epl draft

Gravitational hydrodynamics of large scale

Th. M. Nieuwenhuizen1(a), C. H. Gibson2(b), and R. E. Schild3(c)

1 Institute for Theoretical Physics, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands 2 Mech. and Aerosp. Eng. & Scripps Institution of Oceanogr. Depts., UCSD, La Jolla, CA 92093, USA 3 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA

PACS 98.80.Bp – Origin and formation of the PACS 95.35.+d – PACS 98.20.Jp – Globular clusters in external galaxies

Abstract. - The gravitational hydrodynamics of the primordial plasma with neutrino hot dark matter is considered as a challenge to the bottom-up cold dark matter paradigm. Viscosity and turbulence induce a top-down fragmentation scenario before and at decoupling. The first step is the creation of voids in the plasma, which expand to 37 Mpc on the average now. The remaining matter clumps turn into galaxy clusters. At decoupling galaxies and proto-globular star clusters arise; the latter constitute the galactic dark matter halos and consist themselves of earth-mass MBD. Frozen MBDare observed in microlensing and white-dwarf-heated ones in planetary nebulae. The approach explains the Tully-Fisher and Faber-Jackson relations, and cosmic microwave temperature fluctuations of micro-Kelvins.

(a) [email protected] the first stars should be 100-1000 M population III su- (b)[email protected] perstars. OGCs do not spin rapidly so they cannot be (c)[email protected] condensations, and their small stars imply gentle flows in- consistent with superstars. Other difficulties are posed by Introduction. – Structure formation in the Universe empty supervoids with size up to 300 Mpc reported from starts in the plasma of protons, electrons, He atoms and radio telescope measurements [1], dwarf galaxies with a lot neutrinos, that exists up to some 400,000 yr after the Big of dark matter [2] and a preferred axis of evil spin direc- Bang, the time of decoupling (dc) of photons from matter tion (AE) that appears at scales extending to 1.5 Gpc, (last scattering (L) or recombination). Then the plasma a tenth of the horizon scale [3]. Nearly every month transforms to a neutral gas of H and 24% by weight 4He, new observations arise that pose further challenges to the with the neutrinos remaining free streaming. As this oc- ΛCDM paradigm: Correlations in galaxy structures [4]; curs at about four thousand degrees Kelvin, a moderate absence of baryon acoustic oscillations in galaxy-galaxy plasma temperature, we shall seek an explanation in terms correlations [5]; galaxies formed already when the universe of plasma physics and gravitational hydrodynamics alone. was 4 – 5 billion years old [6]; dwarf satellites that swarm This embodies a return to the top-down scenario of large our own galaxy just like its stars [7]. scale structure formation. The recent conclusion by one of us that dark matter Currently it is assumed that cold dark matter (CDM) particles must have mass of a few eV and probably are 1.5 also exists and, clustered before decoupling, has set seeds eV neutrinos [8], means that dark matter is hot (HDM), for baryon condensation. The so-called the concordance urging once more for an explanation of structure formation or ΛCDM model involves also a cosmological constant or from baryons alone, without a cold dark matter trigger. . It describes a hierarchical bottom-up ap- We shall discuss such baryonic clustering due to a vis- proach to structure formation, stars first, then galaxies, cous instability in the plasma, overlooked by the currently clusters, and, finally, voids. popular linear models of structure formation. CDM is But observations of dense clumps of ancient small stars assumed not to exist, while HDM, though initially impor- in old globular clusters (OGCs) in all galaxies contradict tant to maintain the homogeneity of the plasma, has no the ΛCDM predictions that star formation should begin role in the structure formation. Central in our discussion only after about 300 million years of dark ages and that will be the huge plasma viscosity ν ∼ 6 1027m2s−1 arising

p-1 Nieuwenhuizen, Gibson & Schild from photons that scatter from free electrons. This makes small scales to large, contrary to standard turbulence the- the plasma increasingly viscous, while it is also expanding ories that include in turbulence also irrotational flows and with space. At some age before the decoupling an insta- motions dominated by other forces. bility creates the first structures, proto-voids and proto- Gravitohydrodynamics (GHD). – In his approach galaxy-clusters. At decoupling the viscosity drops to hot with hydrodynamic and diffusive modelling, Gibson 1996 gas values ∼ 1013m2s−1, which creates further structures [10] derives several gravitational Schwarz length scales for at the Jeans scale and at the new, small viscous scale. structure formation by Kolmogorian dimensional analy- The plan of this Letter is to review modern theory of √ sis. With τ = 1/ ρG the gravitational free fall time gravitational hydrodynamical structure formation, to eval- g in the Jeans length L = V τ , there occur first the vis- uate the estimates for various fragmentation scales within √J S g cous length L = τ γν, where ν the kinematic viscos- Friedman , and to compare with observations. SV g ity and γ the rate of the strain, i. e., the magnitude of 1 Hydrodynamics. – The description of gravitational eij = 2 (∂vi/∂xj + ∂vj/∂xi). Second, there is the turbu- 3 1/2 structure formation starts with Jeans 1902. He proposes lent length LST = (ετg ) , where ε is the rate of energy that scales for gravitational condensation of a uniform dissipation per unit mass, and third, the diffusive length p fluid of mass density ρ must be larger than the√ Jeans LSD = Dτg, where D is the diffusion coefficient. Within 1/2 ac acoustic scale LJ = VS/(ρG) , where VS ∼ c/ 3 is the the acoustic horizon scale, dH ∼ ct structures can form at −11 3 2 ac sound speed of the plasma and G = 6.67 10 m /kg s is scale L if dH ≥ L ≥ max(LSV ,LST ,LSD). Newton’s constant. As the plasma Jeans scale is always We shall evaluate these scales within the flat Friedman larger than the horizon scale of causal connection, this for- metric ds2 = c2dt2 −a2(t)dr2. The Friedman equation for bids gravitational structure formation before decoupling. baryonic and neutrino matter reads The Jeans criterion reflects a linear gravitational instabil- ity from acoustics, but it neglects the fact that self grav- 2 itational instability of a gas is absolute [9]. All density a˙ ΩB + Ων Ωγ 2 2 ≡ Ω(a) = ΩΛ + 3 + 4 . (2) variations will grow or decrease unless prevented by the H0 a a a viscous forces, turbulent forces and diffusion effects. √ d R ∞ √ −τ 1+x Conservation of the specific momentum in a fluid is ex- where Ων = −Ων,0 dτ log 0 dx xe with τ = 2 amν c /kBT0 becomes a-dependent above the Compton pressed by the Navier-Stokes equation, p temperature ∼ 17, 000 K. With dt = da/H0a Ω(a) the ∂~v age is R t dt, while the ‘angular’ distance to an object at = ∇B + ~v× ~ω + F~viscous + F~other, (1) 0 ∂t R t0 z = 1/a − 1 reads dA(z) = [c/(1 + z)] t dt/a. averaged over system control volumes exceeding the mo- We adopt the Hubble parameter h = H0/[100km/s Mpc] 3/4 1/2 2 mentum collision length scale. B is the Bernoulli group =0.744 favored in Ref. [8], so that mν = 2 (GF ) me = 1 2 3/2 of mechanical energy terms B = p/ρ + 2 v + lw and the 1.4998 eV and Ων = 0.111/h = 0.173. For baryons we 2 1 2 viscous force is F~viscous = νs∇ ~v + ( νs + νb)∇ · (∇ · ~v), take ΩB = 0.02265/h = 0.0409 from WMAP5 [13], while 3 −5 2 −5 with kinematic shear viscosity νs = η/ρ and bulk viscosity for photons Ωγ = 2.47 · 10 /h = 4.46 · 10 . Finally, νb = ζ/ρ, while other fluid forces may arise. The inertial- ΩΛ = 1 − Ων − ΩB − Ωγ = 0.786 assures a flat space. vortex force per unit mass ~v ×~ω, with ~ω = ∇×~v, produces Viscous instability in the plasma. – GHD starts turbulence if it dominates the other forces; for example, with acknowledging the importance of the photon viscos- ~ Re ≡ |~v × ~ω|/|Fviscous| is the Reynolds number. A large ity. Because it strongly increases in time, already before viscosity corresponds to a small Reynolds number, with c decoupling the plasma becomes too viscous to follow the universal critical value Re ∼ 25 − 100. For adiabatic flows expansion of space [10]. Thus a gravitational instability the “lost work” term lw due to frictional losses is negligible occurs, that tears the plasma apart at density minima, so the enthalpy p/ρ decreases or increases to compensate thus creating voids. Cosmic (super)voids surround us at for changes in the kinetic energy per unit mass 1 v2. 2 any distance and the furthest observable ones are located The turbulence problem is put in a new perspective by at the decoupling redshift. Presently, voids have a 20 times Gibson [10]. Universal similarity laws are explained in under-density with respect to the critical density. In be- terms of the inertial vortex forces ~v × ~ω. From Eq. (1), tween voids the galaxy clusters are located on “pancakes” turbulence is defined as an eddy-like state of fluid motion that join in superclusters. where the inertial-vortex forces of the flow are larger than 2 The shear viscosity ν ≡ νs reads for kBT  mec [14] any other forces that tend to damp the eddies out [11,12]. By this definition, irrotational flows are non-turbulent. All turbulence then cascades from small scales to large be- η 1 5m2ζ(3)(k T )4 ν = = e B , (3) cause vorticity is produced at small scales and adjacent 3 5 2 2 ρB ρB 9π ¯h c αemne eddies with the same spin induce inertial vortex forces that cause the eddies to merge and form bigger structures. with me the electron mass, αem = 1/137 the fine structure Thus, turbulent motions and energy always cascade from constant and ne = 0.76ρB/mN the electron density. With

p-2 Hydrodynamics of structure formation in the early Universe

3 2 p 3 ζp ne ∼ ρB ∼ T , ν increases as 1/T . At WMAP5 values for A test of Gaussianity in CMB, h|∆T | i ∼ h|∆T | i re- 27 2 decoupling it reaches the huge value 5.85 10 m /s, while veals a marked deviation from the Gaussian value ζp = p/3 14 2 the bulk viscosity ∼ 10 m /s is much smaller. In the in the interval 3 < p < 12, with ζ12 ≈ 2.8, and coinciding p plasma the acoustic speed VS = c/ 3(1 + Rz) with Rz = with the ζp of turbulence [19]. In ref. [20] it is deduced 3ΩB/4Ωγ (1 + z) [15] sets the acoustic horizon scale that the data for the first CMB peak involve Re ∼ 100, in striking agreement with our estimate ∼ 158. The pancaked structure of matter in between large voids Z t(z) 0 ac 1 0 VS(t ) arises dynamically since voids expand more than matter. dH (z) = dt 0 . (4) 1 + z 0 a(t ) Towards decoupling. – In the period near last scat- ac At WMAP5 decoupling it takes the value dH = 128 kpc tering, Helium is already formed, so the density of protons ac but, estimating γ = VS/dH , the viscous length LSV = plus H-atoms is n = 0.76 ρB/mN . The fractional ioniza- ac 1/2 (νVs/GρBdH ) is then only 76 kpc, showing that an tion X = ne/n evolves according to Eq. (2.3.27) of [15], instability has occurred. This causes an often over- looked baryonic structure formation in the plasma [10]. ac ac dX nα X2 − (1 − X)/S  T dn  X The crossover of LSV and dH occurs when dH = 1/3 ac = + 3 − ,(7) (Vsν/GρB) . This happens at zvf = 5120, where dH = dT HT 1 + A n dT T 7.3 kpc is the initial void scale. It expands by a factor r 2π S = nλ3 e157,894 K/T , λ =h ¯ , 1 + zvf to become 37 Mpc now, a typical void size, smaller T T m k T than the supervoids of 50–300 Mpc observed by radio tele- e B 1.4377 10−16(T/K)−0.6166 m3 scopes. ΛCDM models predict such voids formed last and α = −3 0.5300 , (8) full of debris, rather than first and empty as observed [1]. 1 + 5.085 10 (T/K) s −3 −39,474 K/T Foreground voids will play a role in the cosmic microwave αλT e A = 3 . background (CMB) structure at large angles [16], espe- Γ2s + 8πH/[λαn(1 − X)] cially due to their neutrino depletion at z ∼ 7 [8]. Voids occur next to condensations with baryonic clustering mass Here S is the Saha function and λT the thermal length, −1 while α and A are factors involving Γ2s = 8.22458 s the two-photon decay rate of the H2s level and λα = 1215A˚ π ac 3 πVsν 14 Mcl = ρB(dH ) = = 1.7 · 10 M , (5) the Lyα wavelength. We added the last term in (7) in order 6 6G to allow that n 6= const.T 3. Baryonic matter will expand which corresponds to the baryonic mass of fat galaxy clus- less after clusters have formed. Let us take the geometric ters (cl). The Reynolds number becomes mean between no and full expansion, thus assuming that the matter clumps expand up till last scattering at zL by p 3/2 vf a factor a/avf ≤ 2.2, implying ρB = (avf /a) ρ . ac 3 5 2 2 ac B dH VS 9π ¯h c αem dH VsneρB Initially S  1, so the Saha law X = 1 − SX2 con- Re = = 2 4 (6) ν 5meζ(3) (kBT ) tinues to hold. H-formation makes X decrease apprecia- bly, from where on we have to solve Eq. (7). The con- At z it equals 158, somewhat above critical. At the vf dition for maximal probability of last scattering [15] can boundaries of the clumps it is much smaller, Re(r, z) = 2 2 be formulated as dJ/dT = J , where J = cσT nX/HT in- Re(z)[ρB(r, z)/ρB(z)] , where z codes the time, r the lo- 2 volves the Thomson cross section σT = 6π(¯h/αemmec) = cal position and the uniform terms refer to the would- 6.6525 10−29m2. This fixes the surface of last scattering be uniform state. While Re = 158 at zvf is already not at T = 2862 K, z = 1050, compared to z = 1090 from large, fragmentation leads to small values at the bound- L L dc WMAP5, and taking place at age tL = 408, 000 yr. The aries, which enhances the effect. As the voids expand, ac p clump size Lcl = dH (zvf ) aL/avf corresponds to an angle baroclinic torques at their boundaries produce vorticity ◦ ◦ θcl = 180 Lcl/πdA(zL) = 0.84 , or spherical index `cl = and turbulence due to misalignment of pressure gradients ◦ 180 /θcl = 215, which agrees with the first CMB peak. At and density gradients. Pressure gradients will be normal this moment X = 0.01 makes the Reynolds number as low to void boundaries, but density gradients need not. The as 0.12, thus exhibiting turbulence throughout the bulk, rate of vorticity and turbulence production at the expand- and predicting more CMB turbulence at smaller lenghts. ing protosupercluster boundaries is ∂~ω/∂t = ∇ρ × ∇p/ρ2. Observations of the Hubble Ultra Deep Field [17] show Magnitude of CMB temperature fluctuations. – chains of protogalaxies and spiral clump clusters, as well The smallness of CMB fluctuations, δT/T ∼ 10−7 is as DM filaments, formed in this way. one of the mysteries of cosmology. Indeed, how can it A connection to turbulence was established [18] in a be consistent with a mass contrast of almost 100% be- study of the CMB temperature difference between two tween clumps and voids? Presently it is described by points at angular separation r, viz. h|∆T |pi ∼ rζp , where inflation, where its size is adjusted in the initial fluctu- the average is taken over angles between 0.9◦ and 4◦. For ation spectrum [15]. In order to explain it from a physical 0.1 < p ≤ 3 the exponent reads ζp ≈ p/3, as in turbulence. mechanism, let us notice that not all clump energy can

p-3 Nieuwenhuizen, Gibson & Schild associate with temperature fluctuation, since in empty Gibson [10] and observations of Schild [24] that galactic space the temperature already decays with the redshift, dark matter is composed from such MBD. Each PGC con- T (z) = (z + 1)T0. Compared to voids, extra energy of a tains about a billion of them. clump that is available for photons must mainly stem from Galaxies. – We may relate galaxies to the Jeans the E = 13.6 eV energy release of H formation. The H 1 mechanism at the end of the plasma epoch. The sole rel- density is low, at decoupling ∼ (1 + z )3Ω ρ /m ∼ dc B c N evant aspect is then the decrease of the speed of sound 300/cc with ρ = 1.04 · 10−26kg/m3 the critical den- c from plasma values to hot gas values. Taking the geomet- sity. At a temperature T < T this amounts to an ex- vf ric mean velocity V = (V plasmaV gas)1/2= 874 km/s, we cess energy density Ω E (1 + z )3ρ /m . By scatter- S S S B 1 vf c N get the Jeans scale L = 1.5 kpc and corresponding mass ings this heats the local photons, while opaqueness pre- J vents it to also heat the voids. Thus it causes a per- 3 turbation in the photon energy density at last scattering π πV 2 4 3 S 11 δuγ (zL) = 4Ωγ ρcc (zL + 1) (δT/T )L and yields Mgal = ρBLJ = = 1.4 · 10 M . (12) 6 3/2 1/2 6G ρB

3 0 δT Ω E (z + 1) The corresponding CMB angle is θG = 4.7 and the angu- = B 1 vf . (9) 2 4 lar index is `G = 2300. For this mass regime the formation T L 4Ωγ mN c (zL + 1) time is limited, because the sound speed continues to de- −7 For zvf = 5120, zL = 1050 we find δT/T |L = 6.8 · 10 , crease to gas values, from where on PGCs are formed. This which corresponds presently to δTcl ≡ Tcl − Tvoid = explains why a lot of baryons are not locked up in galaxies 3 +1.85µK. Given the strong (1 + zvf ) dependence this can with their baryonic dark matter, but located in intraclus- be adapted to the right order of magnitude, observations ter and intercluster X-ray gas. That gas has become hot, −5 7 are ∼ 10 K [13]. Voids do not have this baryonic con- with temperatures up to 100 keV (1 keV/kB = 1.16·10 K), tent, which explains the observed connection hot spots – due to virialization after neutrino condensation on clusters (super)clusters, cold spots – voids. at z ∼ 7 or tνc = 120 Myr [8]. At such high temperatures the gas may allow nuclear fusion up to tellurium [29]. Fragmentation in the gas at two scales. – At last scattering, the plasma turns into a neutral gas and further Role of PGCs. – In some of them, still warm, colli- baryonic structures form. The free fall time is τg = 1.68 sion processes have quickly led to star formation, basically Myr, while the age is tL = 0.41 Myr. The sound speed without a dark period, thus transforming them into OGCs. p of a monoatomic gas is Vs = 5p/3ρ. For H with 24% Other PGCs transformed in ordinary stars. In the major weight of He, p = 0.82ρkBT/mN yields VS = 5.68 km/s. part of the PGCs the MBD have frozen and they still per- The gas fragments at the Jeans scale LJ = Vsτg = 9.78 pc sist without stars. These PGCs are in virial equilibrium into Proto-Globular Clusters (PGCs) with Jeans mass and act as ideal gas particles that constitute the galactic dark matter. Their physical presence explains why the isothermal model describes the basic features of galactic 3 π 3 πVs rotation curves so well, that is, linear growth at small ra- MP GC = ρBLJ = = 38, 000 M . (10) 6 3/2 1/2 6G ρB dius, plateau at large radii. To improve the fit, one may consider mixtures with several isothermal components [8]. This Jeans cluster formation is well known, but not always In the centers of galaxies the near passings of PCGs will welcomed. In our approach it is a standard process, that cause tidal forces which heat their planets and induce star fragments all gas in Jeans clumps, so they should be much formation. Since this is mainly a two-particle effect, the more frequent than globular clusters – see below. luminosity of a galaxy is expected to relate to the PGC At decoupling the viscosity decreases from photon vis- R 3 2 mass density as L ∼ d r ρPCG. In the isothermal model cosity values to hot-gas values. The He viscosity can be 2 2 ρP GC = σ /2πGr , where σv is the velocity dispersion, −5 v estimated as ηHe(TL) = 5.9 · 10 kg/ms. For the 76:24 so the 1/r4 fall off of the integrand makes the luminosity H-He mixture it will be about 0.76/8 + 0.24/4 = 0.155 of finite. This results in the scaling L ∼ σ4/R, which is the 2 1/3 14 v this. The viscous length LSV = (Vsη/GρB) = 3.9 · 10 Faber-Jackson relation [30], with an additional character- m implies a further condensation into masses of order istic bulge scale R. The Tully-Fisher relation is likewise explained, as it involves the rotation velocity, which scales with σv. π 3 πVsη −5 M = ρBLSV = = 13M⊕ = 3.9 · 10 M . (11) In several instances the matrix of dark PGCs is revealed 6 6GρB by new star formation. When agitated by tidal forces We may call these objects MBD, Primordial Fog Parti- the collision frequency of theMBDwill increase causing re- cles or Milli Brown Dwarfs. Their mass is in good agree- evaporation of the frozen gases, increased size and friction, ment with estimates from microlensing of a distant quasar and the possibility of planet mergers to produce largerMB- [24, 25] and so-called cometary knots in the Helix nebula Dand eventually new stars. The existence of galaxy dark [26–28]. It was anticipated independently by theory of matter in the form of clumps of frozen primordialMBDis

p-4 Hydrodynamics of structure formation in the early Universe

−5 clearly revealed in photographs of galaxy mergers such of 2. 10 M [27]. Huggins et al [28] measure a mass −6 as Tadpole, Mice and Antennae. On the respective pho- of 5. 10 M via the radio measurement of CO emis- tographs one can see numerous bright clusters of compa- sion. These findings support the GHD prediction of earth rable size, that are identified here as PGCs turned into massMBDas the baryonic dark matter repository. young globular clusters. They are located in star wakes as Dimming by dense 1013 m planet atmosphere gases or the merging galaxies enter each others dark matter halos realistic quantities of dust is negligible at the 20% levels and heat up theMBDin the PGCs on their path through observed [32]. Such large dimming of obscured lines of the dark matrix. The effect exists only within a certain sight observed in a planetary nebula (e.g. Helix) requires radius, the boundary of the PGC cloud. post turbulent electron density forward scattering [33] as observed by radio telescope pulsar scintillation spectra, Role of MBD. – From the GHD scenario following embedded in the Kolmogorovian “great power law on the decoupling, the first stars form gently by a frictional bi- sky” [11], which can now be understood from GHD as nary accretion of still warm PFPs to form larger planet remnants of supernova powered turbulent mixing in our pairs and finally small stars as observed in OGCs. Thereby local PGC [33]. The planet atmosphere cross section for they create an Oort cavity as clearly exposed in e. g. SNe Ia dimming σ ≈ 1026 m2 gives a photon mean free the Helix planetary nebula. Slow turbulent mixing from path 1/nσ ≈ 3 × 1015 m from the primordial PFP number the rain of planets will not mix away the dense carbon density n0, comparable to the observed Helix planetary core. By conservation of angular momentum the star spins nebula shell thickness and consistent with ≈ 5% of the SNe rapidly as it compresses producing strong spin radiation Ia lines of sight unobscured. Clouds of warm MBDcan be along the spin axis and at the star equator. Stars can form responsible for the Lyα forest – not hydrogen clouds that as binaries in PGC clumps. have remained undetected. At decoupling the entire baryonic universe turns to a fog of earth mass MBD. Due to the expansion they cool and Conclusion. – Within gravitational hydrodynamics the freezing temperature of hydrogen and helium occurs (GHD) for a flat space Friedman cosmology with (hot) at redshift z ≈ 30 a few hundred million years later, pro- neutrino cluster dark matter we have described various ducing the frozen dark baryonicMBDin clumps predicted structures that form due to hydrodynamic instabilities in as the galaxy dark matter [10]. Neutrino condensation the baryonic plasma. The approach accounts for a wealth at z ∼ 7 comes later, showing that the extra-galactic of observations and relations between them. MBDreionize to become hot X-ray gas. That the dark The first step, when photon scattering from free elec- matter of galaxies should be objects of earth mass was trons makes the plasma too viscous, is the creation of independently proposed by the Schild 1996 interpretation proto-voids at zvf = 5120, before decoupling, that expand of 5 hr twinkling periods in quasar microlensing observa- to present average cosmic voids. Proto-supervoids occur tions [24, 25]. Thousands of these planet crossings have too, but are rare. The matter condenses in proto-galaxy- been observed by now. clusters. The coincidence of turbulence properties in the As the universe expands the MBDthat did not turn into CMB and turbulent fluids supports the GHD model. Pan- stars freeze and the PGCs become less collisional and dif- caked galaxy (cluster) structures in between large voids fuse out of the 3 kpc scale protogalaxies to form the ob- arise dynamically, since the voids expand faster, while the served typical R = 100 kpc dark matter halos with a basi- matter remains gravitationally bound. cally isothermal distribution. Consistency of this picture The assumption that the ionization energy of the H- 2 is shown by the isothermal estimate Mgal = 2σvR/G ∼ formation is redistributed to the photons, explains the 12 1.9 · 10 M for σv = 200 km/s. milli-Kelvin scale of CMB fluctuations and the connection When frozen, the MBDare too small to dim light, even cold spots – voids, hot spots – (super)clusters. from remote sources, but they can account for dimming At very large scales the homogeneity of temperature is when they are heated. Warm atmosphere diameters are explained by inflation. Before the viscous instability the ≈ 1013 m, the size of the solar system out to Pluto, bring- plasma was quite homogeneous, due to the free streaming ing them out of the dark. The separation distance be- neutrinos that damped inhomogeneities at the free stream- 14 tweenMBDis ≈ 10 m , as expected if the PGC den- ing scale of 10 kpc at zvf . So, irrespective of their location −17 sity ofMBDis the primordial density ρ0 = 2 × 10 kg on the sky, the fluctuations caused by the viscous insta- m−3. In planetary nebula such as such as the nearby He- bility have the same order of magnitude. This well known lix, darkMBDat the boundary of the 3×1015 m Oort cavity large angle correlation is in GHD an effect of simultane- are evaporated. HST optical images of Helix show ≈ 104 ity (of void formation in the homogeneous plasma), not of “cometary knots”, gaseous planet-atmospheres ≈ 1013 m causality. which we identify as MBDwith metallicity, and Spitzer At decoupling first galaxies are formed and later primor- 5 3 shows ≥ 10 in the infrared from the 10 M available [12]. dial globular clusters (PGCs) of about 38,000 solar masses. Meaburn et al. determine for cometary knots in He- Some of them turn into old globular clusters (OGCs) and −5 lix a mass of 1. 10 M , and conclude that the glob- others form the stars in galaxy bulges. But most PGCs, ules and tails are dusty [26], and later report a mass millions per galaxy, remain dark and constitute the galac-

p-5 Nieuwenhuizen, Gibson & Schild tic dark matter as an ideal gas, which explains why the up in GHD. Galaxy formation when the universe was 4 isothermal model describes galactic rotation curves well. – 5 billion years young may refer to proto-galaxies with A galactic dark PGC matrix also accounts for numerous late-stage star formation by close PGC encounters. Dwarf young globular clusters seen in galaxy mergers. Near PGC satellites that swarm our galaxy just like its stars may just crossings in the center of galaxies will form stars, which relate to single PGCs with modest star formation, popping explains the Tully-Fisher and Faber-Jackson relations. out of the matrix of dark PGCs. At the decoupling the viscous scale becomes much smaller which turns all matter into MBDof a few earth REFERENCES masses. Some of them coalesce to form the first small stars, but most freeze to earth scale. The MACHO [34] [1] Rudnick L., Brown S. and Williams L. R., Astrophys. and EROS [35] collaborations have searched in vain for J. , 671 (2007) 40. such objects. Still, they are not excluded because they [2] Strigari L.E. et al., Nature, 454 (2008) 1096. do not occur uniformly but in PGC clumps. Theoretical [3] de Oliveira-Costa A., Tegmark M., Zaldarriaga M. descriptions of clumped MACHOs in the dark halo were and Hamilton A., Phys. Rev. D, 69 (2004) 063516. started in [36]. But thousands of planets have been ob- [4] Disney M. J. et al., Nature, 455 (2008) 1082. served in microlensing [24, 25] and, reheated, thousands [5] Sylos Labini F., Vasilyev N. L. and Baryshev Yu. V., more in planetary nebula such as Helix [26–28, 37]. Hot arXiv:0903.0950. MBD atmospheres may dim distant supernovas. [6] Bouwens R. J. and Illingworth G. D., Nature, 443 (2006) 189. We have analyzed previous results by two of us within [7] Metz M. et al., Astroph. J., 697 (2009) 269. in the Friedman cosmology, connected CMB temperature [8] Nieuwenhuizen Th. M., Europhys. Lett., 86 (2009) fluctuations with H formation, connected to isothermal 59001. disribution of PGCs and the Tully Fisher relatiion. [9] Gibson C. H., J. Fluids Eng., 122 (2000) 830. We have adopted one set of cosmological parameters, [10] Gibson C. H., Appl. Mech. Rev., 49 (1996) 299. which performed rather well, but not attempted an op- [11] Gibson C. H., Proc. Roy. Soc. Lon. A, 434 (1991) 149. timization. While in the CDM model the main cause of [12] Gibson C. H. and Schild R. E., J. Appl. Fluid Mech., clustering is dark matter with baryons a second order ef- 2 (2009) 1. fect, the GHD scales will be rather sensitive to the precise [13] Dunkley J. et al.,Astrophys. J., () 2009, to appear. parameter values. Large scale numerical hydrodynamics [14] de Groot S. R., van Leeuwen W. A. and van Weert simulations of separate steps of the fragmentation process C. G., Relativistic kinetic theory : principles and applica- tions North Holland, Amsterdam, 1980. are expected to result in precise fits for the mass fractions [15] Weinberg S., Cosmology,Oxford, Oxford, 2008. of baryons and neutrinos, and the Hubble constant. [16] Cover K. S., Europhys. Lett. 87, 69003 (2009) discusses We have not considered the large scale power spectrum that the WMAP5 data fit better to the COBE dipoles with- [15], this should be set by inflation. We may recall that out anisotropy than the anisotropies reported by WMAP. there are reasons to question whether baryons trace the [17] Elmegreen D.M. et al., Astrophys. J., 631 (2005) 85. neutrino dark matter well [8]. [18] Bershadskii A. and Sreenivasan K. R., Phys. Lett. A, Let us sortly connect to the numerical work on the Cold 299 (2002) 149. Dark Matter model by Shapiro et al. [38]. These au- [19] Bershadskii A. and Sreenivasan K. R., Phys. Lett. A, thors find that the Inter Galactic Medium must have con- 319 (2003) 21. tained a substantical amount of the baryon density of the [20] Bershadskii A., Phys. Lett. A, 360 (2006) 210. Universe during and after its epoch, in com- [21] Schild R. E. and Gibson C. H., arXiv:0803.4288. [22] Gibson C. H., Combust. Sci. and Tech., 177 (2005) 1049. plete agreement with our wide distribution of PGCs around [23] Gibson C. H., Apl. Sci. Res., 72 (2004) 161. galaxies. Their problem with quasar absorption lines may [24] Schild R. E., Astrophys. J., 464 (1996) 125. be explained by absorption by hot gas cloud atmospheres. [25] Schild R. E., Astronom. Nachrichten, 327 (2006) 729. The authors do not find a reheating of the Inter Galactic [26] Meaburn J. et al.,Monthly Not. R.A.S., 255 (1992) 177. Medium, also not by quasars. In our picture it is achieved [27] Meaburn J. et al.,Monthly Not. R.A.S., 294 (1998) 201. by the condensation of neutrinos on e.g. galaxy clusters. [28] Huggins P. J. et al., Astrophys. J., 401 (1992) L143. Let us finally see how some problems of the [29] Schatz H. et al.,Phys. Rev. Lett., 86 (2001) 3471. ΛCDM paradigm mentioned in the introduction are solved [30] Binney J. and Tremaine S., Galactic Dynamics, 2nd naturally in GHD. Population III stars may have been Edition,Princeton Univ. Press, Princeton, 2008. rare, since reionization may find its origin in neutrino con- [31] Gibson C. H., J. Appl. Fluid Mech. , 2 (2008) 1. densation on galaxy clusters [8]. Dwarf galaxies with a lot [32] Aguirre A. N., Astrophys. J. , 512 (1999) L19. [33] Gibson C. H. et al.,SPIE optics & photonics 2007, 6680 of (baryonic!) dark matter may pertain to PGCs with (2007) 33, arXiv:00709.0074, arXiv:0712.0115. incomplete star formation. The related fact that OGCs [34] Alcock C. et al.,Astroph. J, 498 (1998) L9. often exhibit stars formed at several epochs is likewise [35] Tisserand P. et al.,Astron. and Astrophys., 469 (2007) explained by further sets of reheated, pre-existing MBD. 387. Correlations in galaxy structures are expected since they [36] Holopainen J. et al.,Mon. Not. R. A. S., 368 (2006) all form early; baryon acoustic oscillations do not show 1209.

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[37] Gibson C. H. and Schild R. E., arXiv:astro- ph/0701474. [38] Shapiro P. R., Giroux M. L. and Babul A., Astro- phys. J, 427 (1994) 25.

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