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.