Dark Matter Free-Streaming: Cold vs Warm vs Hot

Dark Matter Species

Particle mass m 2.0 keV

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Evolution

Simulation speed 1.0×

Live Readouts

Thermal velocity v_rms

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Free-streaming length

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Small clumps surviving

3 / 3

Large clumps surviving

3 / 3

Elapsed (illustrative)

0.0 era-units

How it works

Dark matter that is still relativistic (or mildly so) when the universe becomes matter-dominated keeps moving freely through the early density field, smoothing out — "free-streaming" — any overdensity smaller than the distance a typical particle can travel. Its thermal speed follows the Maxwell–Boltzmann relation:

v_rms = √(3kT/m)

The comoving distance a particle covers before structure can grow, the free-streaming length, scales steeply with particle mass (Bode, Ostriker & Turok 2001, thermal-relic approximation used here for illustration):

λ_fs ≈ 0.2 Mpc × (1 keV / m)^(4/3)

A perturbation of physical size R only survives to seed a bound structure (galaxy, dwarf galaxy, halo) if λ_fs < R — otherwise the particles composing it stream apart faster than gravity can pull them together.

Cold dark matter (m ≳ few GeV, e.g. a WIMP): λ_fs is astronomically small — essentially no structure is erased, down to sub-galactic scales.
Warm dark matter (m ~ 1–10 keV, e.g. a sterile neutrino): λ_fs ~ 0.05–1 Mpc — dwarf-galaxy-scale clumps get washed out while galaxy clusters survive.
Hot dark matter (m ~ 1 eV, e.g. an ordinary neutrino): λ_fs reaches tens to hundreds of Mpc — even galaxy-scale overdensities are erased, which is why neutrino-dominated dark matter was ruled out by observed galaxy clustering.

This simulation seeds two families of overdensities (large "cluster-scale" clumps and small "dwarf-scale" clumps) plus a diffuse background, then evolves them under a toy combination of self-gravity (spring-like pull toward each clump's centre, switchable) and a free-streaming random walk sized from λ_fs above. Watch which clumps hold together and which dissolve as you change the particle mass.

Large (cluster-scale) clumps Small (dwarf-scale) clumps Diffuse background

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