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.
