Thermodynamics sheds light on the nature of dark matter galactic halos

In spherical symmetry, the gravitational potential is uniquely determined by the rotational velocity profile. Numerous galaxies exhibit a universal velocity profile from which a universal gravitational profile is inferred. When treating dark matter as either an ideal gas, a Fermi gas, or a Bose gas, only the latter can produce a gravitational profile consistent with observations, along with a temperature profile that decreases outward. This requires the mass of the boson to be below a certain threshold of 43  eV/𝑐2. Additionally, ensuring that the speed of sound is less than the speed of light yields a lower bound on the boson’s mass.