Postulating dark matter particle mass and properties from two-thirds law
  for self-gravitating collisionless dark matter flow
  Dark matter can be characterized by the mass and size of its smallest
constituents, which are challenging to be directly probed and detected. We
present a new approach to predict the mass and properties of dark matter
particles based on the nature of dark matter flow. The self-gravitating
collisionless dark matter flow exhibits an inverse mass and energy cascade from
small to large mass scales with a scale-independent constant energy flux (the
rate of energy transfer $\epsilon_u$). In this paper, we study the simplest
case with only gravitational interaction involved. In the absence of viscosity,
the energy cascade leads to a two-thirds law for pairwise velocity that extends
down to the smallest length scale, where quantum effects are dominant.
Combining the energy flux $\epsilon_u$, Planck constant $\hbar$, and
gravitational constant $G$ on that scale, the mass of dark matter particles is
found to be around $10^{12}$GeV and size is on the order of $10^{-13}$m. This
suggests a heavy dark matter scenario with a mass much greater than standard
thermal WIMPs.
