https://doi.org/10.1140/epjc/s10052-017-4645-8
Regular Article - Theoretical Physics
Equation of state, universal profiles, scaling and macroscopic quantum effects in warm dark matter galaxies
1
LPTHE CNRS UMR 7589, Sorbonne Universités, Université Pierre et Marie Curie UPMC Paris VI, Tour 24, 5ème. étage, Boite 126, 4, Place Jussieu, 75252, Paris Cedex 05, France
2
Observatoire de Paris, LERMA CNRS UMR 8112, Observatoire de Paris PSL Research University, Sorbonne Universités UPMC Paris VI, 61, Avenue de l’Observatoire, 75014, Paris, France
* e-mail: Norma.Sanchez@obspm.fr
Received:
22
December
2016
Accepted:
24
January
2017
Published online:
8
February
2017
The Thomas–Fermi approach to galaxy structure determines self-consistently and non-linearly the gravitational potential of the fermionic warm dark matter (WDM) particles given their quantum distribution function f(E). This semiclassical framework accounts for the quantum nature and high number of DM particles, properly describing gravitational bounded and quantum macroscopic systems as neutron stars, white dwarfs and WDM galaxies. We express the main galaxy magnitudes as the halo radius 
, mass 
, velocity dispersion and phase space density in terms of the surface density which is important to confront to observations. From these expressions we derive the general equation of state for galaxies, i.e., the relation between pressure and density, and provide its analytic expression. Two regimes clearly show up: (1) Large diluted galaxies for 
and effective temperatures 
K described by the classical self-gravitating WDM Boltzman gas with a space-dependent perfect gas equation of state, and (2) Compact dwarf galaxies for 
K described by the quantum fermionic WDM regime with a steeper equation of state close to the degenerate state. In particular, the 
degenerate or extreme quantum limit yields the most compact and smallest galaxy. In the diluted regime, the halo radius , the squared velocity 
and the temperature 
turn to exhibit square-root of
scaling laws. The normalized density profiles 
and the normalized velocity profiles 
are universal functions of 
reflecting the WDM perfect gas behavior in this regime. These theoretical results contrasted to robust and independent sets of galaxy data remarkably reproduce the observations. For the small galaxies, 
, the equation of state is galaxy mass dependent and the density and velocity profiles are not anymore universal, accounting to the quantum physics of the self-gravitating WDM fermions in the compact regime (near, but not at, the degenerate state). It would be extremely interesting to dispose of dwarf galaxy observations which could check these quantum effects.
© The Author(s), 2017
