Physics Tutorial: Formation of Galaxies and Solar System. Actual Problems

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In this Physics tutorial, you will learn:

  • How were the galaxies formed? When did this process begin?
  • How did the density fluctuations affect the formation of galaxies?
  • How cosmic radiation helps us study the Universe?
  • How did the Solar System emerge? How much did this process last?
  • What is the Observable Universe? How do we know that there are other things beyond it?
  • What is the inflation phase? When did it occur?
  • What is the photon-matter particles ratio in the universe? What does this mean?
  • Why the universe contains more matter than antimatter?
  • What is dark matter? Why it is called so?
  • What is the dark matter - visible matter ratio in the universe?

Introduction

In the previous tutorial, we said that galaxies were formed at a later stage than the primordial helium, cosmic radiation and so on. We showed a chronology of universe from its origin (Big Bang) to 1013 s (300 000 years) after it. However, this period includes early stages of the Universe, prior to galaxy formation. In this tutorial, we will discuss the subsequent period that begins with the formation of the galaxy and continues to current day.

Overview

The picture we have provided so far regarding the first 300 000 years of Universe's existence illustrates a huge amount of gas containing hydrogen and helium which are uniformly distributed in the space around the position in which the Big Bang occurred. At the beginning of this stage this mixture of gas was at temperature T = 3000 K and it was in continuous expansion.

Now, after billions of years, the picture of the Universe is quite different. New structures such as galaxies that contain billions of stars, planets, natural satellites, etc., are present in the space, which on the other hand has expanded a lot since the end of primordial stage of Universe. Matter is no longer uniformly distributed; there are neutron stars in which the density reaches the values of atomic nuclei, but there are also large spaces where there is no matter. This empty space is much larger than the dimensions of galaxies. Galaxies have the tendency to gather in groups and super-groups, where each of these structures increases the distance from the others, making the structure of the Universe highly hierarchic. This results in a continuous expansion of the Universe.

The question that naturally arises at this point is: "How is it possible that from a homogenous Universe (as it was initially), it transformed to a highly partialized Universe as it is now? Maybe the atomic plasma was not as homogeneous as initially thought?"

The presence of structures with varying densities such as galaxies etc., excludes a Universe perfectly homogenous at the initial stage of its existence. The homogeneity must have been either deformed or only partial. These small deformations have acted as "seeds" for later structures we now know. In other words, regions where the density of gas was slightly higher than in the surroundings have acted as centres of new celestial structures such as galaxies etc. This is because gravitational force (that depends on the mass of objects) in these regions, was greater than in the surroundings due to higher density (i.e. higher mass concentration). As a result, matter from the surrounding gathered around these regions, forming the galaxies we now know. All actual models that try to explain the formation of galaxies are based on this assumption.

Formation of Galaxies

There are many models that try to explain the process of galaxies formation but all of them have one thing in common: they rely on the process of increase in matter fluctuation, we introduced this concept in the previous paragraph (without referring to the name of method). Let's explain this process in more detail.

Consider a region of space containing small deformations of matter produced occasionally because of matter fluctuations. In other words, in certain moments there are more particles in a region of space than in another, resulting in regions with higher density than the surroundings. Since gravitational force in these denser regions is greater, they start collecting matter from the surrounding space. As a result, these regions become denser and denser with time at the expense of the surroundings, which on the other hand becomes less and less dense, losing matter continuously until only vacuum is left. Look at the figure.

Physics Tutorials: This image provides visual information for the physics tutorial Formation of Galaxies and Solar System. Actual Problems

Supporters of these theoretical models however, face two main challenges when trying to explain them. The first issue consists on the fact that not every fluctuation of density brings the increase in the amount of matter gathered around it. Some fluctuations disappear after being formed in a region of space. This occurs because of thermal movement which tends to oppose the pulling effect of gravitational force. In order to be able to form new galaxies, the increasing fluctuations must contain enough matter, which based on today's observations must have a mass equal to 1011 solar masses, a value that represents the mass of an average galaxy. The second challenge for theoretical models to overcome consists on finding a reliable version of explanation regarding greater structures such as groups and super-groups of galaxies.

One of the most reliable fluctuation-based models of galaxies formation is that of gradual growth of fluctuations. According to this model, the expansion of Universe favours certain fluctuations while eliminating the others.

As for the gas clouds the absorb matter from the surrounding space and become heavier due to gravitational force, it is obvious that there are two variables to be considered when dealing with their growth: one is the Universe expansion that brings a decrease in matter density and the other is the gravitational attraction that increases the density. After some time, these opposing effects balance each other. As a result, the new structures created (the gas cloud and its components) detach from the rest of cosmic gas. After this critical moment, the galactic cloud collapses as gravitational force prevails over the expansive effect because the expansion process has already stopped.

The collapse of gas cloud (cosmic dust) is very intense; the resulting high speeds produce a circular motion around the centre of this cloud. Hence, the cloud takes an elliptical shape while rotating around itself, which eventually takes a disc shape except the central region, similar to the shape of Milky Way galaxy we have seen in tutorial 22.6. Moreover, a number of smaller fragmentations containing dense matter occur inside this structure that eventually form the stars. We will discuss this process in more detail when explaining the formation of the solar system.

The above model explains how spiral galaxies were formed and also how the revolution of stars around the centre of the corresponding galaxy occur.

Observing Cosmic Radiation

Observation and extraction of useful information from cosmic radiation is the main method used to confirm the possible models of galaxies and other celestial structures formation. Giving that during the first few hundred thousand years of its existence, cosmic radiation has been in equilibrium with matter, it has shared the same features with this matter. Hence, by observing and analyzing the features of cosmic radiation (such as homogeneity and isotropy), scientists have been able to draw conclusions about the homogeneity of matter in the Universe at 300 000+ years after the Big Bang when galaxies began to create.

Careful observations of cosmic radiation made in 1990s have confirmed that it is not completely isotropic, as it was previously believed. Its density changes very slightly when measured in various directions. This difference in density is not more than 1/10000. In this way, the theory of difference in matter fluctuations in the ancient Universe and the versions of galaxies formation resulting from this theory were confirmed.

Formation of the solar system

As we have discussed in tutorial 22.5, the stars experience many changes during their existence, manly resulting from internal explosions. These explosions are more intense in the supernova stage. Hence, despite the primordial Universe has had only hydrogen and helium, it has been enriched with other elements that stars have created at their centre and ejected during internal explosions.

The formation of our Solar System makes no exception from the general rule. Initially it has been just a cosmic cloud (or dust) originating from Milky Way galaxy. After attracting matter from surroundings, it began to collapse about 4.6 billion year ago, where only planets formation era lasted for about 100 million years. However, this dust did not contain only hydrogen and helium; it also contained heavier elements ejected from other stars of the galaxy, which now are found in various celestial bodies of the solar system, especially in the first four, which are earthy planets but also in the core of the gaseous ones.

The following set of figures shows how Solar System has been formed. The first figure shows a cosmic cloud (dust) rotating around itself. In the second figure, gravitational force (which prevails over expanding effect of thermal energy) makes the cloud collapse. As a result, more matter gathers at centre of cloud. It eventually forms the Sun in the third figure (at centre), while smaller amounts of solar dust that were more in periphery and could not get into the centre, form the planets revolving in spiral paths (orbits).

Physics Tutorials: This image provides visual information for the physics tutorial Formation of Galaxies and Solar System. Actual Problems

To summarize, the cosmic cloud detached from the rest of Milky Way has collapsed under the effect of its gravity. As a result, the Sun was formed at centre, where most of dust gathered while the other planets were formed by a smaller amount of gas left outside the central part. The Sun has born as a Main Sequence star when thermonucelar reactions of fusion have started to occur at its centre. As for the remaining gas away from this centre, it has condensed due to lower temperatures, resulting therefore in the formation of small celestial objects that were a few hundred meters in dimensions (asteroids). They later attracted each other forming planets and other celestial bodies. There are still today many such small celestial bodies that were not able to form planets, especially between Mars and Jupiter. This set of celestial bodies is known as the Asteroids Belt, we covered this in detail in tutorial 22.1.

The process of asteroids formation in the Solar System has lasted for about 3 millions of years. At a first glance, it looks a long process, but when compared to the age of Milky Way galaxy (13.7 billion years old) the process of the solar system formation was relatively short. In the scientific viewpoint, it helps us describe in detail many phenomena actually occurring in our Solar System. For example, now it is clear why all planets revolve in the same direction around the Sun. This occurs because initially all of them were part of the same cosmic cloud that was revolving as a whole around its centre. In addition, the rotation of the Sun and planets around their own axis is explained well through this model.

Example 1

The actual density of the observable Universe is about 10-27 kg/m3 and its actual radius is 8.8 × 1026 m. At Planck's time, the density of Universe was 1090 kg/m3. What was the radius of Universe at that instant if we assume that actually we are able to observe the entire Universe?

Solution 1

The quantity that has remained constant over time is the mass m of Universe. This helps us compare the other two related quantities: density and volume in the given instants. If we use the index (1) to represent quantities at Planck's time and the index (2) to represent the same quantities now, we have:

m1 = m2
ρ1 ∙ V1 = ρ2 ∙ V2

If we consider the Universe as a sphere of radius R, we have

ρ14/3 ∙ R31 = ρ24/3 ∙ R32
ρ1 ∙ R31 = ρ2 ∙ R32
R31 = ρ2 ∙ R32/ρ1
R1 = ∛ ρ2 ∙ R32/ρ1
= ∛ (10-27 kg/m3 ) ∙ (8.8 × 1026 m)3 )/1090 kg/m3
= 2.06 × 10-13 m

This value is very small; no actual measuring device can detect such a length. Hence, either the Universe is much bigger than we are able to see, or it began from a very small point (or both versions are true).

Actual Problems. Horizon Issue. Inflation Phase

Now, let's conclude the explanation of Big Bang model by discussing some of its actual problematics that are still under observation in order to take a permanent solution. We will begin this part with the horizon issue.

The techniques used in the last century have made possible to detect signals that come from the most remote sections of the observable Universe, billions of light years away from us. From signals coming from remote galaxies, it became clear that physical features, laws and processes in the Universe are the same throughout it. This is true for all directions and distances in which observations are made.

However, the Big Bang theory is insufficient at a certain extent when trying to explain such a perfect order in the Universe. To make this point clear, let's consider the issue of horizon we have dealt with earlier.

We know that it is impossible to see everything on the surface of Earth from a certain position due to its spherical shape. Our eyes can see the light rays that are incident only from a small section determined by the horizon line. (The concept of horizon line is clearer when we are in midst of ocean and the horizon line is visible in all directions. It represents the borderline that separates the ocean and the sky. We also have explained the concept of sky (celestial) horizon in tutorial 22.8.

We can define the horizon of the Universe in the same way. It represents the border that separates the visible Universe and the part of it that extends beyond our actual ability to see or detect signals coming from the remotest galaxies. Thus, since the Universe is about 13.7 billion years old, we can only see or detect EM waves coming from sources that are closer or equal to 13.7 billion light years away from us. This part of Universe is called the Observable Universe.

However, galaxies diverge from each other at lower speeds than the speed of light. This is because gravitational forces acting on the opposite direction to galaxies moving direction. This means the remotest visible galaxies have never been close to our galaxy since we detect signals coming from them. The question that naturally arises at this point is: How it is possible than two objects that have never been in contact with each other manifest share the same characteristics, have the same behaviour and obey the same laws?

Scientists tried to solve this puzzle that obscured the magnificence of the Big Bang theory by introducing the concept of inflation phase, which we will explain through an analogy - the phase change of steam into water.

Thus, when temperature of steam lowers below 373 K (100°C), it must normally turn into water. However, in temperatures lower than that of liquefaction the steam can overcool without turning into water (especially when its degree of purity is very high). As soon as casual fluctuations create water bubbles, they widen at very high speeds, join other similar bubbles and turn the steam into water. The same thing occurs in the Universe as well. Thus, stars are similar to water molecules, galaxies similar to bubbles and so on.

More specifically, the inflation phase in the Universe is believed to have occurred between 10-38 s and 10-30 s after the Big Bang. As we have said earlier, at t = 10-38 s the Universe experienced a symmetry break, where the electroweak and electro-strong interactions separated from each other. This is similar to the phase change from steam to water. At this instant, cosmic bubbles of a new phase began to appear in the cosmos. They enlarged very quickly including a space where much larger regions than those we can observe today were included.

Prior to 10-38 s after the Big Bang, the Universe was chaotic and non-homogenous. The phase change due to this this quick transformation, i.e. through inflation made most heterogeneities disappear and only small fluctuations did remain. They too disappeared with time in the form of cosmic radiation when it separated from matter. We have explained earlier that such fluctuations were responsible for the galaxies formation.

In general terms the inflation phase today is widely accepted as reasonable, but within this context there exist several models that try to explain it scientifically. All these models are still developing and have not obtained yet a definite shape. If one day this is realized, many questions regarding the origin of the Universe will obtain a definitive answer.

Prevalence of Matter over Antimatter

All reliable physical theories support the idea that an equal amount of matter and antimatter were originally produced in the Universe. This means that at the first instants of its existence, the Universe contained same number of positive and negative charges. However, when the process of the number of particles freeze took place at the first second after the Big Bang, a number of extra matter particles survived over antimatter, creating a misbalance between them. This means that since that time there were more particles than antiparticles available; otherwise the entire matter would have disappeared in one-to-one annihilating processes with antimatter. The reason why by the end of the first second of Universe there were more matter than antimatter is still an enigma to be solved.

The most plausible explanation for this issue is the lack of symmetry in weak interaction. Let's explain what this means.

Physical laws are such that if during the occurrence of a phenomenon all the signs of electric charges change (this is called the action C) and we change the direction of occurrence from left to right and vice-versa (the action P), we obtain a new phenomenon which has the same probability of occur to the original phenomenon. Hence, we say these two phenomena possess the CP symmetry. In weak interaction however, this symmetry does not exist, i.e. a phenomenon may occur more often than the reverse one. Using this reasoning, scientists believe that the process of particles formation has had a higher probability than the reverse process of antiparticles formation during the first second of Universe's existence. Hence the difference in number between particles and antiparticles at this instant.

During the annihilation processes of matter and antimatter a very large number of photons were produced. The ratio of photons to matter particles in the Universe is related to the original particles-antiparticles difference at the first second of the Universe. This ratio is about 109:1 (one billion to one). This means that today there are about one billion times more photons than particles of matter in the Universe. All models must reach this conclusion to be considered as successful.

Dark Matter

Studies carried out in the recent years have found that the Universe contains more matter than we can observe in the form of visible light emitted from bright stars. Gravitational force that is responsible for the creation of galaxies does not justify the actual equilibrium of these systems. It is actually much smaller than the force necessary to make galaxies rotate around their centre.

For this reason, scientists have introduced the idea of the existence of an invisible matter, otherwise known as "dark matter", not detectable by our actual devices. It provides the extra gravitational force required for this process. Calculations have found that the amount of this invisible matter is believed to be about 100 times greater than the visible (or detectable) one.

There are several hypothetic versions that try to explain the identity of this dark matter. It probably consists partially of small white dwarfs that are not observable or other extinct celestial bodies. Many not observable of the primordial Universe may partially be part of this dark matter as well. As an example in this regard we can mention neutrinos and antineutrinos detached from matter in the first second of the universe existence. Their number is very large, so they may produce a considerable gravitational effect. The same role is probably played by other primordial particles of the first instants of the Universe.

The amount of dark matter determines whether Universe is open or close. If the amount of dark matter is too large the Universe is closed while if the amount of matter is less than believed, the universe is open. If the universe is closed, it will stop expanding after some time and then, it will start contracting. In this case, everything discussed so far will occur in the reverse way; the Universe will experience a colossal contraction until it reaches very small dimensions similar to those prior to Big Bang. This process is known as the Big Crunch.

On the other hand, if dark matter is less than believed, the Universe will continue expanding at infinity.

Example 2

What is the minimum mass of universe if it is closed? Express the answer in solar masses. The actual mass of observable universe is Mu = 1.5 × 1053 kg and the mass of Sun as about Ms = 2 × 1030 kg.

Solution 2

The condition for a closed universe is that it must be slightly more massive than it actually is However, we take the actual mass of Universe as a lower limit for this condition. Hence, we have

M(in solar masses) = Mu/Ms
= 1.5 × 1053 kg/2 × 1030 kg
= 7.5 × 1022 solar masses

Summary

There are many models that try to explain the process of galaxies formation, but all of them have one thing in common: they rely on the process of increase in matter fluctuation.

Since gravitational force in some denser regions universe is greater, they start collecting matter from the surrounding space. As a result, they become even denser with time at the expense of the surroundings, which on the other hand becomes less and less dense, losing matter continuously until only vacuum is left.

One of the most reliable fluctuation-based models of galaxies formation is that of gradual growth of fluctuations. According to this model, the expansion of Universe favours certain fluctuations while eliminating the others.

There are two variables to be considered when dealing with growth of fluctuation: one is the Universe expansion that brings a decrease in matter density and the other is the gravitational attraction that increases the density. After some time, these opposing effects balance each other. As a result, the new structures created (the gas cloud and its components) detach from the rest of cosmic gas. After this critical moment, the galactic cloud collapses as gravitational force prevails over the expansive effect because the expansion process has already stopped. In this way, the cloud takes an elliptical shape while rotating around itself, which eventually takes a disc shape except the central region. Moreover, a number of smaller fragmentations containing dense matter occur inside this structure that eventually form the stars.

Careful observations of cosmic radiation made in 1990s have confirmed that it is not completely isotropic, as it was previously believed. Its density changes very slightly when measured in various directions. This difference in density is not more than 1/10000.

Initially, Solar System has been just a cosmic cloud (or dust) originating from Milky Way galaxy. After attracting matter from surroundings, it began to collapse about 4.6 billion year ago. However, this dust did not contain only hydrogen and helium; it also contained heavier elements ejected from other stars of the galaxy, which now are found in various celestial bodies of the solar system.

The Big Bang theory is insufficient at a certain extent when trying to explain the perfect order in the Universe. This is because we can only see or detect EM waves coming from sources that are closer or equal to 13.7 billion light years away from us. This part of Universe is called the Observable Universe.

Scientists introduced the concept of inflation phase to explain discrepancies in the Big Bang theory. Inflation phase is believed to have occurred between 10-38 s and 10-30 s after the Big Bang when the Universe experienced a symmetry break, in which the electroweak and electro-strong interactions separated from each other. This is similar to the phase change from steam to water. At this instant, cosmic bubbles of a new phase began to appear in the cosmos. They enlarged very quickly including a space where much larger regions than those we can observe today were included.

At the first instants of its existence, the Universe contained same number of positive and negative charges. However, when the process of the number of particles freeze took place at the first second after the Big Bang, a number of extra matter particles survived over antimatter, creating a misbalance between them. The most plausible explanation for this issue is the lack of symmetry in weak interaction.

During the annihilation processes of matter and antimatter, a very large number of photons were produced. The ratio of photons to matter particles in the Universe is related to the original particles-antiparticles difference at the first second of the Universe. This ratio is about 109:1 (one billion to one). This means that today there are about one billion times more photons than particles of matter in the Universe.

Studies carried out in the recent years have found that the Universe contains more matter than we can observe in the form of visible light emitted from bright stars. This is because the actual gravitational force produced by the visible universe is not sufficient to make the galaxies rotate around themselves. To explain this phenomenon, scientists have introduced the idea of the existence of an invisible matter, otherwise known as "dark matter", not detectable by our actual devices. It provides the extra gravitational force required for this process. Calculations have found that the amount of this invisible matter is believed to be about 100 times greater than the visible (or detectable) one.

The amount of dark matter determines whether Universe is open or close. If the amount of dark matter is too large the Universe is closed while if the amount of matter is less than believed, the universe is open. If the universe is closed, it will stop expanding after some time and then, it will start contracting. On the other hand, if dark matter is less than believed, the Universe will continue expanding at infinity.

Formation of Galaxies and Solar System. Actual Problems Revision Questions

1. What part of the solar system's existence did the process of asteroid formation occupy?

  1. 3/13700
  2. 3/4600
  3. 4600/13700
  4. 100/4600

Correct Answer: B

2. What is the total mass of the observable universe (expressed in solar masses) including the dark matter?

  1. 7.5 × 1022
  2. 7.5 × 1023
  3. 7.5 × 1024
  4. 1.5 × 1053

Correct Answer: C

3. If the Universe is closed and it actually is at half of its expansion process, when the Big Crunch will occur?

  1. After 13.7 billion years
  2. After 27.4 billion years
  3. After 41.1 billion years
  4. After 54.8 billion years

Correct Answer: C

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