A model for the mass and distribution of particles in dark matter halos

This model is intended for dark-matter-dominated galaxies and galaxy clusters for which the centrifugal force caused by system rotation is negligible. Such systems, ostensibly dark matter halos, would tend to be spherical. Consider a uniform sphere of identical, massive particles in equilibrium (not contracting or expanding). In the quantum model, gravitation pulls the particles together and quantum uncertainty pushes them apart. In the corresponding classical model, gravitation pulls the particles together and thermal motion pushes them apart. This model provides an expression for particle mass as a function of the total mass and density of the system and its quantum state or temperature. Using the measured total mass and density of our dark-matter-dominated galaxy, and assuming the system is in the ground state, the particle mass is found to be 10.5 eV and the temperature 0.042 K. This represents the lowest possible system temperature and particle mass. If, on the other hand, the system is in equilibrium with the cosmic microwave background, the particle mass is found to be 693 eV. This range of inferred particle masses supports the hypothesis of "low-mass dark matter" with approximate mass 100 eV. However, the system temperature is not presently known so it is possible that the temperature is higher and, consequently, the particles are heavier. The average speed of the particles is found to be approximately 1/1000 the speed of light in our galaxy. Remarkably, this result does not depend on the system temperature and, therefore, does not depend on the particle mass. The extension of this model to variable density provides a straightforward solution to the "core-cusp problem" because the distribution of dark matter that minimizes the system energy has a flat central dark matter density profile.