AQUATER PAPER 4.7B SHAPING THE DARK MATTER CLOUD

For updated version—see www.Aquater2050.com/2015/11/

Abstract

In a previous paper (AP4.7), a self-consistent theory called Model 1 was developed that appears to answer twelve major connected questions in astrophysics. The most important of these questions are:

• How can dark matter be explained and described?
• How can dark energy be explained and described?
• Where do the extremely high-energy cosmic rays that occur beyond the GZK cutoff come from?

In working out this model, some problems arose that are connected with it. The most important of the problems are on the detailed characteristics of the dark matter super particle that is the core of Model 1. Those problems were resolved in a companion paper AP4.7A. The next most important of the problems has to do with the formation and shaping of the dark matter clouds. That problem will be addressed and resolved here.

 

The Problem

In AP4.7, several problems were left for future efforts. In this paper, one of these problems, the detailed characteristics of the dark matter cloud have been singled out for effort.

 

The Dark Matter Cloud. AP 4.7 showed how an ionized cloud of super particles would form after entering vacuum space.  Some equations were developed for the cloud, and solved to give a contained, dark matter cloud roughly similar to the one obtained from studying the rotation data of galaxies. That was a simplified, first level treatment. Here, we will move to the next level. We start with the basic equations.

 

We begin with the diffusion velocities of the ionized gaseous components (see Cobine, 51).

 

V⁺ = -D⁺/n⁺ dn⁺/dx + K⁺E + K⁺G

 

V^– =-D^–/n^– dn^–/dx – K^–E + K^–G

 

V^g = K^gG

 

Where:

D = Diffusion coefficient

K = Ion or gravitational mobility under the influence of electric or gravitational force 

V = Ion velocity

n = Ion concentration

E = Electric field

G = Gravitational field tempered by centrifugal force (see below)

n^g = source of particles from the black hole

           

We set:

                        V+ = V- = V^g = V ;  n⁺ = n ^– = n^g = n ;  dn⁺/dx = dn^–/dx = dn/dx

 

We solve these equations, and get:

 

                        n= (N_o/4pDt)^3/2 exp(–r²/4Dt)  

 

                        Where:

                        D = (D⁺ K^– + D^– K⁺ ) / ( K⁺ + K^– –  2 K⁺ K^– / K^g ) 

                                r= Radius from black hole source

                        t= Time

                        N_o = particles diffusing from an “instantaneous” point source  

 

The principal forces being described in this solution are the following:

• A dispersive force due to the motions and collisions of particles stemming from their high temperature (kinetic energy).
• An electromagnetic force E pulling the components of an ionized particle cloud together due to the different diffusion rates of different particles (positive and negative particles} because of different diffusion coefficients.

We see an electric field in the velocity equations, yet the solution is independent of that field. How can this be?

 

In order to obtain this solution, we have simplified the G field into one central vector field pointed toward the particle source (the black hole). In reality, it is composed of the vector sum of a:

• A Newtonian type gravitational field pointed toward the center of the black hole that works on each particle. (Here we have taken advantage of the fact that Loop Quantum Gravity predicts a Newtonian type gravitational force even close to the black hole.  (Smolin, 251). It is known that further from the black hole, a Newtonian type force works well.)
• A Centrifugal force field pointed away from the center of the black hole that works on each particle (Again, it is known that a centrifugal force works well further from the black hole).
• An expansive field that comes from the gravitational potential under some circumstances. Note that this field works on space itself.

 

The last force comes from a single new scalar field, f. The energy density and pressure equations that result are as follows (Peebles, 396):

 

Here, ρ  = f’ ²/2+ V; and p = f’ ²/2 – V)

 

            Where:

            V = a potential energy density

            f = a new real scalar field

            f’ ²/2 = a kinetic energy term

 

Now, we assume V is a slowly varying function of the field, and the initial time derivative of the field is not too large. We also assume that V is large enough to make a significant contribution to the stress-energy tensor. Then the pressure can satisfy the condition p < – ρ /3, which is the condition for the expansion of space. If V is less than f’ ²/2, kinetic energy and gravitational attraction will control.

 

It is necessary to see how V varies with R, the distance from the black hole center. This same potential energy density described here is contained around each super particle by the barrier at a distance of ~ 10^-5 cm and beyond this distance, it has the vacuum value in particle space (10^-5 GeV/cc). Inside the barrier, it has a value of ~10³³ GeV/cc as indicated in AP4.7 Appendix 1. Near the center of the black hole, it is even higher ~10³⁵ GeV/cc, and is generated by the spatial distortion of the tremendous mass of the black hole. There, the potential is used to form the barrier around the incoming particles, fill it with potential energy, and thus make super particles and bounce them into vacuum space. Note that the super particles exist in dynamic equilibrium with particles in the high vacuum potential of vacuum space as shown in AP4.7A The generation zone requires at least a barrier sphere diameter ~ 10^-5 cm to generate super particles. Beyond this distance, V falls off rapidly as potential energy is lost in particle space, but inside the barrier (i.e. in vacuum space), the high potential energy is maintained. The value of V is high enough in this particle space zone near the black hole center to generate the expansion condition mentioned above, and space expands. The use of potential energy to make particles, and the expansion of space reduces V below the kinetic energy (f’ ²/2), and the expansion dies in particle space. Thus the pressure becomes:

 

p(R) = f’ ²/2 – V₀(R)

 

Where:

V₀(R) drops precipitously beyond ~ 10^-5 cm from the center of the black hole down to 10^-5 GeV/cc.  

 

Note here, that when the super particles expand away from the black hole center, they cool, and the super ions recombine into neutral particles. More important, there is an extremely low interaction cross section between visible and dark matter. The low interaction and collision cross section results from the characteristics of the barrier potential shell (see Appendix 1).

 

Note finally that we have here a pump that receives particles from particle space through the black hole, converts them into super particles, bounces them into vacuum space, and then pumps them away from the black hole center. We will call this pump the generation-expansion field.

 

For R far enough from the center of the black hole, the gravitational field is, of course:

 

 G = M₁G₀/R² 

 

Remember that it acts on the center of mass of a mass-energy source such as a particle.

           

Now we have the tools needed to describe what happens to super particles bouncing into vacuum space. The super particle is pushed away from the black hole center, and comes under the influence of the central force. Here again, we see the central field G in the velocity equations, but the solution is independent of G. How can this be?

 

We have seen the problems, and so we must ask what the effect of the electric and the central field has on the solution to the velocity equations. The solution does not seem to show the effect of either the E, or more important, the G field. They seem to be able to be changed without any impact on the particle density function. This is this problem that we will investigate here.

 

The Solution

We will start our explanation by investigating the impact of the electric field. Cobine (see Cobine, 51) describes in detail the interaction of the thermal dispersive and the electromagnetic forces. He shows that the electric field is caused by the different diffusion rates of the positive and negative ions, and so is dependent on those rates. Thus the electric field can be eliminated from the equations because it cannot be changed independently of the diffusion. It should not appear in the final solution. If the initial conditions are changed, they can generate an electric field from a different source that is independent of diffusion. Then, the equations must be handled differently, and we will investigate that case below.

 

Now we investigate the impact of the central G field. Here, there are three cases of interest.

1. Assume the generation-expansion field plus the centrifugal force field roughly balances the gravitational field due to the black hole’s attraction on the particles, so the net radial average motion is roughly zero. Note, however, that the particles are moving through the expanding space under the influence of the gravitational field, so the 2 K⁺ K^– / K^g term in the D equation still has meaning. One would expect in this case, however, that the denominator of the term would be larger than the numerator, so the term would be small. Clearly, the solution to the equations shown above would be valid in this case.
2. Assume the generation-expansion field plus the centrifugal force dominate, and space expands faster than the gravitational attraction of the black hole can pull the particles back. In this case, a particle, trapped in space, moves away from the black hole even though it is attracted toward it. Note that the expansion does not last forever. It lasts only as long as the generation-expansion field is high, and we have seen that it drops fast as it expands and generates super particles. Thus the particle will move out until the generation-expansion field equals the gravitational field, and then it will slow, and move back at the rate demanded by the gravitational attraction tempered by the vacuum value of particle space (~ 10^-5 GeV/cc), which is low. Recall that the super particles involved are in a thermal, Gaussian distribution, so a thermally distributed band of super particles will form where the expansion field equals the gravitational field
3. Assume the gravitational attraction of the black hole to the particle dominates, because the particles are beyond the thermally distributed band of case 2. The particles are then attracted toward the black hole center by the central force. As this happens, the particles try to retreat to the radius where the expansion field equals the gravitational field, and a distributed band of super particles has formed.

 

Thus, we see that the super particles move radially to a quasi-stable minimum shell around the black hole center to form a source of incoming particles. This is an impulse source that gives out super particles as long as the black hole is feeding- a time short compared to the life of the galaxy. The particles do not remain at this equilibrium point, however, they diffuse away from it under the influence of the dispersive force and the electromagnetic force tempered by the gravitational attraction as indicated above. Thus we must make a minor alteration to the above solution as follows:

 

n= (N_o(R)/4pDt)^3/2 exp(–r²/4Dt)  

 

                        Where:

                        D = (D⁺ K^– + D^– K⁺ ) / ( K⁺ + K^– –  2 K⁺ K^– / K^g ) 

                                r= Radius from black hole source

                        t= Time

N_o(R)  = a Gaussian distribution of particles diffusing from a finite spherical shell source whose size R is somewhat larger than ~ 10^-5 cm

 

Here we see that the solution is the same, except that the source is a spherical shell instead of a singularity (a delta function). Thus the solution is still valid, and it should be independent of the central force, because the central force is self-determined. It cannot be changed unless the initial conditions are changed. Note that if the initial conditions change, the central force must be handled separately. We will investigate that case below. 

 

Special Case 1. Electric fields unrelated to diffusion.

Assume the black hole is feeding, and so has formed a rotating cloud of ions around the black hole. This rotating cloud forms an electric field ionizes the particles, and then pumps ions and electrons from the rotating cloud out from the galaxy in a giant fast moving spike of radiating ions. This field is not connected with the diffusion electric field, so it must be analyzed separately.

 

The spike of radiating ions in particle space will not interact with ions in vacuum space, because the barrier from super particles would block the exchange photons that make the interaction possible. However, the gravitational attraction from the spike would tend to gather dark matter along the spike, and make a dark matter corridor coincident with the spike.

 

Special Case 2. Gravitational Fields that are dependent on more that one center of mass (one black hole). 

Assume that two galaxies are close at a distance R₀. Both have central black holes. The total gravitational field from the two galaxies is diminished along the corridor between them as follows:

 

                        G = M₁G₀/R² – M₂G₀/(R_O-R)²  (R> R₀₎

 

In this case, assume a super particle starts moving away from black hole 1 due to the potential expansion field surrounding the black hole center faster than the gravitational field can attract it to the black hole. The gravitational field is less along the radial toward black hole 2 than it is along other radials, so a corridor of diminished field is formed. Thus the super particle moves further along this corridor than along other radials, and a buildup of particles starts along that corridor. The presence of particles in the corridor increases the mass there and increases the resistance to movement, and so particles preferentially accumulate along that corridor. Over time, a lattice of super particle corridors forms using galaxies as nodes. This lattice acts as a nucleation net of dark matter along which dust and gas in particle space will be attracted. This dust and gas will then form galaxies preferentially along the net. This preferential formation of galaxies in strings and clumps and walls has been observed in the universe

 

It is important to note that when the super particles have expanded out to become a dark matter cloud, they cool and some super ions recombine to become neutral super particles. As such, they have a lower interaction and collision rate as super particles. More important, the barrier shell has a very low interaction and collision cross section with visible matter (see Appendix 1). Thus Model 1 correctly predicts the observed fact that when galaxies collide, the visible matter interacts with itself and coalesces while the dark matter passes right through the visible and dark matter.

 

Testing Model 1B with Data

As with Model 1, Model 1B must be tested with data. The tests that support the composite Model (Model1A along with Model 1 and Model 1B) are shown here. The composite Model does the following.

• It correctly predicts interacting dark matter in and around a galaxy, and it shows why the matter is dark.  
• It describes a source for this dark matter, namely a black hole. This source does not violate the laws of physics as presently understood.
• It correctly describes the distribution of this dark matter with respect to the galaxies and shows why this distribution happens.
• It correctly predicts the observed fact that when galaxies collide, the visible matter interacts and coalesces while the dark matter passes right through the visible and dark matter.
• It details the characteristics of the dark matter particles to within our ability to measure them.
• It connects with a property predicted by the standard model of particle physics-namely the unification of forces, and predicts the impact of this unification.
• It provides an explanation for the difference in vacuum potential energies as measured (low) and as predicted (high).
• It provides a physically defendable procedure for describing what happens in a black hole other than “a singularity forms”.
• It describes the cause of the Big Bang, what triggers it, what stops it and where the energy causing it comes from. All of this description is in keeping with the data currently available.
• It correctly describes the immediate aftermath of the big bang; how early thermodynamic contact is maintained, why the expansion, why it stops, and where the energy causing it comes from.
• It correctly describes the later aftermath of the big bang; where the matter and anti matter came from, why we have cosmic background radiation and where our excess of matter over anti matter came from.
• It describes how quantum mechanical state details can be transmitted faster than the speed of light if coherence is maintained. Recent experiments have shown that this happens.
• It correctly predicts extremely high-energy cosmic rays beyond the GZK cutoff, and describes where they come from. These cosmic rays have been observed.
• It correctly predicts dark energy that accelerates the expansion of space, and describes where it came from, and the value of the dark energy. The accelerated expansion of space has been observed.
• It predicts the existence of a future new big bang, and estimates when it will happen.

 

Problems with Model 1B

The primary problem is that to get a simple solution to the equations used, it was necessary to make certain simplifying assumptions. These assumptions can be justified in two ways.

• Each assumption must be shown mathematically to be small.
• The results must be shown to be in agreement with data.

In this set of papers, the latter procedure is the one used.

 

Further Proof of Model 1B

Theoretical Proof

Accomplishing the following tasks would strengthen the theory.

• Although most of the pieces of this development are justified separately, the development would be stronger if the assumptions were proved mathematically.

 

Experimental Proof

Although Model 1B appears to satisfy all of the previous experimental results as shown above, it should also predict and satisfy one or more unique experimental results listed below.

• It is possible to do a simulation of dark matter formation and resultant galaxy formation. If the patterns are similar to those observed by astronomers, that similarity would constitute supporting evidence for this model.

 

Summary and Conclusions

A model (Model 1) has been developed in AP4.7 that predicts dark matter and energy and extremely high-energy cosmic rays, which operate beyond the GZK cutoff. As part of this model, a set of super particles in a new space (vacuum space) was predicted that constitutes this dark matter, and generates this dark energy and the high-energy cosmic rays. The details of these super particles were not pursued in AP4.7, and so they have been pursued in this paper. Initial checks with existing data have been made, and Model 1A has been found to be in agreement with the data. Possible problems with the model have been analyzed, and a theoretical program proposed as a fix. Experiments that would check the accuracy of the model have been proposed. Model 1A has been found to be valid as far as the current checks can determine

 

Appendix 1

Here, we explore the characteristics of super particles to see if they can be observed in particle space- i.e. are they dark? First, super particles do not show charges associated with the electromagnetic, weak, and strong forces. They are combined into one super charge and hidden behind the barrier potential. The super particle spin, if any, would not show beyond the barrier as well. They have only the super charge associated with the unified force. Thus they will not interact with the detectors we normally use. Particles in particle space will scatter off the potential barrier surrounding the super particle, however, so it is necessary to calculate this scattering cross section. This scattering cross section is like the scattering of a proton off a neutron, but with different energies. This scattering cross-section has been calculated (Halliday, 47), and is as follows:

 

s = h²π/M x  1/(V_o + E)

 

Where:

M = m_s m_p/ (m_{s +} m_p)

m_p = mass of particle space baryons = 1 GeV.

m_s = mass of super baryons = 10¹⁷ GeV.

V_o = potential of super baryons = 10¹⁹ GeV

E = kinetic energy of the particle space baryons = 1 GeV or less.

 

Then:   s = 10^-45 cm² 

 

Clearly, this scattering cross section would be difficult if not impossible to detect. So matter is dark or difficult to detect in particle space. Also, the collision cross section of the dark matter particles is low enough that in colliding galaxies, the dark matter particles would pass right through each other, while the visible matter would interact and coalesce, as seen by astronomers.

 

References

1.      L. Smolin, The Trouble with Physics, Boston, New York: Mariner Books, 2006.

2.      G. Kane, Modern Elementary Particle Physics, Ann Arbor, Michigan, Perseus Publishing.

3.      J. Magueijo, New Varying Speed of Light Theories, arxiv.org/pdf/astro-ph/030545v3.pdf

4.      J. Magueijo, Faster than the speed of light, Penguin Books, New York, New York, 2003.

5.      P. J. E. Peebles, Principles of Physical Cosmology, Princeton, New Jersey, Princeton University Press.

6.      J. D. Cobine, Gaseous Conductors, Dover publications, Inc., New York, 1958