Warm Dark Matter Mass

Warm dark matter (WDM) consists of particles with masses in the keV range that remain relativistic longer than cold dark matter. Because they travel faster in the early universe, they can erase density perturbations below a characteristic scale known as the free‑streaming length. This suppression influences the formation of low‑mass halos and can be probed by observations of dwarf galaxies and the Lyman‑α forest.

The free‑streaming mass, (M_{mathrm{fs}}), is the mass contained within a sphere whose radius equals half the free‑streaming length. It provides a convenient way to express the smallest structures that can form in a WDM cosmology. The mass depends on the particle mass (m_{mathrm{wdm}}), the WDM density parameter (Omega_{mathrm{wdm}}), and the reduced Hubble constant (h).

A widely used approximation for the free‑streaming mass is

This expression yields (M_{mathrm{fs}}) in solar masses ((M_{odot})). Larger particle masses produce smaller free‑streaming masses, allowing smaller halos to survive.

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