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Journal of Applied Fluid Mechanics (accepted) 1

Cold Dark Conflicts with Fluid Mechanics and Observations

Carl H. Gibson1

1 University of California at San Diego, La Jolla, California, 92122-0411, USA Email: [email protected]

ABSTRACT

Cold hierarchical clustering (CDMHC) cosmology based on the Jeans 1902 criterion for gravitational instability gives predictions about the early contrary to fluid mechanics and observations. Jeans neglected viscosity, diffusivity, and turbulence: factors that determine gravitational and contradict small structures (CDM halos) forming from non- particle candidates. From hydro- gravitational-dynamics (HGD) cosmology, viscous-gravitational fragmentation produced (1046 kg), cluster, and - (1042 kg) clouds in the primordial with the large fossil turbulence -17 -3 12 (ρ0= 3 ! 10 kg m ) of the first fragmentation at 10 s, and a linear and spiral clump morphology reflecting maximum stretching near vortex lines of the plasma turbulence at the 1013 s plasma- transition. Gas fragmented into proto-globular--cluster mass (1036 kg) clumps of protoplanet gas clouds that are now frozen as earth-mass (1024-25 kg) Jovian of the baryonic dark matter, about 30,000,000 rogue planets per star. All form from these planets. They appear in planetary nebulae and are misinterpreted as dark . Observations contradict the CDMHCC prediction of large explosive Population III first stars at 1016 s, but support the immediate gentle formation of small Population II first stars in globular-star-clusters from HGD.

Keywords: , Gravitational Structure Formation, , Turbulence

1. INTRODUCTION theoretical support for a central gas source in spiral failed to materialize. Modern fluid mechanics requires additional gravitational structure formation The Jeans (1902) acoustic criterion for self- criteria. When viscosity, diffusion and turbulence are gravitational structure formation is derived by linear included in the analysis, a hydro-gravitational- perturbation stability analysis of the Euler fluid dynamics (HGD) cosmology emerges that is in better equations with , giving linear agreement with recent observations of the early acoustic equations by neglecting diffusion, viscous universe than CDM scenarios that assume collisionless forces and turbulence. Density is set to zero (the ρ fluids (Gibson 1996, 2000, 2004, 2005, 2006). Jeans swindle) to derive a critical (Jeans) length scale

1 / 2 L = V / (!G) , where V is speed and G is J S S From HGD cosmology (Figure 1), proto-galaxies and Newton’s gravitational constant, interpreted by Jeans proto-galaxy-clusters were formed by gravitational and astrophysicists (e.g. Springel et al. 2005) as the fragmentation of plasma at the Schwarz viscous scale only gravitational stability criterion, thus forbidding 1 / 2 L = (!" / #G ) , where γ is the rate-of-strain, ν is the gravitational structures at scales smaller than L . Sir SV J kinematic viscosity, ρ is the density, and G is James Jeans (1929) claimed observational support for Newton’s constant, preserving various parameters of his theory is provided by spiral galaxies. He assumed these irreversible transitions as fluid mechanical hot gas from a (mysterious) central spinning source 1 / 2 fossils. Because the Kolmogorov scale L = (! / " ) , collapses to stars in such galaxies only when chilled K

by the coldness of space, thus reducing L . 1 / 2 J and because ! / ( "G ) # 1 for a flat universe, it

follows that L ! L ! L for the conditions of proto- This evidence weakened as better telescopes showed SV N K the “stars” observed were really globular star clusters galaxy formation shown in Fig. 1. The first was to form primordial fog particle (GCs) containing millions of stars. Observational and (PFP) planets in Jeans mass proto-globular-star-cluster Journal of Applied Fluid Mechanics 2

(PGC) clumps as the plasma proto-galaxies became diffusion from PGs to form >1021 m galaxy halos of gas with much smaller viscosity. Stars form as baryonic dark matter (BDM), with diffusivity D ~ 1027 binaries when these planets merge in a binary cascade m2 s-1 calculated from L and the size and ρ of the to form larger and larger mass Jovian planets (JPPs), SD halos. now frozen as the baryonic (-) dark matter. JPPs randomly dim supernovae in planetary Flat rotation curves observed outside the 1020 m spiral nebulae, creating the now commonly accepted “ cores reflect this huge diffusivity. Luminous energy” misconception (Gibson & Schild 2007). >1020 m disks and spiral patterns of in globular-star-clusters (GCs) reflect 2. DILEMMAS OF JEANS’ THEORY torques developed in the chain-like morphology of the proto-galaxy-clusters as they split into spiral galaxies The Jeans criterion presents major dilemmas for hot from the expansion of space. The tiny first stars still cosmology in an expanding universe. In the exist in GCs and dim proto-GCs that are bound by H-He plasma epoch, the Jeans scale of the plasma L J gravity and friction from the evaporated gas provided always exceeds the “horizon” scale of causal by heating of their trillion frozen gas planets. connection L = ct because the enormous sound H 4. CDM COSMOLOGY 1 / 2 speed V = c / 3 is of order the speed of light c, S Orthodox collisionless cosmology explains galaxy and where t is the time, so plasma structures are formation using “cold dark matter” forbidden. The primordial gas at transition has a (CDM): a postulated non-baryonic fluid of 36 13 collisionless massive particles produced during the Jeans mass of a million stars ( M J = 10 kg), t = 10 nucleosynthesis epoch with particle . s (300,000 years), and T0 = 4000 K. Fragmentation vCDM < c in the primordial plasma occurs when the Schwarz Based on Jeans theory and collisionless N-body viscous scale matches the horizon scale at simulations, it is assumed deus ex machina, Binney & LSV LH Tremaine (1987), that gravitationally bound CDM 12 10 s (30,000 years), and in the primordial gas at the chunks form and merge gravitationally like point mass Jeans mass from heat transfer considerations and N-bodies are forced to do in computer simulations. simultaneously at to form Earth-mass primordial Large mergers (“halos”) of CDM chunks then serve as LSV planets. growing bottles that guide the gravitational formation of larger structures by hierarchical clustering (CDMHC) for 300 Myr dark ages without 3 / 2 The Jeans mass M = M (T / T ) ! / ! from the J J 0 0 stars and billions of years without galaxies or galaxy 0 Jeans criterion, so from Jeans’ theory the first stars clusters. are large and explosive, Madau (2006), and can form only after a “dark ages” period of about 300 Myr Pop-III superstars form as the gas cools by radiation (1016 s) to permit sufficient cooling and density and promptly explode in the merging CDM-halos, decrease. These Population III superstars rapidly Mori et al. (2004). Jupiter mass gas planets are ruled disintegrate as dusty class II to re-ionize out by the Jeans criterion because they require an the gas and explain its absence in absorption spectra impossible cooling of their H-He gas to 0.004 K to from early , Mori and Umemura (2006). permit Jeans instability. However, Jovian planets circling the sun in outer orbits and now detected in However, recent γ-ray spectra from refute the great multitudes in tight orbits around other stars, intense high-energy starlight expected, Aharonian et Lovis et al. (2006), contradict the Jeans acoustic al. (2006). The intergalactic medium is free of any criterion and support the basic tenet of HGD that all high density of Pop-III that would scatter the hot gas after transition fragments into dense PGC γ-rays by pair production. Chemical searches globular star cluster mass clouds of Earth mass PFP also fail to detect the large amounts of stardust Pop- primordial fog particles. III superstars would have produced had they existed. How can the postulated CDM chunks remain 3. HGD COSMOLOGY gravitationally bound and merge to form larger After the big bang and a fragmentational cascade to chunks? Because fundamental particles of CDM are form protogalaxies (Fig. 1, Gibson 2006), HGD assumed to be collisionless and the chunks are not cosmology predicts primordial gas planets were the point but must occupy finite volumes, CDM first collapsing gravitational objects. Superstars of chunks have no physical mechanisms to stick to each CDM cosmology are not necessary to explain the other on collision or resist tidal forces 3 missing gas since it was sequestered as planets. F = d Gm M / r , where d is the diameter TIDAL CDM CDM CDM CDM Some of the planets gently formed larger planets and of CDM chunks of mass m attracted by a larger small stars in dark proto-globular-clusters (PGCs) of CDM dense, dark, cooling proto-galaxies (PGs). Freezing chunk of mass M at distance r. weakly collisional PGC clumps expanded by CDM

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triggering star formation as they move through each The tidal distortion x per free fall oscillation is other’s highly combustible BDM halos. TIDAL 2 3 . Diffusivity D = Lv in a gas is mean free path xTIDAL / dCDM = (t / ! ) (DCDM / r) M CDM / 2mCDM > 1 L = m / ! " times the particle velocity Small chunks are torn to smaller and MFP particle gas collision mCDM << M CDM , so whatever fundamental particle emerges as smaller masses by any larger v particle mCDM ! mCDM " particle

#1 / 2 that of the unknown ( or neutrino-like) non- masses M in a few free fall times ! = ("G) CDM baryonic dark matter (NBDM) will certainly have a (Figure 2), contradicting the hierarchical merging very large L and large diffusivity D since the MFP NBDM process postulated in CDM cosmology. Chunks of collision cross sectional area ! is small CDM of any size will not remain gravitationally NBDM bound but will expand indefinitely by diffusion. The !40 2 ( < 10 m ) and the particle velocity v ~ c large. CDMHC hypothesis is therefore false. Observations NBDM show no galaxies with cusp-like central concentrations of density reflecting the collisionless From the size and density of galaxy clusters and the 1 / 4 core collapse expected for CDM halos of CDM 2 Schwarz diffusive scale L = D / !G , the NBDM SD ( ) chunks. -35 particle mass appears to be about 10 kg, Gibson Gravitationally bound CDM chunks are claimed (2000), with diffusivity 30 m2 s-1 and a total DNBDM ! 10 (Binney & Tremaine 1987, chapter 4) to have large NBDM mass about 30 times that of all . With stability periods ! = ! N / ln N much longer than CDM these values, the NBDM diffuses to scales LSD τ if N is large, where N is the number of CDM somewhat larger than the horizon scale ct during the particles. The claim is unwarranted. Any collection plasma epoch and begins fragmentation at galaxy of collisionless particles with any will grow cluster halo scales of about 1023 m after the transition in size indefinitely by diffusion. Assume a spherical of plasma to gas. In the hot plasma period between CDM-chunk initially with perfectly cold, motionless, 102 s and 1011 s when energy dominated mass NBDM particles. All particles fall toward the center of the particles coupled to the plasma to dominate sphere arriving at time t ! " as the density of the momentum transfer in both fluids, preventing both shrinking sphere rapidly increases, the collisionless turbulence and gravitational structure formation. A assumption fails, the particles exchange momentum mechanism like the high MSW scattering and energy, and diffusion increases the size of the of by is anticipated, Mikheyev &

1 / 4 2 Smirnov (1985), Wolfenstein (1978). chunk to a scale L = D / !G larger than its SD ( ) initial size (Figure 3). The free fall time τ increases No cosmological dilemmas arise if collisional, as the CDM-chunk size increases. nonlinear fluid mechanics is applied to cosmology rather than the unrealistic simplifications of Jeans Galaxies of stars in apparent virial equilibrium are 1902 and CDMHC. Self-gravitating fluids are claimed, Binney & Tremaine (1987), as prime absolutely unstable at density minima and maxima and examples of relatively permanent gravitationally- form structures unless prevented by fluid forces or * bound (! ! ! N / ln N ) collisionless systems. diffusion. Fossil turbulence from preserves galaxy patterns of the big bang turbulence, Gibson (2004). However, stars are actually not collisionless because on average 30 million planets surround each star as Only viscous and turbulence forces were relevant in the from which stars are formed. the primordial plasma until buoyancy forces of the The planets supply gas and friction in response to any first self-gravitational structures (at 1012 s) appeared to rapid relative motions, and reveal themselves as inhibit large scale turbulence† and to preserve the contrails of stars (as in the Tadpole, Mice, and plasma density (ρ ~3 ! 10-17 kg m-3) and rate-of-strain Antenna systems) formed in galaxy baryonic dark 0 matter halos when galaxies frictionally merge, Gibson & Schild (2003, 2007), Gibson (2006). * Fossil turbulence is defined as a fluctuation in any hydrophysical field produced by turbulence that Schild (1996) has shown by observations of persists after the fluid ceases to be turbulent at the microlensing twinkling frequencies that the lensing scale of the perturbation. galaxy mass is dominated not by stars but by planets, † Turbulence is defined as an eddy-like state of fluid which he proposed as the galaxy missing mass. motion where the inertial vortex forces of the eddies ! ! Numerous claims that the collisionless tidal tails of v ! " are larger than any other forces that tend to ! ! computer simulations of galaxy mergers have been damp the eddies, v is the velocity and ! is the observed in nature are therefore false. Star trails vorticity. Turbulence by this definition always between merging and separating galaxies are never cascades from small scales to large. collisionless tidal tails but evidence of galaxies

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-12 -1 (γ0 ~10 rad s ) as fossils of the turbulence. ends , , . All the eigenvalues are the (! ij ) = (+ + ") Diffusion dominates gravity for the NBDM in the eigen same magnitude because ! + " + # = 0 from the plasma epoch since L > L = ct during this period SD H continuity equation and incompressibility. Thus, two (Gibson 2000). types of gravitational fragmentation regions are

expected from turbulence induced stretching; the strain Coupling to the plasma ceased soon after 1011 s. dominated vortex line regions giving linear chains of Condensation on density maxima was inhibited by the protogalaxy clumps, and the ! and spin dominated rapid expansion rate of the early universe, so the first ends of vortex tubes giving clump clusters of gravitational structures were formed by fragmentation protogalaxies with a spiral pattern. The resulting at density minima when the viscous Schwarz scale protogalaxy morphology expected from HGD is 1 / 2 20 L = (!" / #G ) > L decreased to less than observed, as shown in Fig. 5. The constant 10 m SV H viscous-gravitational scale of all protogalaxies at L = ct at 1012 s, forming voids and clouds of H plasma-gas transition is termed the Nomura scale L . plasma when viscous forces matched those of gravity, N where is the rate of strain (10-12 s-1) and ! 0 ! 1 / t 0 ν 26 2 -1 The Schwarz viscous scale of the 4000 K hot gas at is the kinematic viscosity (4 10 m s ). 13 14 ! 10 s was about 10 m giving a small- mass of 1024-25 kg. Simultaneous fragmentations at 1036 kg Substituting these values gives =3 1020 m LSV ! LH ! were from radiative heat transfer density changes at 12 45 at t0=10 s with plasma mass ~10 kg corresponding the Jeans scale , not by the Jeans 1902 mechanism. LJ to that of a galaxy supercluster. The horizon scale The viscous dissipation rate ε was a very gentle ~10-12 Reynolds number 2 ~250 for the plasma 2 -3 Re H = c t / ! m s . was only slightly above critical, so the turbulent and

1 / 2 3 / 4 Gravitational condensation of matter first began in the viscous Schwarz scales L = ! / ("G) # L were ST SV #1 / 2 universe as planetary cloud collapse with ! = ( " G ) nearly identical. The viscous dissipation rate ε was 0 0 ~800 m2 s-3. Patterns of big bang fossil turbulence in proto-globular-clusters (PGCs). The collapse time that triggered the fragmentation are preserved by the ! was 3 ! 1013 s (600,000 years) which is also the cosmic microwave background, Gibson (2005). 0 time to first star formation in the tidally agitated PGC

cores near protogalaxy centers, not the 300 million 5. OBSERVATIONS dark ages years (1016 s) predicted by CDMHC after assembly of CDM halos and cooling of the gas to Gravitational fragmentation of the plasma continued permit the first stars as Population III superstars by the to smaller scales, forming protogalaxy mass clouds Jeans criterion. Recent star formation occurs in the 42 (10 kg) prior to gas formation, with density ρ0 and strongly agitated PGCs of galaxy accretion disks, as an initial protogalaxy size 3 ! 1019 m (1 kpc). shown in Figure 6 and GALEX ultraviolet galaxy Density minima and maximum rates of strain γ images, Gil de Paz et al. (2005). When strongly provide sites for fragmentation near vortex lines of agitated, the PFP planets of PGCs form detectable the weak turbulence, giving dim straight chains of massive clumps termed “globulettes” with total mass 6 ! 1019 m protogalaxy clumps (Figure 4) and spiral larger than the large (O and B) stars they produce, clusters of protogalaxy clumps as observed by the Gahm et al. (2007). Spiral structure in galaxies Hubble Ultra Deep Field, Elmegreen et al. (2005). reflects PGC star trails of spiral shaped gravitational accretion, not Lindblad-Lin-Shu density waves. Direct numerical simulations of turbulence, Nomura and Post (1998), show that the maximum γ values 6. CONCLUSIONS required for gravitational structure formation by The standard ΛCDM cosmology based on collisionless fragmentation occur near turbulence vortex lines and fluid mechanics, cold dark matter and dark energy is at the end of vortex tubes (Figure 5). The obsolete and should be abandoned because it gives 2 Hessian ! = " p / "x "x describes the complex non- predictions contrary to observations, and relies on i j i j ! many faulty assumptions. Hydro-gravitational- local interactions of the vorticity ! and the rate of dynamics star formation and cosmology predictions strain tensor S = (!v /!x + !v /!x ) / 2 , resulting in give protosupercluster to protogalaxy formation in the ij i j j i plasma epoch (1012 to 1013 s) by fragmentation maximum values of S eigenvalues triggered by density patterns of big bang turbulent (! ) = (", #,! );" $ # $ ! along the vortex lines mixing, preserved as the first fossils of turbulence, and ij eigen positive straining along vortex lines of the weaker , , but with the average 0 (! ij ) = (+ " ") ! > plasma turbulence (Fig. 1). Evidence of protogalaxy eigen dominated by stretching in two directions near the formation in clump chains (Fig. 4) and in spiral clump clusters (Fig. 5) is reported from HST/ACS images at

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20 Nomura (Kolmogorov) scales 10 m with patterns Rev., 49, no. 5, 299–315. reflecting those computed for turbulence at maximum Gibson, C.H. (2000). Turbulent mixing, diffusion and and average stretching rates, Nomura and Post (1998). GALEX UV images (Fig. 6) reveal gravity in the formation of cosmological previously invisible PGC dark matter accretion disks. structures: The fluid mechanics of dark matter, J. Fluids Eng., 122, 830–835. Gibson, C.H. (2004). The first turbulence and the first From HGD, small stars formed in the protogalaxies from 1024-25 kg planets (PFPs) fragmented at Schwarz fossil turbulence, Flow, Turbul. and Combust., 72, viscous scales in Jeans mass 1036 kg clumps 161–179. LSV (PGCs) immediately after the 1013 s plasma to gas Gibson, C.H. (2005). The first turbulent combustion, transition. The large baryonic density #17 !0 = 3 " 10 Combust. Sci. and Tech., 177: 1049–1071. kg m-3 and large strain-rate ! " 10 #12 s-1 of the 1012 s 0 Gibson, C.H. (2006). The fluid mechanics of protosupercluster fragmentation is fossilized by the density of globular star clusters and the masses of the gravitational structure formation, frozen planets. Gentle motions prevailing at the 1013 http://xxx.lanl.gov/astro-ph/0610628. s time of first stars made possible the small star sizes. Gibson, C. H. and Schild, R. E. (2003). Interpretation The interstellar medium and the baryonic dark matter of the Tadpole VV29 merging galaxy system using are metastable proto-globular-star-clusters of frozen hydro-gravitational theory. http://xxx.lanl.gov/ small planets, as predicted by the Gibson 1996 HGD cosmology and observed by the Schild 1996 quasar astro-ph/0210583. microlensing. These planets give a systematic Gibson, C.H. and Schild, R.E. (2003). Interpretation dimming error when small stars die in planetary of the Helix planetary nebula using hydro- nebulae. This has been misinterpreted as dark energy gravitational theory, http://xxx.lanl.gov/astro- with a ! " 0 , Gibson & ph/0306467. Schild (2007). Gibson, C.H. and Schild, R.E. (2007). Interpretation of the Helix planetary nebula using hydro- CDM hierarchical clustering cosmology gives gravitational-dynamics: planets and dark energy, gravitationally bound structures forming first at small http://xxx.lanl.gov/ astro-ph/0701474. scales and clustering by impossible fluid mechanics (Figs 2&3). These structures gradually form stars Gil de Paz, A., Madore, B., et al. (2005). Discovery of that are much too large and too late, and that explode an extended ultraviolet disk in the nearby galaxy to form light that is found not to exist by the NGC 4625, ApJL , 627, L29-L32. Aharonian et al. 2006 blazar observations. Lovis, C. et al. (2006). An extrasolar planetary system Galaxies and galaxy clusters are observed at times with three Neptune-mass planets, Nature, 441, 3-5- earlier than predicted by CDMHC cosmology, but as expected from HGD cosmology. 309. Madau, P. (2006). Trouble at first light, Nature, 440, 1002–1003. REFERENCES Mikheyev, S., Smirnov, A. (1985). Sov. J. Nucl. Phys., 42, 913. Aharonian, F. et al. (2006). A low level of Mori, M. & Umemura, M. (2006). The evolution of extragalactic background light as revealed by γ- galaxies from primeval irregulars to present-day rays from blazers, Nature, 440, 1018–1021. ellipticals, Nature, 440, 644–647. Binney, J. and Tremaine, S. (1987). Galactic Mori, M., Umemura, M. & Ferrara, A. (2004). The Dynamics, Press. nature of Lyα blobs: dominated Elmegreen, D.M., Elmegreen, B.G., Rubin, D.S., primordial galaxies, ApJ, 613, L97–L100. Schaffer, M.A. (2005). Galaxy morphologies in Nomura, K.K. & Post, G.K. (1998). The structure and the Hubble Ultra Deep Field: Dominance of linear dynamics of vorticity and rate of strain in structures at the detection limit, ApJ, 631:85-100. incompressible homogeneous turbulence, J. Fluid Jeans, J. H. (1902). The stability of a spherical Mech., 377, 65-97. nebula, Phil. Trans., 199 A, 0–49 Schild, R.E. (1996). Microlensing variability of the Jeans, J.H. Sir (1929). and Cosmogeny, gravitationally lensed quasar Q0957 561 A,B. 2nd Ed., Cambridge University Press. ApJ, 464, 125–130. Gahm, G. F. et al. (2007). Globulettes as seeds of Springel, V. et al. (2005). Simulations of the brown dwarfs and free-floating planetary-mass formation, evolution and clustering of galaxies and objects, AJ, 133, 1795-1809. quasars, Nature, 435, 629-636. Gibson, C.H. (1996). Turbulence in the ocean, Wolfenstein, L. (1978), Phys. Rev. D, 17, 2369. atmosphere, galaxy and universe, Appl. Mech.

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7. FIGURES

Figure 1. Gravitational structure formation according to HGD cosmology (Gibson 2006). Proto- supercluster-voids form at minimum density points along vortex lines of weak turbulence in the hot plasma at 1012 s (top center). Fragmentation continues to 1013 s when plasma proto-galaxies turn to gas (right top bottom). These fragment into proto-globular-star-cluster (PGC) clouds of primordial-fog-particle planets (PFPs) that form the first stars (bottom center). The freezing PGCs diffuse out of the galaxy core to form its baryonic (bottom left).

Figure 2. Three hypothetical CDM chunks interact gravitationally. Because they have no sticking mechanism to hold them together, the collisionless CDM chunks are shredded to in a few free fall times ! by tidal forces and cannot grow by CDM hierarchical clustering.

Figure 3. A perfectly cold chunk of CDM with motionless particles collapses in a free fall time to a ! 0 size small enough for the collisionless assumption to fail. The “chunk” then expands to size with particle kinetic determined by the initial gravitational potential energy. LSD

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Figure 4. Elliptical galaxies magnify light from the first galaxies, which are in linear structures reflecting viscous-gravitational formation along vortex lines of the weakly turbulent plasma just before transition to gas (Fig. 1). Star formation is triggered in the BDM between the 2 kpc (6 ! 1019 m) protogalaxies (clumps).

Figure 5. Direct numerical simulations of turbulence by Nomura & Post (1998) show maximum stretching rate occurs on vortex lines where , , , but the average stretching rate ! (! ij ) = (+ " ") eigen 0 comes from the end of vortex tubes where , , . From HGD, ! " # > (! ij ) = (+ + ") eigen protogalaxy formation in the turbulent plasma is triggered where ! is large, which can explain the clump-chains and clump-spirals observed by Elmgreen et al. (2005). The Nomura scale 20 LN ! 10 m is that of central bulge regions of most spiral galaxies, suggesting these are fossils of their

protogalaxy clump origins at the plasma Kolmogorov scale LK ! LN just before transition to gas.

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Figure 6. M81 reveals its dark-matter accretion disk in the ultraviolet (GALEX satellite) that is invisible from optical telescopes on earth (lower right). Point-like blue disk objects are not stars but million-solar-mass proto-globular-star-clusters (PGCs) illuminated by a few very hot young short-lived (O and B) stars and their ionized bubbles triggered into formation by viscous and tidal stresses of M81 separated from M82 by the expansion of the universe. Strong agitation of the trillion dark-matter PFP planets per PGC leads to large stars with short lives. Weak agitation produced the ancient small stars of the central core with the Kolmogorov (Nomura) scale

LK ! LN of the plasma epoch. The baryonic dark-matter halo is comprised of PGCs diffused from proto-galaxy central cores of M81 and M82, and occupies a cylinder larger than the region shown by the optical insert (lower right). The non-baryonic dark matter has diffused about ten times larger to form the galaxy cluster halo ! 1022 m. Dust trails on the face of the central core reflect spiral accretion in O and B supernovae stardust.