Filament Width-Mass Scaling

The width of cosmic filaments — the transverse scale over which the density profile drops from the spine to the mean field — scales with the total mass of the filament in a way that ΛCDM reproduces only approximately. Observed filaments tend to be somewhat wider than pure gravitational collapse from ΛCDM initial conditions predicts, and the width-mass relation shows scatter that correlates with environment. SCT explains filament width through the interplay of angular momentum inheritance and gravitational superposition. The angular momentum deposited into each filament by the collision creates a centrifugal barrier that prevents matter from collapsing all the way to the filament spine, setting a minimum transverse scale determined by the specific angular momentum inherited rather than by thermal or turbulent pressure alone.

The centrifugal barrier from inherited angular momentum sets the filament width such that ρ(r) ∝ r⁻² in the outer profile — the same mechanism that flattens galaxy rotation curves operates at the filament scale. More massive filaments, which descend from collision regions with higher angular momentum per unit mass, therefore have systematically wider profiles, naturally generating the observed positive width-mass correlation. The scatter in this relation reflects the variance in impact parameter across different filament orientations relative to the primary collision axis: filaments aligned with the collision axis inherited more angular momentum and are consequently wider for their mass than transversely oriented filaments. ΛCDM, which relies on stochastic tidal torquing alone, cannot produce this coherent, axis-correlated scatter.