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Mass density structuring around galaxy formation sites: impact on galaxy basic properties

Using the EAGLE50 simulation, this study reveals that the anisotropic evolution and final shape of Lagrangian volumes around galaxy formation sites, characterized by their deformation and the timing of Cosmic Web spine emergence, significantly influence the resulting galaxy's mass and kinematic properties, with prolate or flattened configurations favoring low-mass or rotation-dominated systems.

Original authors: Sandra Robles, Rosa Domínguez-Tenreiro, Susana E. Pedrosa

Published 2026-03-20

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CC BY 4.0

Original authors: Sandra Robles, Rosa Domínguez-Tenreiro, Susana E. Pedrosa

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 static backdrop, but as a giant, evolving piece of dough being kneaded by gravity. This paper is a detailed study of how that dough shapes itself around the "seeds" where galaxies are born, and how those shapes determine what kind of galaxy eventually grows there.

Here is the story of the paper, broken down into simple concepts and everyday analogies.

The Big Picture: The Cosmic Web as a Construction Site

Think of the early universe as a vast, foggy construction site. Gravity is the foreman. It doesn't just pull things together randomly; it pulls them into a specific structure called the Cosmic Web. This web looks like a giant spiderweb made of:

Nodes: Where galaxies cluster (like busy city centers).
Filaments: Long, thin strands connecting the nodes (like highways).
Walls: Flat sheets of matter (like large apartment blocks).
Voids: Empty spaces where nothing much happens (like empty fields).

The authors wanted to know: Does the shape of the "construction site" (the local environment) determine the size and personality of the "building" (the galaxy) that gets built there?

The Method: Tracking a "Time-Lapse" Bubble

To answer this, the scientists used a supercomputer simulation called EAGLE. Instead of just looking at galaxies today, they went back in time to when the universe was very young (about 1 billion years old, or redshift $z=15$ ).

The Bubble (Lagrangian Volume): Imagine placing a perfectly round, transparent bubble around a spot where a galaxy is about to form.
The Time-Lapse: They watched this bubble evolve over 13 billion years. As gravity pulled matter in, the round bubble got squashed, stretched, and twisted.
The Ingredients: They tracked two types of "dough" inside the bubble:
- Dark Matter: The invisible, heavy skeleton that holds everything together.
- Cold Baryons: The normal stuff (gas and stars) that actually lights up and forms the galaxy.

They measured how the bubble changed shape using a mathematical tool called the Reduced Inertia Tensor. Think of this as a way to measure if the bubble is becoming a pancake (flat), a sausage (long and thin), or a football (triangular).

Key Findings: How Shape Dictates Destiny

1. The Shape of the Bubble Determines the Galaxy's Size

The study found a strong link between the shape of the bubble and the mass of the galaxy inside it.

The "Sausage" (Prolate) Shape: If the bubble stretched out into a long, thin sausage shape, it tended to host small, low-mass galaxies. It's like trying to build a skyscraper on a narrow, unstable foundation; you can't get much mass there.
The "Pancake" or "Football" (Oblate/Triaxial) Shape: If the bubble flattened out or became a complex 3D shape, it tended to host massive galaxies. These shapes allow matter to flow in from many directions, like a wide highway system feeding a massive city.

2. The "Skeleton" vs. The "Flesh"

One of the most interesting discoveries is that the Dark Matter (the skeleton) and the Gas/Stars (the flesh) don't always evolve at the same speed or in the same way.

The Skeleton Sets First: The dark matter structure usually stabilizes first. It sets the "spine" of the cosmic web.
The Flesh Takes Its Time: The gas and stars (Cold Baryons) are messy. They get heated up by supernovae (stellar explosions) and black holes, causing them to swirl and move differently than the dark matter.
The Analogy: Imagine a steel frame of a building being erected (Dark Matter). Once the frame is up, the workers start putting up drywall and painting (Gas/Stars). The workers might move around, get distracted, or change the layout slightly, so the final painted building looks a bit different from the steel frame underneath.

3. Rotation: The "Spin" of the Galaxy

The paper also looked at why some galaxies spin like a top (disc galaxies like the Milky Way) while others are just puffy blobs (elliptical galaxies).

The "Thin Sheet" Effect: Galaxies that end up spinning rapidly tend to form inside bubbles that became very thin and flat (like a sheet of paper).
Why? If the gas is confined to a thin sheet, all the particles are moving in the same direction, like cars on a circular racetrack. This creates a strong, organized spin.
The "Messy Pile" Effect: If the bubble stays somewhat round or chaotic, the gas particles crash into each other from different angles, canceling out the spin and creating a puffy, non-rotating galaxy.

The "Freezing Out" Concept

The authors noticed that the universe doesn't change shape forever. Eventually, the "construction" stops, and the shape "freezes."

Early Freezing: In some places, the shape froze very early (within the first 2 billion years). These places usually ended up with massive galaxies.
Late Freezing: In other places, the shape kept changing for a long time (up to 10+ billion years). This late, chaotic rearrangement often resulted in smaller galaxies or those with different spin characteristics.

The Takeaway

This paper tells us that galaxies are not just random collections of stars. Their size and how they spin are deeply connected to the "room" they were born in.

If you are born in a long, thin corridor (prolate), you are likely to be small.
If you are born in a wide, flat hall (oblate), you are likely to be massive and spin rapidly.
And just like a building, the invisible steel frame (Dark Matter) sets the stage, but the actual construction workers (Gas and Stars) add their own messy, dynamic flair that can change the final look of the galaxy.

In short, the universe is a sculptor, and the shape of the clay (the local environment) determines the final statue (the galaxy).

1. Problem Statement

The paper addresses the gap in understanding how the local evolution of the Cosmic Web (CW) around galaxy formation sites influences the fundamental properties of the resulting galaxies, specifically their mass and rotational support (kinematic morphology).

While previous studies have established correlations between large-scale environments and galaxy properties (e.g., the Tidal Torque Theory for spin alignment), there is a lack of detailed analysis on the local anisotropic evolution of mass density from high redshift ( $z \sim 15$ ) to the present ( $z=0$ ). Specifically, the authors aim to determine:

How initially spherical Lagrangian volumes (LVs) deform into the filamentary and wall-like structures of the CW.
Whether the shape and orientation of these local environments differ between Dark Matter (DM) and Cold Baryons (CB).
How the timescales of this structural "freezing-out" correlate with the final stellar mass and kinematic state (rotation-dominated vs. dispersion-dominated) of the central galaxy.

2. Methodology

Simulation Data

Simulation: The study utilizes the EAGLE50 large-volume reference simulation (50 Mpc box, $\Lambda$ CDM cosmology).
Sample Selection: Central galaxies at $z=0$ with identified progenitors at $z \approx 15$ .
Lagrangian Volumes (LVs): For each galaxy seed at $z \approx 15$ , a spherical region with a radius of $K \times R_{vir}$ (where $K=10$ ) is defined. This volume contains all particles (DM, gas, stars) that will eventually contribute to the galaxy and its halo. The mass within the LV is conserved over time (excluding black hole formation).

Analytical Tools

Reduced Inertia Tensor (r-TOI): The authors compute the r-TOI for each LV to quantify its shape and orientation. This method is chosen because it is invariant under radial mass rearrangements and less sensitive to substructure at the LV outskirts compared to standard inertia tensors.
Shape Parameters: The eigenvalues and eigenvectors of the r-TOI are used to derive:
- Principal axes ( $a, b, c$ ).
- Axis ratios ( $b/a, c/a$ ).
- Triaxiality ( $T$ ): Distinguishes prolate ( $T > 0.7$ ), triaxial ( $0.3 < T < 0.7$ ), and oblate ( $T < 0.3$ ) shapes.
- Ellipticity ( $e$ ) and Prolateness ( $p$ ).
Freezing-out Timescales: The authors define specific cosmic ages ( $t_U$ $t_{U}$ ) when the LV evolution stabilizes:
- $t_{\delta A}$ : When eigen-directions (principal axes orientation) stop changing significantly (within a 10% threshold).
- $t_f$ : When the principal axis lengths stop changing (mass rearrangement ceases).
Galaxy Properties:
- Mass: Stellar mass ( $M_*$ ) and Halo mass ( $M_{vir}$ ).
- Kinematics: The kinematic morphological parameter $\kappa_{rot}$ , measuring the fraction of kinetic energy in ordered rotation. Galaxies are classified as rotation-dominated ( $\kappa_{rot} > 0.5$ for stars) or dispersion-dominated.

3. Key Contributions

Decoupling of DM and CB Evolution: The study explicitly separates the evolution of Dark Matter (DM) and Cold Baryons (CB) within the same Lagrangian volumes. It demonstrates that while DM drives the overall gravitational potential, CBs exhibit distinct hydrodynamic behaviors (cooling, heating, feedback) that lead to different shape evolutions and freezing-out timescales.
Quantification of "Freezing-Out": The paper provides a rigorous statistical framework for defining when the local Cosmic Web spine is "set" and when anisotropic mass flows cease, linking these timescales directly to galaxy formation outcomes.
Linking Local Geometry to Galaxy Kinematics: It establishes a direct causal link between the specific geometric configuration (flattened vs. prolate) of the baryonic environment at high redshift and the rotational support of the galaxy at $z=0$ .

4. Key Results

A. Shape Evolution and Mass Correlations

Anisotropy: Most LVs evolve from spherical to highly anisotropic configurations. By $z=0$ , ~67% of DM-LVs are prolate, while only ~4% are oblate.
Mass Dependence:
- Low-mass galaxies tend to form in prolate (filament-like) LVs.
- Massive galaxies tend to form in triaxial or oblate (flattened/wall-like) LVs.
DM vs. CB: CB-LVs often reach more extreme anisotropic configurations (lower $c/a$ ratios) than their DM counterparts, particularly in the flattened regime.

B. Freezing-out Timescales

Directional Freezing: One principal direction (usually the major axis) freezes out very early (within the first 2 Gyr).
Spine Emergence: The local CW spine (defined by fixed eigen-directions) emerges earlier for massive haloes than for low-mass haloes.
Mass Rearrangement: Anisotropic mass rearrangements cease late, on average at $t_U \sim 10.5$ Gyr for DM and even later for CB.
Massive vs. Low-Mass: Massive haloes have their principal axes freeze out later (up to $t_U \sim 11-12$ Gyr) compared to low-mass haloes, suggesting a longer period of mass accretion for massive systems.

C. Impact on Rotational Support ( $\kappa_{rot}$ )

Baryonic Flattening: Rotation-dominated galaxies are strongly correlated with flattened CB-LVs (low $c/a$ ratio, high ellipticity).
Prolate Filaments: Interestingly, highly prolate (filamentary) DM-LVs also host a significant fraction of rotation-dominated galaxies, suggesting that accretion along filaments can also align angular momentum.
Timing: The emergence of the CB spine ( $t_{\delta A, CB}$ ) is significantly delayed for rotation-dominated galaxies compared to dispersion-dominated ones. This delay allows for a longer period of coherent angular momentum alignment via cold gas flows.
Formation Sequence: For rotation-supported galaxies, the data suggests a sequence where cold gas organizes into a thin, flattened structure (low $c/a$ ) at $z \sim 0.5-0.1$ , forming a rotation-supported gaseous disc, which then forms stars.

5. Significance and Conclusions

Baryonic Physics is Crucial: The study confirms that baryonic processes (cooling, feedback, heating) cause CBs to deviate from the DM distribution. CBs can form more extreme flattened structures than DM, which are critical for the formation of disc galaxies.
Environmental Determinism: The local shape and evolution timescale of the environment are strong predictors of galaxy properties.
- Mass: Determined by the degree of anisotropy (prolate = low mass; flattened/triaxial = high mass).
- Rotation: Determined by the presence of flattened, coherent baryonic structures and the timing of their formation.
Methodological Advancement: The use of the Reduced Inertia Tensor on Lagrangian volumes provides a robust, global description of the local environment that avoids the smoothing issues of point-based tensor methods, successfully capturing the "fossil" record of the Cosmic Web's assembly.
Implications for Disc Formation: The results support a scenario where disc galaxies form from the accretion of cold gas that has been organized into flattened structures (walls or filaments) by the local Cosmic Web, with the timing of this organization dictating the final kinematic state of the galaxy.

In summary, the paper demonstrates that the local anisotropic evolution of the Cosmic Web, particularly the geometry and freezing-out timescales of the baryonic component, plays a decisive role in shaping the mass and rotational support of galaxies.