One Halo, Two Boundaries: Relating Accretion Shocks and Splashback Radii in Galaxy Clusters

Abstract: The boundaries of dark matter and gas in clusters are delineated by the splashback radius and the accretion shock, respectively. Theoretically, both of these boundaries are expected to coincide at the outskirts of halos. However, hydrodynamic cosmological simulations have highlighted significant displacement between them. In this study, we utilise the IllustrisTNG simulation suite to investigate the statistical relationship between the splashback and shock surfaces in a sample of 812 cluster-mass halos. We compute the full angular distribution of both boundaries and examine their relationship, also considering how different moments of this distribution correlate with halo properties. We employ a dispersion-based measure for the splashback boundary and the maximum entropy distance for the shock location. Despite examining various boundary definitions, we consistently observe an offset between the splashback and shock boundaries, with $R_{\rm sh}/R_{\rm sp} \sim 1.3-2$, depending on specific methodological choices. This offset predominantly occurs along void directions. We analyse the redshift evolution of these boundaries for a subset of halos and find that splashback and shock boundaries are not necessarily distinct at earlier times. During mergers, gas dissipates energy and resists contraction via pressure, unlike collisionless dark matter, leading to the observed boundary offset. We also find that the feature in pressure profiles arising from the outer accretion shock is sensitive to the exact method of stacking, which has important implications for observations.