Numerical effects on the stripping of dark matter and stars in IllustrisTNG galaxy groups and clusters

Imagine the universe as a giant, cosmic kitchen where galaxies are the main dishes being cooked. In this kitchen, smaller galaxies (satellites) often get swallowed by larger ones (hosts). As they get eaten, they get stripped of their ingredients—stars and dark matter—which then scatter around the host galaxy, creating a faint, glowing "soup" known as the stellar halo or intra-cluster light.

This paper is like a team of chefs (the authors) checking their recipe books to see if the size of their measuring spoons (numerical resolution) changes how the dish turns out. They used a massive set of computer simulations called IllustrisTNG to cook these cosmic meals at different levels of detail, from "rough sketches" to "4K ultra-high definition."

Here is what they found, broken down into simple concepts:

1. The "Pixel" Problem: Why Resolution Matters

Think of a digital photo. If you have a low-resolution image, a galaxy might look like a blurry blob made of just a few big pixels. If you have a high-resolution image, that same galaxy is made of millions of tiny, sharp pixels.

In these simulations, the "pixels" are particles of gas, stars, and dark matter.

Low Resolution: The "pixels" are huge (like giant boulders).
High Resolution: The "pixels" are tiny (like sand grains).

The scientists wanted to know: Does using giant boulders instead of sand grains change how the galaxies get stripped apart?

2. The Dark Matter: The Invisible Skeleton

Dark matter is the invisible scaffolding that holds galaxies together.

The Finding: The scientists found that the dark matter is surprisingly tough. Even with the "giant boulder" simulations, the dark matter held together just fine until it lost about 90% of its mass.
The Analogy: Imagine a house made of steel beams (dark matter). Whether you measure the house with a ruler or a tape measure, the steel beams don't suddenly collapse just because your measurement tool is a bit clunky. The "stripping" of this invisible skeleton is not heavily affected by the resolution.

3. The Stars: The Delicate Flowers

Stars are the visible part of the galaxy, like flowers in a garden.

The Finding: This is where the resolution matters a lot. In the low-resolution simulations (big boulders), the "flowers" got plucked off much faster. In the high-resolution simulations (fine sand), the flowers stayed attached longer.
The Analogy: If you try to blow on a dandelion using a giant fan (low resolution), the seeds fly off immediately. If you use a gentle breath (high resolution), the seeds stay on the head a bit longer.
The Result: Every time they improved the resolution (made the particles 8 times smaller), the stars survived for about 2 billion years longer before being stripped away.

4. The "Ghost" Disruption

There was a fear among scientists that low-resolution simulations might be "breaking" galaxies that shouldn't be breaking. This is called spurious disruption.

The Finding: They checked this carefully. They found that while low-resolution simulations strip stars faster, they don't completely destroy the galaxies in a "fake" way that high-resolution ones wouldn't eventually do. The galaxies are actually quite resilient, especially because they orbit in oval paths rather than perfect circles.
The Analogy: It's like thinking a low-resolution video game character falls apart because the graphics are bad. The authors found that the character is actually still holding together; it just looks like it's falling apart faster because the "camera" isn't sharp enough to see the details.

5. The Big Surprise: More Stars, More Soup

Here is the twist. Even though high-resolution simulations keep stars attached longer, the final result is actually more scattered star soup (stellar halo) in the outer regions.

Why? Because in high-resolution simulations, the galaxies are not only holding onto their stars longer, they are also growing bigger in the first place. They form more stars overall.
The Analogy: Imagine two bakeries.
- Bakery A (Low Res): Makes small cakes and drops crumbs on the floor quickly.
- Bakery B (High Res): Makes huge, fluffy cakes. Even if they keep the cake together longer, they are so big that they still drop more crumbs on the floor in the end.
The Problem: Observations of the real universe show less star soup in the outer edges than the high-resolution simulations predict. This suggests that while the simulation is getting better at physics, it might still be making too many stars or keeping them too dense.

Summary for the Everyday Reader

The Goal: To understand how galaxies eat each other and how their "leftovers" (stellar halos) form.
The Method: They ran the same cosmic recipe 9 times, changing the "grain size" of the simulation from coarse to fine.
The Verdict:
1. Dark Matter: Doesn't care much about the resolution. It gets stripped at the same rate.
2. Stars: Are very sensitive. High resolution makes them stick around longer and form more of them.
3. The Outcome: The best simulations (like TNG100) are reliable enough to trust for studying how galaxies are destroyed. However, they still predict slightly too much "star soup" in the outer universe compared to what we see through telescopes.

The Bottom Line: The computer models are finally sharp enough to stop worrying about "fake" galaxy destruction. The problem now isn't that the models are too blurry; it's that they might be a little too good at making stars, leading to a universe that looks a bit too crowded with starlight in the deep outskirts.

Here is a detailed technical summary of the paper "Numerical effects on the stripping of dark matter and stars in IllustrisTNG galaxy groups and clusters."

1. Problem Statement

The formation of stellar haloes and intra-cluster light (ICL) serves as a critical test for galaxy formation models and dark matter (DM) physics. These diffuse stellar components are built primarily from the accretion and tidal stripping of satellite galaxies. However, cosmological hydrodynamical simulations face significant challenges regarding numerical resolution:

Spurious Disruption: Previous studies (e.g., van den Bosch & Ogiya 2018) suggested that finite mass and spatial resolution in simulations could lead to the artificial (spurious) disruption of subhaloes, causing them to dissolve faster than physically expected.
Resolution Dependence: It is unclear whether the stripping rates of DM and stars, and the resulting stellar halo profiles, converge as resolution improves.
Observational Discrepancies: Simulations like IllustrisTNG have been observed to overpredict the surface density of stellar haloes at large radii compared to observations (e.g., Dragonfly Nearby Galaxies Survey). It is necessary to determine if this discrepancy is driven by physical model deficiencies or numerical resolution artifacts.

2. Methodology

The authors utilized the IllustrisTNG cosmological simulation suite, specifically comparing 9 different resolution runs across three volumes:

Volumes: TNG50 (51.7 Mpc), TNG100 (100 Mpc), and TNG300 (302.6 Mpc).
Resolution Levels: Each volume was simulated at three resolution levels (L1, L2, L3), differing by factors of 2 in spatial resolution and 8 in particle mass.
- Baryonic Mass Resolution: Ranges from $8.5 \times 10^4 M_\odot $(TNG50-1, highest) to$ 7.0 \times 10^8 M_\odot$ (TNG300-3, lowest).
Lagrangian Matching Technique: A key methodological innovation was the development of a Lagrangian-region matching algorithm. This allowed the authors to identify the exact same physical objects (satellite galaxies and host haloes) across different resolution simulations of the same volume. This enables a direct, case-by-case comparison of how the same galaxy evolves under different numerical resolutions, controlling for stochastic variations in initial conditions.
Sample Selection:
- Host haloes: $M_{200c} = 10^{12} - 10^{15} M_\odot$ .
- Satellites: Stellar mass $> 10^7 M_\odot$ at infall.
- Infall time: Satellites entering hosts at $z \approx 2$ (providing ~10 Gyr of evolution).
Metrics:
- Stripping Times: $t_{50}$ (time to lose 50% of infall mass) and $t_{90}$ (time to lose 90% of infall mass, a proxy for disruption).
- Concentration ( $C$ ): Ratio of mass within 5 kpc to mass within 30 kpc.
- Ex-situ Stellar Mass: Mass stripped from satellites and deposited into the host halo.

3. Key Contributions

Systematic Resolution Study: This is one of the most comprehensive studies of resolution effects in the TNG suite, covering a factor of >8,000 in baryonic mass resolution.
Public Catalogues: The authors released a public catalogue of matched haloes and satellites across resolution levels, facilitating future comparative studies.
Decoupling DM and Stellar Physics: The study explicitly separates the resolution dependence of collisionless DM stripping from baryonic stellar stripping, revealing distinct behaviors for each.
Convergence Analysis: It establishes specific resolution thresholds where key physical quantities (stripping rates, disruption times) converge.

4. Key Results

A. Dark Matter Stripping and Disruption

Stripping Rate: The rate at which DM is stripped from satellites is largely independent of resolution (converged to within a few percent) for satellites with sufficient particle counts ( $>100$ DM particles).
Disruption: While the rate of stripping is stable, the disruption time (complete dissolution) does depend on resolution for low-mass satellites. However, for the mass ranges considered ( $M_* > 10^7 M_\odot$ ), the TNG100-1 resolution is sufficient to prevent spurious disruption.
Orbital Eccentricity: The authors refute the "spurious disruption" hypothesis for TNG satellites. Unlike the idealized circular orbits in van den Bosch & Ogiya (2018) which dissolve quickly, TNG satellites typically have high eccentricity (ratio of apocentre to pericentre $\approx 2$ ). These eccentric orbits make them more resilient to tidal forces, allowing them to survive for >10 Gyr even at lower resolutions.
Conclusion: DM stripping is robust; spurious disruption is not a dominant factor for satellites with $M_* > 10^7 M_\odot$ in TNG100-1 and better.

B. Stellar Mass Stripping and Disruption

Strong Resolution Dependence: Unlike DM, stellar mass stripping is strongly resolution-dependent.
- Higher resolution leads to slower stripping.
- Each factor of 8 improvement in particle mass resolution adds approximately 2 Gyr to the stripping time ( $t_{50}$ ).
Mechanism: Improved resolution leads to:
1. Higher Stellar Mass: Satellites form more stars at fixed halo mass (due to better feedback modeling).
2. Higher Concentration: Stellar profiles become more centrally concentrated, making the core more resistant to tidal stripping.
Convergence: Stellar stripping rates converge at the TNG100-1 / TNG50-2 resolution level (baryonic mass $\sim 10^7 M_\odot$ ).

C. Impact on Stellar Haloes and ICL

Increased Stellar Mass: Because higher resolution simulations produce more massive satellites that are also more concentrated, the total amount of ex-situ stellar mass deposited into the host halo increases with resolution.
Profile Concentration: The stellar haloes in higher-resolution simulations are more centrally concentrated (steeper inner profiles).
Outer Halo Mass: Crucially, despite the steeper inner profiles, the total stellar mass at large radii ( $>0.1 R_{200c}$ ) increases with resolution. This is because the satellites start with significantly more stellar mass (due to higher star formation efficiency in high-res runs), and even though they are stripped more slowly, the absolute amount of mass available to be stripped is larger.
Observational Discrepancy: The paper concludes that numerical resolution cannot explain the overprediction of stellar halo surface density in TNG compared to observations (Merritt et al. 2020). In fact, moving to higher resolution increases the discrepancy by adding more mass to the outer halo. The issue likely lies in the galaxy formation physics (e.g., feedback efficiency) rather than numerical artifacts.

5. Significance and Conclusions

Robustness of TNG100: The flagship TNG100 simulation (and TNG50-2) is robust against resolution-dependent artifacts regarding satellite stripping and disruption for galaxies with $M_* > 10^7 M_\odot$ .
Physical vs. Numerical: The study confirms that the "spurious disruption" seen in idealized circular orbit simulations does not apply to the realistic, eccentric orbits found in cosmological volumes like TNG.
Implications for Models: The overprediction of stellar haloes in TNG is likely a physical model issue (e.g., feedback is not strong enough to suppress star formation in satellites or eject gas efficiently), not a numerical resolution error.
Recommendation: For studies of stellar haloes and ICL, researchers should use simulations with baryonic mass resolution equal to or better than $\sim 10^7 M_\odot$ (TNG100-1, TNG50-1, TNG300-1). Lower resolution runs (e.g., TNG300-3) artificially suppress stellar mass and overestimate stripping rates, leading to inaccurate predictions.

In summary, the paper demonstrates that while numerical resolution significantly affects the amount of stellar mass formed and the concentration of satellites, the dynamical process of stripping is physically robust in the TNG model at standard resolutions. The discrepancy with observations regarding stellar halo mass is therefore likely due to the galaxy formation model itself, not the numerical resolution.