PART IV
The Mystery of the Solar Corona.
Errors in the Theory of Stellar Structure.
The Psychology and Causes of Errors in Theoretical Astrophysics.

Chapter 8
The Mystery of the Solar Corona

WHY is the temperature of the Solar Corona (over 2 million K) higher than that of the Photosphere and Chromosphere (4,400 – 20,000 K)?

The solutions to physical mysteries proposed by modern astrophysicists are astonishing. Either contemporary astrophysicists do not know physics, or they fail to understand which laws of physics operate and how they function in physical phenomena and processes. Or, under the pressure of outdated theories and authoritative theorists, they are unable to apply their knowledge of physics to explain physical phenomena, processes, and scientific research.

In this section (article), we will examine the mystery of the solar corona. Through this example, we will see that the enigmas in astrophysics have simple physical explanations—explanations that, unfortunately, elude modern astrophysics educators.

And so, the mystery of the solar corona—or rather, the solution to the mystery of the solar corona.

According to the outdated, yet still prevailing and dominant theory of stellar structure by A. Eddington, thermonuclear fusion occurs in the star’s core. The entire star is heated from its center outward, from the core. In the star’s core, the temperature reaches between 15 million and 40 million Kelvin (according to various astrophysicists).

The errors in this theory are discussed in other sections and articles of “Analytical Astrophysics.”

According to this outdated theory, the temperature of the lower layers of the Sun’s atmosphere should exceed that of the upper layers. In reality, however, the opposite occurs: the lower layers of the Sun’s atmosphere are colder than the upper layers. Let me provide an example—data compiled from various sources:

- The lowest layer of the solar atmosphere is the Photosphere.
The photosphere’s thickness ranges from 100 to 400 km, with temperatures between 4,000 and 6,600 K.

- The Chromosphere lies above the photosphere.
The chromosphere’s thickness ranges from 2,000 to 5,000 km, with temperatures between 4,000 and 20,000 K.

Above the chromosphere lies the Corona.
The corona extends millions of kilometers into space. The temperature of the solar corona reaches between 1 million and 2 million K, and in some places up to 8 million K, and even as high as 20 million K, according to data gathered from various sources.

Why???

One of the physical mysteries of the Sun is: “Why is the temperature of the Corona higher than the temperature of the Sun’s surface (the photosphere and chromosphere)?” — even though the corona should be heated by the chromosphere and photosphere.

The main mystery of astrophysics lies in the absence of real physics in theoretical astrophysics!

Let us examine this mystery of the solar corona from the standpoint of the laws of physics.

The Sun radiates energy into outer space. This energy is emitted in the form of light waves, radio waves, gamma radiation, X-ray radiation, and streams of particles and atomic nuclei.

The Sun, like any other star, is a source of powerful gravity.

Consequently, in order to leave the Sun’s surface, a particle or atomic nucleus must overcome the star’s gravity. That is, particles and atomic nuclei must attain a velocity sufficient to escape the Sun’s surface.

The minimum velocity required to overcome the Sun’s gravity from its surface is the first cosmic velocity, equal to 436.8 km/s. To travel great distances from the star’s surface, particles and atomic nuclei must reach the second cosmic velocity, equal to 617.7 km/s.

A similar physical process occurs in chemical combustion—for example, when a candle or campfire burns. The hottest part of the flame is at its top, even though the chemical combustion itself takes place at the base of the flame, in the region where fuel comes into contact with oxygen. Why is the upper part of the flame hotter than the lower part? The answer is quite simple: the combustion process is influenced by Earth’s gravity. Particles and ions that acquire high temperature, energy, momentum, and velocity during combustion are able to overcome Earth’s gravity and rise to the upper layers of the flame.

An analogous process occurs on the Sun’s surface. Particles and atomic nuclei that achieve high velocities leave the star’s surface. The minimum velocity for escaping the Sun’s surface is the first cosmic velocity of 436.8 km/s. Particles and atomic nuclei attain such velocities through participation in nuclear and thermodynamic processes. These processes occur both inside the star, near its surface, and on its surface. Thus, to overcome the Sun’s gravity and escape its surface, particles and atomic nuclei must reach velocities of 436.8 km/s or higher. By participating in nuclear and thermodynamic processes, particles and atomic nuclei acquire high velocities due to the momentum imparted to them and their heating to extremely high temperatures.

The high velocities of particles and atomic nuclei resulting from momentum gained in nuclear and thermodynamic processes are examined in “Analytical Physics. Analytical Astrophysics.” This analytical study explores the scenario in which particles and atomic nuclei achieve high velocities through heating and exposure to high temperatures.

And so, using the laws of physics and logic, we have understood the physics of the processes leading to the high temperatures of particles and atomic nuclei in the solar corona. The temperature of particles and atomic nuclei comprising the stellar corona is higher than on the Sun's surface because particles with lower energy and temperature cannot escape the Sun's surface. Conversely, particles possessing high energies and temperatures overcome the Sun's gravity and become part of the stellar corona.

For a particle (or atomic nucleus) to be able to leave the Sun's surface, it must acquire kinetic energy during nuclear fusion (or other nuclear reactions). Alternatively, it might be ejected from the star through a "sunspot" following powerful nuclear explosions inside the Sun. Another possibility is achieving high temperature as a result of heating. In the nuclear and thermodynamic processes occurring within a star, a combined scenario is highly probable: acquiring high temperature through thermodynamic processes, supplemented by momentum and additional high temperature from nuclear reactions, as well as through the repeated alternation of such physical processes.

Let us calculate the temperature a particle or atomic nucleus must have to overcome solar gravity and escape the star's surface. In these calculations, we will rely solely on temperature.

Let us assume that the increase in the velocity of a particle (atomic nucleus) due to the kinetic momentum acquired in nuclear and thermodynamic processes is zero (kinetic momentum = 0).

For the calculations, we will adopt certain assumptions. The minimum particle velocity is taken to be 436.8 km/s, corresponding to the first cosmic velocity for the Sun's surface. We will also perform temperature calculations for the second cosmic velocity from the Sun's surface, which is 617.7 km/s.

Particles and atomic nuclei reaching such velocities have a very high probability of escaping the Sun's surface and becoming part of the solar corona and solar wind.

For our calculations, we will use the formulas from the molecular-kinetic theory. Specifically, the equation for the root-mean-square velocity of a molecule is:

V - Velocity of the particle or atomic nucleus;

T - Temperature of the particle or atomic nucleus;

m - Mass of the particle or atomic nucleus;

k - Boltzmann constant.

Since our calculation does not claim engineering precision—much like all calculations in astrophysics—it is reasonable to assume that calculations based on this formula will clarify the range of temperatures required for particles to attain the first and second cosmic velocities from the Sun's surface.

Let us calculate the temperature to which a proton must be heated in order for its velocity to reach 436.8 km/s.

Where

Let us calculate the temperature to which a proton must be heated in order for its velocity to reach 617.7 km/s.

The calculation results for the proton, neutron, alpha particle, lithium nuclei, iron nuclei, and nickel nuclei are presented in Table 8.1.

             (55) TABLE #  8.1

Based on the data from Table 8.1, Graph 8.2 has been plotted. Graph 8.2 illustrates how the temperature required to heat particles or atomic nuclei—in order to impart velocities of 436.8 km/s and 617.7 km/s—varies with changes in particle mass.

(56) Graph 8.2

From the calculations and the graph, it is evident that for a particle to leave the Sun's surface without any kinetic momentum, it must be heated to temperatures of millions of degrees. For a proton and neutron, this ranges from 7.7 million K to 15.4 million K. For an alpha particle, the required temperature ranges from 30.6 million K to 61.2 million K. The heavier the particle, the higher the temperature required for it to escape the Sun's surface.

Consequently, particles with a lower temperature cannot become part of the solar corona unless they have received a kinetic impulse from nuclear and thermodynamic processes. That is, the components of the solar corona and solar wind include:

1. Particles and atomic nuclei that have acquired sufficient kinetic impulse to escape the star's surface;

2. Particles and atomic nuclei heated to temperatures of millions of degrees, enabling them, due to their high temperature, to reach the first and second cosmic velocities needed to escape the Sun's surface;

3. Particles and atomic nuclei that are heated to high temperatures and receive a kinetic impulse from nuclear and thermodynamic processes.

For stars, the third option holds true. By undergoing nuclear and thermodynamic processes, a particle or atomic nucleus inevitably attains both a high temperature and a kinetic impulse.

Therefore, the high temperature of the solar corona can be explained by the (indirect) influence of the Sun's gravity. Solar gravity acts as a kind of filter, preventing the star's energy and mass from leaking away (unproductively) and returning them to the nuclear thermodynamic (productive) process. This ensures the star's long-life cycle of energy production.

Particles and atomic nuclei with lower temperatures, lacking high kinetic energy, cannot overcome the star's gravity and become part of the Solar corona.

When particles receive the same kinetic impulse in nuclear and thermodynamic processes, particles with smaller mass attain the highest velocity.
I= m . v

where  I - is the impulse (momentum) of the particle; m - is the mass of the particle; v - is the velocity of the particle. 

I= Const = m1 . v1 = m2 . v2

If  m1 >m2  then   v1 > v2

Gravity exerts a stronger influence on a particle with greater mass, hindering its escape from the Sun's surface into space.
Light particles and light atomic nuclei have a higher probability of leaving the star's surface than heavier nuclei. This is because, upon receiving a kinetic impulse, the velocity of light particles and light nuclei will be higher than that of heavier nuclei. Furthermore, the temperature to which light particles and atomic nuclei must be heated to achieve high velocities is lower than that required for heavier nuclei. Light particles and light atomic nuclei distribute the received kinetic and thermal energy toward increasing their velocity. Due to these physical properties, when receiving the same amount of energy, the velocities of light nuclei and particles are higher than those of heavier nuclei. The majority of heavier nuclei do not attain sufficient velocity to overcome gravity and escape the Sun's surface. This explains the dominance of light particles—protons, hydrogen nuclei, and helium nuclei—in the composition of the corona and solar wind.

A particle's escape from the star's surface, driven by thermal energy and high temperature, is directly dependent on the mass of the particle (atomic nucleus). The greater the mass of the particle, the higher the temperature it must possess.

That is, the force of a star's gravity creates a filter that restricts the ejection of the star's mass and energy into outer space. The star possesses a gravitational shield-reflector of energy and mass, directed inward toward the star. This gravitational reflector returns mass and energy to the star's energy-producing process. In the design of nuclear reactors, shields (made of graphite and beryllium) are used to reflect neutrons back into the core, which increases the efficiency of the neutrons. The presence of such a gravitational shield-reflector increases the energy and mass efficiency of the star's operation as a nuclear reactor. It enhances the efficiency of the energy and mass expenditure involved in the process of evolution and transformation of matter within the star (and in outer space). The presence of a gravitational energy reflector reduces the effective size and parameters of the star. An increase in the star's mass strengthens its gravity and enhances the properties of this "shield-reflector," returning mass and energy to the star. It is possible that this enhancement of the "shield-reflector" properties fundamentally affects the physics of medium and high-mass stars, accelerating nuclear processes, shortening their lifespans, and leading to supernova explosions (collapse).

The photosphere and chromosphere, acting as a plasma-energy envelope, also perform the function of a shield-reflector, preventing energy and matter from leaving the star. Energy and matter attempting to escape the star's interior, upon colliding with the plasma-energy envelope (the photosphere and chromosphere), are partially reflected back into the star and partially engage in nuclear and thermodynamic reactions within the envelope itself. By participating in these reactions, the energy and matter sustain the existence of the photosphere and chromosphere. Energy and matter from the star that manage to break through the photosphere and chromosphere are partially returned under the influence of the star's gravity and, possibly, other fields. This process of matter returning is clearly observable in the example of prominences. Nuclear explosions of immense power occurring inside the star can breach the star's plasma-energy envelope (photosphere and chromosphere) and, through sunspots, release excess, "accidental" energy into space. In such cases, the non-rigid plasma envelope of the star functions as safety valves.

Such valves are used in the design of thermal boilers. They release thermal energy into the environment, protecting the thermal boiler from destruction. A star is both a nuclear reactor and a thermal boiler, the entire structure of which is composed of nuclear fuel. As an energy-producing object (a structure) operating over a long period, a star, by its very design, requires systems that support, regulate, and functionally ensure its operation. Systems to prevent the star's destruction are also necessary. Its plasma envelope serves as such a system.

What functions does a star's plasma envelope perform?

1.     The casing or shell of the star.

2.     A shield-reflector, directing energy and matter back into the star.

3.     The generator of the star's thermonuclear reaction.

4.     A generator of dynamic waves, thermodynamic, and nuclear processes inside the star.

5.     A mechanism that prevents the star's destruction by releasing critical energy into space through sunspots.

6.     Protection from the kinetic impact of cosmic objects.

7.     Generation of the Corona, Stellar Wind, and Heliosphere of a Star. It creates an environment with favorable conditions for a planetary system. It protects the star and its planetary system from the influence of gas flows in outer space.

Thus, for a particle and an atomic nucleus to leave the surface of the Sun and become part of the star's corona and the solar wind, they must:

1.     Be heated to temperatures above one million Kelvin, as shown in Table # 8.1 (allowances must be made for assumptions and errors in calculations).

2.     Receive an impulse from nuclear synthesis and other nuclear reactions near the Sun's surface. This impulse must be sufficient for the particle and nucleus to escape the star's surface.

3.     The particle and atomic nucleus must be partially heated to a high temperature and additionally gain an impulse from participation in nuclear and thermodynamic reactions and processes.

4.     Become part of the ejected (gas-plasma) mixture through dark spots on the Sun's surface, during powerful nuclear explosions inside the star. These explosions inside the Sun may possibly be explosions both from thermonuclear fusion reactions of light atomic nuclei and from the fission and decay of heavy nuclei.

Particles and atomic nuclei from these four listed options become part of the solar corona, the solar wind, and form the star's heliosphere.

Particles and atomic nuclei that do not fall under these options (according to the current level of knowledge) cannot enter the composition of the solar corona.

Particles and atomic nuclei heated to temperatures of thousands of degrees that do not additionally receive sufficient kinetic impulse return back into the star. We observe this return process during prominence flares.

Matter ejected from the Sun's surface that does not gain sufficient kinetic impulse to escape the star returns to the Sun under the influence of gravity and other fields (magnetic, electric, etc.) and continues to participate in nuclear reactions, in the evolution of stellar matter, and in the processes of outer space.

Solar Prominence
(57) Figure # 8.3

Another enigma explained.

We have identified the options for particles and atomic nuclei to become part of the solar corona and solar wind. In this study, we are interested in particles and atomic nuclei that enter the solar corona by being heated to high temperatures. To what temperature must a particle and an atomic nucleus be heated in order to leave the surface of the Sun using the thermal energy they have acquired?

Of great interest are the cases involving stars of intermediate and high mass. The gravitational field of such stars is much stronger than the Sun's gravity. Does the density of particles and atomic nuclei in the stellar wind and corona change? Will high-velocity particles become part of the stellar wind? After all, for stars of intermediate and high mass, the first and second cosmic velocities must be greater than those of the Sun.

In such cases, several scenarios are possible:

1.     In stars with greater mass. Due to higher energy, the particles in the stellar wind have greater velocities and energy. In this case, the question regarding the size of the heliosphere around the star is of particular interest. Do the dimensions of the heliosphere increase or decrease?

o   The change in the size of a star's heliosphere and the influence of this change on the star's motion through space is an interesting topic worthy of serious investigation and analysis.

2.     As the mass and volume of a star increase, its surface area and energy production (power output) also increase. Volume increases by a cubic function (v ~ R³), while the star's surface area increases by a square function (s ~ R²).

o   What function describes the increase in a star's energy output?

o   What is the relationship between a star's parameters—mass, volume, surface area, and energy output?

o   Does the thickness of the photosphere and chromosphere change? Does the radiation flux from the star's surface, the temperature of the corona, and the velocity of particles and atomic nuclei in the stellar wind change?

There are many interesting questions, the answers to which lie in space.

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