Scaling Relations for Collision-less Dark Matter Turbulence

TL;DR

This paper proposes that collision-less dark matter behaves like a turbulent fluid, deriving scaling laws that explain various cosmic observations and suggesting a universal energy flow rate in dark matter structures.

Contribution

It introduces the concept of dark turbulence in collision-less dark matter and derives scaling laws from Navier-Stokes equations applicable to cosmic structures.

Findings

Consistent scaling relations for dark matter systems are explained by dark turbulence.

Derived a universal energy flow rate of 0.3 cm^2/sec^3 in cosmic structures.

Application of turbulence theory to observations like velocity dispersion and power spectra.

Abstract

Many scaling relations are observed for self-gravitating systems in the universe. We explore the consistent understanding of them from a simple principle based on the proposal that the collision-less dark matter fluid terns into a turbulent state, i.e. dark turbulence, after crossing the caustic surface in the non-linear stage. The dark turbulence will not eddy dominant reflecting the collision-less property. After deriving Kolmogorov scaling laws from Navier-Stokes equation by the method similar to the one for Smoluchowski coagulation equation, we apply this to several observations such as the scale-dependent velocity dispersion, mass-luminosity ratio, magnetic fields, and mass-angular momentum relation, power spectrum of density fluctuations. They all point the concordant value for the constant energy flow per mass: $0.3 cm^2/sec^3$, which may be understood as the speed of the hierarchical coalescence process in the cosmic structure formation.