Thermodynamics sheds light on the nature of dark matter galactic halos

In spherical symmetry, the gravitational potential of galaxies and their halos are univocally derived from the rotational velocity profile. Thousands of galaxies are well-fitted by a universal velocity profile and thus, the gravitational profile is well known. By considering that dark matter can be treated either as an ideal gas, a Fermi, or a Bose gas, we found that only the latter can generate such a gravitational profile with a decreasing temperature profile if the mass of the boson is below 20,eV/c^2. If we demand that the sound speed is less than the speed of light, a lower bound on the boson’s mass is obtained.