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.

Figures (15)

• Figure 1: A 2-dimension (2D) projection of the shock boundary found by our algorithm for one of the massive clusters from the TNG-Cluster suite with $M_{200m}=1.9 \times 10^{15}\, M_\odot$. Left panel: Shock boundaries found from entropy maxima (red) and the logarithmic slope of entropy (orange), overplotted on the gas entropy. A particular sightline along the void is shown with the blue solid arrow and along the filament by the black solid arrow. Middle panel: Shock boundaries overplotted on DM density with a black dashed circle marking the $R_{\rm 200m}$ of the cluster. Right panel: Shock boundaries overplotted on the Mach number of the gas, as detected by a shock finder. The complex morphology of the various shocks would make it difficult to find a well-defined accretion shock based on Mach numbers alone.
• Figure 2: Radial profiles (top row) and their logarithmic slopes (bottom row) for gas properties in the same individual cluster from Figure \ref{['fig:shock_algorithm']}. The columns compare the angular median profiles (left) with profiles along a representative void (middle) and filamentary (right) direction. The specific sightlines for the void and filament are identified by blue and black arrows, respectively, in Figure \ref{['fig:shock_algorithm']}. The vertical dashed lines correspond to the location of shock from entropy maximum (top row) and minimum of entropy slope (bottom row).
• Figure 3: The radial profile (top panel) and its logarithmic-derivative (bottom panel) of dark matter density (dark blue) and radial velocity dispersion (red) for the same cluster shown in Figure \ref{['fig:shock_algorithm']} and Figure \ref{['fig:352_profiles']}. The left panel corresponds to the angular median profiles, the middle panel corresponds to profiles along a void direction (blue arrow in Figure \ref{['fig:splashback_algorithm']}) and the right panel corresponds to a filamentary direction (black arrow in Figure \ref{['fig:splashback_algorithm']}). The vertical dashed lines correspond to the location of minimum of the slope.
• Figure 4: A 2D projection of the splashback boundary found by our algorithm for the same cluster shown in Figures \ref{['fig:shock_algorithm']}-\ref{['fig:dm_tracers']}. Left panel: Splashback boundary over-plotted on a slice of the DM density. The orange and black dashed circles are the spherical estimate of splashback from the logarithmic derivative of the median dispersion profile and $R_{\rm 200m}$ of the cluster, respectively. Middle panel: The phase space density ($\mathcal{N}$) along the void indicated by the blue arrow in the left panel. Right panel: The phase space density ($\mathcal{N}$) along the filament indicated by the black arrow in the left panel. The blue and red vertical line corresponds to the estimated splashback from density and our dispersion-based algorithm.
• Figure 5: An example of the shock and splashback boundaries in a massive galaxy cluster shown in Figure \ref{['fig:shock_algorithm']}. Top panel: Maps of gas entropy (left) and dark matter density (right). The identified splashback radius (blue) and accretion shock radius (green) are overlaid. Bottom panel: Angular distribution of the splashback radius (right) and shock radius (left). For this halo, the median and mode of each distribution agree to within 5%.