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

Using the IllustrisTNG simulation suite, this study reveals a persistent offset between the splashback radius and accretion shock in galaxy clusters, where the shock typically lies 1.3 to 2 times farther out than the splashback boundary, particularly along void directions, due to gas pressure resisting contraction during mergers.

Original authors: Siddhant Sen, Susmita Adhikari, Daisuke Nagai, Benedikt Diemer

Published 2026-02-24

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CC BY 4.0

Original authors: Siddhant Sen, Susmita Adhikari, Daisuke Nagai, Benedikt Diemer

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Two Different Fences for One Castle

Imagine a galaxy cluster as a massive, invisible castle floating in space. This castle is made of two very different materials:

Dark Matter: The "ghost" walls. You can't see them, they don't bump into each other, and they just fall straight into the castle's center.
Hot Gas: The "fog" inside the castle. This is real stuff (atoms) that gets hot, squishes together, and crashes into other gas.

For a long time, scientists thought these two materials would stop falling into the castle at the exact same distance from the center. They imagined a single, perfect fence line where the "ghosts" stopped and the "fog" stopped.

This paper says: "Nope, that's not how it works."

The researchers found that the Dark Matter stops falling at one distance, but the Gas keeps going much further out before it finally stops. It's like the ghost wall is a small inner fence, and the gas wall is a much larger outer fence. There is a gap between them.

The Two Boundaries Explained

To understand why there is a gap, we need to look at how these two materials behave when they fall into the cluster.

1. The Dark Matter: The "Splashback" (The Bouncing Ball)

Imagine throwing a rubber ball into a deep, empty well. It falls down, hits the bottom, and bounces back up to a certain height before falling again.

The Physics: Dark matter particles are like these rubber balls. They fall into the cluster, miss the center, and swing out to their furthest point (the "apocenter") before swinging back in.
The Boundary: The "Splashback Radius" is the line where these balls reach their highest point on the bounce. It's the edge of the "bouncing zone."

2. The Gas: The "Accretion Shock" (The Traffic Jam)

Now, imagine a car driving fast toward a wall of thick, hot fog. When the car hits the fog, it doesn't bounce. Instead, it slams into it, the engine revs up, and the car stops dead, turning its speed into heat.

The Physics: Gas is "sticky." When it falls into the cluster, it crashes into the hot gas already there. It can't bounce. Instead, it creates a massive shockwave (like a sonic boom), heating up instantly and stopping its fall.
The Boundary: The "Accretion Shock" is the line where this crash happens.

The Discovery: The Gap Between the Walls

The researchers used a super-powerful computer simulation (called IllustrisTNG) to watch 812 of these galaxy clusters form. They looked at the "fences" from every possible angle.

What they found:

The Gap: The gas wall (Shock) is usually 1.3 to 2 times further out than the dark matter wall (Splashback).
The Shape: The castle isn't a perfect sphere. It's more like a potato.
- Along "Filaments" (The Roads): Matter falls in along giant cosmic highways. Here, the gas and dark matter boundaries are close together. The gas crashes right where the dark matter bounces.
- Along "Voids" (The Open Fields): This is where the magic happens. In the empty space between highways, the gas keeps flying outward much further before it finally crashes and stops. The dark matter bounces back much sooner. This is where the biggest gap exists.

Why Does This Happen? (The Analogy of the Merger)

Think of a galaxy cluster growing like a city getting bigger. Sometimes, a smaller city (a sub-cluster) crashes into the big one. This is a merger.

Dark Matter (The Ghosts): When the crash happens, the ghosts just keep moving. They get jostled, but they don't lose energy easily. They bounce back quickly.
Gas (The Fog): The gas is like a crowd of people in a panic. When they crash, they bump into each other, lose their speed, and turn that energy into heat. Because they are hot and pressurized, they resist being squished back in. They stay pushed out further.

The Result: Every time a merger happens, the gas gets pushed out a little further than the dark matter, creating a permanent gap between the two fences.

Why Should We Care? (The "Cosmic Detective" Work)

Why does this gap matter to astronomers?

Measuring Mass: When we look at the universe, we often try to guess how heavy a galaxy cluster is by looking at the gas (using X-rays or the Sunyaev-Zel'dovich effect). If we assume the gas stops at the same place as the dark matter, we will get the wrong answer. We might think the cluster is smaller or less massive than it really is.
Reading the History: The size of the gap tells us about the cluster's history. A big gap means the cluster has been through some violent crashes (mergers) recently. A small gap means it's been quiet.
The "Blurry" Problem: The paper also found that if you take an "average" picture of a cluster (looking at it from all angles at once), the sharp edge of the gas shock gets blurred out. It's like looking at a crowd from far away; you can't see the individual people. To see the shock clearly, you have to look specifically at the "void" directions (the open fields), not the "filament" directions (the crowded roads).

Summary in One Sentence

This paper proves that the "fence" where hot gas stops falling into a galaxy cluster is significantly further out than the "fence" where invisible dark matter bounces back, and this gap is a permanent scar left by the violent crashes that build these cosmic giants.

1. Problem Statement

Theoretical models of hierarchical structure formation suggest that the boundaries of dark matter (DM) halos and the hot intracluster gas should coincide. Specifically, the splashback radius ( $R_{sp}$ ), defined as the first apocenter of recently accreted DM particles (marking the outer density caustic), and the accretion shock radius ( $R_{sh}$ ), where infalling gas shocks and converts kinetic energy to heat, are predicted to align in spherical, self-similar collapse models.

However, recent hydrodynamic cosmological simulations (e.g., Omega500, ThreeHundred) have revealed a significant offset, with the gas shock boundary typically located significantly farther out than the DM splashback radius ( $R_{sh} > R_{sp}$ ). The physical origin of this offset, its dependence on halo properties (mass, accretion rate), and its evolution with redshift remain subjects of debate. Furthermore, observational detection of these boundaries is complicated by the aspherical nature of halos and the difficulty of distinguishing gas boundaries from DM boundaries in stacked data.

2. Methodology

The authors utilize the IllustrisTNG simulation suite, specifically combining two datasets to maximize statistical power and resolution:

TNG-Cluster: 352 high-resolution "zoom-in" re-simulations of massive clusters ( $M_{200m} \ge 10^{15} M_\odot$ ).
TNG300-1: A large cosmological volume ( $\sim 300$ Mpc) containing 460 clusters ( $M_{200m} > 10^{14} M_\odot$ ).
Total Sample: 812 cluster-mass halos.

Key Algorithmic Innovations:
Instead of assuming spherical symmetry, the authors compute the full angular distribution of both boundaries for each halo using $50 \times 50$ solid angle bins.

Shock Finding Algorithm ( $R_{sh}$ ):
- Tracer: The authors identify the accretion shock using entropy ( $S$ ) rather than temperature or density. While temperature jumps and density drops occur at shocks, entropy exhibits a distinct, sharp maximum precisely at the shock front ( $S \propto T/\rho^{2/3}$ ).
- Definition: $R_{sh}$ is defined as the radial location of the maximum entropy along each line of sight.
- Robustness: A strict criterion ( $S_{max}/S_{min} > 2$ ) is applied to distinguish physical shocks from numerical noise and substructure. A temperature cut ( $T > 0.3 T_{halo}$ ) ensures the shock is associated with the main halo rather than infalling subhalos.
Splashback Finding Algorithm ( $R_{sp}$ ):
- Tracer: The authors employ a novel radial velocity dispersion ( $\sigma_r$ ) method rather than the traditional density minimum.
- Definition: $R_{sp}$ is identified as the location of the minimum in the logarithmic derivative of the radial velocity dispersion.
- Advantage: This kinematic tracer is more robust in filamentary directions where density profiles are noisy due to substructure. The dispersion transition marks the outermost boundary of the velocity phase space, separating the infall region from the multi-streaming region.

3. Key Results

A. The Offset and Angular Distribution

Systematic Offset: A persistent offset exists between the two boundaries, with the shock radius typically extending further than the splashback radius.
- Median Ratio: $R_{sh}/R_{sp} \approx 1.31 - 1.34$ (depending on the simulation suite).
- Directional Dependence: The offset is highly anisotropic. It is most pronounced along void directions ( $R_{sh}/R_{sp} \approx 1.42 - 1.47$ ), where gas travels unimpeded to larger distances before shocking. Along filamentary directions, the shock is pushed inward, and the ratio approaches unity ( $R_{sh}/R_{sp} \approx 1.00 - 1.03$ ).
Scatter: The shock boundary exhibits significantly larger directional scatter than the splashback boundary, reflecting the complex, filamentary nature of gas accretion.

B. Dependence on Halo Properties

Halo Mass: When normalized by $R_{200m}$ , the splashback radius is largely scale-free (weak correlation with mass). However, the shock radius shows a strong negative correlation with mass ( $R_{sh}/R_{200m}$ decreases as mass increases). This suggests gas physics (pressure, cooling, pre-heating) introduces scale-dependence not present in collisionless DM.
Accretion Rate ( $\Gamma$ ): Both boundaries contract (move to smaller radii in units of $R_{200m}$ ) as the accretion rate increases, consistent with theoretical expectations.
Dispersion Depth: The sharpness of the velocity dispersion transition correlates with the splashback radius in massive clusters but not the shock radius.

C. Redshift Evolution and Merger Dynamics

Evolution: The offset is not static; it is established early and amplified by mergers.
Merger Response: During a merger event:
1. Both $R_{sp}$ and $R_{sh}$ contract rapidly.
2. The splashback radius contracts more significantly than the shock radius.
3. During the subsequent relaxation phase, the shock expands to a larger fraction of $R_{200m}$ than the splashback.
Physical Mechanism: The offset arises because gas is collisional and subject to pressure support and dissipative heating (shocks), whereas DM is collisionless and relaxes via violent relaxation and Landau damping. The gas resists contraction more effectively during the post-merger relaxation phase.

D. Stacked Profiles and Observability

Smearing Effect: When stacking clusters and taking an angular mean (density-weighted), the sharp outer shock feature in the pressure profile is washed out. This is because the mean is dominated by filamentary accretion, which lacks a sharp shock edge.
Median vs. Mean: The angular median profile retains the sharp shock signature.
Implication: Observational studies relying on spherically averaged thermal Sunyaev-Zel'dovich (tSZ) profiles may fail to detect the outer shock or misinterpret the boundary location, potentially explaining why some observations suggest aligned boundaries.

4. Significance and Conclusions

Theoretical Validation: The study confirms that the offset between gas and DM boundaries is a robust feature of cosmological hydrodynamics, driven by the differential response of collisional gas and collisionless DM to mergers and accretion.
Observational Calibration: The paper provides a simulation-calibrated correction for observational studies. Interpreting gas-based boundaries (SZ/X-ray) as direct tracers of the DM splashback radius without accounting for this offset leads to systematic biases in mass and concentration estimates.
Future Probes: The results highlight the necessity of multi-probe observations (separating void and filament directions, using kinematic SZ, and FRBs) to resolve the outer accretion shock. The offset serves as a new probe of the halo's merger history and dynamical state.
Methodological Contribution: The use of velocity dispersion for splashback and entropy maxima for shocks offers a more robust, directionally resolved framework for defining halo boundaries in future simulations and observations.

In summary, this work establishes that "one halo" possesses two distinct, dynamically driven boundaries that are separated by a factor of $\sim 1.3-2$ , with the separation being a sensitive tracer of the cluster's accretion history and merger activity.