Acquired scaling relations in dark matter turbulence

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 collisionless 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 collisionless 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 massangular momentum relation, power spectrum of density fluctuations. They all point the concordant value for the constant energy flow per mass: 0.3cm 2 /sec 3 , which may be understood as the speed of the hierarchical coalescence process in the cosmic structure formation. PACS numbers: Cosmology: theory, Gravitation, Turbulence, Cosmology: dark matter, Cosmology: observations, Hydrodynamics 98.80.-k 95.35 +d 98.65.-r

Galaxies nurtured by mature black holes

“…The scaling relation derived from this equation is applied to various observations such as the scale dependent mass density, L/M ratio, magnetic field distributions, etc. They all consistently point the value ǫ ≈ 0.3cm 2 /sec 3(Nakamichi, & Morikawa. (2010)).…”

“…The latter is the scaling velocity vout ≡ (ǫr) 1/3 , where ǫ is a constant. This is derived by the scaling property of the cosmic turbulence (Nakamichi, & Morikawa. (2010)).…”

Supermassive Black Holes and Dark Halo from the Bose-Condensed Dark Matter

“…However, an appropriate amount of angular momentum may be important to get the coexistence of SMBH and DH, because the whole system would collapse into BH otherwise. In this context, from various observations, the individual angular momentum A of the cosmological objects shows the following scaling [Nakamichi 2010], In our case, if we start from the wave function…”