# Presentation: 116033

## The Hydrodynamics of Galaxy and MBH formation: Z<,~3(No “early”  BH-BH Mergers )Stirling Colgate, Nathan Currier, Chris Fryer, Mike Warren, Hui Li, T-6 Los Alamos Nat. Lab 

- Ten billion thin, flat rotation curve galaxies with a SMBH, ~108 Msolar at near their exact center, (~10-2  of luminosity center) is a monumental puzzle for most of the barryonic matter, BM, of the universe.  (Apologies for immense complexity of explanation, 1019 dynamic range of scale .)
-  For such coordinated structures to occur requires a highly coordinated mass flow within the filaments after voids and filaments of structure are formed, --- requiring:
- A depletion wave in  DM and BM at the virial velocity for a Hubble time,
- 	~ 1 Mpc at vv ~ 100 km/s, MBM ~ 1012 Msolar  = ~ 10 L* galaxies.
- 2) 	A surprisingly low Reynolds number, Re ~100, due to ionic and atomic viscosity.
- 3) 	A viscous, cooling collapse to a self-sustaining scale, 1/6 Mpc, (x200 in density)
-  	Lyman- clouds, heating and growing by cloud-cloud mergers.  When gravitational scattering exceeds collisions, this becomes the source of most angular momentum.

- S.A.Colgate, Pop III, 7/17/07

## 4) 	Barryonic mergers with the largest structure, the Lyman- cloud or proto galaxy,  rapidly deplete smaller scales.  Zeldovich spectrum: Nsmaller = Mlargest / Msmaller . We observe ~ 1/10 to 1/100 Nsmaller .  

- The depletion of mergers allows: (a) rapid viscous, turbulent relaxation to a uniform, slowly rotating cloud of constant , (b) rapid cooling with the termination of merger heating, and (c) a rapid, free-fall, transparent, inviscid collapse to a rotation supported structure.  (Inviscid because of high density and short time, < 1/.)
- The inviscid collapse of a rotating, uniform density,  constant cylinder leads analytically and exactly to a flat rotation curve disk, FRC disk, where vrot = 2vviral =  const.,  M~r and ~1/r .  (Gravity is approximated by the inside mass.)
- When the initial rotation velocity of the Lyman-cloud is chosen as
-  =< vrot/vvirial > = 0.05 (from dozens of dark matter simulations), then the outer rotational support radius of the FRC becomes r0 = 10kpc, as observed, and the MMBH---- relation comes from 4 .
- 8) When r = 10-6 r0,  MSMS  = 105Msolar ,   = 106 0 = 104 g/cm2  radiation during collapse is trapped and a supermassive star is born.

- S.A.Colgate, Pop III, 7/17/07

## How Galaxies are Formed ?

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**Cylinder:**
**M****<R**** = M****0**** r****2**
**J = v r = J****0**** r****2**
**M****<R**** = J : a Flat Rotation Curve disk, FRC**
**A  Mestel disk; **
**R****0**** = 9.7 < ********2**** R****cloud**** **
**= 10 kpc**
**M****<R**** = M****0**** R/R****0**
******0**** / R, ********0**** = 0.035 g cm****-2**

- Lyman- cloud

- 1

- 2

- 3

- = vcloud / vKeplerian = 0.05

- 10-4 g/cm2

- Angular Momentum from
- Tidal Torquing

## Supermassive star GR collapse

- Nearly all the greats of astrophysics have modeled, and calculated this problem:
- Feyman, 1963, Iben, 1963; Fowler and Hoyle, 1964;  Dicke and Peebles, 1968;
- Larson and Starfield, 1971; Zeldovich and Noovikov, 1971; Truan and Cameron,
- 1971; Orzernoy and Usov, 1971; Yoneyama, 1972;  Fricke, 1973, 1974;
- Begelman and Rees, 1978, 2004; Shapiro and Teukolsky, 1979; Bethe, Brown,
- Applegate, and Lattimer, 1979;  Thorne, 1980;  Goldreich and Weber, 1980;
- Tohlin 1980; Ostriker and Cowie, 1981; Woosley and Weaver, 1982; Brown,
- Bethe, and Baym, 1982; Stoner and Ptak, 1984; Fuller Woosley, and Weaver, 1986;  more .... and recently;  Linke, Font, Janka, Muller, and Papadopoulos, 2001.
- We believe that  none of these works considered the non-homologous evolution
- of the  inner most solar mass and its possible collapse to a neutron star. We also include the mechanism to form such a massive star in the process of formation of galaxies.
- Entropy, S =~ 200 set by rSMS ~, SMS ~ 3x104 g/cm2, a unique structure, radiation supported,  neutrino pair cooling, and one per universe per year.

- S.A.Colgate, Pop III, 7/17/07

## SMS GR collapse, S=200, MSMS = 105 MsolarExplosion energy ~ 1052 ergs (C. Fryer)

- S.A.Colgate, Pop III, 7/17/07

## rg  = 3x1013 cm, (108 Msolar);  rSMS = 3x103 rg,   rgalaxy = 109 rg

- rg  = 3x1013 cm, (108 Msolar);  rSMS = 3x103 rg,   rgalaxy = 109 rg
- MSMS = 5x105 Msolar ;   MSMBH = 108 Msolar  ; Mgalaxy = 1011 Msolar

- S.A.Colgate, Pop III, 7/17/07

## Weather vortices on earth:Vortex radius > 100 H, H = atmosphere scale height ~10 km.RVI transport of atmospheric angular momentum. 

- Accretion disk, H/r ~ 10-4, 3-D turbulent diffusion: Diff = (H cs/3) cm2/s.
- Diffusion  time of angular momentum = r2 / Diff = (r/H) (3r/cs) = 1011
- years (1000 x life-time of quasar) at r = 1 pc = 3 x1018 cm, ~10% of mass.

- S.A.Colgate, Pop III, 7/17/07

## Self-gravity waves and Rossby vortices in an Accretion disk

- 2-D calculations, Keplerian, radial
- pressure, gradient,  Numerical
- dissipation, ~ 10-7 per turn. Alpha
-  ~ few %. Hui Li, et al., 2001,
- ApJ 551, 874.

- 2-D calculations, self gravity,
- Flat rotation curve, m ~ r ,  Sigma ~  1/r ..
- N. Currier, SAC, in rev.

- Galaxy formation starts with the invisid collapse of a uniform, constant omega rotating
- gaseous cloud leading to a flat rotation curve disk and Self Gravity Instabilities.  Only
- after a neutron star or BH forms will a Keplerian disk appear.

- S.A.Colgate, Pop III, 7/17/07

## Black Collapse ? and the Formation of a Keplerian Accretion Disk

- The supernova (2 x 1052 ergs) destroys the SMS and ejects
- the mass at  vvirial (2 x107 cm/s).
- 2) New mass has high angular momentum (x 100), and is accreted
- from the FRC by self gravity waves, SGI, and from the Keplerian,
- disk by the Rossby instability, RVI next to the  neutron star and
- growing BH.
- 3) Does the SGI overwhelm the RGI leading to a black collapse?
- or does the Eddington limit stabilize the SGI leading to a quasar?
- 4) A warped disk would seem to us the only solution?

- S.A.Colgate, Pop III, 7/17/07

## Massive black hole, an accretion disk, self-gravity instabilities,  Rossby vortices, and star-disk colloisions

- These are all needed
- to make an AGN. But
-  “who ordered that?”
- A  quasar is half a magnetic phenomena:
- A dynamo, force-free magnetic helix, and a radio lobe,
- Elobe ~ (1/10) MMBH c2
- !

- S.A.Colgate, Pop III, 7/17/07

## This is what  is there:

**              ****~1 Mpc**
**Frequency   10****10**** Hz**
**L****lobe**** ~ 10****45-46 ****  ergs/s**
**~few% MBH c****2**** / 10****8**** years**

**Hydra radio lobes (inside):**
** ****Rotation Measure ---B**
**E = (B****2****/8********x Vol  = 10****58**** ergs**

**Galaxy energy 10****55 ****ergs**
**Insignificant energy**

**Hy’**

**field**

**clusters**

**High z**

**Hydra radio lobes outside**
**the Hydra Cluster, **
**E ~ = 10****60**** ergs.**
**(Burbidge, 1953:) min energy**
**B****2****/8**** = n****e******** m****e****c****2****; ******** = 3x 10****4**
**B = 10****-5****G.**

- MBH c2 = 1062 ergs, Source of energy

**3C219 Radio Lobe, **
**(intergalactic)**

- S.A.Colgate, Pop III, 7/17/07

- A dynamo generates poloidal and toroidal flux.
- The Keplerian motion winds up
- the poloidal flux outside the
- disk and makes a force-free
- helix, (jet). Instability makes a spheromak, a radio lobe, the
- magnetic fields of the universe .
-  The Keplerian motion winds
- up the internal radial flux
- within the disk making an enhanced toroidal field.
- The plumes driven by star disk
- collisions are a unique source
- of helicity that translates and
- rotates by ~ this toroidal
- flux into the poloidal plane.
- Two coherent fluid motions make the dynamo possible.
- Turbulence must be weak.

- How it Works

- Force-free field; Grad-Safronoff:
- J(perpendicular) = 0;
- J(parallel) ~ curl B
_**Not**_ a mass-dominated jet.
- Hui Li et al., 2001,
- ApJ., 561,915
- A self-luminous force-free
- helix.

- S.A.Colgate, Pop III, 7/17/07

## The black hole selectively advects toroidal flux.No Back-reaction limit:  Plume pressure > Btoroidal2/8

- Inductance: L =106 henries
- I = 1018 amperes
- L dI/dt = 1020 volts
- Current closes through fire ball.
- T~ 100 kev,   ohms.
- Toroidal Fire Ball

- S.A.Colgate, Pop III, 7/17/07

## From Cosmic Density Fluctuations to SMBH  Formation

-  Dark matter (DM) halos form within the volume defined by the virial velocity times the Hubble time.
- Baryonic collapse and merger heating form a viscous, damped Lyman-alpha cloud with solid body rotation.
- As the Lyman-$\alpha$ cloud collapses within the DM halo, it loses its viscosity and ultimately becomes a galaxy-mass gaseous Flat rotation Curve  FRC disk;
- M<r  ~ r;  Sigma ~ 1/r .
- Subsequent  star formation within the thin gaseous disk depletes gas all the way "down" to an inner galaxy mass fraction or radius of 10-3 rgalaxy , the SMBH mass.
-  At a still  smaller radii, ~ 106 rgalaxy, since Sigma ~ 1/r ,  the disk becomes thick enough, ~ 103 g/cm2,  to trap the radiation energy of collapse and a “quasi-star” or SMS of  gas is formed at the center  of the disk.
*The quasi-star becomes a $\sim 10^5 \msun$ seed black hole, by (1) the general relativistic instability, and  (2) by neutrino-driven cooling followed by (3) by a supernova, which would eject ~ 10^5 M**solar** of gas from the disk, but then quickly*
*undergoes a black collapse to a BH.  (Begelman, Volonteri, and Rees, 2006, Mon.Not 370,289 *
- Plus seven more steps to make a quasar.

- S.A.Colgate, Pop III, 7/17/07

## Summary

- Galaxy  formation of ~ 1011 Msolar in a thin FRC disk and
- a massive black hole of ~ 108 Msolar form as a natural consequence
- of hydrodynamics and emerging structure formation of the universe.
- 2) Along the way a high entropy, super massive star of ~ 105 Msolar
- forms making a supernova and neutron star by GR collapse.
- 3) Accretion of matter onto the NS makes the SMBH from the
- FRC disk by Rossby vortices and self-gravity instabilities.
- 4) A natural dynamo in the Keplerian accretion disk makes the
- magnetic phenomena, non-thermal emission, jets, and radio lobes
- of quasars.
- 	(job security for eons)

- S.A.Colgate, Pop III, 7/17/07

## From Cosmic Density Fluctuations to SMBH  Formation

-  Dark matter (DM) halos form within the volume defined by the virial velocity times the Hubble time.
- Baryonic collapse and merger heating form a viscous, damped Lyman-alpha cloud with solid body rotation.
- As the Lyman-$\alpha$ cloud collapses within the DM halo, it loses its viscosity and ultimately becomes a galaxy-mass gaseous Flat rotation Curve  FRC disk;
- M<r  ~ r;  Sigma ~ 1/r .
- Subsequent  star formation within the thin gaseous disk depletes gas all the way "down" to an inner galaxy mass fraction or radius of 10-3 rgalaxy , the SMBH mass.
-  At a still  smaller radii, ~ 106 rgalaxy, since Sigma ~ 1/r ,  the disk becomes thick enough, ~ 104 g/cm2,  to trap the radiation energy of collapse and a “quasi-star” or SMS of  gas is formed at the center  of the disk.
*The quasi-star becomes a $\sim 10^5 \msun$ seed black hole, by (1) the general relativistic instability, and  (2) by neutrino-driven cooling followed by (3) by a supernova, which would eject ~ 10^5 M**solar** of gas from the disk, but then quickly*
*undergoes a black collapse to a BH.  (Begelman, Volonteri, and Rees, 2006, Mon.Not 370,289 *
- Plus seven more steps to make a quasar.

- S.A.Colgate, Pop III, 7/17/07

## The Super Massive Star and GR Collapse

- Virial velocity, vv = 200 km/s
- To trap radiation or heat during free-fall: tau = ~ 20(c/3)/vv = 104 ; ~ 104 g/cm2).
- Thickness of galaxy, Sigma of galaxy at 10kpc = 0.035 g/cm2
- Radius ratio = Sigma ratio  ~ 1/r =  3 x 105
- Radius of self supporting cloud, SMS,  rgalaxy / 3x105  or  rSMS  = 1017  cm
- MSMS =  Mgalaxy / 3x105  =   3 x 105  Msolar
- Density = MSMS / 4 rSMS3  =   = 2 x 10-12   g/cm3
-  a T04  =  vv2/2)  ; 	 T0 = 1.3 eV
- Beta, the radiation adiabat,  = nkT /aT4  = 0.01;  high entropy, S = 100, polytrope index 3
- T ~ T0 r0/r	  =  (r03/r3)
- GR unstable,   aT4 /(c2 )  ~ 1,  rGR = 2x 1010  cm
- collapses in pressure equilibrium until pair neutrino emission =
- free-fall compression heating.
- Ppp neutrino emission = 1.9 x 1025 T9MEV  ergs cm-3 s-1,
- 9th power beats free-fall compression heating at
- Tpair  = 7 x 105  eV  (high S, low Beta, nuclear neutrino emission small.)
- Radius of pair emission  = 2 x 1011 cm , rGR = 2 x1010  cm.
- Pair neutrinos cools adiabat at near constant T, nuclear neutrino emission  exceeds pair emission and neutron star forms at S ~1 before matter can cross event horizon.

- S.A.Colgate, Pop III, 7/17/07