Predicting the dark matter particle mass, size, and other properties from the mass and energy cascade and two-thirds law in dark matter flow

How can the fluid mechanics help us understand the dark matter mystery - the biggest quest of contemporary astrophysics? After years of null results in the search for thermal WIMPs, a different prospective might be required. We present a new fluid mechanics approach to estimate the dark matter particle mass, size and many other relevant properties based on the nature of flow of dark matter. A comparison with hydrodynamic turbulence is presented to reveal the unique features of dark matter flow, i.e. an inverse mass and energy cascade from small to large scales with a scale-independent rate of energy cascade ε_u=-4.6x10^-7m²/s³. If gravity is the only interaction involved and viscosity is absent, the energy cascade leads to a two-thirds law for pairwise velocity that can be extended down to the smallest scale, where quantum effects become important. Combining the rate of energy cascade ε_u, Planck constant h, and gravitational constant G on that scale, mass of dark matter particles is found to be around 10¹²GeV with a size around 10^-13m. This strongly suggests a heavy dark matter scenario with a mass much greater than standard WIMPs. The accompanying slides and datasets for this work can be found on Zenodo.org by searching "dark matter flow" or https://doi.org/10.5281/zenodo.6569901.