PART III
The Origin and Formation of Galaxies.
Galaxy Clusters.
Voids in Galaxy Clusters.

How do galaxies form and come into being?
How do galaxy clusters form?
How are voids in galaxy clusters formed?

Revealing the evolutionary process of globular star clusters will provide answers to these questions.

Chapter 5

Globular Star Clusters and the Evolution of a Globular Star Cluster.

The vertical genealogy and fractality of galaxies, globular clusters, and halo stars are clearly manifested in their structure and kinematics. To demonstrate the evolution of globular star clusters into galaxies, an analytical study of scientific data obtained from research on globular star clusters must be conducted.

5.1. Globular Star Clusters

Outer space is neither a human being nor a human society; it does not attempt to conceal from researchers the processes and events occurring within it.

An astrophysicist acting as an analyst must be able to discern the physics of past and ongoing processes in space based on facts, events, and the residual traces of those processes.

Competent analysis of ongoing events, the search for and analysis of traces left by past events—with mandatory consideration of the time dimension—makes it possible to identify the physical processes taking place in space.

Such analytical research requires: knowledge of the laws of physics, research data, and a system for the analytical examination of scientific data.

However, for researchers in the process of inquiry, the ability to logically and coherently generate questions for analytical investigation is also necessary.

In logically well-constructed questions, the pathways for finding correct answers are psychologically embedded. Sometimes, the correct answers are already contained within the properly formulated questions themselves.

When analyzing scientific facts, it must be taken into account that the examination of a single fact does not provide a complete answer to the questions posed in the study. Yet, in combination with analyses of other facts, the investigation will be partially or fully successful. After analyzing individual facts, it is necessary to conduct an analysis of all facts collectively. In such an analysis, facts that either confirm or refute the conclusions and results of the study must be identified. The study itself may be part of a broader investigation and constitute a singular analytical examination of a group of scientific facts.

The aggregation of analytical studies reveals the operation of the laws of physics in the processes and events occurring in space.

Analysis of the data collected in studies of globular star clusters uncovers patterns in the physical events and processes affecting and taking place within globular clusters.

Uncovering the causes and regularities of the physical events and processes occurring in globular star clusters reveals the mysteries of the origin of galaxies and their clusters.

Let us examine and analyze the scientific facts gathered by space researchers concerning globular star clusters.

5.2. Globular Star Clusters: Scientific Facts and Their Analysis

Analysis of the scientific facts obtained from studies of globular star clusters indicates the evolution of globular star clusters into galaxies. That is, a globular star cluster represents the initial stage of galaxy formation.

We shall analyze the scientific facts derived from research on globular star clusters and identify the signatures of galaxy formation within these clusters. We shall identify the indicators that the evolution of globular clusters leads to the formation of galaxies.

In the process of analyzing the facts obtained from studies of globular star clusters, we shall predict the physical processes involved in the birth, formation, and evolution of globular star clusters.

In order to make a prediction regarding the evolution of globular star clusters, we shall define the questions that require answers:

1.     Where are globular star clusters born, and how do they form?

2.     The kinematics and trajectory of globular star clusters.

3.     The evolution of globular clusters into galaxies.

4.     The genealogical relationship between globular star clusters and galaxies.

How does one determine the connection between the objects under study?
Is this connection genealogical?
And is this genealogical connection between the objects vertical?

It is quite simple!!!
The greater the similarity, resemblance, and identity between the objects under study, the stronger their genealogical connection!

Vertical genealogy between globular star clusters and galaxies is manifested in external features, internal structure, kinematic motion, and the process of star formation.

We shall identify and substantiate this genealogical connection by conducting an analysis of research data.

Where do globular star clusters originate? What do the facts indicate?

- Globular star clusters are concentrated in the region of the galactic center.
Globular star clusters—being part of the halo—are located in the halos of galaxies. Half (50%) of the globular star clusters in our galaxy lie at a distance of 10 Kpc from the galactic center. The remaining clusters are situated within a zone up to 50 Kpc from the galactic center, and some extend even farther.

- Globular clusters consist of Population II stars, as do the halo stars of the parent galaxy. The stars in globular clusters have a low abundance of heavy chemical elements. This fact indicates that the stars of globular clusters are old.

Where do star clusters that already contain old stars come from?
Where are the globular clusters that contain young stars? Why are there no globular clusters with young stars? Where are globular star clusters born and formed?

To unravel the mystery of the birth and formation of globular star clusters—which comprise old stars—it is necessary to analyze the trajectory and kinematics of globular cluster motion. The trajectory of globular star clusters is elongated and takes the form of a spiral. The motion of globular clusters is directed along a spiral, from the galactic center toward the periphery.

By analyzing the facts—the age of the stars and the trajectory of the clusters—it can be established with high probability that the origin, birth, and formation of globular star clusters occur in the centers of their parent galaxies.

The formation and evolution of young globular clusters take place in the center of the parent galaxy, within a region of high gas and dust density. The high density of gas and dust in the galactic center—in its bulge—prevents observation of the evolution of young globular clusters. By the time globular clusters emerge from this high-density zone, their stars have already aged. It is precisely because the evolution of young globular clusters is concealed within dense gaseous regions that researchers observe only aged stars in globular clusters. Globular star clusters undergo the same evolutionary life path as Population II stars—the halo stars.

Let us conduct an analysis of the scientific data obtained from studies of globular star clusters.

1. Vertical genealogy between globular star clusters and galaxies is manifested in external features.

Globular star clusters are aggregations of stars with a spherical or ellipsoidal shape.

The similarity in geometric form between globular clusters and elliptical galaxies indicates a vertical genealogical connection between them.

The shape of a globular star cluster and that of an elliptical galaxy suggest that at the center of both the star cluster and the galaxy lies the primary source of star formation—an object that generates accretion: a black hole. In the early stages of evolution, a globular cluster may alternatively have a neutron star or a white dwarf at its center.

It is precisely these objects—those that generate an accretion disk—that are involved in the production of stars within globular clusters and galaxies. Given the ideal sphericity and ellipsoidal form of globular clusters, the accretion disk at the cluster center is likely attributable to a black hole. It is possible that, following the initial star formation processes during the formation of globular clusters, neutron stars and white dwarfs became incorporated into newly formed stars as their cores. Meanwhile, at the center of the globular cluster, a stable black hole formed—or possibly several black holes. Star formation propagating outward from the center can produce globular star clusters of ideal geometric shape.

1. Conclusion:

- The shape of a globular star cluster and that of an elliptical galaxy indicate a genealogical connection between them.

- The shape of a globular star cluster and that of an elliptical galaxy indicate the presence at their centers of the primary source of star formation—a black hole.

- Indirect observational data confirm the presence of black holes, neutron stars, accretion sources, and star formation within globular star clusters.

2. Vertical genealogy between globular star clusters and galaxies is manifested in internal structure.

Globular clusters contain stars of advanced age, with high and intermediate masses. The rapid evolution of high-mass stars has caused some of these stars to transition into the white dwarf, neutron star, and black hole stages. The existence of stellar remnants in globular clusters is supported by indirect evidence. Emissions originating from globular star clusters indicate the presence within these clusters of stellar remnants—black holes, neutron stars, and white dwarfs. Likewise, galaxies are composed of stars, white dwarfs, neutron stars, and black holes.

Galaxies and globular star clusters consist of the same components: stars, white dwarfs, neutron stars, and black holes. This fact confirms not only their common genealogy but also the fractality of galaxies. And the primary elements of galactic fractality are globular clusters.

The distribution of stars within globular clusters is analogous to the distribution of stars in elliptical galaxies.

Ellipticity of form and isophotal structure are observed in globular clusters.
In both galaxies and globular clusters, stellar isophotes uniformly surround their centers. The age of stellar isophotes in a globular cluster increases with distance from the cluster center. Elliptical galaxies exhibit the same structure.

The uniform age of stars in a globular cluster can be explained by the fact that stars at the periphery of the cluster are close in age to one another and represent the oldest stars in the cluster.
Young stars are located in the interior of the globular cluster and are visually inaccessible due to the obscuration by older stars at the cluster periphery. The existence of young stars in a globular cluster depends on the presence of conditions favorable for star formation within the cluster at different stages of its lifetime.

2. Conclusion:

- Indirect observational data confirm the presence of black holes, neutron stars, accretion sources, and star formation within globular star clusters.

- The compositions of galaxies and globular star clusters are identical. They consist of the same components: stars, white dwarfs, neutron stars, and black holes.

- The similarity between galaxies and globular star clusters is manifested not only in geometric form and kinematic motion but also in the set of components of which they are composed.

- Globular clusters and galaxies share not only a common genealogy but also fractality. The primary elements of galactic fractality are globular clusters.

- The absence of globular star clusters within the compositions of globular star clusters indicates the youth of globular clusters as galaxies, as well as the weakness of the primary star formation source—the central black hole.

3. Where are globular star clusters born?

All galaxies possess globular star clusters.
Globular star clusters are part of the galactic halo.
The centers of mass of globular clusters are the galactic centers.

The density of globular clusters increases toward galactic centers.
One third of the globular clusters in our galaxy are located in the constellation Sagittarius—that is, in the direction of the galactic center.
More than half (50%) of the globular clusters in our galaxy lie within 10 Kpc of the galactic center, surrounding it with their halo. The remaining globular clusters of our galaxy are situated up to 50 Kpc from the center and beyond.

When analyzing the distribution of halo stars and globular star clusters in galaxies, their kinematic motion must be taken into account. Analysis of the kinematics and concentration of halo stars and globular star clusters indicates their place of birth and formation. The motion of halo stars and globular star clusters is directed away from galactic centers.

Taken together, these facts indicate that halo stars and globular star clusters are formed, born, and originate in the centers of galaxies. The center of a galaxy is its black hole.

3. Conclusion:

The black hole at the galactic center and the region of space surrounding it constitute the birthplace and formation site of globular star clusters.

4. Vertical genealogy between globular star clusters and galaxies as manifested in the kinematics of motion in space.

Globular star clusters move along elongated orbits around the galactic center.
More precisely, the orbits of globular star clusters are identical to the orbits of halo stars and take the form of spirals.

Halo stars and globular star clusters recede along spiral trajectories from their place of birth. The fact that halo stars and globular star clusters move away from the black hole at the galactic center indicates the absence of a gravitational bond between these objects and the galactic center.

Beyond the galaxy, globular clusters transform into galaxies, and their trajectories become the orbits of satellite galaxies around the parent galaxy (Figure 5.1).

(23) Figure #5.1

That is, satellite galaxies are daughter galaxies formed from globular star clusters of the parent galaxy. Satellite galaxies are not galaxies captured by the gravitational field of another galaxy.

These facts indicate that globular clusters share a genealogical connection with halo stars. More precisely, globular clusters share a genealogical connection with stars born in the galactic center—just as halo stars do.

The paradox of globular clusters:

- Globular star clusters exhibit a genealogical connection both with halo stars and with galaxies.

Halo stars and globular star clusters move along a spiral trajectory, receding from the galactic center. The spiral pattern of motion is indicated by the spatial distribution of halo stars and globular clusters within the galaxy.

In Figure 5.2, halo stars and their isophotes are shown. In the arrangement of the isophotes of halo stars in galaxies, a pattern exists: as the age of the stars increases, their distance from the galactic center also increases. This distribution of stars can be explained by the fact that halo stars are moving away from the galactic center. That is, the motion and trajectories of these stars are directed away from the center of the galaxy, away from its central black hole. The motion and trajectories of globular star clusters are analogous to those of halo stars.

(24) Figure #5.2

The fact of such motion of globular star clusters and halo stars indicates that they share a common mechanism of production (birth, formation). That is, the formation and birth of halo stars and globular star clusters occur in the same location. And that location is the black hole at the center of the galaxy. The birth of a globular cluster—with all its stars and with a black hole at its center—is impossible, even theoretically. Consequently, the formation of globular star clusters must result from certain physical processes and events.

The genealogical connection between globular star clusters and halo stars is expressed in the fact that their formation and birth occur at the galactic center, with identical kinematic characteristics. Such a genealogical chain suggests that globular star clusters may be born as halo stars and, after collapse and transformation into a black hole, evolve into globular clusters.

Further evolution transforms a globular cluster into a galaxy, revealing a genealogical link between globular clusters and galaxies.

Thus, this analytical study has uncovered and identified a vertical genealogical connection among halo stars, globular clusters, and galaxies.

Let us predict the physical processes and events that result in the formation of globular star clusters, taking into account their genealogical connection with halo stars. Let us predict the most probable scenario for the formation of globular clusters at the centers of galaxies.

Prediction of a Probable Scenario for the Formation of Globular Clusters

Globular star clusters arise in regions favorable for star formation—areas of space with elevated gas density.

Such regions include the centers of galaxies, their nuclei, and bulges.
In these zones, the density of gas and dust is high. Due to this high density, the study of physical processes in galactic centers is inaccessible.
The majority of globular clusters in galaxies are located around these very regions. The identity in kinematics and spatial distribution within galaxies indicates the existence of regularities in the formation and physics of globular clusters.

The density of gas and dust in the gas flows, disks, and spiral arms of galaxies is also high and favorable for star formation; however, the formation of globular clusters does not occur in these zones. This fact suggests that globular clusters form only in the centers of galaxies, in the bulge, and possibly in the galactic nucleus.

Why? What is the difference between a star-formation-favorable zone at the galactic center and a star-formation-favorable zone in the disks and arms of galaxies?
How does star formation at galactic centers differ from star formation in galactic disks and arms?

The difference lies in the masses of the stars!

In the disks and spiral arms of galaxies, low-mass stars are formed; the evolution of these stars does not lead to the formation of neutron stars or black holes.

At the galactic center, by the central black hole, high- and intermediate-mass stars are formed, the evolution of which leads to the formation of neutron stars and black holes.

Since globular clusters are not formed in the disks and arms of galaxies, a prediction can be made regarding the involvement of halo stars in the formation of globular star clusters.

Some of the stars born at the galactic center, those with high masses, do not reach the galactic halo. For simplicity, we will consider these to be halo stars, as they share a common birth mechanism with halo stars. These stars collapse while still within the bulge, without exiting into the galactic halo.

Let us consider the prediction concerning the role of halo stars in the birth of globular clusters.

In galaxies, high-mass stars—halo stars—are ejected from the central zones into outer space. The ejection of high-mass stars at the galactic center occurs with the direct or indirect involvement of the central black hole.

It is possible that under the influence of physical, nuclear, and dynamical processes, the accretion disk is disrupted. It is also possible that stars form around the black hole and, upon the dynamical disruption of the accretion disk, these stars are ejected into space. How exactly stars form and are ejected from the region containing the central black hole remains unknown. What is known is that the formation and ejection of stars from the galactic center does occur. And these stars are halo stars.

Globular star clusters form in the nucleus and bulge of the galaxy, under conditions favorable to star formation.

Let us make a permissible simplification: it is possible that in the accretion disk of the black hole at the galactic center, a high-mass star has formed. As a result of physical, nuclear, and dynamical processes, this high-mass star was ejected from the accretion disk of the black hole, as illustrated in Figure 5.3.

(25) Figure #5.3

The region of space surrounding the black hole at the galactic center has a high density of gas and dust and is a favorable zone for star formation.
The high density of gas and dust in the space around the black hole is created by the black hole itself, via its accretion disk. The black hole draws gas and dust from space into its accretion disk, forming around itself a zone with an elevated concentration of gas and dust.
The formation of globular star clusters begins with the birth of a massive halo star. This halo star is born in the zone of the parent galaxy's central black hole.
This massive star, along with other stars, is ejected into space from the black hole's accretion disk. During its journey, this star passed through all stages of its evolution while remaining within the zone favorable for star formation.

Its white dwarf collapsed, transitioning into the black hole stage while still in the galactic bulge, not far from the parent black hole.
The short interval between the star's birth and the collapse of its white dwarf in the galactic bulge space indicates that it is indeed a black hole that is forming. The probability of a neutron star forming after the collapse of a white dwarf is very low, but possible.
There is no fundamental difference in what forms a globular star cluster—a white dwarf, a neutron star, or a black hole.
To simplify the prediction of physical events, let us adopt the scenario of globular cluster formation by a black hole.
The black hole formed an accretion disk, which initiated star formation processes. The young black hole began to form and produce stars, ejecting them into the space around itself, thereby creating a globular star cluster.

Since the density of gas and dust in the galactic center is high, star formation within the globular cluster proceeds intensively, and the age difference between stars is small. That is, having produced one group of stars, the accumulation of gas for the next group of stars occurs within a short period of time. Consequently, the age difference between groups of stars produced by the daughter black hole is not large.

The young, daughter black hole forms a globular cluster around itself. In a zone favorable for star formation, the rate of star formation within the globular cluster is high. However, after the globular cluster exits the favorable zone, the star formation rate declines. Located at the outer boundary of the globular cluster are the oldest stars of the cluster, born at the beginning of its formation. Due to the location of these old stars on the outer boundary of the globular cluster, one can infer the age of the cluster itself.

Why do old stars tend to occupy the outer regions of a globular cluster?

The structural scheme of elliptical galaxies and globular clusters is identical, and this regularity indicates their vertical genealogical connection. In galaxies and globular clusters, the production of stars and the subsequent formation of galaxies and globular clusters from these stars are analogous (identical).

Stars are ejected from the galactic center, where the black hole resides, along unwinding spiral trajectories. This spiral motion is directed from the center toward the outer boundary. A globular star cluster inherits its kinematic motion from the parent star that was ejected from the galactic center as a result of physical, nuclear, and dynamic processes.

Other Theoretically Possible Scenarios for the Origin of Globular Clusters

- A possible scenario involves the participation, in the formation of halo stars and globular clusters, of stellar remnants born in the gas flows of galactic disks and spiral arms. In the disks and spiral arms of galaxies, low-mass stars are formed, which move toward the galactic center along a converging spiral. This is because the gas in the disks and arms moves in a converging spiral toward the galactic center, toward the central black hole. Stars born in these gas flows inherit their kinematics of motion. Consequently, their ultimate destination is the central black hole. What reaches this final destination are the remnants of stars, which may be reborn as stars multiple times. That is, during their journey within the gas flow, under favorable conditions, these stellar remnants can form a star by becoming its core. Such a process of rebirth may repeat. Upon reaching the galactic center—the central black hole—the former star from the disk and spiral arms may, as a stellar core, become part of a halo star. It is possible that the birth of high-mass stars is associated with such a chain of events. Perhaps the remnants of stars, which have accumulated a large amount of heavy chemical elements, became part of high-mass halo stars. These stars then collapse at the galactic center and form globular star clusters.

- Theoretically, a scenario is possible where a black hole is born within the accretion disk of the parent black hole, or in the space surrounding that black hole. That is, within the gas flow of the accretion disk, due to turbulent motion of the gas, a gas vortex or a gaseous tornado could form. During the dynamic ejection or escape of halo stars, this gaseous tornado is ejected into space, just like the halo stars. The accretion disk of the gaseous tornado then initiates the star formation mechanism as it passes through space favorable for star formation.

The probability of such a scenario developing is low, but possible.

How the formation and birth of globular star clusters actually occurs remains unknown. Based on the laws of physics and the analysis of observational facts, the described scenario involving the collapse of a high-mass star has a high probability.

Clarification:
To simplify the examination of physical processes, the scenario of globular cluster formation through the birth and collapse of a high-mass star at the galactic center will be adopted as the primary model. In subsequent research, we will rely on this model of globular cluster formation.

We do not know exactly how the birth and formation of a globular cluster occurs; what matters is that it does occur. That is, the important point is that globular star clusters exist, and that they are formed and created at the galactic center, with the direct or indirect participation of the parent black hole.

If there are errors in this prediction, they do not affect the outcome of the globular star cluster formation process.

4.     Conclusion:

- In globular star clusters, a genealogical connection is evident, both with halo stars and with galaxies.

- The origin and formation of globular clusters occur at the galactic center, in the bulge region. The birth of globular clusters most likely involves high-mass stars, born within a black hole or with its participation. After the collapse of such a star's white dwarf, an accretion disk forms around the resulting black hole or neutron star. The accretion disk of the black hole, located at the center of the cluster, then forms the globular star cluster. Similarly, the central black hole of a galaxy forms an elliptical galaxy.

- Beyond the galaxy, globular clusters move into regions with an elevated gas content. Star formation increases, and the globular clusters transform into satellite galaxies of the parent galaxy. The trajectories of these former globular clusters become the orbits of the satellite galaxies.

5. Chemical Composition of the Atmospheres of Stars in Globular Clusters.

What does the chemical composition of stellar atmospheres indicate?

Throughout its entire life, a star and its surroundings undergo changes—physical, nuclear, chemical, and dynamic. Its mass, velocity, energy output, chemical composition, and other properties change. By analyzing many parameters of a star, it is possible to predict the processes occurring within it. By analyzing a star's size, color, and luminosity, researchers can determine its age and mass.

Changes in color and luminosity indicate age-related changes taking place inside the star.

A star's color and luminosity are determined by the color and luminosity of its atmosphere—that is, by the chemical composition of the star's atmosphere and the energy released within it. What parameters affecting the color and luminosity in a star's atmosphere can indicate to researchers the age-related changes occurring in the star?

One parameter influenced by a star's age is the chemical composition of its atmosphere.

The abundance of heavy chemical elements in a star's atmosphere is a parameter by which the star's age can be determined.

What internal changes in a star can indicate its age?

As a star ages, its chemical composition changes.
Changes in the chemical composition of a star have both quantitative and qualitative effects on both its energy release and the nuclear reactions occurring within the star.
Changes in the chemical composition of a star also influence changes in the nuclear reactions taking place in the star's atmosphere.
Changes in the nuclear fusion reactions in the star's atmosphere alter the chemical composition of the star's atmosphere.
Consequently, the increase in a star's age changes the chemical composition of its atmosphere.

Space researchers have noticed that the chemical composition of the atmospheres of young stars contains more heavy elements than that of old stars. The presence of heavy chemical elements in a star's atmosphere is explained by their penetration into the star's atmosphere from surrounding space. However, such a view is erroneous! If the density of the solar wind at Earth's orbit is 15 particles/cm², then the density of the solar wind at a distance of 1000 km from the Sun's surface is more than 690,000 particles/cm². With such a density of radiation emanating from the star's surface, the penetration of any chemical elements into the star's atmosphere is impossible!

What if these chemical elements became part of the star during its formation?

In the upper layers, in the star's atmosphere, are atoms and ions of hydrogen and helium—the lightest chemical elements.

For heavy atoms and ions to rise into the upper layers of the star's atmosphere, they would have to travel enormous distances, overcoming the resistance of the laws of physics.

Within a star, atoms of chemical elements undergo nuclear changes.

Is it possible for heavy chemical elements to rise into the upper layers of a star's atmosphere without changing their chemical formula? No!

Why, then, does the chemical composition of stellar atmospheres change?

In the atmospheres of stars, researchers are not observing the chemical composition of the stars themselves, but rather the synthesis of chemical elements within those stellar atmospheres. That is, in stars and their atmospheres, not only helium (He) is synthesized, but also heavy chemical elements. As a star ages, its energy capacity and the parameters of its energy output change. Do changes in the parameters of the energy released affect the synthesis of chemical elements in stellar atmospheres? Of course they do!!! The higher the energy release in a star, the higher the probability of synthesizing heavy chemical elements. Young stars have a higher specific density of energy release than old stars. Consequently, the probability of synthesizing heavy chemical elements in the atmospheres of young stars is higher than in the atmospheres of old stars.

What, then, does the increased abundance of heavy chemical elements in the atmospheres of young stars signify? And what is the connection between the abundance of heavy chemical elements in a star's atmosphere and its age?

The answer to these questions likely lies in the ratio of hydrogen to other chemical elements synthesized in the star's atmosphere per unit of time.

The chemical composition of a star's atmosphere indicates which chemical elements are being synthesized in that atmosphere at a given moment. These chemical elements did not penetrate into the star's atmosphere from outer space; they were synthesized within the star's atmosphere!!!

The more hydrogen a star contains, the more energy is released during the synthesis of light chemical elements. The speeds of the synthesized chemical elements are high. Under such conditions, the synthesis of heavy chemical elements occurs more frequently.

As a star ages, the proportional relationship of its chemical elements changes. The proportion of hydrogen, relative to the other chemical elements, is lower in an old star. The degree of contamination, or nuclear "slag," within the star is higher. The volumetric energy release is less than that of young stars. Consequently, the synthesis of heavy chemical elements in the star's atmosphere decreases. The synthesis of heavy chemical elements inside the star does occur and continues, but in its deeper layers.

Perhaps the reason for the similar composition of chemical elements in a star's atmosphere and the surrounding space is the ejection of these chemical elements from the stellar atmosphere into the surrounding environment.

The difference in the chemical compositions of stellar atmospheres determines the age of stars. Determining age through the chemical composition of stellar atmospheres helps the researcher predict and trace the temporal chain of stellar evolution and the evolution of star clusters.

A change in a star's color is linked to the change in the chemical composition of its atmosphere and to age-related changes within the star itself.

Changes in energy release, both indirectly and directly, affect the changes in a star's color and the chemical composition of its atmosphere. Changes in the quantitative content of heavy chemical elements in a star's atmosphere influence the change in its color.

That is, a star's color changes as a consequence of the change in the chemical composition of its atmosphere.

What does the chemical composition of the atmospheres of stars in globular clusters indicate?

In globular clusters, the stars are old, with a low abundance of heavy elements in their atmospheres. The stellar composition of globular clusters is analogous to the stellar composition of the galactic spheroidal component—the Population II stars.

This fact indicates that the stars in globular clusters were born and formed in the galactic center and underwent the same evolutionary path as other halo stars, the stars of the spherical component of the galaxy.

This fact points to the similarity in the conditions of birth and formation for halo stars and globular cluster stars.

If globular clusters form and are born in the galactic center, then their stars traverse the same evolutionary and distance-related path as halo stars, under identical conditions.

The high probability of this predicted scenario is indicated by:

- the identical age of stars in globular clusters and halo stars;

- the identical chemical composition of the atmospheres of stars in globular clusters and halo stars;

- the identical kinematics of stars in globular clusters and halo stars;

- the identical distances from halo stars and globular clusters to the galactic center.

These identical parameters of the stars suggest a common birthplace for halo stars and the stars of globular clusters.

Classification of Globular Clusters Based on the Chemical Composition of Stellar Atmospheres.

Based on the abundance of heavy chemical elements in their stars, globular clusters in galaxies are divided into two groups. In the first group of globular clusters, the stars have a higher abundance of heavy chemical elements; consequently, this group is younger. In the second group of globular clusters, the stars have a lower abundance of heavy chemical elements; consequently, this group is older in age.

How are these two groups of globular clusters spatially distributed within the galaxy?

The first, younger group of globular clusters, within the space of the Milky Way galaxy, is located closer to the galactic center and is associated with the bulge.

The second, older group of globular clusters, within the space of the Milky Way galaxy, is located farther from the galactic center than the first group and is associated with the galactic halo.

That is, globular clusters located closer to the galactic center are younger, while globular clusters located farther from the galactic center are older. In such a spatial arrangement of globular clusters within galaxies, there is nothing surprising. Halo stars are distributed in exactly the same sequence.

The fact of this age-dependent distribution of globular cluster stars and halo stars points to their place of birth and formation being the galactic center, with the participation of the central black hole.

The totality of these coincidences reveals a pattern.

5.     Conclusion:

- The chemical composition of a star's atmosphere determines its color and age.

- The identity of the kinematic and age-related characteristics of stars in globular clusters and halo stars (the spherical component of the galaxy), taken together, indicates an identical mechanism of their formation and a common birthplace.

- The chemical composition of stellar atmospheres, the kinematics, and the location of globular clusters within galaxies unequivocally point to the galactic center as the place of their formation and birth.

- The observed regular age dependence in the distribution and kinematics of halo stars and globular cluster stars allows us to predict the evolution of globular star clusters from halo stars into galaxies.

6. Star Formation in Globular Clusters

The low rate of star formation in many globular clusters is explained by the low density of gas in the space through which the globular cluster has passed. The beginning of a globular cluster's life cycle occurs in the galactic center. The nucleus and center of the galaxy contain a large amount of gas and dust. When passing through a region of space with a high gas density, the star formation rate within the globular cluster increases. Upon leaving the galactic center, exiting the bulge, star formation in the globular cluster decreases because the density of the gas in the space surrounding the cluster has diminished. However, if the path of the globular cluster takes it through a region of space with an increased gas density, star formation can resume and continue. This is confirmed by the existence of globular clusters containing stars of multiple generations, such as Omega Centauri in the Milky Way galaxy and Mayall II in the Andromeda galaxy.

6. Conclusion:

Star formation in globular clusters depends on the density of gas within the cluster and in the space surrounding it. A decrease in the gas density in the space around a globular cluster reduces and eventually halts star formation within it. However, when passing through zones favorable for star formation, the process resumes. This resumption of star formation involves retained star formation sources: black holes, neutron stars, and white dwarfs. Massive stars may also participate in this process; their collapse generates an accretion disk, which triggers the star formation mechanism.

7. Concentration of Stars Toward the Center of Globular Clusters

As one approaches the center of a globular cluster and the center of a galaxy, the concentration of stars increases. That is, both in the centers of globular clusters and in the centers of galaxies, there is a high concentration of stars.

The facts of increasing stellar concentration when approaching the center, observed in both globular star clusters and galaxies, confirm the following conclusions:

- The main epicenter of star formation is located in the centers of globular star clusters and in the centers of galaxies.

- The identical shape of the objects and the identical location of the primary star formation source confirm the existence of a kinship between globular star clusters and galaxies.

A comparison of the facts regarding stellar concentration in globular clusters and galaxies indicates their similarity and fractality.

Galaxies possess fractal properties. These fractal properties of galaxies are manifested in globular clusters.

Visually and physically, a globular cluster is a prototype of an elliptical galaxy. That is, fractality exists between an elliptical galaxy and globular clusters. A galaxy is fractal, meaning it is a set possessing the property of self-similarity. In form and content, a galaxy coincides with a globular cluster.

7.     Conclusion:

The structure of globular star clusters is identical to the structure of galaxies. Since globular star clusters are part of galaxies, the structure of galaxies is a fractal structure.

Globular star clusters are elements of galaxies, similar to galaxies not only in the composition of their constituent elements but also in their structure.

8. Stellar Density in Globular Clusters

Globular clusters are classified according to their degree of stellar concentration, on a scale from 1 to 12. Class 1 corresponds to the maximum concentration of stars in the cluster, while class 12 corresponds to the minimum stellar concentration. Several factors influence the degree of stellar concentration within a globular cluster.

- The rate of star formation in the globular cluster.
The rate of star formation in a globular cluster is influenced by the density of gas within the cluster itself and in the surrounding space. A globular cluster moves through space, where the gas density is not uniform. Consequently, the gas density within and around the globular cluster changes over time. These temporal variations in gas density affect star formation and, subsequently, the stellar density within the cluster.

The galactic nucleus and its bulge are the zones with the highest gas content. When passing through this region of space, a globular cluster experiences its maximum rate of star formation. Therefore, the stellar density during the period of traversing this zone tends towards its maximum.

- The rate of star formation in a globular cluster is also affected by the cluster's own velocity when passing through zones favorable or unfavorable for star formation. The longer a globular cluster remains in a zone favorable for star formation, the more stars will be formed within the cluster, and the higher its stellar density will be. Conversely, if the cluster passes through a zone unfavorable for star formation—a region with low gas density—star formation within the cluster may cease.

If the parameters of the surrounding space do not change favorably for star formation, the cluster will transition into the stage of an open cluster. Star formation may resume when passing through zones with increased gas content, provided that the star formation sources are not lost. However, even if the star formation source is lost, star formation in a globular cluster can still resume when the cluster passes through a zone with increased gas content. The collapse of a white dwarf within the globular cluster will lead to accretion, and accretion will set the star formation mechanism in motion.

That is, star formation and the stellar density in a globular cluster depend on temporal changes in the gas parameters within the cluster itself and in the space surrounding it.

The function of stellar density in a globular cluster incorporates the function of variable star formation. This star formation function, in turn, includes the parameters of the globular cluster's motion through space.

- The stellar density in globular clusters is neither stationary nor constant. The stellar density within a globular cluster is influenced by the motion parameters of the cluster's constituent stars themselves. That is, stars within a globular cluster move through space. The motions of stars in globular clusters occur along spiral trajectories directed away from the cluster's center. In other words, the movement of stars in globular clusters is directed towards the expansion of the globular cluster and its volume. The expansion of the globular cluster and its volume leads to a decrease in the stellar density within the cluster.

Consequently, star formation in a globular star cluster and in an elliptical galaxy leads to an increase in stellar density. The motion of the stars themselves, within globular clusters and galaxies, is directed towards decreasing their density in the clusters and galaxies. These facts reveal the fractal properties of galaxies and globular star clusters.

8. Conclusion:

Several factors influence the degree of stellar concentration in a globular cluster.

- The rate of star formation in the globular cluster.
The rate of star formation in a globular cluster is influenced by:

- The density of gas within the globular star cluster and in the surrounding space.

- The velocity of the globular cluster itself when passing through zones favorable or unfavorable for star formation.

- The loss of a star formation source does not lead to the demise of the globular cluster. The collapse of a white dwarf, upon passing through a zone favorable for star formation, will restore star formation in the globular cluster.

- The stellar density in globular clusters is neither stationary nor constant. The stellar density within a globular cluster is influenced by the motion parameters of the cluster's constituent stars themselves.

- Star formation leads to an increase in stellar density within a globular star cluster and within an elliptical galaxy. Conversely, the movement of stars away from the center, in both a globular star cluster and an elliptical galaxy, reduces the stellar density in the clusters and galaxies.

9. The Genealogical Connection of Globular Clusters to the Parent Black Hole.

Space researchers have established a relationship between the parameters of the black hole at the center of a galaxy and the parameters of globular clusters located in the galactic halo.

The parameters of globular clusters in the galactic halo depend on the parameters of the black hole at the galactic center.

This fact indicates a parental connection between the black hole at the galactic center and the globular clusters. That is, the globular star clusters of a galaxy are born and formed with the participation of the black hole. How exactly the birth and formation of globular clusters occur, and what specific role the galaxy's central black hole plays in these processes, remains unknown. Analysis of indirect observational data suggests that it is indeed the central black hole that participates in the birth and formation of globular clusters.

It is possible to predict scenarios for the formation of a globular cluster involving the parent black hole.

The most realistic prediction points to a scenario in which a black hole or a neutron star forms a globular star cluster. That is, a star of great mass is born within the galaxy's central black hole. The black hole ejects this star into the galactic space. The density of gas and dust in the galactic nucleus is high. Since the lifespan of massive stars is short, the star ejected from the black hole collapses while still within the galactic nucleus region. Passing through the gas flows of the galactic nucleus, the young black hole (formed from the collapsed star) forms a globular star cluster. The mass of stars forming in association with a black hole depends on the parameters of that black hole; this genealogical connection is transmitted, via the progenitor star, to the globular cluster. Star formation in the galactic nucleus also depends on the parameters of the black hole.

The stars of the bulge, the halo stars, and the stars of globular clusters follow the same path along spiral trajectories. The velocities of bulge stars, halo stars, and globular cluster stars are similar in value, and they share the same ages and trajectories of motion. These facts point to a common birthplace and explain the identical ages of these stars at the same distance from the galactic center.

9.     Conclusion:

- The parameters of globular star clusters depend on the parameters of the central black hole of the parent galaxy.

- There is a genealogical connection between the globular star clusters and the halo stars of a galaxy.

10. Dependence of the Evolution of Globular Clusters on the Gas Flows of the Parent Galaxy.

In globular clusters, there is little gas between the stars.

This fact indicates that the gas within a globular star cluster is consumed for star formation, and the gaseous environment of the cluster depends on the influx of gas from outer space. The accretion disk within the cluster is still weak and unable to form its own gas flows. The accretion disks of parent galaxies are many times stronger than those of globular clusters. Due to the weakness of their own accretion disks, globular star clusters utilize the gas flows of their parent galaxies as they move through their space. If a globular cluster passes through a region of space with a high gas content, the intensity of star formation increases.

If the zone of space through which a globular cluster passes has a low gas content, star formation in the cluster decreases. If a globular cluster remains in a zone of low gas content for a long period, star formation in the cluster ceases. In the event of an extended absence of star formation, the cluster may transition into the stage of an open cluster.

10.  Conclusion:

- While residing within the space of its parent galaxy, star formation in globular clusters depends on the gas flows of that parent galaxy.

11. The Milky Way and the Magellanic Clouds

Let us analyze the scientific data obtained from the study of globular star clusters in the galaxies: the Milky Way, the Large Magellanic Cloud, and the Small Magellanic Cloud.

- In the Magellanic Cloud galaxies, relatively young globular clusters are observed, containing stars of different ages. This contrasts with the Milky Way galaxy, which contains old globular clusters.

- Globular clusters in the Large Magellanic Cloud galaxy are larger than those in the Milky Way galaxy.

If we analyze the evolutionary conditions of globular clusters in the Large Magellanic Cloud and Small Magellanic Cloud galaxies, the facts we predicted become apparent.

- The Large Magellanic Cloud and the Small Magellanic Cloud are located in a zone of increased gas density and are satellites of the Milky Way; the conditions within them are more favorable for star formation than those within the Milky Way.

The globular clusters of the Magellanic Cloud galaxies are immersed in interstellar gas. Consequently, star formation occurs within these globular star clusters, the number of stars increases, and the clusters evolve. The stellar density within the clusters increases.

The Large Magellanic Cloud and the Small Magellanic Cloud are satellites of the Milky Way. For the Milky Way, these galaxies are daughter galaxies.

They formed within the Milky Way and are therefore younger than our galaxy.

That is, these two galaxies were formed from globular clusters of the Milky Way. Before becoming galaxies, the Magellanic Clouds were globular clusters and were part of the parent galaxy, the Milky Way. Consequently, the Large Magellanic Cloud and the Small Magellanic Cloud are younger than our galaxy, and their globular clusters are younger than the globular clusters of the Milky Way galaxy.

Within the space of the parent galaxy, gas is consumed by star formation within the galaxy itself, and its density constantly decreases. When globular clusters move beyond the confines of the parent galaxy, they enter denser gas flows that are favorable for star formation. In these gas flows outside the parent galaxy, star formation within the globular cluster increases, and it transitions into the stage of a satellite galaxy.

Globular star clusters and daughter satellite galaxies recede from the parent galaxy along a spiral trajectory. They move towards the gas flows that are directed toward the parent galaxy.

Since the Magellanic Cloud galaxies move through space with an increased gas content, star formation in their globular clusters occurs more intensively than in our galaxy.

In the globular clusters of the Large Magellanic Cloud galaxy, stars of different generations (ages) can be distinguished.

11.  Conclusion:

- The motion of globular clusters and daughter satellite galaxies is directed away from the center of the parent galaxy along a spiral trajectory. These movements are directed towards the gas flows that are moving toward the parent galaxy.

- The encounter of globular clusters with gas flows is a favorable factor for the evolution of globular clusters into galaxies.

The totality of these coincidences reveals a pattern.

A vertical genealogy between globular star clusters and galaxies is manifested in external features, internal structure, kinematic motion, and the process of star formation.

This section has analyzed the facts obtained from the study of globular star clusters in galaxies.

The study has established a vertical genealogical connection between the following cosmic objects:

- the black hole of the parent galaxy;

- massive stars (halo stars), born with the participation of the galaxy's central black hole;

- the galaxy's globular star clusters;

- satellite galaxies of the parent galaxy.

That is, all the listed objects are linked by a single evolutionary chain.

The parent black hole produces a massive star, which, after the collapse of its white dwarf, transitions into the black hole stage and forms a globular star cluster around itself. Under favorable conditions, this globular star cluster evolves into a satellite galaxy of the parent galaxy.

CONCLUSIONS:

- Galaxies give rise to galaxies.

- Galaxies in galaxy clusters are born and formed by neighboring parent galaxies.

- A massive star, born in the center of a parent galaxy, under favorable conditions evolves into a galaxy, passing through the stage of a globular star cluster.

5.3. What the Facts Indicate.

The conclusions of our study are confirmed by astronomical research.
"Astronomers have conducted a study of four faint dwarf galaxies close to us, which were discovered several years ago and are satellites of the Milky Way. Some of these objects turned out to be more similar to globular clusters than to galaxies, while others may have actively interacted with the Milky Way in the past. The paper was published in The Astrophysical Journal."

A team of astronomers led by Burçin Mutlu-Pakdil has presented the results of photometric observations of four nearby ultra-faint dwarf galaxies, whose discoveries in the data from the Pan-STARRS and Dark Energy Survey surveys were announced in 2015. They have been designated Sagittarius II (Sgr II), Reticulum II (Ret II), Phoenix II (Phe II), and Tucana III (Tuc III).

Maps of the brightness distribution of the newly discovered dwarf galaxies
Burçin Mutlu-Pakdil et al./The Astrophysical Journal (2018)

The galaxy Sagittarius II, possessing a total gas mass of 1300 solar masses, turned out to be unusual in that its size (its effective radius is estimated at 32 parsecs) is small even by the standards of dwarf galaxies, and its structure is more similar to that of a large globular star cluster.

Phoenix II turned out to be the most massive dwarf galaxy among the studied group (its total gas mass is estimated at 1400 solar masses); initially, there were also attempts to classify it as a globular cluster.

Alexander Voytyuk
Source: https://nplus1.ru/news/2018/10/02/four-new-Milky-Way-satellites
Burçin Mutlu-Pakdil et al./The Astrophysical Journal (2018)
The Astrophysical Journal.

Recent studies confirm our prediction – Globular clusters are young galaxies, "galaxies in their infancy."

Under favorable conditions, a black hole evolves into a globular star cluster. Under favorable conditions, a globular star cluster evolves into an elliptical galaxy.

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