🔭 astrophysics

Galaxy Populations in the IllustrisTNG Caustic Skeleton

This study utilizes the parameter-free caustic skeleton formalism on IllustrisTNG simulations to demonstrate that galaxy properties form a continuum across the multiscale cosmic web, revealing how the hierarchical formation history of cosmic structures systematically influences the color and star formation activity of galaxies.

Original authors: Benjamin Hertzsch, Job Feldbrugge, Rien van de Weygaert

Published 2026-04-21

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Benjamin Hertzsch, Job Feldbrugge, Rien van de Weygaert

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

Imagine the universe not as a random scattering of stars, but as a giant, intricate spiderweb stretching across billions of miles. This is the Cosmic Web. It's made of invisible "dark matter" that acts like the frame, and visible galaxies that sit on the strands like dewdrops.

For decades, astronomers have known that where a galaxy lives on this web matters. Galaxies in dense "cities" (clusters) look different from those in lonely "countryside" (voids). But until now, we've been looking at this web through a blurry, single-lens camera. We knew the shapes, but we didn't fully understand how the web was built or when its different parts formed.

This paper, written by Hertzsch, Feldbrugge, and van de Weygaert, introduces a new, crystal-clear way to map this universe. They use a mathematical tool called the Caustic Skeleton.

Here is the story of their discovery, broken down into simple concepts:

1. The "Origami" of the Universe

Imagine the early universe as a smooth, flat sheet of dough. As gravity pulls on it, the dough starts to fold, crumple, and stretch.

The Problem: When you fold a sheet of paper, the layers stack on top of each other. In the universe, this means dark matter flows cross over each other. This is called "multistreaming."
The Old Way: Previous maps tried to draw the web by looking at how thick the dough is right now. It's like looking at a finished cake and guessing how the baker mixed the batter.
The New Way (Caustic Skeleton): The authors look at the folds themselves. In mathematics, these sharp folds are called "caustics" (think of the bright, curved lines of light you see at the bottom of a swimming pool). These folds are the "skeleton" of the universe. By tracing these folds, they can see the exact history of how the web was built, from the very first crinkle to the massive clusters we see today.

2. The "Scale" of the Web

The universe is fractal-like, meaning it has big structures and tiny structures nested inside them.

The Analogy: Think of a tree. You have the massive trunk, then big branches, then smaller twigs, and finally tiny leaf stems.
The Discovery: The authors realized that if you look at the web with a "wide-angle lens" (looking at huge scales), you see massive, thick walls and clusters. But if you zoom in with a "magnifying glass" (looking at small scales), you see that those massive walls are actually made of smaller, thinner filaments.
The Result: They found that galaxy properties aren't just "City vs. Country." They exist on a continuum. A galaxy in a small, thin filament looks a lot like a galaxy in a massive wall. The "type" of galaxy depends entirely on how big the structure you are looking at is.

3. The "Age" of the Neighborhood

One of the most exciting findings is that the age of the web structure matters just as much as its density.

The Analogy: Imagine two neighborhoods.
- Neighborhood A (Old): Built 100 years ago. The houses are settled, the trees are huge, and the streets are quiet. The "galaxies" here are old, red, and stopped having babies (star formation) long ago.
- Neighborhood B (New): Just built last year. The construction is loud, the paint is fresh, and there is lots of activity. The "galaxies" here are young, blue, and actively making new stars.
The Discovery: The authors found that galaxies living in the oldest parts of the cosmic web (the parts that folded first) are the "red and quiet" ones. They have been stripped of their gas and stopped forming stars.
The Twist: Even in a dense cluster, if the cluster is young (just formed recently), it still has some blue, active galaxies. But if a cluster is old, it is completely dead. The "birth date" of the web structure is a secret code that predicts how the galaxies inside it behave.

4. The Two Types of "Strings"

The paper also discovered that not all "strings" (filaments) in the web are the same.

The Swallowtail Filaments: These are the long, thin, tenuous strands. They are like the delicate threads of a spiderweb. Galaxies here are a mix of blue and red.
The Umbilic Filaments: These are the thick, heavy, junction points where three walls meet. They are like the thick cables holding up a suspension bridge. Galaxies here are redder and more "dead" because they are denser and older.
Why it matters: Previous studies treated all filaments as the same. This study shows they are actually two different families with different histories and different types of galaxies.

5. The Big Picture: Why This Matters

For a long time, we thought the "Color-Density Relation" (the rule that says "dense places have red galaxies, empty places have blue galaxies") was a simple rule.

The New Insight: This paper shows that the rule is actually a spectrum.
- If you look at the universe on a small scale, the "empty" voids are actually full of tiny, active galaxies.
- If you look at the universe on a huge scale, the "dense" clusters are the only places with dead galaxies.
- The "blue" galaxies are mostly hiding in the walls and voids of the large-scale web, while the "red" galaxies are in the large-scale clusters.

Summary

Think of the universe as a giant, evolving city.

Old Maps: Showed us the city blocks (clusters) and the suburbs (voids).
This Paper: Gives us a time-traveling map that shows us when each block was built and how the roads connected.
The Lesson: A galaxy's personality (its color and activity) isn't just about how crowded its neighborhood is. It's about how old the neighborhood is and how big the map is you are using to look at it.

By using this "Caustic Skeleton," the authors have given us a rigorous, mathematical way to understand the history of the universe's structure, proving that the story of a galaxy is written in the folds of the dark matter web it lives in.

1. Problem Statement

The Cosmic Web is a multiscale network of dark matter, gas, and galaxies comprising voids, walls, filaments, and clusters. While observational and simulation studies have established a "colour-density relation" (where galaxies in dense environments are redder and quenched, while those in voids are bluer and active), traditional analyses suffer from two main limitations:

Single-Scale Bias: Most web classification methods (e.g., DisPerSE, T-web, NEXUS) operate at a single characteristic smoothing scale, failing to capture the inherent multiscale and hierarchical nature of the cosmic web.
Lack of Dynamical History: Traditional methods classify structures based on the present-day density field or morphology, ignoring the formation history and the phase-space dynamics (multistreaming) that define the web's geometric backbone.
Morphology-Colour Decoupling: The relationship between galaxy morphology and environment is complex; colour is often a more sensitive tracer of environmental density than morphology, yet simulation-based studies of morphology across web environments remain scarce.

The paper aims to address these gaps by utilizing the Caustic Skeleton formalism—a parameter-free, mathematically rigorous framework based on catastrophe theory—to trace the multiscale formation history of the cosmic web and analyze how this history influences the properties of embedded galaxy populations in the IllustrisTNG simulations.

2. Methodology

A. Theoretical Framework: The Caustic Skeleton

The authors employ the Caustic Skeleton formalism, which identifies cosmic web elements through singularities (caustics) in the dark matter flow.

Phase-Space Dynamics: The method relies on the multistreaming nature of dark matter. As the universe evolves, the dark matter sheet folds, creating regions where particle trajectories cross (shell-crossing).
Catastrophe Theory: The structural elements are identified by specific conditions on the deformation tensor (eigenvalues $\lambda$ $λ$ and eigenvectors $\mathbf{v}$ $v$ ) of the primordial displacement potential $\Psi$ $Ψ$ :
- Folds ( $A_2$ ): Mark the onset of multistreaming.
- Cusps ( $A_3$ ): Correspond to cosmic walls.
- Swallowtails ( $A_4$ ) and Umbilics ( $D_4$ ): Correspond to filaments. The paper distinguishes between these two families, noting $D_4$ filaments are denser and shorter.
- Butterflies ( $A_5$ ) and Parabolic Umbilics ( $D_5$ ): Correspond to cluster nodes.
Scale-Space Analysis: By smoothing the primordial potential with a Gaussian filter of varying scale $\sigma$ , the authors construct a scale-space caustic skeleton. This allows them to trace web features from small (galaxy-scale) to large (supercluster-scale) simultaneously.

B. Simulation Data & Computational Implementation

Datasets: The study uses the IllustrisTNG suite, specifically TNG100 ( $75^3 h^{-3} \text{Mpc}^3$ ) and TNG300 ( $205^3 h^{-3} \text{Mpc}^3$ ).
Lagrangian Reconstruction Challenge: IllustrisTNG uses "glass" pre-initial conditions rather than a regular grid of primordial displacements. To apply the Caustic Skeleton (which requires Lagrangian coordinates), the authors developed a novel pipeline:
1. Discrete Natural Neighbour Interpolation: Used to reconstruct the primordial displacement field $\mathbf{s}$ and potential $\Psi$ from the irregular particle positions of the glass initial conditions.
2. Phase-Space DTFE (PS-DTFE): A method to evaluate the multistreaming dark matter density field from the $N$ -body particle data.
3. Caustic Evaluation: The caustic conditions are evaluated on the smoothed primordial potential $\Psi_\sigma$ and evolved into the final configuration space ( $z=0$ ) using the displacement field.

C. Galaxy Analysis

Sample: Luminous galaxies are identified as subhalos with stellar mass $M_* > 0$ and at least 20 stellar particles.
Classification: Galaxies are assigned to web environments (voids, walls, filaments, clusters) based on their proximity (within $1 h^{-1}\text{Mpc}$ ) to the numerically calculated caustic simplices.
Metrics: The study analyzes four key properties as a function of web environment and formation time:
1. Colour ( $g-r$ ): Indicator of star formation history.
2. Specific Star Formation Rate (sSFR): Activity level.
3. Stellar Metallicity ( $Z$ ): Chemical enrichment.
4. Baryon Fraction ( $f_{bar}$ ): Retention of gas.

3. Key Contributions

First Lagrangian Application to TNG: Successfully reconstructed the primordial potential from the glass initial conditions of IllustrisTNG, enabling the first application of the Caustic Skeleton formalism to this state-of-the-art simulation suite.
Multiscale Web Classification: Provided a continuous, scale-space classification of the cosmic web, moving beyond single-scale definitions to show how web definitions (and thus galaxy populations) evolve with the smoothing scale $\sigma$ .
Filament Sub-Structure: Identified and analyzed two distinct filament families ( $A_4$ swallowtail and $D_4$ umbilic), demonstrating that $D_4$ filaments are denser, shorter, and host redder, more quenched galaxies than $A_4$ filaments.
Formation Time Dependence: For the first time, explicitly correlated galaxy properties with the formation time of their embedding web element (defined by the first shell-crossing time $b_c = \lambda_1^{-1}$ ), rather than just present-day density.

4. Key Results

A. Multistreaming and Gas Properties

The dark matter density field follows a log-normal distribution arising from the summation of multistreaming configurations.
Baryonic Gas: Gas density traces dark matter linearly across all environments. However, gas temperature and metallicity show strong bimodality.
- Temperature: Transitions from cool ( $T \lesssim 10^4$ K) in walls to hot ( $T \gtrsim 10^5$ K) in filaments and clusters.
- Metallicity: Highly bimodal; negligible in voids/walls but significant in filaments and clusters, indicating that significant stellar enrichment occurs only in dense environments.

B. Galaxy Properties in Web Environments

Hierarchical Quenching: A clear progression exists:
- Voids: Bluest, highest sSFR, lowest metallicity, highest baryon fraction.
- Walls: Intermediate properties.
- Filaments: Redder, lower sSFR, higher metallicity.
- Clusters: Reddest, most quenched, lowest baryon fraction.
Filament Families: Galaxies in $D_4$ (umbilic) filaments are systematically redder and more quenched than those in $A_4$ (swallowtail) filaments, acting as an intermediate environment between standard filaments and clusters.

C. Scale-Space Dependence

Continuum of Properties: Galaxy properties form a continuum in scale-space.
- At small scales ( $\sigma \sim 0.5$ ), "clusters" include galaxy-sized halos, and "voids" are nearly empty.
- At large scales ( $\sigma \sim 2.5$ ), "voids" contain significant substructure and host $\sim 60\%$ of all blue galaxies.
- The traditional "quadripartite" distinction blurs; small-scale filaments resemble large-scale walls in terms of galaxy populations.
Blue Galaxy Distribution: The fraction of blue galaxies depends heavily on scale. At large scales, walls and voids host 90% of all blue galaxies, whereas at small scales, this fraction is much lower.

D. Formation Time vs. Density

Formation Time Correlation: There is a strong correlation between the age of a web element and the properties of its galaxies.
- Older Web Elements: Host redder, more metal-rich, and more quenched galaxies (even within the same environment type).
- Younger Web Elements: Host bluer, more active galaxies.
Density vs. Time: While the colour-density relation is strong, the dependence on formation time is of a similar order of magnitude. Older structures have had more time to accrete mass and quench star formation, leading to a degeneracy between age and density.

5. Significance

Theoretical Rigor: The paper moves cosmic web classification from heuristic, single-scale morphological filters to a mathematically rigorous, parameter-free, phase-space dynamical framework.
Refining the Colour-Density Relation: It demonstrates that the "colour-density" relation is actually a "colour-scale-density-formation-time" relation. The environment's definition is scale-dependent, and the formation history is a critical, previously under-explored variable.
Observational Relevance: As upcoming surveys (DESI, Euclid, LSST) provide deeper 3D maps, this work provides a theoretical basis for interpreting galaxy populations in a multiscale context. It suggests that the "environment" of a galaxy cannot be defined by a single density threshold but must account for the scale of observation and the dynamical age of the structure.
Future Directions: The framework opens avenues for studying the evolution of galaxy spin alignments, morphologies (red spirals/blue ellipticals), and the dynamical origin of atypical populations by tracing their specific caustic origins.

In summary, this study establishes that the multiscale nature and formation history of the cosmic web are fundamental drivers of galaxy evolution, offering a more nuanced and physically grounded understanding of the colour-density relation than previously available.