameter of the cluster. (3) MA-shocks may lead to the misalignment of the ICM boundary and the splashback radius.
