Sub-filaments in the cosmic web showed a different pattern of surrounding density and motion from their parent filaments in cosmological simulations, even after the comparison was matched by the mass of the nodes at each end and by relative distance from the filament. The sub-filaments were more often linked with larger endpoint-node masses, denser surroundings, stronger coherent inflows, larger tangential motions and higher velocity dispersions. The study set out to determine whether sub-filaments are a distinct subset of the filament population or simply a random sample of it.
Mapping the cosmic-web hierarchy
To make the comparison, the analysis used five independent ΛCDM N-body realizations with identical cosmological parameters. Each realization evolved 10,243 particles in a periodic box 300 h−1 Mpc on a side, with particle mass about 2 × 10^9 h−1 M⊙. The analysis was at redshift z = 0, and all five realizations were pooled for the profile and distribution measurements.
Skeletor built the hierarchy by lowering tracer-mass thresholds to bring smaller structures into view. It then smoothed and refined the filament spine using the surrounding dark-matter distribution, reconstructing three hierarchy levels.
The labels were based on geometric overlap. A current-level filament became a candidate sub-filament when more than 50% of its spine lay inside a filament from the previous level. If more than 80% of a spine lay within 3 × ds, detections were treated as the same structure; after that, remaining embedded candidates were labelled sub-filaments and non-embedded filaments parents.
Before comparing classes, the catalog was cleaned. The cuts removed portions within one halo radius of endpoint nodes, filaments too short relative to endpoint-node radii, structures whose enclosed density never exceeded 10 times the mean, and the 10% of segments with the highest curvature. The retained catalog contained 82% of the original sample, or 27,789 filaments classified as parent or sub-filaments.
Where the profiles separate
Parent and sub-filament profiles were compared in three approximately equal bins of total endpoint-node mass. Distance from each filament was scaled by its Rv, and each stacked profile was weighted by the length over which it was measured. This made the comparison at matched node mass and relative filament radius.
The distributions pointed to different kinds of connections. Sub-filaments were preferentially associated with larger total endpoint-node masses, so they occurred more often near massive nodes and denser environments. Their node-mass-ratio distribution also had a more prominent high-ratio tail, consistent with connections between nodes with more unequal masses.
At the lowest node masses, the outskirts of sub-filaments beyond r/Rv > 1 were approximately 1.5 times denser than the outskirts of parent filaments at the same node mass. That contrast weakened at higher node masses. The sub-filaments also showed a deeper dip in radial infall, meaning stronger inward motion. The location of the minimum changed little, but in low-node-mass outskirts the stronger infall continued to larger radii.
Motion differed in other ways, too. At fixed node mass—especially at the low-mass end—sub-filaments had roughly twice or more the angular momentum of parent filaments, indicating stronger rotation in their surroundings. Radial and tangential velocity dispersions, a measure of how widely particle velocities were spread in those directions, were consistently higher for sub-filaments across all three node-mass bins.
Together, the density and motion profiles showed a systematic difference between the two classes after node mass and filament radius were accounted for. Sub-filaments had enhanced densities, stronger coherent inflows, larger tangential motions and higher velocity dispersions. The combined pattern is consistent with the view that parent and sub-filaments are physically distinct populations.
A result tied to one simulation setup
The result is tied to how the structures were defined and to the simulation setup. Sub-filaments were identified through spine overlap, so the finding describes a geometric hierarchy rather than a directly tested account of how individual structures formed or evolved. The calculations used identical-parameter simulations at z = 0, and the comparisons covered the cleaned catalog, which retained 82% of the original structures.
Within those boundaries, the comparisons suggest that a filament’s place in the hierarchy is associated with different surrounding conditions. After node mass and relative radius were matched, sub-filaments still differed from parent filaments across several density and motion measures.
The manuscript is a preprint identified as arXiv:2608.25840v1. Its front matter gives August 27, 2026, while the arXiv header states August 26, 2026.
Paper data and sources
Original title: Filaments within filaments: unraveling the hierarchy of the cosmic web
Authors: Saee Dhawalikar, Aseem Paranjape, Shadab Alam
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text