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.

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