Chapter 6
Galaxy Clusters

When studying and analyzing the processes of void formation, it is impossible to bypass the processes of galaxy cluster formation.

That is, in order to answer the question of how voids appear in galaxy clusters, we must first find the answer to the question: "How do galaxy clusters appear?"

How are galaxy clusters formed?
Where did the enormous number of galaxies in space come from?
How do galaxies populate space?
Why do galaxies not move in a single direction, as predicted by the Big Bang theory?
Why do galaxies move in different directions?

Let us attempt, based on the analysis of research data, to predict the answers to all these questions.

Galaxy clusters—where do they come from?
Why is it specifically clusters of galaxies, and not clusters of stars?
Why are star clusters packed into galaxies?
Why are galaxies packed (grouped) into clusters?
Why cannot stars unite into a single structure?
Why? Why? Why?

Outdated astrophysical theories contradict the very concepts of a galaxy and galaxy clusters. The Big Bang theory presupposes a uniform distribution of matter in space. The theory of star formation through the gravitational formation of protostars physically precludes the existence of galaxies. The gravitational interaction of stars within a galaxy contradicts the kinematics of stellar motion in the galaxy.

Halo stars move away from the galactic center, from the black hole, along a diverging spiral trajectory. Meanwhile, the stars of the disk and the spiral arms of the galaxy likely approach the galactic center, moving within their gas flows along a converging spiral trajectory.

A galaxy and a galaxy cluster are structural associations of stars. That is, there exist physical laws that unite stars into galaxies, and galaxies into clusters.

In order to understand how galaxy clusters are formed, it is necessary to investigate not only the process of the birth of galaxies, but also to investigate and understand the process of the origin of galaxies.

The Physics of Galaxy Clusters

6.1. Elements of the Physics of Galaxy Evolution.

The existence of a galaxy is connected to a common site of star formation and birth, and not to gravity between stars or to non-existent dark matter. The formation and birth of stars depend on the parameters of the surrounding space. The main parameter is the presence and density of gas, cosmic dust, and matter in the surrounding space. Gas, dust, and matter in space are the building materials for stars and galaxies. However, the matter of space must be delivered to the site of star formation and birth. For the movement and distribution of matter in space, there exist gas flows. Gas flows in space are the "circulatory system" of the universe. It is gas flows that distribute and deliver the building material of stars to galaxies. What creates gas flows in space? One of the main sources of gas flows in space is black holes.

Black holes form and create gas flows, which deliver the building material for stars into their accretion disk.

The design of a black hole is simple and astonishing. Or, more precisely – astonishingly simple.

The design of a black hole is the design of a gas cyclone, a tornado, or even a gas vortex, Fig. 6.1.

                   (26) Figure # 6.1

At the center of a black hole is a region of reduced pressure, zone "A", surrounded by a gas ring, the accretion disk, zone "B". The region of reduced pressure draws in gas from the surrounding space, creating primary gas flows. The primary gas flows form and create a circular gas flow around the region of reduced pressure, isolating this region from gas inflow. However, this gas cyclone, zone "B", not only isolates the region of reduced pressure from being filled with gas, but also extracts gas and matter from this region, from zone "A", into its flow. The extraction of gas and matter from the region of reduced pressure maintains the level of reduced pressure in zone "A". The jet of the black hole isolates the region of reduced pressure, zone "A", from gas penetration along the axial directions. Through its circulatory flows, the jet maintains the reduced pressure in this region. That is, the design of a black hole is the design of a self-sustaining cosmic tornado, or cyclone. This self-sustaining cosmic cyclone draws matter from space into the accretion disk of the black hole to form stars from it. What can stop this cosmic cyclone? A cosmic cyclone can only be stopped by the absence of gas and gas flows in the surrounding space. Star formation in a galaxy can be stopped by the absence of building material for star formation. Star formation can be stopped by the absence of gas flows delivering gas and matter to the site of star formation, to the accretion disk. That is, star formation in a galaxy can stop if obstacles appear in the path of its gas flows. These obstacles could be other galaxies or the gas flows of other galaxies, which redirect the passing gas flows and take their gas.

If, in some region of space, there is gas, matter, and gas flows, then star formation also exists in that region.

How does the origin of galaxies occur?

The Birth of a Galaxy

A galaxy consists of stars, stellar remnants, black holes, and gas flows. And the most important part of galaxies is black holes and gas flows. No gas flows, no galaxy! If a galaxy has no gas flows, it dies!

 Looking at the night sky, we see the glow of stars, and we do not see the movement of gas flows, yet it is gas flows, and within gas flows, that stars and galaxies are built (created).

Gas flows deliver and distribute the building material—gas and dust—to the sites of star and galaxy formation and birth.

What causes gas to move in the gas flows of a galaxy?

The gas flows of a galaxy are formed and created by the galaxy's black holes. It is black holes that are the most important and crucial mechanism in a galaxy. No black holes, no gas flows, no galaxy! The birth of a galaxy begins with a black hole and within a black hole!

The main and only mechanism of a black hole is the accretion disk!!! There are no unnecessary parts! And most importantly, it is the gas of space from which the accretion disk of a black hole is created. Gas is the building material of the universe. A gas flow is the collection of the universe's building material, its delivery (logistics) to the construction site of stars and galaxies. Within a gas flow, the formation and birth of stars and galaxies occur. Gas flows, stars, and galaxies are formed from the gas of space. The main and only mechanism of a black hole, the accretion disk, consists of gas, of building material. A star, as a nuclear reactor, consists of gas, but now as nuclear fuel. There are no unnecessary parts! We perceive the Greatness of the Creator through the perception of His Creations!!!

Conclusion: The birth of a galaxy begins with a black hole and within a black hole! The main and only mechanism of a black hole is the accretion disk!!!

The Origin of a Galaxy

The evolution of a galaxy was examined in other sections of "Analytical Astrophysics."

In this section, we are interested in how galaxies originate.

Halo stars, which have large masses, are the parents of galaxies.

If the birth of a new galaxy begins with the birth of a black hole that will become its center, then the origin of a galaxy begins with the birth of a massive halo star.

The birth and evolution of a massive halo star is a physical process representing the origin of a galaxy, preceding its actual birth. There are possible scenarios where the origin of a galaxy does not lead to its birth. That is, there are possible developments where the birth and evolution of massive halo stars do not result in the birth or formation of a full-fledged galaxy. Disruptions in the evolution of a halo star into a galaxy can occur both before the birth of a black hole and after its birth, during the formation period of a globular star cluster or a galaxy. One of the main reasons for such disruptions is a lack of gas for star formation, or a cessation of the gas flows heading towards the forming galaxy.

The birth of a new galaxy begins with the birth of a black hole at its center.

Suppose, in some zone of space filled with gas and matter, with a density ρ = 10⁻²⁹ g/cm³, a black hole forms.

This central black hole of a young galaxy draws in gas and matter from space. From this matter, the black hole forms stars and ejects them back into space, creating a globular star cluster around itself.

Globular star clusters are future galaxies, which will be formed under favorable conditions of the surrounding space.

By increasing the number of stars, the globular cluster evolves into a galaxy.

Where and how does this black hole, from which a galaxy forms, originate???

It is very simple...

A black hole forms after the collapse of the white dwarf of a star that had a large mass.

The task simplifies: we need to find a star with a large mass.

Where and how does a star with a large mass, whose collapse creates a black hole from which a galaxy forms, originate?

The outdated theory of gravitational star formation through a protostar has not received a single confirmation. Consequently, there is no point in considering this option.

Then, where are the stars from which galaxies form formed, and how are they born?

If we examine the structure of galaxies more carefully, we can discover that among the halo stars, there exist stars with large masses. There is another very important fact: galaxies contain globular star clusters.

Analysis of recent research on globular star clusters indicates their evolution into galaxies. Consequently, the formation of new galaxies occurs within the globular clusters of neighboring parent galaxies!!!

The parent black hole in a neighboring galaxy forms and ejects halo stars into space. Among these stars, massive stars are ejected, whose evolution proceeds through collapse. The collapse of a massive star forms a black hole. This black hole then evolves, through a globular cluster, into a galaxy.

A massive halo star collapses while still within the halo space of its parent galaxy. A black hole forms in its place. The kinematics of motion for this black hole are inherited from the parent halo star. Moving through the space of the parent galaxy, the black hole evolves into a globular star cluster. Upon leaving the halo space of the parent galaxy, the globular cluster transitions into the stage of a dwarf galaxy. The globular star cluster transforms into a galaxy which, having exited the confines of the parent galaxy, becomes a satellite of that parent galaxy.

Galaxies give birth to galaxies!!!
Stars born in galaxies give birth to galaxies.

FACTS:

The Andromeda Galaxy has four hundred globular star clusters and 35 satellite galaxies. Our galaxy has 157 globular star clusters and 63 satellite galaxies.

A new galaxy is born and formed while still being part of a neighboring parent galaxy. Stars born in parent galaxies give birth to daughter galaxies.

Consequently, the central black hole of a new galaxy appeared while still within the space of a neighboring parent galaxy. Let us attempt to identify the source of the formation and birth of the massive star whose collapse created the central black hole of the young galaxy. Let us consider two facts that confirm our predictions.

Firstly, stars with medium and large masses are stars belonging to the galactic halo. Stars of the disk and spiral arms do not have large masses.

Secondly, globular star clusters in galaxies possess the parameters and trajectories of motion characteristic of halo stars. This fact indicates that the progenitors of globular star clusters in a galaxy are halo stars.

Thus, through a reverse analysis of the facts, it has been determined that halo stars from neighboring galaxies are the progenitors of the central black holes of young galaxies.

If this prediction is correct, then all galaxies within galaxy clusters are satellites of neighboring, parent galaxies. It is possible that the very first parent galaxies have already "perished" and in their place are voids, or younger galaxies which are themselves satellites of other galaxies.

The reproduction of galaxies occurs through massive halo stars. Consequently, a galaxy that possesses satellite galaxies is a parent galaxy to those satellite galaxies. And the satellite galaxies are daughter galaxies relative to the galaxies around which they orbit. A galaxy moving around a daughter galaxy is both a satellite of that daughter galaxy and its own daughter, Fig. 6.2.

Figure 6.2 depicts a simplified diagram of the reproduction of galaxies in space. The reproduction of galaxies resembles a chain reaction in nuclear physics. A galaxy produces a certain number of halo stars, which, through evolution, become daughter satellite galaxies of the parent galaxy. Each of these galaxies, under favorable conditions, produces a certain number of its own halo stars, which, through evolution, become daughter satellite galaxies of their respective parent galaxies. And these galaxies continue the chain of reproduction, similar to a chain reaction.

Figure 6.2 shows the first parent galaxy, which produced six satellite galaxies through the evolution of its halo stars. These satellite galaxies are first-generation daughter galaxies. These first-generation daughter galaxies produced five second-generation daughter galaxies. The second-generation daughter galaxies are satellites of their parent galaxies, the first-generation daughter galaxies. Such a chain-like and spontaneous reproduction of galaxies is only possible under favorable conditions for star formation in the surrounding space. The globular star clusters within galaxies are the future satellite galaxies of that galaxy.

- It is known that the Milky Way galaxy has 157 globular clusters and 63 satellite galaxies, while the Andromeda galaxy has 400 globular clusters and 35 satellite galaxies.

       (27) Figure # 6.2

In the chain reproduction scheme of galaxies, it is evident that the velocity of daughter galaxies is always higher than the velocities of parent galaxies. This is because the daughter galaxy, in addition to inheriting the kinematic parameters of the parent galaxy, receives an additional ejection impulse at the birth of the halo star, as well as an acceleration of the star's motion during its lifetime. It is possible that this acceleration persists throughout the life of the galaxy.

Let us predict the kinematic characteristics of galaxies in the case of the chain reproduction scheme. The prediction of the kinematic characteristics of galaxies must begin from the moment of the formation and birth of a halo star.

Where are halo stars born?

Where are halo stars formed and born?

Analysis of the location of isophotes of halo stars indicates that the birthplace of halo stars is the central black hole of the parent galaxy. Two facts point to this prediction:

Firstly, the isophotes of halo stars uniformly surround the galactic center and appear as closed lines, at the center of which is located the black hole. There are large distances between isophotes, and no mixing of stars from different isophotes occurs.

Secondly, the arrangement of halo star isophotes exhibits a temporal and age-related pattern. As the distance from the central black hole increases, the age of the halo star isophotes also increases. This fact indicates that the birthplace of halo stars is at the center of the galaxy, at the location of the black hole. The same pattern is present in globular star clusters, which is logically evident.

Such an arrangement of isophotes suggests that the birth of an elliptical galaxy begins with the appearance of its central black hole.

Thus, it has been analytically established that galaxies begin their formation with the appearance and with the participation of a black hole at their center.

Where do these black holes at the centers of young galaxies come from?

The central black holes of new galaxies are formed as a result of the collapse of halo stars from neighboring, parent galaxies.

Massive halo stars collapse and create a black hole while still within the space of their parent galaxy. During their outward journey from the center, and while still residing in the parent galaxy's space, the young black hole produces stars and forms a globular cluster. Beyond the confines of the parent galaxy, this globular cluster evolves into a galaxy.

- Let us predict and analyze the physical events occurring during the formation and birth of halo stars.

- Let us predict the physical events occurring during the ejection of halo stars from the black hole's accretion disk.

- Let us predict the evolution from halo stars to galaxy clusters.

Formation and Birth of Halo Stars

The origin of future galaxies occurs within the accretion disk of a black hole in a parent galaxy.

The black hole's accretion disk draws gas and matter from the surrounding space into its gas flow. The collected gas and matter in the accretion disk serve as the building material for stars. Within the black hole's accretion disk, halo stars are formed and constructed from this collected "construction" matter.

As matter is drawn in, the mass of the accretion disk increases. Stars form within the accretion disk. As the mass of the accretion disk increases, the gravity in the zone of this accretion disk also increases.

The level of gravity in a black hole's accretion disk is equal to the level of gravity of the matter collected within it, namely the gas, dust, and cosmic objects drawn into the accretion disk by the gas flow.

Dark matter does not exist, and it is not present in a black hole. In modern astrophysics, the action of the forces of attraction created by gas flows is mistakenly taken for the action of gravitational forces from non-existent dark matter.

Let us analyze the scientific data obtained from the study of black holes. Based on this analysis, let us predict the physical processes and events occurring in the accretion disk of a black hole. Let us predict the processes of formation and birth of halo stars, and the processes occurring when these stars exit the parent black hole.

Physical Processes Occurring in the Accretion Disk.

The accretion disk is a circulating flow of gas and matter around the center of a black hole.
The linear velocity of gas and matter particles in the accretion disk reaches
170,000 km/s.

- The gas flow, moving at high speed, creates a enormous force that draws matter from the surrounding space into the gas flows of the accretion disk.

- The second function of the accretion disk's gas flow is to accelerate matter particles within the accretion disk to speeds at which thermonuclear fusion occurs.

Let us consider the structure of a black hole, Fig. 6.3.

Structure of a Black Hole.

The structure of a black hole consists of four parts, Fig. 6.3:

- The cyclonic gas flow, zone "B";

- The gas jet, "Jet";

- The vacuum zone at the center of the black hole, zone "A";

- Gas flows directed towards the accretion disk of the black hole from space, from zone C, Fig. 6.3. These gas flows are formed under the influence of the black hole's drawing force FBr. Although these gas flows are not part of the black hole itself, they physically sustain its existence.
Zone C is the space surrounding the black hole.

                                     (28) Figure # 6.3

We have already examined the physics of processes within a black hole under the influence of the forces drawing matter in, FBr (Bernoulli forces), and the centrifugal force. However, gas and matter accumulate in the accretion disk of a black hole, from which a certain number of massive stars are formed. Consequently, the processes occurring in the accretion disk of a black hole are also influenced by the force of gravity. That is, matter is gathered in the accretion disk of a black hole, from which massive stars are formed. And this mass of matter is a source of gravity. As the mass of matter in the accretion disk increases, the force of gravity increases.

Let us predict the influence of gravity on the processes and events occurring in a black hole during star formation and during the departure of halo stars from the parent black hole.

There are mathematical difficulties in predicting the gravitational interaction of more than two objects. Predicting the actions of forming stars within the accretion disk is currently practically impossible. This is a topic for future research.

Let us consider the influence of gravitational forces on the physical processes within the accretion disk.

Figure 6.4 depicts the forces acting within the accretion disk and on the accretion disk.

(29) Figure # 6.4

In an accretion disk, the following primary forces act, as shown in Figure # 6.4:

Centrifugal forces FCB. Centrifugal forces FCB are directed from zone A to zone B, and from zone B to zone C;

 FCB = MZ . ω02 . R0 = MZ . ω0 . V0

Where: MZ – Mass of the star or protostar located within the accretion disk;
ω0 – angular rotational velocity of the protostars in the accretion disk around the center of the black hole;
V0 – linear rotational velocity of the protostars around the center, within the accretion disk;
R0 – radius of rotation of the protostars around the center of the black hole, within the accretion disk;

- Gravitational forces FG. Gravitational forces FG are directed toward the center of mass of the accretion disk, toward the center of the black hole.

Where:
G – gravitational constant;
MAC – mass of the accretion disk, excluding the mass MZ;
MZ – mass of the star or group of stars leaving the accretion disk;
Rg – distance from the star with mass MZ to the center of mass of the accretion disk,

      Rg~ R0.

- Bernoulli forces, or inflow forces, FBr. The forces FBr are directed from zones A and C into zone B, into the interior of the accretion disk. The black hole's jet is shaped and formed under the influence of the forces FBr. The forces that shape the jet are not examined here, as they are not relevant in this context.

Over the course of star formation within the accretion disk, nuclear reactions occur, synthesizing chemical elements heavier than hydrogen and helium. The cores of stars are formed from these synthesized chemical elements, dust, and objects located within the gas flow of the accretion disk.

It is possible that the cores of halo stars are formed from white dwarfs and neutron stars that have been drawn into the accretion disk by gas flows.

It is possible that stars and white dwarfs from the galactic disk and spiral arms, moving within their respective gas flows along a spiral trajectory, travel toward the galactic center.

It is possible that neutron stars are also captured by these gas flows.

Once these white dwarfs and neutron stars enter the accretion disk of the central black hole, they may become the cores of future halo stars. It is possible that during their journey within the gas flows of the galactic disk and spiral arms, neutron stars and white dwarfs repeatedly served as stellar cores.

It is possible that within the accretion disk, stellar cores are formed, while the gas-plasma mixture is captured by the stellar core as it passes through the gas flows of the black hole's accretion disk and the surrounding space.

It is possible that centrifugal forces acting on the stellar cores, in combination with other dynamic processes and forces, tear apart the black hole's accretion disk.

A star formed within the accretion disk must eventually leave its parent black hole.

The effects of the dynamic processes occurring within the accretion disk on the star are unknown and are not taken into account due to the lack of observational data.

The centrifugal force is directed toward ejecting the star from the accretion disk. Let us assume that all forces directed toward the ejection of stars from the accretion disk are included within the centrifugal force.

For a star to be ejected from the accretion disk, the forces acting toward its ejection must exceed the gravitational pull of the accretion disk, as illustrated in Figure # 6.5.

(30) Figure # 6.5

This requires changes in the internal structure of the accretion disk. In other words, constructive transformations of matter within the black hole's accretion disk are necessary.

Centrifugal force can also be expressed through acceleration.
FCB = MZ . a

Where: FCB – centrifugal force;
MZ – mass of the star or protostar within the accretion disk;
a – acceleration of the star as it leaves the accretion disk.

That is, FCB = MZ . ω02 . R0 = MZ . ω0 . V0= MZ . a

The actions of the forces FBr, FCB, and FG within the accretion disk tend toward equilibrium. However, under the influence of the inflow (Bernoulli) forces FBr, the mass of the accretion disk increases. Consequently, the gravitational force FG and the centrifugal force FCB change. The increase in the mass of the accretion disk also affects the inflow force FBr, but indirectly, through changes in the dynamic and gaseous parameters of the accretion disk. For matter to be ejected from the accretion disk, the centrifugal force must increase and exceed both the inflow forces FBr and gravity FG. The interaction between inflow forces and centrifugal forces is examined in another section. This section focuses on the interaction between gravitational forces and centrifugal forces.

How stars form inside the accretion disk and how they leave the parent black hole remains unknown. What is known is that halo stars do leave the black hole's accretion disk. Consequently, these stars are formed within the accretion disk.

The accretion disk of a black hole is enormous in size. Despite the high linear velocities, the angular velocities of the forming stars are low.

FCB = MZ . ω02 . R0 = MZ . ω0 . V0

Whether the velocity within the accretion disk increases as mass increases is unknown.

For stars to form, a vast amount of matter must be gathered, and nuclear and thermonuclear reactions must be initiated within this accumulated mass. The accretion disk acts as a gigantic natural compressor, collecting matter from space, and as a particle accelerator for this matter, initiating and sustaining nuclear reactions. In other words, the accretion disk functions as a colossal natural "collider."

What functions does the core of a forming star perform?

To leave the accretion disk, a star must gain momentum. The momentum imparted by centrifugal force increases as the star's mass increases. Consequently, to escape the black hole's accretion disk, the star must increase its mass.

The greater the mass of an object, the greater the centrifugal force applied to it. Centrifugal force and dynamic processes act more effectively on objects with larger mass and dimensions than on gas molecules.

In other words, centrifugal force acts more efficiently on the star's core than on the gas particles within that star.

It is possible that the influence of dynamic processes and centrifugal force, during the ejection of stars from the accretion disk, is exerted precisely on the stellar cores.

The longer a star forms while remaining within the accretion disk, the greater the mass of its core.

Since white dwarfs, neutron stars, and other cosmic objects are drawn into the accretion disk along with gas flows, it is possible that they form the cores of halo stars.

Under the influence of high temperatures and dynamic processes, cosmic objects pulled into the black hole's accretion disk merge and form the cores of future stars.

It is possible that within the accretion disk, the cores of stars are formed, while the gas-plasma mixture of the star forms around the core.

The core of a star is a crucial component in the structure of a star.

- First, the core of a star is the source of gravity that holds the gas-plasma mixture around it.

- Second, the core of a star performs functions necessary for sustaining thermonuclear reactions. The stellar core is a source of radioactive radiation that provokes nuclear reactions. It is a source of: gamma radiation, X-rays, protons, neutrons, alpha rays, and beta rays.

- Third, the core of a star is a source and reflector of dynamic waves generated by nuclear reactions and thermonuclear fusion.

- Fourth, dynamic and nuclear processes occur within the stellar core, which provoke thermonuclear fusion in the star.

It is possible that in the accretion disk of a central black hole, medium-mass stars form in pairs or in larger numbers. High-mass stars, however, may form either as single stars, in pairs, or in groups of more than two. That is, a single high-mass star possesses sufficient mass to escape the accretion disk.

An increase in the mass of the accretion disk intensifies its gravity, which hinders the star's escape from the accretion disk and prevents its disruption. However, an increase in the mass of the accretion disk also leads to an increase in the masses of protostars and their cores, which in turn increases the centrifugal force acting on the star. In other words, the disruption of the accretion disk becomes possible when the masses of the stars and their cores reach critical values.

Thermonuclear fusion increases the temperature and pressure within the accretion disk. The increase in temperature and pressure may reduce the inflow force drawing matter in and hinder the growth of the accretion disk's mass. At the same time, under the influence of thermonuclear fusion and dynamic processes within the accretion disk, the masses of stellar cores increase. The increase in the mass of stellar cores amplifies the centrifugal forces acting on these stars.

The rise in temperature and pressure within the accretion disk also increases the forces ejecting stars from the accretion disk.

How dynamic processes, along with changes in temperature and pressure, affect the ejection of a halo star from the accretion disk remains unknown.

How stars form inside the accretion disk and how they leave the parent black hole is still unknown. What is known is that this process occurs.

Let us predict the physical processes involved in the ejection of halo stars from the accretion disk of their parent black hole.

The accretion disk is a unified structure that, through inflow forces, gathers matter from space. By the gravitational force of the accumulated mass, it holds the protostars forming from this matter.

To leave the accretion disk, a halo star must acquire momentum directed away from the parent black hole.

Such momentum could be imparted to future halo stars by centrifugal forces. However, since nuclear and dynamic processes occur within the accretion disk, it is possible that impulses from these processes also affect the star. As a result of the physical processes taking place in the accretion disk, the parameters (pressure and temperature) of the matter within the accretion disk change.

Changes in the internal parameters of the accretion disk affect the momentum acquired by a halo star as it exits the black hole's accretion disk.

Izg = ∑ Ii =Icb + Icr + Idp + Ipt

Where: Izg = ∑Ii – total momentum of the halo star, acquired upon its exit from the black hole's accretion disk;

Icb = f(FCB) – momentum acquired by the halo star from the influence of centrifugal force upon its exit from the black hole's accretion disk;

Icr = f(Fcr) – momentum acquired by the halo star from the influence of forces accompanying nuclear processes upon its exit from the black hole's accretion disk;

Idp = f(Fdp) – momentum acquired by the halo star from the influence of forces accompanying dynamic processes upon its exit from the black hole's accretion disk;

Ipt = f(Fpt) – momentum acquired by the halo star from the influence of forces accompanying changes in parameters (temperature, pressure, and others) within the accretion disk upon its exit from the black hole's accretion disk.

To simplify the understanding of the physical processes involved in star formation within the accretion disk, and given the lack of observational data, the parameters Icr, Idp, and Ipt will be simplified by temporarily equating them to zero. Alternatively, these impulses will be incorporated into the momentum acquired by the star from centrifugal force.

Icb = f(FCB) + Icr + Id + Ipt = f(FCB) + f(Fcr) +  f(Fdp) + f(Fpt).

We assume that upon exiting the black hole's accretion disk, halo stars acquire momentum from the influence of centrifugal force. That is, 

Izg = Icb.

However, there is also momentum that stars acquire while still within the accretion disk. This momentum is inherited from the circulating motion of matter in the accretion disk around the center of the black hole, denoted as Iω. The momentum Iω causes halo stars to move around the galactic center.

Iω – the momentum of a halo star, directed toward motion around the parent black hole's center.

Consequently, halo stars in galactic space move under the influence of the momenta they have acquired: Izg and Iω. The trajectory of halo stars, shaped by the combined influence of Izg and Iω, forms a spiral along which the stars recede from the center of the parent black hole, as illustrated in Figure 6.6.

                                                           a                                                                                                                                                b

ω – angular rotational velocity of halo stars around the galactic center, after the stars have exited the influence of the accretion disk;
V – linear rotational velocity of halo stars around the galactic center, after the stars have exited the influence of the accretion disk;
R – radius of rotation of halo stars around the galactic center, after the stars have exited the influence of the accretion disk.

(31) Figure # 6.6

As R increases, the angular velocity ω of halo stars decreases; that is, R > R0, ω < ω0. As the stars age, their linear velocity increases, but this increase does not compensate for the decrease in angular velocity.

The motion of halo stars along a spiral trajectory explains the observed pattern in the distribution of isophotes of halo stars in elliptical, disk, and spiral galaxies.

Upon exiting the accretion disk, under the influence of centrifugal force and the circulatory forces acting within the accretion disk, a halo star recedes from the parent black hole along a spiral path. The recession speed of the halo star depends on the centrifugal force and the dynamic momentum acquired by the star upon exit (if any). Inheriting the momentum gained during their ejection from the accretion disk, halo stars, globular clusters, and satellite galaxies recede from the parent galaxy along a spiral trajectory.

As the distance from the galactic center to the halo star increases (due to the increasing radius), the angular rotational velocity decreases, although the linear velocity increases with age. Figure 6.7 illustrates possible evolutionary paths of halo stars.

       (32) Figure # 6.7

In Figure 6.8, the evolution of halo stars is divided into three frequently occurring scenarios.

Scenario I: Evolution of a halo star into a neutron star.
Scenario II: Evolution of a halo star into a high-velocity star escaping the parent galaxy.
Scenario III: Evolution of a halo star into a galaxy.

       (33) Figure # 6.8

Let us briefly examine each scenario of halo star evolution.

Scenario I: Evolution of a halo star into a neutron star.
Figure No. 6.9 illustrates the evolutionary path of a halo star into a neutron star.

(34) Figure # 6.9

After a halo star exits the black hole's accretion disk, it undergoes a transformation process from a star to a white dwarf. The white dwarf then collapses, transforming into a neutron star. Under extremely favorable environmental conditions, the neutron star may further transform into a stellar core. There is also a possibility that a neutron star could transform into a globular cluster. If the surrounding space of the neutron star does not intersect with gas flows and contains no significant amount of gas, the neutron star may instead transform into a planet.

Scenario II: Evolution of a halo star into a high-velocity star escaping the parent galaxy.
Figure # 6.10 illustrates the evolutionary path of a halo star into a high-velocity star.

                                                                                        (35) Figure # 6.10

This type of evolution is characteristic of stellar systems containing two or more stars. One of the stars collapses and transforms into a neutron star. There is also a possibility of transformation into a black hole. Following the collapse of one star, the velocity of the stellar system increases and may reach 700–1000 km/s. The velocity of the stellar system increases due to the reduction in the system's mass and due to a jet propulsion effect—that is, from the asymmetric ejection of mass during the collapse.

Scenario III: Evolution of a halo star into a galaxy.

Let us examine the evolution of halo stars into galaxies in greater detail, as it is precisely this evolutionary path that leads to the formation of galaxy clusters.

Figure 6.11 illustrates the evolutionary path of a halo star into a globular cluster, and the subsequent evolution of the globular cluster into a galaxy.

(36) Figure # 6.11

A halo star, having left the accretion disk, recedes along a spiral trajectory from the parent black hole. The lifespan of stars with large masses is short. Due to their great mass, abundant nuclear fuel, and large volume, the intensity of nuclear synthesis of chemical elements is high. Transuranic chemical elements accumulate in the star's core. The mass of accumulated transuranic elements in the core of the halo star exceeds the "critical mass," triggering a powerful nuclear explosion of the white dwarf. This powerful nuclear explosion of transuranic elements ejects the entire mass of the white dwarf into space. At the epicenter of the explosion, a black hole forms.

This black hole draws in gas and matter from the surrounding space, forms stars from this matter, and ejects them into space. Around the black hole, a globular cluster of stars forms. This globular cluster of stars takes shape within the space of the parent galaxy.

Having exited the parent galaxy, the globular cluster evolves into a galaxy. This galaxy is a first-generation daughter galaxy and a satellite of its parent galaxy. As it evolves, the daughter galaxy will produce its own daughter galaxies. The galaxies produced by these daughter galaxies are second-generation galaxies relative to the original parent galaxy and satellites of the first-generation daughter galaxy.

Let us now turn to the facts.

- The Milky Way galaxy is known to have 154–157 globular star clusters and over 60 satellite galaxies.

- The Andromeda galaxy is known to have 400 globular star clusters and over 20 satellite galaxies.

In the Milky Way, the total mass of halo stars is 10⁹ solar masses, of which 1% are stars in globular clusters. That is, it is possible that a few percent of halo stars may evolve into globular clusters and galaxies.

Figure 6.12 illustrates the motion patterns of first-, second-, and third-generation daughter galaxies relative to the original parent galaxy.

The trajectories of first-generation daughter galaxies relative to their parent galaxies are spiral. That is, relative to the parent galaxy, the trajectory of a halo star that has transformed into a globular cluster and then into a galaxy is a spiral.

The trajectories of second-generation and subsequent daughter galaxies, relative to the original parent galaxy, follow paths of logarithmic spirals. The degree of logarithmic spiral in the trajectories of daughter galaxies increases with each successive generation.

                     (37) Рисунок № 6.12

(37) Figure # 6.12

Figure 6.12 schematically depicts the motion of daughter galaxies of three generations—"1," "2," and "3"—relative to the original parent galaxy "A."

Galaxy "1" is a satellite and daughter galaxy of the original parent galaxy "A."

Galaxy "2" is a satellite and daughter galaxy of galaxy "1."
Galaxy "3" is a satellite and daughter galaxy of galaxy "2."

Let us assume that:
Galaxy "1" moves along a spiral trajectory around its parent galaxy "A."
Galaxy "2" moves along a similar spiral trajectory around its parent galaxy "1."
Galaxy "3" moves along a similar spiral trajectory around its parent galaxy "2."

As can be seen from the figure, the trajectories of galaxies "2" and "3" relative to the original parent galaxy "A" take the form of logarithmic spirals, the degree of which increases with the generation number of the galaxy relative to the original parent galaxy "A."

Conclusion:

- Galaxies give birth to galaxies. Galaxies reproduce through the evolution of high-mass halo stars. Galaxies within galaxy clusters are interconnected by "kinship" relationships. That is, there existed one or several galaxies that were the progenitors of a given galaxy cluster.

- The motion of galaxies through space follows spiral trajectories relative to their parent galaxies. As the generation number of a daughter galaxy increases, the degree of the logarithmic spiral in its trajectory relative to the original parent galaxy also increases.

- The power-law variation in galactic trajectories complicates the determination of "kinship" relationships between galaxies. Galaxy clusters can only form through such "kinship" connections.

The acceleration of daughter galaxies.

The accelerating expansion of the universe is, in modern astrophysics, a mystery that contradicts the outdated gravitational concept.

One of the reasons for the accelerating expansion of the universe is the acceleration of galactic motion. In the process of analytical study of galaxy clusters, it has been established that galaxies within clusters are linked by kinship relationships. That is, the study has determined that all galaxies in clusters are daughter galaxies to some galaxies and parent galaxies to others. It is precisely these kinship relationships between galaxies that constitute one of the causes of the accelerated motion between them.

Figure 6.12 schematically depicts the trajectories of daughter galaxies relative to the original parent galaxy "A." In other words, in Figure 6.12, the original parent galaxy "A" is shown as stationary, while the daughter galaxies "1," "2," and "3" (of the 1st, 2nd, and 3rd generations) are in motion. Since galaxy "1" was born from a halo star of the original parent galaxy, and that halo star was ejected from the galaxy's center, this halo star possessed a velocity relative to the center of galaxy "A"—meaning its velocity was greater than that of galaxy "A" itself. The velocity of galaxy "1" is expressed by the formula:

V1 = V0 + ∆V1

Where:
V0 – velocity of the original parent galaxy "A";
∆V1 – velocity of the first daughter galaxy relative to the parent galaxy "A."

This velocity value includes:

- the velocity imparted to the halo star upon its exit from the accretion disk,

- the acceleration of the star over the course of its lifetime.

It is possible that velocity changes occur during the motion of the globular cluster and the daughter galaxy itself. However, as of now, there are no observational data regarding such changes in galactic velocity.

Velocity may also change during the collapse of a white dwarf. However, if the halo star is single, the ejection of its mass into space likely occurs uniformly in all directions. Possibly, due to such a symmetrical mass ejection, changes in the velocity and direction of motion of the future galaxy are minimal.

Thus, a daughter galaxy has a higher velocity than its parent galaxy.

  Where:
V2 – velocity of the second-generation daughter galaxy "2";
V3 – velocity of the third-generation daughter galaxy "3";
∆V2 – velocity of the second daughter galaxy relative to its parent galaxy "1";

∆V3 – velocity of the third daughter galaxy relative to its parent galaxy "2."

Conclusion:

The process of accelerated motion between galaxies has two physical causes:

First, the reproduction of galaxies inherently involves an increase in the velocity of daughter galaxies. Each daughter galaxy, upon formation, possesses a velocity greater than that of its parent galaxy.

Second, measurements of galactic and stellar velocities are based on stars, which throughout their lives accelerate due to mass loss from radiating energy into space.

6.2. Formation of Galaxy Clusters

We have predicted and examined the physical processes involved in the origin and birth of galaxies. Let us now predict the process of galaxy cluster formation.

To form a star, it is necessary to gather gas and matter from space. To form a galaxy, it is necessary to gather gas and matter billions of times greater than that required for star formation.

To form a galaxy cluster, it is necessary to gather gas and matter hundreds of millions of times greater than that required for a single galaxy.

That is, a necessary condition for the formation of stars, galaxies, and galaxy clusters is the presence of gas and matter in the region where these objects form. More precisely, the presence of gas flows that collect matter from the surrounding space and transport it to stellar formation sites. These gas flows are shaped and generated by the black holes within galaxies.

For example: The Milky Way galaxy contains one hundred million black holes, which shape and generate the gas flows of our galaxy.

Consequently, the existence of gas and gas flows is a necessary condition for the formation of stars, galaxies, and galaxy clusters.

Gas flows in space are shaped and generated by the accretion disks of black holes. Therefore, the presence of black holes in the region where stars form and are born is a necessary condition.

The necessary conditions for the formation and birth of stars, galaxies, and galaxy clusters are:

- Space. A region of space where the formation and birth of stars occurs;

- Gas and gas flows. Gas and gas flows collect and deliver "building material" and nuclear fuel for star formation;

- Black holes. Black holes are the sources that generate gas flows.

That is, a galaxy cluster forms in a region of space where gas flows, created by the black holes of the galaxies themselves, are present.

Why are stars packed into galaxies?
What is a galaxy?
How can one explain, in simple terms, the ingeniously simple, ingenious construction of the galaxy, Created by the Almighty?

The theory of star formation through gravitational collapse of protostars is erroneous. Stars form and are born within black holes, in the gas flows created by black holes or by the accretion disks of stellar remnants.

- A galaxy is a mechanism for producing stars. And this entire mechanism consists of a black hole, or of black holes. If you were to remove all the stars from a galaxy, leaving only the black holes and their flows, stars would continue to be born within the space of the galaxy.

- A galaxy is a mechanism that collects gas and matter from space, builds nuclear reactors—stars—from this gas, ignites nuclear reactions within them, and then releases these stars back into space.

- A galaxy is a gigantic compressor for gathering matter and a factory for producing nuclear reactors.

- The ingenuity of the galaxy's construction is fantastic. A mechanism that produces hundreds of billions of stars consists of a gas tornado, of circulating, cyclonic gas flows.

The black hole at the center of a galaxy is the main mechanism of the galaxy, collecting matter from space. The stars of galaxies are produced within black holes or within gas flows shaped by black holes. The stars in a galaxy are united by their place of birth.

However, galaxies give birth not only to stars; galaxies also give birth to galaxies. Galaxies born from galaxies form galaxy clusters.

Let us consider a possible scenario for the formation of a galaxy cluster.

Let us predict the physical processes involved in the inception of a galaxy cluster.

A star, or a white dwarf, of high or intermediate mass entered a region of space containing hydrogen gas. Following the collapse of this white dwarf, an accretion disk formed around a black hole or neutron star in that region. This accretion disk, in turn, generates its own gas flows.

   To simplify the prediction, let us assume that the collapse of a white dwarf resulted in the formation of a black hole's accretion disk. It is possible that, under favorable conditions, the accretion disk of a neutron star may also possess the capability to produce groups of stars, similar to black holes.

   The prediction of the evolution of a black hole into a galaxy was discussed above. Let us now forecast the development of physical events during the evolution from a galaxy to a galaxy cluster.

   Following the collapse of the white dwarf, a black hole's accretion disk formed in a region of space. In this region, hydrogen gas and matter are present with a density of ρ = 10⁻²⁹ g/cm³.

   The black hole, by forming and ejecting stars into space, gradually assembled a globular cluster of stars around itself. As the number of stars increased, the black hole transformed this globular cluster into a galaxy. During the formation of the galaxy, the black hole produced halo stars. A fraction of these stars possess large masses.

These high-mass stars, while still within the space of the parent galaxy, evolve into white dwarfs and subsequently collapse, transitioning into the black hole stage. These black holes, moving within the space of the parent galaxy, form globular clusters, which, beyond the boundaries of the parent galaxy, evolve into dwarf galaxies and galaxies.

   The motion of halo stars through space after their ejection from the accretion disk follows a spiral trajectory relative to the parent black hole.

By inheritance, this spiral trajectory is passed down from the parent halo star to its white dwarf, then to the black hole, then to the globular cluster, and finally to the daughter galaxy.

Consequently, a daughter galaxy recedes along a spiral trajectory relative to its parent galaxy. The production of daughter galaxies by daughter galaxies increases the generation number of daughter galaxies relative to the original parent galaxy. Starting from the second generation of daughter galaxies, their recession from the original parent galaxy follows a logarithmic spiral. An increase in the generation number increases the degree of the logarithmic spiral in the recession trajectory of daughter galaxies from the original parent galaxy.

Let us predict the evolution of a galaxy cluster through the evolution of daughter galaxies produced by the original parent galaxy.

Let us make a theoretical assumption:

- In this example, each galaxy can produce only five daughter galaxies.

Thus, the original parent galaxy produces five first-generation daughter galaxies. These five first-generation daughter galaxies produce twenty-five second-generation daughter galaxies. The twenty-five second-generation daughter galaxies produce one hundred twenty-five third-generation daughter galaxies. The one hundred twenty-five third-generation daughter galaxies produce six hundred twenty-five fourth-generation daughter galaxies. The total number of galaxies in this theoretical space amounts to seven hundred eighty-one galaxies. And this is with a reproduction coefficient of five.

In reality: our galaxy contains over 154 globular clusters and more than 60 satellite galaxies; the Andromeda galaxy contains 400 globular star clusters and over 20 satellite galaxies.

Research findings confirm our prediction regarding the population of galaxy cluster space by parent and daughter galaxies.

That is, galaxies located within galaxy cluster spaces are linked by kinship relationships, being mothers and daughters to one another.

Let us graphically examine the spatial distribution of galaxies in a hypothetical cosmic space, as shown in Figure 6.13.

At the center of Fig. 6.13 lies the original parent galaxy. It was its black hole that first appeared in this region of hypothetical cosmic space. And it was its halo stars that initiated the process of populating this space. Surrounding the original parent galaxy are five first-generation daughter galaxies, labeled "1." The motion of these daughter galaxies follows spiral trajectories.

The motion of galaxies along spiral trajectories expands the space populated by galaxies. The motion of galaxies along logarithmic spirals is directed toward the periphery, increasing the extent of the galaxy cluster at its outer regions.

That is, younger galaxies, with a higher degree of logarithmic trajectory, tend to occupy peripheral regions of space. Meanwhile, older galaxies, with a lower degree of logarithmic trajectory, remain closer to the center, nearer to the original parent galaxy. Such a system of trajectories creates streams of galaxies moving toward incoming gas flows. It also leads younger galaxies away from the central zones occupied by older galaxies, where there is a scarcity of gas for star formation. In Fig. 6.13, it can be seen that younger galaxies tend to populate the peripheral space.

(38) Figure # 6.13

By populating the periphery, young galaxies, with their spatial presence and their gas flows, isolate the central zone of the galaxy cluster from the influx of gas from intergalactic space. In this central zone, older galaxies are located. The lack of gas and gas flows within galaxy clusters may lead to the formation of voids after the "death" of the old galaxies, as illustrated in Figure 6.14.

          (39) Figure # 6.14

Figure 6.14 illustrates the process of void formation inside a galaxy cluster. Old galaxies, surrounding themselves with daughter galaxies, isolate their own space from the influx of gas from intergalactic space. The gas of the old galaxies is taken by their children. Star formation in the old galaxies declines and eventually ceases. After the death of most stars, voids form in the spaces of the old galaxies, as shown in Figure 6.14. Such voids may be referred to as exhausted voids.

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