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James Edward Gunn coauthored work connecting the microscopic nature of a proposed dark matter particle with the macroscopic structure of a galaxy. The argument uses limits on the phase-space occupancy of fermions to constrain whether a light neutral particle could supply a measured galactic mass distribution.^[ref]

It illustrates a bridge between particle and stellar dynamics: a gravitationally inferred density is not independent of the allowed velocities and statistical properties of the particles supplying it.

Standard Model active neutrinos decouple while relativistic and retain a thermal momentum distribution. They therefore constitute hot dark matter for the light masses compatible with the standard cosmological picture. Their collisionless free streaming erases linear cosmological density perturbations below a characteristic scale. Making them the dominant gravitating matter would delay small-scale structure formation and suppress the observed matter power spectrum.

For standard thermal abundances and nonrelativistic neutrinos today,Increasing the mass sum enough to provide all the stipulated dark matter conflicts with the successful cold dark matter description of cosmological structure. Independently, the Tremaine-Gunn bound on the fermionic phase-space occupation limits the density light neutrinos can supply in small galactic haloes.^[ref] Oscillations establish nonzero neutrino mass differences, but do not make the relic neutrinos cold. Active neutrinos can contribute some matter; they cannot supply the dominant cold component. A heavier sterile neutrino candidate would be a different hypothesis, not an ordinary Standard Model relic.

Scott Tremaine coauthored a phase-space constraint on fermionic dark matter. The analysis connects the phase-space density needed in a galaxy with an upper bound arising from the microscopic statistics of a proposed particle.^[ref]

The result shows why matching a total gravitational mass is not sufficient for a viable matter model. The candidate must also be able to occupy the measured spatial and velocity distribution. Both the dynamical inference and assumptions about the particle distribution enter the test.

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]