The Tremaine-Gunn phase-space constraint giving lower limits on the mass of dark-matter particles that were once in kinetic equilibrium is generalized to arbitrary decoupling temperatures and chemical potentials for fermions as well as bosons. It is stressed that even in the cases where no exact limit exists (e.g., for bosons with a chemical potential approaching the mass) a statistical limit can be obtained. In most cases particle masses of several eV or more are necessary to explain the dark matter in galaxy halos.

• Received 21 March 1991

DOI:https://doi.org/10.1103/PhysRevD.44.999