Turbulent Mixing, Diffusion and Gravity in the Formation of Cosmological Structures: the Fluid Mechanics of Dark Matter

The theory of gravitational structure formation in astrophysics and cosmology is revised based on real fluid behavior and turbulent mixing theory. Gibson's 1996-1998 theory balances fluid mechanical forces with gravitational forces and density diffusivity with gravitational diffusivity at critical viscous, turbulent, magnetic, and diffusion length scales termed Schwarz scales LSX. Condensation and void formation occurs on non-acoustic density nuclei produced by turbulent mixing for scales L≥LSXmax rather than on sound wave crests and troughs for L≥LJ as required by Jeans's 1902 linear acoustic theory. Schwarz scales LSX = LSV, LST, LSM, or LSD may be smaller or larger than Jeans's scale LJ. Thus, a very different "nonlinear" cosmology emerges to replace the currently accepted "linear" cosmology. According to the new theory, most of the inner halo dark matter of galaxies consists of planetary mass objects that formed soon after the plasma to neutral gas transition 300,000 years after the Big Bang. These objects are termed primordial fog particles (PFPs) and provide an explanation for Schild's 1996 "rogue planets ... likely to be the missing mass" of his observed quasar-lens galaxy, inferred from the twinkling frequencies of both quasar images and their phased difference. The more massive nonbaryonic dark matter (possibly neutrinos) is super-diffusive because of its small collisional cross-section with ordinary (baryonic) matter, and can only condense at LSD scales much larger than galaxies to form massive halos of galaxy superclusters, clusters and outer galaxy halos. In the beginning of structure formation 30,000 years after the Big Bang, viscous Schwarz scales LSV matched the Hubble scale ct of causal connection at protosupercluster masses of 1046 kg, with photon viscosity values of 5x1026 m2 s-1, where c is the velocity of light and t is the age of the universe, decreasing to 1041 kg protogalaxy masses at plasma neutralization. Diffusivities of this magnitude are indicated by LSD values of 1022 m for dark matter dominating luminous matter by a factor of about 800, observed in a dense galaxy cluster by Tyson and Fischer (1995). NOMENCLATURE AU = astronomical unit, 1.4960x1011 m a(t) = cosmological scale factor as a function of time t c = speed of light, 2.9979x108 m s-1 D = molecular diffusivity of density, m2 s-1 ε = viscous dissipation rate, m2 s-3 G = Newton's gravitational constant, 6.7x10-11 m3 kg-1 s-2 γ = rate of strain, s -1 kB = Boltzmann's constant, 1.38x10-23 J K-1 l = collision length, m ly = light year, 9.461x1015 m LGIV = gravitational-inertial-viscous scale, [ν2/ρG]1/4 LSV = viscous Schwarz scale, (ν γ /ρG)1/2 LST = turbulent Schwarz scale, ε1/2/(ρG)3/4 LSD = diffusive Schwarz scale, (D2/ρG)1/2 LH = Hubble or horizon scale of causal connection, ct LJ = Jeans scale, VS/(ρG)1/2