Locations of Accretion Shocks around Galaxy Clusters and the ICM properties: insights from Self-Similar Spherical Collapse with arbitrary mass accretion rates

Accretion shocks around galaxy clusters mark the position where the infalling diffuse gas is significantly slowed down, heated up, and becomes a part of the intracluster medium (ICM). They play an important role in setting the ICM properties. Hydrodynamical simulations have found an intriguing result that the radial position of this accretion shock tracks closely the position of the `splashback radius' of the dark matter, despite the very different physical processes that gas and dark matter experience. Using the self-similar spherical collapse model for dark matter and gas, we find that an alignment between the two radii happens only for a gas with an adiabatic index of $\gamma \approx 5/3$ and for clusters with moderate mass accretion rates. In addition, we find that some observed ICM properties, such as the entropy slope and the effective polytropic index lying around $\sim 1.1-1.2$, are captured by the self-similar spherical collapse model, and are insensitive to the mass accretion history.