Observational rotation curves and density profiles versus the Thomas-Fermi galaxy structure theory

The Thomas-Fermi approach to galaxy structure determines self-consistently the gravitational potential of the fermionic warm dark matter (WDM) given its distribution function f(E). This framework is appropriate for macroscopic quantum systems as neutron stars, white dwarfs and WDM galaxies. Compact dwarf galaxies are near the quantum degenerate regime, while large galaxies are in the classical Boltzmann regime. We derive analytic scaling relations for the main galaxy magnitudes: halo radius rh, mass Mh and phase-space density. Small deviations from the exact scaling show up for compact dwarfs due to quantum macroscopic effects. We contrast the theoretical curves for the circular galaxy velocities vc(r) and density profiles ρ(r) with those obtained from observations using the empirical Burkert profile. Results are independent of any WDM particle physics model, they only follow from the gravitational interaction of the WDM particles and their fermionic nature. The theoretical rotation curves and density profiles reproduce very well the observational curves for r ≲ rh obtained from 10 different and independent sets of data for galaxy masses from 5 × 109 to 5 × 1011M⊙. Our normalized theoretical circular velocities and normalized density profiles turn to be universal functions of r/rh for all galaxies. In addition, they agree extremely well with the observational curves described by the Burkert profile for r ≲ 2 rh. These results showthat the Thomas-Fermi approach correctly describes the galaxy structures.