Tremaine-Gunn bound

The maximum primordial occupation of a collisionless fermion distribution limits the coarse-grained phase-space density attainable in a halo. Combining that bound with an observed velocity dispersion and mass density gives a lower candidate mass. This tests light-fermion halo models independently of whether the candidate is optically visible.^[ref]

Fine-grained occupation is conserved along trajectories of a collisionless distribution. Coarse graining cannot increase its maximum. For fermions the primordial occupation is bounded, so a measured halo density and velocity scale restrict the particle mass required to produce that halo.