Possible Evidence of Thermodynamic Equilibrium in Dark Matter Haloes
  After deducing the density profiles and gravitational potential functions of
eight galaxies from the rotation velocity data from THINGS, we find that the
density decreases exponentially with the potential in substantial regions of
the haloes. Such behavior is in agreement with that of a single-component
isothermal Boltzmann gas, and suggests that an effective description in terms
of a Boltzmann gas is possible for dark matter in these regions. This could be
an indication that dark matter self-interactions are sufficient in strength and
number to lead to thermal equilibrium in these regions. We write down the
dynamics and boundary conditions for a Boltzmann gas description and examine
some of its qualitative and quantitative consequences. Solutions to the
dynamical system are determined by three dimensionfull parameters, and provide
reasonable fits to the rotational velocity data in the regions where the
Boltzmann-like behavior was found. Unlike in the usual approach to curve
fitting, we do not assume a specific form for the dark matter density profile
and we do not require a detailed knowledge of the baryonic content of the
galaxy.
