Tracing the branching roots of dark-matter haloes

A history drawn in particle paths

The cosmic web connects galaxies and galaxy clusters through a vast network of matter. Mark Neyrinck, Miguel Aragón-Calvo and István Szapudi examine a different view of that network: the accumulated paths of particles that eventually belong to one dark-matter halo. Their paper, Galaxy and Halo Root Systems: Fingerprints of Mass Assembly, is available on arXiv in a revision whose record states that it matches the version accepted to Monthly Notices of the Royal Astronomical Society.

The researchers call these accumulated trajectories a halo’s root system. Unlike a conventional merger tree, which records hierarchical relationships between objects, this representation preserves spatial geometry. It shows where matter travelled as smaller concentrations gathered into a larger structure.

Crucially, the image combines different times. It is not a snapshot of filaments all existing simultaneously, nor a set of streamlines calculated from the velocity field at one moment.

Removing motion to reveal assembly

The main analysis uses TNG50-3-Dark, a dark-matter-only simulation in the IllustrisTNG collection. It contains 540 cubed particles in a box 35 megaparsecs per h across, where h expresses the Hubble constant in conventional scaled units.

Starting with haloes identified at the present-day endpoint, the team follows their constituent particles through 100 simulation snapshots. At every snapshot, it recentres the selected particles to remove the halo’s bulk motion. Positions are expressed in comoving coordinates, which factor out cosmic expansion and make inward movement easier to recognize.

The particles are deposited onto three-dimensional grids, with contributions weighted by the time intervals between snapshots. Combining these deposits produces a record of where the selected matter spent time. Concentrated paths appear as roots, while some material contributes a more diffuse background rather than an obvious branch.

Larger haloes, richer branching

Across the sample, larger haloes generally display more roots and more branching than smaller ones. The most massive objects correspond to the scale of galaxy clusters, rather than individual galaxies.

To move beyond visual impressions, the researchers examine spherical shells around each root system’s centre. A multiscale image filter identifies blob-like concentrations where roots cross a shell. These responses contribute to a quantity called filamentarity, rather than a definitive count of individually mapped branches.

Averaging measurements in groups of 20 haloes, the team finds that filamentarity generally increases with halo mass at a fixed radius over part of the measured range. Its outward rise also suggests branching: more paths become distinguishable farther from the centre. Lower-mass systems tend to show an earlier downturn.

The images additionally suggest that haloes with greater final angular momentum have more curved roots. This is a visual finding, not a calibrated formula for predicting spin from root curvature.

Distant streaks and numerical checks

Many root systems contain narrow streaks extending well beyond their compact central regions. These indicate contributions from particles that began far away, without all the intervening matter joining the same final halo.

Their interpretation depends partly on how a halo is defined. The study uses the friends-of-friends method, which links nearby particles but does not remove every particle that is not gravitationally bound. The authors therefore caution against treating every distant streak as an unambiguous feature of a permanently bound object.

A comparison of eight systems with a simulation having eight times better mass resolution, alongside finer rendering grids, finds broadly similar structures. Many distant streaks persist. This supports their physical interpretation and the mass-dependent branching trend, although it is a limited resolution check rather than an exhaustive convergence study.

A diagnostic, not a complete explanation

Stacking root systems also reveals evidence of preferred infall directions relative to the simulation’s coordinate axes. The authors present this as a possible diagnostic of finite-box effects. Small contributing samples at large radii and the need for further analysis prevent a definitive claim that the simulation is unsuitable for a particular application.

Connections to galaxy evolution remain more tentative. Disrupted supply filaments could help explain reduced star formation, but this analysis follows dark matter, not star-forming gas, and does not establish that mechanism as the dominant cause of quenching.

The immediate contribution is a geometric way to inspect assembly history. Turning those branching images into objective root maps—and establishing how reliably they predict galaxy properties—remains unfinished research.