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Baryonic Feedback across Halo Mass: Impact on the Matter Power Spectrum

Using IllustrisTNG simulations, this study demonstrates that group-scale halos ( $\log M_{\rm 200m}/h^{-1}M_\odot \in[13, 14]$ ) are the primary drivers of baryonic suppression in the matter power spectrum and that their associated weak-lensing signals offer a powerful observational test for feedback models to enable unbiased cosmological inference.

Original authors: Kyle Miller, Surhud More, Bhuvnesh Jain

Published 2026-03-19

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CC BY 4.0

Original authors: Kyle Miller, Surhud More, Bhuvnesh Jain

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: The Cosmic "Cosmic Soup"

Imagine the Universe as a giant, invisible soup made mostly of Dark Matter (the heavy, invisible stuff that holds galaxies together) and Baryonic Matter (the normal stuff we can see: stars, gas, planets, and us).

For a long time, scientists thought this soup was stirred only by gravity. Gravity pulls everything together, forming clumps called halos (which are basically the "homes" of galaxies). If you only had gravity, you could predict exactly how the soup would look.

But, the Universe isn't just gravity. Inside these galaxy homes, there are violent events: stars exploding (supernovae) and super-massive black holes eating gas and shooting jets out (Active Galactic Nuclei or AGN). These events act like cosmic blowtorches. They heat up the gas and blast it out of the galaxy, changing how the "soup" is distributed.

This paper asks: How much do these "blowtorches" mess up our predictions of the Universe's structure? And more importantly, which galaxies are doing the most messing?

The Experiment: The "Frankenstein" Simulation

To figure this out, the authors used a supercomputer to run two different simulations of the Universe:

The "Gravity-Only" Universe: A world where only gravity exists. No explosions, no black holes, just smooth, predictable clumping.
The "Full-Physics" Universe: A realistic world where stars explode and black holes blast gas away.

The Clever Trick:
Instead of just comparing the two finished movies, they played a game of "cut and paste."

They took the Gravity-Only Universe.
They found a specific galaxy (a halo).
They cut out the matter around that galaxy and replaced it with the matter from the same galaxy in the Full-Physics Universe.
They did this for galaxies of different sizes: small ones, medium ones, and huge ones.

By doing this, they could isolate exactly how much "messing up" was caused by small galaxies versus big ones.

The Big Discovery: The "Goldilocks" Zone of Chaos

The scientists expected that the biggest galaxies (the massive clusters) would cause the most chaos because they have the biggest black holes. They were wrong.

The Result: The biggest troublemakers are the medium-sized galaxy groups.

Think of it like a neighborhood:

Small Houses (Low Mass Galaxies): They have small blowtorches. They mess up the local garden a little bit, but not much.
Mansions (Massive Clusters): They have massive blowtorches, but the houses are so heavy and deep (deep gravity wells) that the gas gets trapped. The blowtorch tries to blast it out, but gravity pulls it back in.
Suburban Neighborhoods (Group-Scale Halos): This is the sweet spot. These galaxies are heavy enough to have powerful black holes, but light enough that the black holes can successfully blast gas far away. These are the ones causing about 60% of all the "mess" in the Universe.

The Analogy:
Imagine trying to blow a feather out of a bucket.

A tiny fan (small galaxy) can't move it.
A giant industrial fan (massive cluster) is so powerful it creates a vacuum that sucks the feather back in before it flies away.
A medium-sized leaf blower (group-scale galaxy) is just right. It blasts the feather high into the air, scattering it everywhere.

Why Does This Matter? (The "Blurry Photo" Problem)

Scientists use a technique called Weak Gravitational Lensing to map the Universe. Imagine looking at the night sky through a slightly foggy window. By measuring how the fog distorts the light of distant stars, they can figure out where the invisible Dark Matter is hiding.

However, if the "fog" (the gas and stars) gets blown around by the blowtorches, the distortion changes. If scientists don't account for this, they might think the Universe is expanding faster or slower than it actually is, or that there is more/less Dark Energy than there really is.

The Paper's Solution:
The authors found that because the "mess" is concentrated in those medium-sized groups, we can fix our models by focusing on them.

If we look at the light from background galaxies passing through these specific groups, we can see a unique "signature" of the blowtorches.
This signature acts like a fingerprint. If we see this specific pattern of distortion, we know it's caused by galaxy feedback, not by a change in the laws of physics.

The "Add-Up" Rule

One of the coolest findings is that the chaos caused by different galaxy sizes is additive.

If you have a small galaxy messing things up, and a medium galaxy messing things up, the total mess is just the sum of the two. They don't really interfere with each other.
This is great news for computer models. It means scientists don't need to simulate the whole complex interaction at once; they can calculate the effect of each galaxy size separately and just add them together to get the total picture.

Summary in a Nutshell

The Problem: Normal matter (gas/stars) gets blasted around by exploding stars and black holes, messing up our maps of the invisible Dark Matter.
The Method: The authors swapped parts of a "perfect" gravity-only universe with a "realistic" universe to see who was causing the most trouble.
The Surprise: It's not the biggest galaxies causing the most trouble. It's the medium-sized groups (the "Goldilocks" zone) that blast the most gas around.
The Benefit: By understanding exactly where this gas is being moved, we can build better models. This allows future telescopes (like the ones looking at the "fog" of the Universe) to measure the expansion of the Universe with much higher precision, without getting confused by the "wind" of galaxy feedback.

In short: The Universe isn't just a quiet, gravity-driven dance. It's a chaotic party where the middle-sized galaxies are the ones throwing the most confetti, and we finally figured out how to clean it up in our math.

1. Problem Statement

Upcoming weak gravitational lensing surveys (e.g., LSST, Euclid, Roman) aim to measure the matter distribution of the Universe with percent-level precision on nonlinear scales ( $k > 1 \, h \, \text{Mpc}^{-1}$ ). However, baryonic feedback processes associated with galaxy formation (e.g., supernovae, AGN outflows) significantly alter the matter distribution on these scales, suppressing the matter power spectrum.

Current cosmological inference often requires marginalizing over these baryonic effects or excluding small scales, which degrades statistical power. While hydrodynamical simulations exist, there is a lack of understanding regarding which specific halo mass ranges and what radial scales contribute most to this suppression. Furthermore, it is unclear if the suppression contributions from different halo mass bins are additive or if complex cross-correlations exist between them. This paper seeks to isolate and quantify the contribution of halos across different mass bins to the total suppression of the matter power spectrum.

2. Methodology

The authors utilize the IllustrisTNG-300 simulation suite, specifically comparing the TNG300-1 (full-physics) and TNG300-1-Dark (gravity-only/collisionless) runs, which share identical initial conditions.

Hybrid Snapshot Construction:
To isolate the impact of baryonic feedback by halo mass, the authors developed a "hybrid" approach:

Halo Matching: They bidirectionally match halos between the full-physics and gravity-only simulations using the LHaloTree algorithm, focusing on the most massive subhalo (firstSub) within Friends-of-Friends (FoF) groups.
Particle Replacement: For specific logarithmic mass bins (spanning $\log_{10}(M_{200m}/h^{-1}M_\odot) \in [12, 14.5]$ ), they replace particles in the gravity-only simulation with their counterparts from the full-physics simulation.
Radial Extent: Replacements are performed within spherical regions of radius $R = \alpha R_{200m}$ , where $\alpha \in \{0.5, 1.0, 1.5, 2.0\}$ .
Mass Conservation: A critical step involves enforcing mass conservation. Since baryonic feedback often ejects mass beyond $R_{200m}$ , simply replacing particles within a fixed radius creates a mass deficit. The authors redistribute this missing mass uniformly to the surrounding gravity-only particles in a shell extending to $2R_{replace}$ . This prevents spurious boosts in large-scale power caused by global mass loss.
Power Spectrum Measurement: They compute the matter power spectrum ( $P(k)$ ) for these hybrid snapshots using FFTs (via Nbodykit) up to $k \approx 31.3 \, h \, \text{Mpc}^{-1}$ . They analyze the ratio $P/P_{GO}$ (Full-Physics / Gravity-Only) to quantify suppression.

Weak Lensing Analysis:
The authors also compute the excess surface density ( $\Delta\Sigma$ ) and tangential shear ( $\gamma_t$ ) for matched halos to determine how these mass-dependent feedback effects manifest in observable weak lensing signals.

3. Key Contributions

Mass-Dependent Isolation: The study is the first to systematically quantify the contribution of specific halo mass bins to the total matter power spectrum suppression using a controlled particle-replacement method.
Identification of the Dominant Regime: It identifies group-scale halos ( $\log M_{200m} \in [13, 14]$ ) as the primary drivers of baryonic suppression, rather than clusters or low-mass galaxies.
Linearity of Suppression: The authors demonstrate that the suppression contributions from different mass bins are approximately additive, implying negligible cross-correlations between mass scales in the context of power spectrum suppression.
Radial Dependence: They quantify how far feedback effects extend, showing that for group-scale halos, the suppression is largely established within $R_{200m}$ , whereas for massive clusters, feedback can eject matter to larger distances.
Observational Predictions: They provide specific predictions for group-galaxy weak lensing signals, suggesting that stacking lenses by mass (or richness) can serve as a direct test of feedback models.

4. Key Results

A. Halo Mass Dependence of Suppression

Group-Scale Dominance: Halos with masses in the range $\log M_{200m} \in [13, 14]$ contribute approximately 60% of the total suppression observed in halos with $M > 10^{12} h^{-1}M_\odot$ . The maximum suppression for this bin is $\sim 10\%$ at $k \sim 10 \, h \, \text{Mpc}^{-1}$ .
Low-Mass Halos ( $\log M \in [12, 13]$ ): Contribute a moderate suppression ( $\sim 5\%$ ) due to shallow potential wells and stellar feedback (supernovae).
Cluster-Scale Halos ( $\log M > 14$ ): Despite having powerful AGN, their contribution is modest ( $\sim 2-3\%$ ) because their deep potential wells retain more baryons, and they are less numerous.
Non-Monotonicity: The suppression is non-monotonic with mass, peaking at the group scale. This is attributed to the combination of efficient AGN feedback and the specific abundance of halos in this mass range.

B. Radial Dependence

Extending the replacement radius from $0.5 R_{200m}$ to $2.0 R_{200m}$ has little additional impact on the suppression for group-scale halos, suggesting the feedback redistribution is largely contained within the virial radius.
For massive clusters ( $\log M > 14$ ), extending the radius increases suppression slightly, indicating AGN can eject matter to larger distances.
For low-mass halos, extending the radius slightly decreases the measured suppression, likely due to the inclusion of gas that has fallen back or mixed with neighboring halos.

C. Additivity and Cross-Correlations

The total suppression of the matter power spectrum can be accurately reconstructed by summing the suppression contributions of individual mass bins.
There are no significant cross-correlations between different mass bins. This validates the "halo-by-halo" treatment used in semi-analytic "baryonification" models, where the 2-halo term (dependent only on dark matter) dominates the cross-correlation, and baryonic effects are treated as local 1-halo modifications.

D. Weak Lensing Signal

The suppression in the matter power spectrum translates directly to the weak lensing signal ( $\Delta\Sigma$ ).
Low-mass halos: Show an enhancement of the lensing signal in the very center ( $< 0.2 R_{vir}$ ) due to baryonic contraction, followed by suppression at larger radii.
Group-scale halos: Show the maximum suppression in the lensing signal, mirroring the power spectrum results.
The signal converges to the collisionless case beyond a few virial radii.

5. Significance and Implications

Cosmological Inference: The results suggest that future weak lensing analyses can recover significant cosmological information from small scales by modeling the specific mass-dependent feedback of group-scale halos, rather than treating baryonic effects as a generic nuisance parameter.
Modeling Emulators: The finding of linear additivity supports the development of emulators that predict the matter power spectrum and halo-matter cross-correlation jointly. It validates semi-analytic "baryonification" approaches that treat halos independently.
Observational Strategy: The paper proposes that group-galaxy lensing (stacking lenses by group richness or mass) is a powerful observational test. Since group-scale halos dominate the feedback signal, measuring the lensing profile of groups provides a direct constraint on feedback models, potentially breaking degeneracies between cosmological parameters and baryonic physics.
Synergy with other Probes: The results highlight the importance of combining weak lensing with Sunyaev-Zel'dovich (SZ) and Fast Radio Burst (FRB) dispersion measures, as these probes are sensitive to the same redistributed baryons in the group-mass regime.

In conclusion, this work provides a rigorous, simulation-based decomposition of baryonic feedback, identifying group-scale halos as the critical regime for understanding and modeling the suppression of the matter power spectrum in the era of precision cosmology.