The Three Hundred project: The relationship between the shock and splashback radii of simulated galaxy clusters

Observations of the intracluster medium (ICM) in the outskirts of galaxy clusters reveal shocks associated with gas accretion from the cosmic web. Previous work based on non-radiative cosmological hydrodynamical simulations have defined the shock radius, r_shock, using the ICM entropy, K ∝ T/n_e²/³, where T and n_e are the ICM temperature and electron density, respectively; the r_shock is identified with either the radius at which K is a maximum or at which its logarithmic slope is a minimum. We investigate the relationship between r_shock, which is driven by gravitational hydrodynamics and shocks, and the splashback radius, r_splash, which is driven by the gravitational dynamics of cluster stars and dark matter and is measured from their mass profile. Using 324 clusters from The Three Hundred project of cosmological galaxy formation simulations, we quantify statistically how r_shock relates to r_splash. Depending on our definition, we find that the median r_shock ≃ 1.38r_splash(2.58R₂₀₀) when K reaches its maximum and r_shock ≃ 1.91r_splash(3.54R₂₀₀) when its logarithmic slope is a minimum; the best-fit linear relation increases as r_shock ∝ 0.65r_splash. We find that r_shock/R₂₀₀ and r_splash/R₂₀₀ anti-correlate with virial mass, M₂₀₀, and recent mass accretion history, and r_shock/r_splash tends to be larger for clusters with higher recent accretion rates. We discuss prospects for measuring r_shock observationally and how the relationship between r_shock and r_splash can be used to improve constraints from radio, X-ray, and thermal Sunyaev-Zeldovich surveys that target the interface between the cosmic web and clusters.