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The Thomas-Fermi approach to galaxy structure determines selfconsistently thefermionic warm dark matter (WDM) gravitational potential given the distributionfunction f(E). This framework is appropriate for macroscopic quantum systems:neutron stars, white dwarfs and WDM galaxies. Compact dwarf galaxies followfrom the quantum degenerate regime, while dilute and large galaxies from theclassical Boltzmann regime. We find analytic scaling relations for the maingalaxy magnitudes as halo radius r_h, mass M_h and phase space density. Theobservational data for a large variety of galaxies are all well reproduced bythese theoretical scaling relations. For the compact dwarfs, our results showsmall deviations from the scaling due to quantum macroscopic effects. Wecontrast the theoretical curves for the circular velocities and densityprofiles with the observational ones. All these results are independent of anyWDM particle physics model, they only follow from the gravity interaction ofthe WDM particles and their fermionic nature. The theory rotation and densitycurves reproduce very well for r < r_h the observations of 10 different andindependent sets of data for galaxy masses from 5x10^9 Msun till 5x10^{11}Msun. Our normalized circular velocity curves turn to be universal functions ofr/r_h for all galaxies and reproduce very well the observational curves for r <r_h. Conclusion: the Thomas-Fermi approach correctly describes the galaxystructures (Abridged).

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