How stars form, function, and evolve

AstroNuclPhysics Nuclear Physics - Astrophysics - Cosmology - Philosophy Gravity, black holes and physics

Chapter 4
4.1. The role of gravity in the formation and evolution of stars
4.2. The final stages of stellar evolution. Gravitational collapse
4.3. Schwarzschild static black holes
4.4. Rotating and electrically charged Kerr-Newman black holes
4.5. The "black hole has no hair" theorem
4.6. Laws of black hole dynamics
4.7. Quantum radiation and thermodynamics of black holes
4.8. Astrophysical significance of black holes
4.9. Total gravitational collapse - the biggest catastrophe in nature

4.1. The role of gravity in the formation and evolution of stars

For centuries, to astronomers observing the night sky, the stars seemed completely unchanging and eternal. They did not change their position *) or brightness (except for rare phenomena such as a nova or supernova flare up). However, a simple physical reasoning - even without knowing the specific nature and structure of the stars - shows that this stability and immutability is only apparent. Stars emit a large amount of light and other radiation (only thanks to this can we observe them at such great distances), thus losing energy, which must necessarily cause certain changes in their interiors - the stars must therefore evolve. Because their energy reserves cannot be unlimited, radiation to the surrounding universe necessarily leads to the depletion of the star's internal energy sources. Thus, the time of active existence of each star is necessarily finite. Only the length of human life (and even the duration of human civilization) is too short to notice any significant changes in the properties of the stars during it. Fortunately, stars formed (and still arise) at different times and evolved at different speeds, so that they have now reached various stages of their evolution. By observing a larger number of "differently old" stars, we can get an idea of the dynamics of stellar evolution.
*) As for the relative position of the stars, it is now also clear that they are not "fixed" - on the contrary, the stars move relative to each other relatively quickly, at speeds of the order of tens of km/s. and higher. This is both a proper peculiar motion with respect to the surrounding stars, as well as drift by the motion of galaxies and the overall expansion of the universe. However, due to the long distances, these movements are not directly visible visually. The relative motions of stars in binary stars and multiple systems are well demonstrable and measurable. The speeds of stellar motion are now determined spectrometrically from the frequency Doppler shifts of spectral lines.
   Thus, stars are not immutable objects - they arise, evolve and perish. The speed of a star's development and its lifespan depends mainly on how intensely it shines. It will be shown below that the radiant power
(and thus the pace of its evolution and the time of active life) depends mainly on the mass of the star. Stars in the universe form, evolve and disappear continuously, they are irreversible events, so it can be expected that the material for the formation of stars and thermonuclear reactions in them will gradually be depleted. The formation of new stars eventually ceases, the last stars go out, the universe plunges into eternal "darkness and cold" (5.6 "The Future of the Universe") ...
Atypical order of interpretation of the origin, properties, composition and evolution of stars
Since our book "Gravity, black holes and the physics of space" is focused on the role of gravity for the functioning and evolution of stars and the entire universe, we adapted to that even the interpretation of stellar astrophysics, which is described in this chapter. First of all, this paper is a brief, mostly at the popular level - it is not a systematic astronomical interpretation. Its aim is to show how gravity and other physical interaction governed by grandiose processes in stars, with the accent on the final stage of life of stars. Therefore, we first outline the "phenomenology" of stars and related astronomical aspects
(HR diagram, structure of stars, variability, multiple systems, planets around stars, etc ....) and only then is the term origin and "Evolution of stars" included, which is then directly continues the the following chapter 4.2 "Final phases of stellar evolution. Gravitational collapse.". The author apologizes if perhaps this atypical sequence of interpretation from an astronomical point of view seems incoherent..?..

Basic essence of stars
Contrary to notions in the distant past, which stars considered to be a kind of glowing "dots", perennials visible in the night sky, we now know that stars are essentially huge spheres of hot gas
(mostly in a plasma state) held together by gravity. Thanks to the high temperature (thousands of degrees) of its surface, the star shines with the bright light that we observe, as well as electromagnetic radiation of longer and shorter wavelengths. The temperature of the star's surface layers determines what wavelengths will predominate in the spectrum, what "color" the emitted radiation will have.
   This radiation is a consequence of the laws of Maxwell's electrodynamics, according to which every uneven (accelerated, decelerated or change of direction) movement of an electric charge emits electromagnetic waves - see 1.5 "Electromagnetic field. Maxwell's equations.", Larmor's formula (1.61 '). It is mainly realised for electrons, that are light and their velocity vector can change easily and abruptly during interactions. At high temperatures, electrons in an ionized gas collide (interact electromagnetically) at high velocities with atoms and ions, while electromagnetic waves with a continuous spectrum are emitted due to abrupt changes in their velocities. Depending on the temperature (ie the speed and intensity of electron collisions) is dominated by either longer-wave infrared radiation, visible light, at very high temperatures, X and gamma radiation are also emitted.
   In addition to the continuous radiation generated by free electrons, weak radiation with a line (discrete) spectrum comes from the stars, resulting in electron jumps between energy levels in excited atoms located in surface layers with a lower temperature in the stellar atmosphere. The emission lines of atoms are mostly over-radiated by continuous radiation, but excitation and deexcitation are manifested mainly by the opposite effect - dark absorption lines on a continuous background
(see the section "Excitation and spectra of atomic radiation" 1.1 in the monograph "Nuclear physics and physics of ionizing radiation") .
   The energy "engine" generating this heat and light of the stars are basically two types of physical processes :
Shrinkage of star material due to gravity - a gravitational contraction, in which the gravitational binding energy is converted by adiabatic compression into the kinetic energy of gas particles, ie into heat. Gravitational contraction is only a secondary, short-term and not very strong source of thermal energy of stars (with the exception of the smallest stars of the brown dwarf type, where it can be the only source of energy). However, gravitational contraction is necessary - it causes the formation of stars and is a necessary condition for realization of thermonuclear reactions.
Thermonuclear reactions - nuclear fusions in which light nuclei of a star's material fuse into heavier nuclei to release large nuclear binding energy of nucleons in the nuclei. This energy intensively heats the interior of the star, from where the heat spreads radiatively and convectively to the surface layers. Most often it is a fusion of hydrogen nuclei - protons - to helium, in massive stars at a more advanced stage of evolution it is also a fusion of heavier nuclei (it is discussed in more detail below in the section "Thermonuclear reactions inside stars"). Thermonuclear reactions are the main and long-term source of energy for the luminosity of stars.
   However, even after the end of the energy-generating processes - thermonuclear reactions or gravitational contractions - some stars can still, due to the huge heat capacity, shine for a long time with the remaining heat accumulated in the previous stages.
   The knowledge that our Sun is also a star, which, due to its proximity, is far more accessible to study, made a decisive contribution to understanding the nature and functioning of stars. Spectral analysis of the radiation of atoms in terrestrial laboratories, light from the Sun and other stars then showed, that the same chemical elements occur everywhere: the world has a unified material nature. The properties of stars and other cosmic objects can thus be studied and explained using physical methods and laws - this is the content of astrophysics.

Hertzsprung-Russell diagram
Great progress in stellar astronomy occurred in the early 20th century in connection with the introduction of astronomical
photometry and spectrometry, which allows to analyze not only the brightness but also the composition of the surface parts of stars and their temperature. In the years 1911-1913, astronomers E.Hertzsprung and H.N.Russel, by processing a large number of observations of stars, found significant patterns between the luminosity and the surface temperature of stars; a graphical representation of this dependence is the well - known Hertzsprung-Russell (HR) diagram. Later it turned out that these regularities are closely related to the evolutionary processes in the stars.

Hertzsprung-Russell (HR) diagram of the relationship between temperature and luminosity of stars
(color redrawing of an earlier black and white sketch) .

The mentioned HR diagram is created by plotting on the horizontal axis the effective surface temperature of the star (derived from its spectrum - the color of the emitted light) and on the vertical axis the luminosity of the star (expressed in multiples of the luminosity of the Sun L). A logarithmic scale is used on both axes - it is a log-log diagram.
Note: For the horizontal temperature axis on the HR diagram, the scale of temperature increase from right to left is used, ie the opposite direction than is usual for other graphs. This peculiarity arose from the fact that the spectral type stars was originally plotted on the horizontal axis (astronomically, stars are divided into 7 main spectral types O, B, A, F, G, K, M, finely divided by numerical indices, eg G2, A1, K5, etc.). In optical spectrometry, the wavelength is plotted from shorter to longer, which is inversely proportional to the temperature of the radiating body or to the energy of the photons.
   The points in this diagram, each representing one particular star (only a few more prominent stars are explicitly plotted in the figure), are not evenly or randomly distributed in the graph, but are grouped predominantly in several banded regions, along three distinct "branches", "succesions" or "sequences" :
Main sequence
The main group of observed stars cluster in the diagram in an almost straight (sigmoid) diagonal band, stretching from the upper left corner (very bright and glowing stars) to the lower right corner (dimmer and cooler stars). This branch, containing the
largest number of known stars (about 90% - almost every star went through the main sequence during its evolution ), is called the main sequence and includes even our Sun (it is a yellow dwarf star of spectral class G). It is true here that the brighter the star, the hotter its surface. The luminosity and temperature are determined by the mass of the star (the radiant power of the star is proportional to the approximately 3th power of the mass) - the main sequence is also the sequence of the masses of the stars. In the lower right of the main sequence, there are dimmer and cooler stars smaller than the Sun - the "red dwarfs", which are the most common types of stars. Even lower and further to the right, already outside the scope of the HR diagram, are the so-called "brown dwarfs", whose mass is not enough to create sufficient temperature and pressure to ignite thermonuclear reactions; by gravity contraction they heat to surface temperatures around a thousand degrees and glow faintly dark red and mainly in the infrared.
l Sequence of giants
Above this diagonal of the main sequence and somewhat to the right are stars that are brighter but have a lower temperature. This means that their dimensions are significantly larger than the luminosity
- corresponding star of the main sequence; these are stellar "giants", respectively red giants, because they usually emit more in the longer-wavelength in red region of the spectrum. These are mostly late stages of stellar evolution (helium combustion) of stars, originally located in the middle of the main sequence. After tens of millions of years, their interior collapses into a white dwarf, or explodes like a supernova to form a neutron star that is no longer part of the HR diagram (4.2).
l Group supergiants
Even higher in HR diagram, there are very bright stars with a large surface, referred to as "supergiants". They are the largest stars we observe in space, with a diameter of up to 109 km. And also the brightest, up to a million times brighter than the Sun. Some radiate spectrally, especially in the red region, others in the blue region (according to the stage of their evolution). These are very massive stars (tens of M, originally located in the upper left of the main sequence), which are in the late stages of evolution, burning carbon. After several million years, they explode like supernovae, the most massive then gravitationally collapse into a black hole and thus leaving the HR diagram (4.2).
l Sequence of white dwarfs
Below the diagonal of the main sequence is a group of stars that have a high surface temperature but relatively low luminosity. As a result, they have a very small surface - they are called "
white dwarfs". These are the final stages of stars with a lower mass (<1.4 M) after the depletion of all nuclear fuel, which are gravitationally compressed to an average of only a few thousand kilometers (similar in size to the Earth but mass to the Sun). Nuclear reactions no longer take place in them (or except for short episodes of thermonuclear fusion of accretion-absorbing matter).
   HR diagram showing significant regularities  in the great variety of sizes, luminosities, and spectral types of stars, it brings order to the "zoology" of stars *) and is of great importance for elucidating the structure and evolution of stars. To understand this, however, nuclear astrophysics had to develop, leading to the recognition that the source of energy inside stars is the nuclear fusion of light elements into heavier elements.
*) The HR diagram has a similar systematizing significance for stellar astronomy as the Mendeleev's periodic table of elements for chemistry. The periodic table groups chemically similar elements, the HR diagram groups into sequences those stars that are currently going through a similar stage of their evolution. At the time of the creation of the Periodic Table, neither Mendeleev nor the other chemists knew anything about the structure of the atoms on which the periodicity of the properties of the elements is based. Similarly, Hertzsprung, Russel, and other astronomers who, based on empirical observations, compiled the first tables and diagrams of stars according to spectral colors and luminosities, did not know why stars shine or how stars form, evolve, and disappear. Nor did they know that the stars gave rise to most of the elements that make up the planets, the Earth, and our organisms, and that are systematized in Mendeleev's periodic table. The HR diagram significantly contributed to the discovery of all this, in co-production with laboratory knowledge of atomic and nuclear physics.
   It should be noted that significant selection effects are applied when compiling the HR diagram. This is a sample of relatively close and brighter stars, as it is difficult to accurately measure the spectrum of distant and less bright stars. In terms of time, the HR diagram captures a kind of "snapshot" of the current state of the surrounding stars; this condition occurs over longer time scales (> 106 -109 years) varies significantly (as mentioned above and will be discussed in more detail below). In particular, the stars go through the stage of giants and super giants relatively quickly; according to astronomical observations in our galaxy, the 10 million stars of the main sequence account for about 1 million white dwarfs, about 1,000 giants, and just 1 supergiant. Nevertheless, even this sample of stars in the HR diagram is sufficiently representative for the analysis of the properties and evolution of stars.
Evolution of stars in the HR diagram

HR diagram
, that captures the current static "snapshot" representation of each type of stars, seen in the light of the dynamics of stellar evolution "come alive" : the position of each star in the HR diagram is not fixed and unchanging, but only temporary. It changes over time as it evolves surface temperature of stars and their luminosity - stars shift in the HR diagram. For a long time (about 90% of their lives), the stars remain in one place in the main sequence, but then move from the main branch to the giant region and eventually, after depletion of "nuclear fuel", become white dwarfs or even more "exotic" compacts formations, that are no longer captured in the HR diagram.
   Stars are formed by the gravitational shrinkage of large gas-dust clouds in space. Pressure and temperature rise inside them, such a formation is called a protostar. When the temperature inside the interior reaches about 10 million degrees, thermonuclear fusion of hydrogen nuclei (protons) to helium nuclei begins to take place (for more details, see "Star formation" below). With the released nuclear energy, the star born in this way shines for a long time on the main sequences in the HR diagram. As we will see below, the primary and decisive variable for the properties and course of evolution of a star is its initial mass, which is already established when the star formed from the germinal cloud. The greater this mass, the brighter and hotter the star, and the faster its evolution. The final fate of a star is then determined by the remaining mass M' at the end of its evolution (ie the initial mass minus the mass of all matter, particles and radiation that the star ejected during its evolution), after exhaustion of thermonuclear reactions.
If the initial weight is very small , only of the order of hundredths mass of the Sun M, then so-called "brown dwarf" is formed, whose mass is not enough to create sufficient temperature and pressure to ignite the thermonuclear reactions of hydrogen combustion (for a short time only a small amount of deuterium and lithium can be burned). The brown dwarf is not a star in the true sense, because there are no thermonuclear fusions, it glows faintly in the red and infrared fields due to gravitational contraction.
Stars of small masses - from a few tenths to about 1.4 M - live a very long time , more than 10 billion years ago, on the main sequence of the HR diagram (bottom right), where thermonuclear fusion "burns" hydrogen to helium. Towards the end of its evolution, after depletion of the hydrogen inside, the star begins to shrink under its own gravity, causing the temperature to rise, and further thermonuclear fusions of helium-to-carbon combustion ignite inside. The star expands significantly: the outer layers "inflate" and cool - these stars move from the main sequence to a group of red giants, where thanks to the large surface it shines with significantly higher intensity. After the depletion of helium, there is another contraction of the star's core (and possibly other thermonuclear fusions), but due to the low mass, other nuclear reactions can not continue intensively enough, the energy flow stops and the star begins to shrink gravitationally. Eventually, all of the star's mass collapses into a compact structure just a few thousand kilometers in diameter with a very high density and temperature - a white dwarf is formed. A large supply of thermal energy (originating from earlier thermonuclear reactions and gravitational contraction) is collected inside it, which radiates only very slowly due to the small surface area. Therefore, the white dwarf can shine even without ongoing nuclear reactions for hundreds of billions of years. It is only after this very long time that it gradually cools down and becomes a black dwarf (it moves below the lower right edge of the diagram).
The possibility of a white dwarf thermonuclear explosion (type Ia supernova) is discussed in 4.2, passage "Supernova explosion. Thermonuclear explosion. Core collapse.".
Medium-mass stars - from 1.4 to about 10 M - burn hydrogen faster and their life on the main sequence (they are from the middle left) is shorter, in the order of hundreds of millions or a few billion years. As in the previous case, after the depletion of hydrogen, the star's interior shrinks and helium is burned there, while the outer layers open and the star moves from the main sequence to the giant region. After the consumption of helium due to the large mass of the star during gravitational contraction, such high temperatures and pressures arise in its core that other nuclear reactions take place - burning of carbon, oxygen, nitrogen, ... up to iron. At the same time, the star further increases its dimensions and luminosity - in the HR diagram, it enters the realm of giants. After all the thermonuclear fuel has been depleted, the star begins to collapse unstoppably by gravity. In gravitational collapse and specific gravitational-nuclear reactions (injection of electrons into nuclei -> neutronization, see 4.2, section "Supernova explosion. Neutron stars. Pulsars.") a huge amount of energy is suddenly released inside the star, which scatters the outer parts of the star during a gigantic supernova explosion. This supernova (lying beyond the boundaries of the HR diagram - above the upper edge) glows with the intensity of many millions of Suns for several days to weeks. After radiating enormous energy for several months, its core remains in place of its original star, collapsed into a compact formation of only a few kilometers in diameter and an unimaginable density of the order of 1014 g/cm3, composed mainly of neutrons - a neutron star; due to its slight luminosity, it leaves the HR diagram below the lower edge.
Very massive stars - tens of M - have a rapid evolution, remaining on the main sequence (in its upper left part) of the order of 100 million years, the most massive even shorter. They go quickly through the stage of giants, and after consuming nuclear fuel and exploding a supernova, they completely collapse into a black hole with zero luminosity *), which is also not part of the HR diagram (well below the lower edge).
*) Zero luminosity refers to the black hole itself (excluding the Hawking effect of quantum radiation), not to the accretion disk around the black hole, which in turn can radiate strongly, including intense jets (see 4.8).

   We have sketched various scenarios of stellar evolution here only preliminary and mostly phenomenologically, in connection with the HR diagram. A more detailed analysis from an astrophysical point of view will be given below in this 4.1 (section "Evolution of stars") and further in 4.2 and 4.3.

"Chemical" composition of stars
According to current astrophysics, all astronomically observed stars (including our Sun) are huge gas spheres held together by their own gravity. From an energetic point of view, they function as gigantic
thermonuclear reactors, which in their interior "burn" lighter atomic nuclei into heavier nuclei by thermonuclear fusion - especially hydrogen to helium (as described in more detail below). The energy released is a source of the radiant power of stars, whereas as a "by-product" they create heavier elements from lighter elements (the relevant processes of nuclear fusion, energy release and production of heavier elements are described in more detail below).
   Most current stars (main sequences) have the following "chemical" composition on average *): 83% hydrogen, 15% helium, 8% oxygen, 3% carbon, 1.5% iron, 1.3% neon, 0.9% nitrogen, 0.7% silicon, 0.5% sulfur, ... + lower concentrations of other elements ... (it is graphically shown in detail below in the picture "Elements-represented " in the passage "Planets around stars").
*) We cannot talk about chemical composition in the usual sense! There are no atoms in the fully ionized hot plasma that makes up stars, and therefore no chemical reactions can occur (that's why we put the word chemical in quotation marks); only nuclear reactions occur. Only nuclei, or nuclides of potential chemical elements are present here, and the free electrons. Atoms occur only in surface parts, in the stellar "atmosphere".
   This "chemical" composition of current stars was established in the distant past as a result of two types of astrophysical processes :
Primordial cosmological nucleosynthesis in the early stages of space evolution - in the Lepton era, when about 75% hydrogen and 25% helium were established (analyzed in more detail in 5.4, section "Lepton era. Initial nucleosynthesis"). After cooling and the formation of the relevant atoms in the era of substance from the gas clouds of this composition, the first stars were formed by the gravitational contraction. The stars of the first generation consisted only of hydrogen and helium (if we omit trace amounts of primordial nuclides deuterium, lithium, beryllium).
  Stellar nucleosynthesis in earlier generations of stars, which synthesized heavier elements and enriched gas dust clouds with them during the explosion of supernovae, from which later stars formed (the current stars are mostly 3rd generation).
   The "chemical" composition of stars is not constant, but changes during the evolution of the star. The younger the star, the higher the proportion of hydrogen, while the older stars have a higher proportion of helium and other heavier elements - this is a consequence of the ongoing stellar nucleosynthesis. The composition of the stars also depends on the overall evolution of the universe. The first stars were made only of hydrogen and helium, while in the distant future (tens and hundreds of billions of years) higher generation stars will form with a larger proportion of heavier elements - greater "metallicity"
(discussed in more detail below).

Rotating disks - typical formations in the universe
Before we begin to deal with the formation, properties and evolution of stars, we will briefly mention some common features of the distribution of matter in the universe. One of the most common shapes in which the observed matter in the universe is concentrated are flattened disk-shaped or "pancake-shaped" shapes in a variety of sizes. A more detailed analysis shows that these are
rotating disks composed of gas, dust and larger bodies - stars, planets. In space, we observe several types of rotating disks, differing in their nature and size :
Small disks around planets, such as Saturn's rings.
Protoplanetary disks around young stars, from whose gas and dust the planets condense. Even our solar system was probably born of a rotating disk (see "Planets around stars" below).
Accretion disks around stars and compact objects, in which the captured material orbits a gravitational body and slowly descends to its surface in a spiral motion resembling a vortex. In the inner parts of the disk (according to Keppler's laws) the circulation period of the material is shorter than in more distant areas. This creates "shear" friction, which slows down the faster circulating inner regions and, conversely, accelerates the slower circulating outer regions - the angular momentum is transmitted from the inner to the outer regions. The retarded material in the inner areas therefore loses the centrifugal force acting against gravity and falls further inwards. The result is a gradual spiral movement of the circulating mass towards the central body. Shear friction converts some of the energy into heat, so the disk material can heat up to high temperatures and emit large amounts of visible, UV and X-rays. Accretion disks form also in some binary stars, where gas escapes from one component, which captures the gravity of the other star and creates a rotating disk around it. Massive accretion disks exist around supermassive black holes in the centers of galaxies, where they emit a colossal amount of energy like quasars (see 4.8, section "Accretion disks around black holes").
The largest disks are spiral galaxies, which usually have a diameter of more than 100,000 light-years (see 5.4, section "Structure and evolution of galaxies").
Disks are formed by the co-production of two opposing forces :

Gravity, trying to shrink matter towards the center or center of gravity of the system ;
Centrifugal force arising from the rotation of the system, with the interaction of the law of conservation of the angular momentum.
   At the beginning is a cloud of interstellar gas, which slowly rotates *) and shrinks under the influence of its own gravity. Due to the law of conservation of angular momentum, gravitational shrinkage accelerates the rotation of the cloud ("pirouette" effect), which takes on an elliptical shape. In the "equatorial" plane, the centrifugal force of rotation begins to balance the attractive effect of gravity, so that the gas then moves inwardly more and more slowly. The material distributed along the axis of rotation (above and below the equatorial plane) falls inwards, vertically to the equatorial plane, much faster. The gravitational shrinkage of a rotating cloud is therefore asymmetric: it is slower in the equatorial plane, faster shrinkage occurs in the perpendicular direction of the axis of rotation. Over time, most of the cloud material "falls" into the equatorial plane, where the rotational centrifugal force will already hold it against the effect of gravity. The resulting formation is a rotating disk whose stability is maintained by a balance between gravity and the centrifugal force of rotation.
*) Origin of rotation in universe
Almost everything rotates in space at different levels. Rotational motion generally occurs when a force acts in a direction other than the velocity vector of the moving body, e.g., perpendicular to the direction of velocity. In space formations, this situation occurs during their mutual movement and "collision", which is usually not exactly central, but with a certain impact parameter - a non-zero (and usually quite large) angular momentum. The gravitational forces acting perpendicular to the movement then curve the paths of these formations into a circular or spiral motion. The resulting rotary motion then persists due to the law of conservation of angular momentum. In gas clouds, vortex rotational motion arises during movement and due to the mutual electromagnetic interactions of gas particles, during which the particles exchange small amounts of energy, momentum and angular momentum. If a sufficiently large velocity gradient ("shear") occurs due to friction, the gas flow becomes turbulent and the resulting rotational motion is maintained with inertia (the law of conservation of angular momentum).

Measures of distances of space objects - a basic condition of astrophysics
Determining the distances of space objects is a basic condition of objective astrophysics research. The intensity of the observed radiation from stars and other radiant objects decreases with the square of the distance
(this applies to distances large compared to the dimensions of the source, which is always met when observing distant objects in space). The star may appear bright to us *) either because it is relatively close (even at low radiant power), or it can be far away, but it has a high radiant power - luminosity. Similarly for other objects.
*) In observational astronomy, the brightness of stars is expressed by a photometric quantity called stellar magnitude or stellar "size". It is apparent brightness of a star (or other luminous object) in the sky, the perceived when observing eye or a telescope. Qualitatively was introduced in antiquity (6 groups of 1.-6. magnitude stars), in the 18th century logarithmic Pogson quantification was introduced for magnitude. According to her, the difference in brightness of 1 mag. corresponds to a brightness ratio of 2.5: 1. The logarithmic scale was chosen on the basis of psychophysical knowledge that if the light or sound stimuli acting on our senses change by a geometric series, we subjectively perceive their changes only by an arithmetic series. From the historical reasons, higher magnitude means lower star brightness. Of course, the stellar magnitude ("size") has nothing to do with the size of the stars and usually even not with their true brightness (radiant power). In addition to its true luminosity, the observed brightness of the star is also affected by its distance from the Earth. Therefore, distance normalization is performed to compare the actual brightnesses of the stars - the so-called absolute stellar magnitude is introduced. It's the magnitude a star would have if it were 10 parsecs away. The absolute stellar magnitude depends only on the actual luminosity of the star. We do not use magnitude in our (astro) physical materials, we express the luminosity of stars either in absolute radiant power, or in multiples of the luminosity of the Sun L.
 "Ladder" of astronomical distances
The cardinal problem of astronomy and astrophysics of the distant universe is the correct determination of distances of stars, nebulae, star clusters, galaxies and other objects. Only in this way can we determine the radiant powers of these objects, which makes it possible to analyze the physical mechanisms that lead to such energy powers. Distances in outer space are often determined by a relatively, careful comparison of the luminosities of stars of a certain type in our galaxy (the distance of which we more or less know) and similar stars in other galaxies
(the luminosity method ). We then extrapolate this method to compare the brightness of closer and more distant galaxies. Previously, these results were often burdened with considerable inaccuracy. Contemporary astronomy has at is disposal four basix (+ one auxiliary) interconnected methods for measuring the distances of space objects :
The trigonometric method - parallax - is based on a change in the angle of view (position in the sky), under which the object is observed from two different places of known distance. For nearby objects (such as planets in the solar system), it is sufficient to measure angles from two different places on the earth's surface. For astronomical trigonometry, however, the Earth's orbit around the Sun is used: the so-called annual parallax is measured - the change in the angle (position in the sky) of a given object at two opposite points in the Earth's orbit. This method only works for relatively close objects. The distances of a number of stars in our Galaxy were thus measured relatively reliably. However, for more distant objects, the changes in viewing angle are immeasurably small and the trigonometric method no longer works.
Luminosity method is based on the above basic law that the intensity I of the observed radiation from stars and other radiating objects decreases with the square of the distance r : I = L/4p r2, where L is the absolute luminosity of the star. The stars of the same spectral class have the same or close mass M and luminosity L; more precisely, it is determined from the HR diagram. Thus, if we compare the observed relative brightness of a more distant star with the brightness of a closer star of the same spectral class (whose distance is known, for example, from the trigonometric method), we can determine the unknown distance of the star under investigation based on the law of inverted squares. This method is applicable up to distances of about 200 thousand light-years (it is difficult to measure spectra with more distant stars).
Pulsating variable stars of type d Ceph, called cepheids, have become an important tool for measuring the distances of very distant objects (they are described below in the section "Variable stars"). As early as 1912, the American astronomer H.Leavitt noticed a remarkable relationship between the absolute luminosity (radiant power) of these stars and the period of their variability. Cepheids can thus serve as "standard candles", the actual radiant power of which can be determined from a period of variability. From the ratio of the actual and photometrically observed luminosity of the Cepheids, it is then possible to determine their distances - and thus the distance of the star cluster or galaxy of which these Cepheids are a part. Using Cepheids, galaxy distances up to about 100 million light-years can be measured (in more distant galaxies, Cepheids are no longer distinguishable).
The relationship between the mass-luminosity of galaxies and the speed of their rotation
The more mass a galaxy has - the more stars it contains and therefore has a higher luminosity, the
faster it must rotate to balance its attractive gravity by centrifugal force. The speed of a galaxy's rotation can be measured by the Doppler broadening of the spectral lines. This makes it possible to determine the absolute luminosity of the galaxy according to the empirical so-called Tully-Fisher relation (5.4, section "Forming the large-scale structure of the universe", passage "Structure and evolution of galaxies"); we then compare it luminositically with the observed brightness ("star size") of the galaxy, thus obtaining the resulting distance of the galaxy.
Type Ia supernovae
For the greatest distances of many billions of light-years, where Cepheids are no longer observable, stronger sources can be used, which are a special type of supernova Ia.
A type Ia supernova is formed in a close binary star from a giant star and a white dwarf, where matter overflows from the giant to the white dwarf. This leads to a gradual accumulation of matter, until the white dwarf eventually exceeds the Chandrasekhar stability limit (1.44 M), it gravitationally collapses and thermonuclear explodes, which manifests itself as a supernova explosion (discussed in 4.2., Passage "Supernova types and their astronomical classification"). Because the mass to Chandrasekhar limit increases gradually between, the initial mass of the collapse and therefore the amount of energy released - absolute magnitude- is practically the same in each case, so that the distance of such a type Ia supernova can be determined (by the luminosity method) from the relative observed brightness. Supernovae Ia can therefore serve as a kind of "standard candle", replacing Cepheids in extragalactic astronomy; they allow the measurement of large intergalactic and cosmological distances of the order of billions of light-years.
The advantage of supernovae Ia is the high accuracy given by the same mechanism of reaching the Chandrasekhar mass limit. However, for the longest distances
(corresponding to a universe less than about 5 billion years old) , these supernovae are scarce, are weak, rarely explode and may not be observable. However, another path to even greater distances appears :
The only observable objects in the outermost universe are the quasars - giant black holes at the center of galaxies, which in a large accretion disk absorb large amounts of rurrounding gas, part of which is ejected along the rotation axis in the massive jets (sprays) - see 4.8 passage "
Thick accretion disks .Quasars". The absolute magnitude (actual radiant power) of quasars is different, it depends on the mass and rotational angular momentum of the black hole and especially on the amount of absorbed gas - accretion flow. However, it turns out that this absolute magnitude is related to the emission spectrum of the quasar, especially to the ratio of radiation in the ultraviolet and X-ray fields. At present, these spectrometric measurements are performed on a number of quasars of different distances, which will make it possible to determine the calibration dependence between the spectrum and the absolute magnitude of the quasar. It will then be possible to use quasars as "standard candles" for measuring the greatest cosmological distances (4.8, passage "Quasars as standard candles") .
Fluctuation of homogeneity of relic microwave radiation in correlation with large-scale distribution of galaxies
In the relict microwave background, small inhomogeneities (anisotropy) originating from the end of the radiation era are observed. During the long-term expansion of the universe, these small inhomogeneities spread over long distances (.......), where they stimulated the formation of galaxies. From a cosmological point of view, it is interesting to compare - correlate - the distribution of small structures at the time of recombination, observed by CMB fluctuations, with the current astronomical observations of large-scale clustering of galaxies
(large sky surveys with statistical evaluation). It would help to better analyze the dynamics of the expansion of the universe throughout its long existence.
Hubble's law of redshift .
To determine the distance of the farthest objects, the measurement of the red spectral shift
z according to Hubble's law (5.2) is also used - see 5.1, section "Dynamically expanding universe". Hubble's law was established on the basis of the analysis of cepheids in distant galaxies, it is in a way an extrapolation of cepheid method. However, this method depends on the dynamics of cosmological expansion, on the cosmological model.
   These interconnected methods represent a kind of degrees or "rungs" on the imaginary "ladder" of cosmic distances. Reliable direct measurements of nearby objects are extended outward using "standard candles" such as Cepheid variables and type Ia supernovae, up to cosmological scales. The use of the ladder of cosmic distances consists in "stitching" different cosmic scales with careful elimination of uncertainties in the places where the different "rungs" of the ladder join. Today's advanced astronomical observation - measuring - methods have greatly refined the scale of cosmic distances. More than 1700 Ia supernovae are already available, the calibration of supernova light curves and the measurement of their redshifts have been improved... All measurements agree very well, the uncertainties in the various measurements on the distance ladders are around 1%.
   All the above methods determine the distance of the examined object at the time when the observed radiation was emitted by its source. For very distant objects (>106 light years) may be - due to the cosmological expansion of the universe - their current distance (where the object is today) much greater. It should also be noted that the light beam was emitted a long time ago, and during its long journey to us, space "stretched out" to him (cf. again 5.1, section "Dynamically expanding universe").
A certain additional method of determining the distance of some radio astronomical sources may, in certain circumstances, be the analysis of the Faraday rotation of the polarization planes of the received electromagnetic waves (1.1, section "Electromagnetic radiation - the basic source of information about space", passage "Faraday rotation of the polarization planes").
Gravitational waves - "standard siren"
This is a new prospective way of determining the distances of neutron stars. The detection of gravitational waves from the fusion of neutron stars
(4.8, passage "Collision and fusion of neutron stars"), together with the simultaneous detection of electromagnetic radiation from their optical counterparts, also has astrophysical-cosmological significance for the independent determination of the distance of the respective objects. This measurement makes it possible to combine the determination of the distance to the source derived from the gravitational wave analysis, with the receding velocity derived from the redshift measurement using electromagnetic signal spectrometry. This approach not requires the use of a cosmic distance "ladder" (discussed above). The analysis of gravitational + electromagnetic waves can thus be a measurement of the direct determination of the relationship distance <--> luminosity in cosmological scales, without the use of intermediate distances, with sometimes problematic continuity. Gravitational wave detection is therefore sometimes metaphorically referred to as a "standard siren" - a gravitational-wave analogue of the electromagnetic "standard candle" (Cepheids, Ia supernovae) used to determine large cosmological distances...
   Objective determination of the distances of the outermost cosmic objects is of cardinal importance, especially in cosmology (will be discussed primarily in 5.4 "Standard Cosmological Model. The Big Bang. Shaping the Structure of the Universe." and 5.5 "The Future of the Universe. Arrow of Time. Hidden Matter. Dark energy.") . In the passage "How fast is the universe expanding? - accurate measurement of the Hubble constant" 5.4, we outline different methods of measuring the Hubble cosmological constant of the expansion of the universe.

Age of objects in universe
Different objects in the universe (stars, planetary systems, galaxies) have gradually formed over time and evolved at different speeds, they have very different ages (for our human scales, in any case, unimaginably large!). The age of our planet Earth and the Solar system has been determined with high accuracy ( 1%) to 4.56 billion years - using radiometric dating by radioactive decay of long-lived radionuclides, especially uranium 238U -> ......--> 206Pb per stable lead. It is discussed in detail in 1.4 "Radionuclides", passage "Radioisotope (radiometric) dating" in monograph "Nuclear physics and physics of ionizing radiation".
   Remote space objects are not available for direct laboratory investigation, their age is assessed on the basis of spectrometric analysis of emitted radiation using astronomical methods.
   To estimate the age of stars, it is important to determine their mass. Below in the section "Evolution of stars" we will see that it is the mass of a star that determines the speed of its evolution. Massive stars have more pressure in their nuclei, which causes significantly faster thermonuclear combustion of hydrogen. The most massive stars live only a few million years, while stars with minimal mass - red dwarfs - burn their fuel very slowly and can live for tens or hundreds of billions of years.
By spectrometric measurement (determination of the spectral class) we find out the approximate position of the star in the H-R diagram and thus the stage of its evolution. The age of a large number of stars in star clusters is most often determined. The age of most stars is on the order of 1 - 12 billion years (but several stars with an estimated age of more than 13.2 billion years are known). However, new stars are still forming (104-107 years old) - protostars are observed in dense nebulae.
   The age of galaxies is the time before these large stellar systems formed into the currently observed structure (it may not directly correspond to the age of their stellar populations). We basically estimate the age of the galaxy by determining its distance from us by measuring the Hubble redshift z of the spectrum of the emitted radiation. The color of the stars in the galaxy can also be an indicator of the age of the galaxy, reddish stars indicate greater age (the age of elliptical galaxies is estimated at 7-10 billion years).
   The age of most galaxies is estimated to be in the range of about 10-13 billion years. Thus, most galaxies formed relatively soon after the universe formed. So far, the oldest and most distant astronomically observed galaxy is GN-Z11 - a small irregular galaxy (weighing about 1% of our Milky Way) with a spectrometric redshift of z = 11.1, which corresponds to 13.4 billion years, just 400 million years after the Big Bang.
   However, "young" galaxies, which were formed about 500 million years ago, have also been observed rarely. Galaxies in space are probably created (gradually forming) even now, althout much slower rate than in the early universe. In addition, there are interactions and "collisions" of galaxies, which can develop into new galaxies, whose "age" is debatable...
   The mechanisms of galaxy and galaxy clusters formation in the material era are discussed in more detail in 5.4, section "Formation of the large-scale structure of the universe" and "Structure and evolution of galaxies".
   The age of the whole universe is determined by two methods :
- Analysis of the observed dynamics of the expansion of the universe (galaxy distances, redshift) and its back extrapolation to the initial time t = 0 (5.3 "Friedman's dynamic models of the universe").
- Detailed study of microwave relic radiation, including minor local inhomogeneities (5.4, section "Microwave relic radiation - a unique messenger of early space news").
Within the standard LDCM cosmological model, these methods have determined the age of the universe to be 13.8 billion years. It is comprehensively discussed in 5.4 "Standard Cosmological Model. The Big Bang. Shaping the Structure of the Universe.".

Stars formation
According to current astrophysic
al knowledge, stars are formed by gravitational contraction in large gas-dust clouds of "interstellar" *) substances. The substance in these gigantic formations (weighing on the order of 105 M and measuring dozens of parsecs), consisting mainly of hydrogen and 25% helium, is very sparse, but has a complex inhomogeneous structure and turbulent motions. In order for gravitational contraction to occur, this gas must be cold enough, otherwise the kinetic energy of the thermal motion of the atoms would predominate over the originally weak gravity and contraction would not occur (hot gas tends to expand...).
*) The quotation marks next to the word "interstellar" are because it refers to a situation where there are already some stars in space; so it is now. In the early stages of substances era, however, the first stars were only formed from gas-dust nebulae - in "free space"... The basic chemical composition of substances was formed during primordial cosmological nukleogenesis - is analyzed in more detail in 5.4, part "
Lepton era. Initial nucleosynthesis".
   If the dynamic balance between some inhomogeneities and the environment is more significantly disturbed, gravitational instability may occur in cold gas, leading to the given part of the cloud starting to shrink by its own gravity (one of the causes of the formation of a gravitationally unstable cloud can sometimes be the pressure of radiation from suitably distributed surrounding stars, or from a supernova explosion). There are a larger number of such areas of gravitational instability in the original cloud, young stars are almost always observed in groups.

In a shrinking cloud the districts can form, in which gravitational contractions occur faster than in the surroundings (gravitational instabilities). From these individual districts, protostars are formed and finally stars, which usually form in groups.

The initial phase of gravitational contraction is actually a gravitational collapse, ie a process in which the gravitational force completely prevails over all other forces and drives the individual particles to move almost in free fall towards the center of gravity. If there were no obstacles, the cloud would collapse completely by gravity theoretically to a point - singularity. However, during the gravitational contraction of this cloud ("protostar"), lasting about units up to tens of millions of years, its density, pressure and temperature constantly increase inside it (adiabatic compression), which gradually slows down the collapse and turns into a slower contraction. This stage, in which the contracting cloud is already shining predominantly in the infrared, is referred to as protostar.
   When the germinal cloud shrinks, the potential binding gravitational energy Ep of the cloud mass is released. For gravitational binding energy ball body mass M and the radius R we are in the introductory part 2.8 "Specific features of gravitational energy" derived relationship
                             E p = [ G . M 2 / R ] . f ,
where the coefficient f depends on the distribution of the density of the substance in the body; in most cases it is close to 1. Numerically therefore is Ep 7.1041.M2/R [Joule]. When shrinkage of the cloud (protostars) with a speed dR/dt releases energy power output
                             - d E p / dt = - 1/2 [ G . M 2 / R ] . dR / dt ,
which initially changes to the increasing kinetic energy of the particles of collapsing gas and dust, later as the density increases
, with particle collisions it changes into thermal energy. The rate of contraction is largely determined by the efficiency with which the protostar radiates energy generated by the shrinkage of gas-dust material. In the initial stages, the outer layers of the cloud are transparent and the radiation outwards is almost perfect, the contraction takes place quickly and undisturbed. As the radius decreases, the density of not only the inner but also the outer layers increases, the opacity of the material increases, the radiation from the inner parts becomes more difficult to reach the surface, the internal temperature increases; contraction with resulting thermal back pressure slows down. In this phase, the solid dust particles also evaporate and then the gas atoms are ionized, the inner parts are formed by a hot plasma .
   About half of the released binding gravitational energy GM
2/R is converted into heat warming the interior of the protostar (in the kinetic energy of the motion of ions and electrons), the other half of the gravitational energy is electromagnetically radiated into the surrounding space as photons. This distribution of 1/2 1/2 gravitational energy between star particles and photons emitted into interstellar space is related to the virial theorem in classical mechanics, according to which the sum of potential energy and twice the kinetic energy of a stationary system of bodies is zero (1.2, passage "The distribution of kinetic and potential energy. virial theorem"). Thermal radiation outwards is a necessary condition for the continuation of the gravitational contraction, in which the originally cold cloud of the protostar in its interior is heated to temperatures of up to millions of degrees, at which thermonuclear reactions can ignite.
   Gravitational binding energy - gravitational contraction - is a source of radiant energy of stars only for very short periods compared to the time of active "life" of the star (except for the smallest stars of the brown dwarf type, where gravitational contraction may be the only source of energy). This is especially in the early stages of protostar contraction, before the ignition of thermonuclear reactions. And then again in the final stages of star evolution, when after depletion of thermonuclear "fuel" contractions of the star's core occur due to gravity, or even a massive gravitational collapse may occur (as described in 4.2 "Final Stages of Stellar Evolution. Gravitational Collapse.").
The scenario of star formation is outlined here only in the roughest features. Due to the rotation of the germinal cloud, for example, a number of fragmentations can occur ("excess" rotational angular momentum thus passes to the orbital motion of the fragments) and subsequent collapses or contractions of these fragments - multiple systems are formed. Turbulence in the germinal cloud can lead to similar effects. However, details of this kind are beyond the scope of this book. We will also not deal with the classifications of star classes and special types of stars - this is the content of stellar astronomy and astrophysics. We will summarize only the most important findings necessary to understand and assess the role that gravity plays in the structure and evolution of stars.

When the temperature inside the protostar reaches about 107 K, the kinetic energy of the nuclei begins to overcome the electrostatic repulsion Coulomb barrier and ignites the main fusion reactions - synthesis of hydrogen nuclei into helium accompanied by the release of large amounts of the binding of nuclear energy (the details of these fusion reactions, including the initial reaction of deuterium, see "Star Evolution" below). As a result, the contraction of the protostar, now actually a star, stops and for a long time (~106 -1010 years) the weight of the outer layers will be balanced by the pressure of radiation and the pressure of the thermal motion of the ions of the hot gas inside the star, heated by the released nuclear energy - the star was born. The pressure of the emitted radiation and particles of considerable kinetic energy (stellar "wind", which we also know from the Sun, see below) "blows away" the peripheral parts of the original cloud (globules) - the star "peeks-trought" clear and already shines undisturbed into space in visible, infrared and UV spectrum, depending on the temperature of the surface layers. The dynamics of stellar evolution is the coarsest features captured below at Fig.4.1 in the form of time dependence of some important parameters of star.
Note: A short episode of the very first thermonuclear reactions in which deuterium, lithium, beryllium and boron are converted to helium are mentioned below in the section "Evolution of stars".
 Initial mass - a determining parameter of the dynamics of stellar evolution
The dynamics of stellar evolution depends significantly on the
mass of the germinal contracting cloud. As we will see below, the initial mass of the star also determines the stage to which the star's evolution will reached in the future. The more massive a star, the higher the temperatures and pressures inside it - the higher the kinetic energy of moving and collapsing particles and the heavier atomic nuclei can react thermonuclear with each other: the greater the kinetic energy of the collision overcomes the greater electrical repulsive force of heavier nuclei with greater proton number Z. The evolution of more massive stars is therefore faster and in their interior there is a synthesis of heavier elements.
In low-mass stars (about 0.1 M
), the contraction stage lasts for hundreds of millions of years, and later only hydrogen can burn to helium. And with even smaller weights, less than about 0.05M, there is no longer enough temperature inside them for the hydrogen to helium synthesis - a real star is not formed, but only a so-called brown dwarf (see below).
 The participation of dark matter in the formation of early stars
In the early periods of the universe, about 200 million years after the formation of the universe, when the first stars began to form, the initial densities of gas may have contained a relatively high percentage of dark matter. In the protostar phase, a certain amount of dark matter collapsed together with molecular clouds of hydrogen and helium. Early
massive stars of the 1st generation could thus contain, in addition to the usual atomic-baryonic substance, a smaller amount of dark matter. How this absorbed dark matter behaves during the formation of a star and its further development, depends on the properties of the particles it is made of - we don't know that yet, we can only discuss some hypothetical possibilities :
   Due to the weak interaction of dark matter, kinetic collisions with ordinary matter particles produce little energy (could only be effective at high mass, which is sometimes assumed..?..).
 Early stars powered by annihilating dark matter ?
Interesting and somewhat bizarre is the hypothesis of the mutual
annihilation of dark matter particles: that dark matter particles are mutually anti-particles and their collisions would result in annihilation with to the emission of photons, neutrinos, electrons, positrons. The annihilation energy of the absorbed dark matter would be stored in the gas (except for neutrinos). If the effective cross-section of the annihilation interaction of dark matter particles were high enough, estimated to be about 3x10-26cm3/s, it would produce a significant amount of thermal energy (thermonuclear fusion of hydrogen has an energy efficiency of about 1%, while annihilation has an efficiency of 70%, with substraction of neutrinos). A concentration of dark matter of about 1% would be enough to stop the contraction of the protostar cloud and thermal and hydrostatic equilibrium could be reached at a temperature of about 10,000 K. Nuclear fusion would not occur at this stage, the radiation of such a hydrogen-helium "star" would be driven by the annihilation of dark matter *). And during this phase, accretion of additional matter could take place continuously, since the surface is relatively cold and baryons from the dense surrounding matter can fall onto it without significant resistance. The star can thus acquire extremely large masses of 103-107 M. .....
*) The authors of this interesting scenario D.Spolyar, K.Freese and P.Gondolo [Phys. Rev. Lett. 100 (2008) 051101] proposed the name "dark stars" for these hypothetical objects. However, this name is somewhat misleading, as they are composed of about 99% ordinary hydrogen and helium, the dark matter content is assumed to be less than 1%; and they are not dark, but intensive shine with the energy released during the annihilation of dark matter. So they are glowing stars powered by dark matter.
   After the dark matter is exhausted, star it could continue the contraction again, with the subsequent ignition of thermonuclear fusion - the evolution of the star would continue in the standard way. However, if this "star" in the previous stage of dark matter packed a large amount of mass onto itself (sometimes up to 106 M!), it would collapse into a black hole. After all, such massive "dark stars" after collapse could form seeds for the formation of supermassive black holes in the center of galaxies (4.8, section "Mechanism of quasars and active galactic nuclei", passage "How did supermassive black holes form?").

The structure of stars
Stars, as gas spheres, of course, have no "construction" in the mechanistic sense. We can, however, recognize some notable areas - layers, shells, zones - with the characteristics properties and events taking place there :

The core of the star

is the central part, very hot and dense, in which the ongoing
nuclear reactions, and there all the energy of star is created (see below "Thermonuclear reaction inside the stars"). For ordinary stars, it occupies only about 1% of the total volume (it has a diameter of about 0.2 of the star's diameter), but contains more than 30% of the star's mass. Helium (and later other elements) produced by thermonuclear fusion also accumulates in the star's core. This gradually reduces the efficiency of thermonuclear reactions, in stars of the mass of the Sun, only about 10% of the hydrogen supply is consumed by nuclear fusion. In small stars of the red dwarf type, which are fully convective, "waste" helium is evenly stir and distributed throughout the star and does not accumulate in the core - the usability of hydrogen is much higher.
Radiant equilibrium area - the radiation zone
extends between the
core and the convective zone. Here, thermal energy is radiated transmits from the core towards the star's surface. Originally high-energy photons are constantly absorbed and re-emitted here, while their energy decreases (wavelength increases). Energy transfer is very slow here, it takes hundreds of thousands of years (see below "Evolution of stars", passage "The long path of energy and radiation from the interior to the star's surface").
convective zone
is located above the radiation zone and extends almost to the star's surface; its thickness is about 200-400 thousand kilometers
(occupies about 20-40% of the star's internal volume)*). The temperature and energy of the photons are no longer enough to completely ionize the gas, and some of the electrons begin to associate with the nuclei to form atoms.The energy transfer by radiation becomes less efficient and further energy transfer takes place mainly by convection. The cooled substance then descends towards the center of the star, heats up again from the radiation zone and begins to rise again, but these convective currents are chaotic - strongly turbulent ("bubbling") .
*) For very small stars - red dwarfs, the convective zone occupies the entire interior of the star, they are fully convective.
The surface and atmosphere of the star

Stars are gas spheres that do not have a solid surface or a sharp edge, pass
ing freely and smoothly into the surrounding cosmic environment (we do not consider neutron stars here). However, as the optical surface of a star can be considered its photosphere - the last region in which the star's material is not yet transparent to photons. This layer (thickness about 100-200km) is observable as the surface of a star, it emits about 99% of the star's radiation. The tortuous and slow path of photons from inside the star changes to a straight one here - photons emerge from inside the star and at a speed of 300,000 km/s they fly into the surrounding space. The relatively small thickness of the photosphere (compared to the diameter of a star) causes us to see the Sun as a disk with a relatively sharp edge. Due to the magnetic field, inhomogeneous areas of reduced luminosity (such as observed sunspots) or arcuate plasma outbursts may form on the star's surface - solar protuberances are observed (visible as "bumps" or "protrusions" on the sun's disk), which may disconnect and expand rapidly into space like an eruption.
   Above the photosphere is located   chromosphere, formed by a transparent sparse gas. The highest layer of the stellar atmosphere is the corona, formed by a sparse but very hot gas with a temperature of several million degrees. This high temperature is probably caused by the supply of energy by plasma waves and a magnetic field generated by convective plasma currents (magnetohydrodynamic effect).
Note: These areas are, of course, best explored at the Sun. The corona can be observed during total solar eclipses and in the coronograph - a special telescope with a central shading disc that covers the central, highly radiant disk of the Sun.

Left: Protuberances and eruptions occur in the surface layers of stars. From the hot atmosphere of the star, plasma particles are released by thermoemission and radiation pressure. A stream of these charged particles flies away from the star like a "stellar wind".
Right: The stellar wind from the Sun - the solar wind - also flows towards our Earth, where the absolute majority of it is deflected by the Earth's magnetic field, goes around the Earth's magnetosphere and does not penetrate the Earth's surface.

Stellar wind
The hot gases are held firmly in the star by gravity. Nevertheless, thermoemission and the pressure of radiation release gas particles (plasma) in smaller amounts from the hot surface of the star, which are carried into the surrounding space. This stream of charged particles, especially protons, electrons and alpha-particles (helium nuclei) and possibly a small number of heavier nuclei, heading from the star's surface into interstellar space, is called the stellar "wind". In this way, a star can lose much of its initial mass over its lifetime, in the order of billions of years. The stellar wind in outer space becomes part of interstellar matter and cosmic rays (1.6, passage "Cosmic rays" in the book "Nuclear physics and physics of ionizing radiation") .
   In the later stages of the evolution of stars the turbulent flow brings from the interior of the star to the surface some heavier nuclei, which then also become part of the stellar wind. The stellar wind can thus continuously enrich the interstellar space with heavier elements. This phenomenon is more pronounced for faster rotating stars, where there is stronger turbulence and mixing of light and heavier nuclei, and also there is more intense emission of the stellar wind. The stellar wind can thus, together with the far more significant explosion of supernovae, cooperate in the release of heavier elements from the stars - in the chemical evolution of the universe (cf. below the passage "Alchemical cauldrons of the universe").
   In the colder stars of the main sequence (including the Sun), a stellar wind is formed mainly in the hot corona ("coronary wind "), wherein the thermal motions of many particles exceeds the escape velocity and leave star. The outer layers of the corona thus expand and escape into interstellar space. In the surface layers of the star also occurs from time to time eruptions accompanied by the outpouring of plasma - from the star then spreads large clouds of energetic particles at speeds of many hundreds of kilometers/s; the stellar wind temporarily intensifies greatly.
   In very hot stars, the intensity of the radiation can be so great that when these photons are absorbed, the substance of the surface layers can be accelerated to a speed higher than the escape. This is seen especially in heavier elements (carbon, nitrogen, oxygen, ...). In the case of large, colder stars in unstable phases, part of the surface layers reach relatively greater distances during pulsations, where dust particles can condense at a lower temperature; these can then be accelerated by absorbing radiation from the star and carried into interstellar space .
Solar wind - impact on life

These phenomena are well known in our Sun - the solar "wind ". Solar wind particles also hit our Earth. If the clouds of the solar wind hit the earth's surface fully, it would be dangerous for all life. Fortunately, our planet has an atmosphere and a magnetic field. The orbits of charged particles curve in the Earth's magnetic field, and most particles deflect or bounce further into space - clouds of charged particles seem to "wrap" us along the curves of magnetic field lines. The Earth's magnetic field thus creates an extensive "cavity" in the incoming plasma of the solar wind - the so-called magnetosphere. Solar wind particles flow around the magnetosphere and ussally do not reach Earth.
   Only a small part of them enter the atmosphere, especially in the polar regions, where magnetic field lines approach the Earth's surface. In the upper layers of the atmosphere, a stream of solar wind particles interacts with nitrogen and oxygen atoms, causing their excitation and ionization. During deexcitation, light is then emitted, observed as aurora borealis. It is a beautiful phenomenon in which spectral colors are radiated from red and green (derived from oxygen) to blue and purple (formed by nitrogen radiation), depending on the height of the interaction in the atmosphere. Aurora Borealis occurs mainly in the greater northern and southern latitudes, where a small part of the charged particles of the solar wind penetrates along magnetic field lines.
   The solar wind carries away gases from the upper layers of the atmosphere in small quantities, mainly nitrogen and oxygen. E.g. trace amounts of oxygen of terrestrial origin have also been found on the Moon (during a full moon, the Earth's magnetosphere is stretched in direction of the Moon by tidal forces and the solar wind comes from the opposite side; the deformed magnetosphere then allows the ejected nitrogen and oxygen atoms to escape towards the Moon, where a small part of them falls) .
   The magnetic field of terrestrial-type planets is generated in the rotating semi-fluid outer part of the core, which acts as a magnetohydrodynamic "dynamo". In the later stages of the planet's evolution, this core cools and solidifies, causing the planet's magnetic field to disappear. For possibly life on the planet that has two negative consequences :
Larger amounts of hard ionizing radiation, harmful to living organisms, begin to enter the biosphere from outer space.
b) An intense stream of charged particles emitted by the star destroys the atmosphere and can "spray" it into the surrounding universe. The loss of the atmosphere leads to faster evaporation of water, whose steam is also carried into space by the stellar wind. The loss of the atmosphere and water is incompatible with the continuation of life on such an affected planet - see "
Anthropic principle or cosmic God", the "Stars-Planets-Life" passage.
   The stellar wind enriches the surrounding space with gases, including heavier elements thermonuclear "cooked" inside the star. Under certain circumstances *), stellar wind clouds could theoretically form new stars of the next generation, partially enriched with heavier elements - even before the supernova's explosion of the stars of the previous generation.
*) Stellar wind particles fly out at a considerable speed of the order of thousands of kilometers per second, so that this gas dilutes very quickly and escapes from around the star. However, if another gas around the star is dense enough, the stellar wind may slow down. Similarly, with a larger accumulation of stars (eg in star clusters), streams of wind particles from different stars can collide and slow down. Gases from the stellar wind could thus accumulate, thicken and eventually succumb to gravitational collapse with the formation of new stars next generation. The resulting stars would be partially enriched with heavier elements from stellar wind emitting stars, especially in the later stages of their evolution. However, this way of increasing metallicity is far from comparable to a supernova explosion.
Star Density
We will first consider "ordinary" stars, not compact gravitationally collapsed objects such as white dwarfs and neutron stars
(these will be discussed in the following 4.2). The local density of a star, ie the mass of stellar material in a unit volume, varies significantly in the direction from the surface to the star's core. The surface layers around the photosphere have a very low density of the order of 10-9 g/cm3 - lower than what is the best vacuum achievable in our earthly conditions. The surface layers of the stars can therefore be described with a bit of exaggeration as a "glowing vacuum". Towards the center, the density increases and in the core of ordinary stars of the main sequence it reaches relatively high values of about 100-200 g/cm3 (10 times heavier than terrestrial iron). However, in end-evolutionary stars, where thermonuclear hydrogen combustion is depleted and helium, carbon and higher nuclei fuse, the central density reaches huge values higher than 105 g/cm3 (1000 times higher than the density of any known material on Earth, except atomic nuclei).
   Average stellar density, ie the ratio of the total mass of a star and its volume, is quite different for different types of stars. For our Sun it is 1.6 g/cm3, for red giants only 10-7 g/cm3. For giants, the average density is a slight 10-9 g/cm3, again lower than the vacuum achievable by us - the whole such giant is again metaphorically "glowing vacuum", but with a huge radiant power... The average density of a white dwarf is 105 g/cm3, a neutron star has an unimaginable density of 1014 g/cm3, the same as atomic nuclei.

Eddington's limit of luminosity
Radiation, when interacting with matter, exerts
pressure, which in principle limits the greatest possible luminosity that a (cosmic) body held by gravity can achieve. This maximum possible luminosity, the so-called Eddington limit LEd , is such a radiant power, at which the gravitational attraction inwards is balanced with the pressure of radiation acting in the opposite direction to gravity (this maximum possible luminosity was determined by A.Eddington in 1924) .
   If we have a star of mass M and radius R, then an gravitational force Fg = G.M.m/R2 acts on each particle of mass m in the direction of the center. The force of radiation pressure Frad = I. s/c acts in the opposite direction on this particle, where I is the flux (intensity) of radiation, which is related to the total luminosity L by the relation I = L/4p R2 and s is the effective cross section of radiation interaction with particles (for the concept of effective cross-section see 1.5, section "Interactions of elementary particles", passage "Effective cross-section of particle interactions" monograph "Nuclear physics and physics of ionizing radiation"). The condition Frad = Fg for the Eddington limit then gives LEd = 4p.G.M.m.c/s. The critical (maximum) luminosity therefore depends only on the weight of the object and on the mechanisms of radiation-substance interaction.
Interaction of radiation with matter and pushing the radiation pressure is also sometimes expressed in terms of opacity (opaquenes) O of the upper layers of the star. The Eddington limit can then be equivalently expressed by the relation LEd = 4p G.M.c/O.
   Assuming the outer layers of a star composed of hydrogen, then we substitute the mass of the proton (hydrogen nucleus ) for the mass of the particle m : m = mp. If the radiation interaction is caused by classical Thomson scattering on electrons in an ionized gas, it is s = sT= (8p/3).(e2/me2)2, where e is the charge and me the electron mass *). Using the parameters of the Sun, the Eddington limit can then be calculated as LEd 1,3.1031M/M [J.s-1], or LEd 3,3.104(M/M).L. However, the exact value of the Eddington luminosity depends on the chemical composition of the surface layers of the gas and on the spectral distribution of the emitted radiation.
*) The radiation pressure acts mainly on the electrons, which thus move from the center. For protons, the pressure (transfer of momentum) by Thomson scattering is negligible due to their high mass. As a result of these different radiation forces on electrons and protons, a certain charge separation and electric field of the radial direction is created, which "pulls" the protons upwards - the radiation pressure thus ultimately acts uniformly on all ionized gas.
   The luminosity of ordinary stars (including the Sun) is only about 10-4 LEd . At higher luminances than LEd , called super-eddington luminosity, the pressure of the radiation would prevail and the body would "blow" or "scatter" into the surroundings - this really happens especially in the final stages of stellar evolution in red giants, novae and supernovae (see the following 4.2). The Eddington limit applies only under the assumption of isotropic radiation from spherical objects. In 4.8 we will see that in the case of strongly anisotropic radiation from accretion disks around black holes, the Eddington limit can be exceeded many times over.

Planets around stars
A newly forming star is surrounded by a rotating disk of residual material, gas and dust. The disk has an inhomogeneous structure, creating vortices and turbulence in it. Over the course of several million years, this gas-dust disk, called protoplanetary (planets form from it), decays - part of it is absorbed by the central star, part is ejected, but some parts of the disk remain in orbit around the star, gradually fragmenting, they absorb more matter by gravity; they grow and thicken. The dust grains slowly combine to form gradually larger bodies. As their weight increases, so does their gravity, and so they attract more matter. Planets gradually form from these fragments *), which then orbit the parent star. Moons can form around them, and smaller bodies, asteroids, and comets form from the remaining material. Due to the law of conservation of angular momentum, the rotation of the protoplanetary disk is maintained as the orbit of planets and other objects in elliptical (sometimes almost circular) orbits around the central star, according to Kepler's laws .
*) The name "planets" comes from a time when nothing was known about their true nature. Greek word "plantes" = "wanderer"; "the one who walks here and there" in antiquity and the Middle Ages, he referred to celestial bodies that, when viewed from Earth, moved in the sky differently from "motionless" stars with an apparent circular motion. They were then Mercury, Venus, Mars, Jupiter, Saturn; sometimes they included the Sun and the Moon. Copernicus' heliocentric system clarified the nature of the planets as bodies orbiting the Sun (the Sun disappeared from the list of planets and the Earth was added). Bodies orbiting planets have been called moons (by analogy with our Moon). When it was later discovered that a large number of smaller bodies - asteroids and comets - orbited the Sun, the term planet was clarified in the sense that it is a body so large in mass that it maintains an approximately round shape by gravity, and it gravitationally controls its surroundings, which it can "cleanse" of other smaller bodies, gas and dust (along its orbit). From current ideas and knowledge about star formation, it follows that almost every star has some planets (and undoubtedly asteroids), although for most stars so far we can't find out yet...
 Specification of the term planet
Based on the accumulated amount of astronomical knowledge about a large number of stars, objects in the Solar System and around other stars, the general specification of the term planet was precised - four conditions were established for a cosmic body to be called a planet :
1. The body must orbit a star (a classical star, a white dwarf, a neutron star, brown dwarf, or around a black hole) after a sufficiently stable orbit (also related to Lagrange libration points, L4/L5 stability) .
2. It must be enough large - mass, so that due to its own gravity it overcomes the resistance of material forces (including the rigidity of solids such as ice and rocky minerals) and the body in hydrostatic balance thus permanently maintains an approximately spherical shape (or an elliptical shape if it rotates). This minimum size and weight depends on body composition. In order for a body to form a sphere by its own gravity, it should have a mass of at least 6x1020 kg (1/10,000 of the mass of the Earth) and a diameter of about 600 km for a rocky body and about 400 km for a body composed of ice.
3. It must create a sufficiently strong gravity around itself to attract nearby bodies and thus "clean" its orbit from other smaller bodies (this condition is not met by Pluto, in whose orbit many smaller bodies move; Pluto is therefore not considered a true planet, but a dwarf planet).
4. The body should not be so large - massive, that thermonuclear reactions can start in its interior and later become a star (perhaps a brown dwarf). For bodies composed of material of average solar metallicity, this limiting mass for deuterium thermonuclear fusion is estimated to be around 10-13 Jupiter masses.
 Chemical composition of the planets
In the protoplanetary disks of the oldest stars of the 1st generation, only gaseous planets (similar to our Jupiter, but without a dense core of heavier elements) composed only of hydrogen and helium could form, other elements were essentially non-existent at the time. In the later 2nd and 3rd generation stars, the original mass in the gas dust disk consisted of about 98% from light elements formed in primordial cosmological nucleosynthesis (see 5.4 "
Standard cosmological model. The Big Bang. Shaping the structure of the universe.", passage "Primary nucleosynthesis") - hydrogen and helium with trace amounts of lithium. Only 2% was made up of heavier elements created by nucleosynthesis in previous generations of stars (described below in the section "Thermonuclear reactions inside stars"), which in the final stages of their lives ejected these stars into interstellar space (4.2 "Final stages of stellar evolution. Gravitational collapse", part "Supernova explosion , neutron stars, pulsars"). The central star also has this initial composition (during the later stages of nucleosynthesis it is slightly enriched with heavier elements). However, some physical and chemical processes may occur in the surrounding protoplanetary disk, which may lead to significant differentiation in chemical composition of various formations and emerging planets (compare the graphs of the representation of elements in universe and on terrestrial planets).

Relative abundance of elements in nature depending on their proton (atomic) number Z, related to hydrogen Z = 1.
Above: The current average abundance of elements in space. Bottom: Occurrence of elements on Earth (in the Earth's crust) and terrestrial planets.
Due to the large range of values, the relative abundance of the elements (relative to hydrogen Z = 1) on the vertical axis is plotted on a logarithmic scale; however, this can optically distort a large difference in the share of hydrogen and helium compared to heavier elements, especially in the upper graph.
The picture is taken from the monograph "
Nuclear physics and physics of ionizing radiation", 1.1 "Atoms and atomic nuclei", part "Origin of atomic nuclei and origin of elements - cosmic alchemy".

The distribution of planets by mass, composition, and orbit
depends on the mass and density of the protoplanetary disk, as well as the mass and luminosity of the central star. If the protoplanetary disk is relatively sparse and the star's luminosity is higher, three mechanisms are manifest to differentiate different types of planets (besides gravity, which is of course the main driving force) :
- Thermal effects of star radiation , which heated the inner parts of the disk to relatively high temperature, in which light substances (such as water, or carbon compounds such as methane) are in the gaseous state. Only solids with a high melting and boiling point, such as silicates and metals and their compounds, could be and are newly formed in the solid state of dust particles (and subsequently their clusters or mineral crystals). It was from these heavier substances that the core of the inner planets were formed.
- The pressure of the radiation near the star "sweeps out" gases mainly from light atoms (especially hydrogen and helium, or lighter molecules) to greater distances - it pushes them into higher orbits in the protoplanetary disk. Gases from heavier elements and heavy dust particles are expelled more slowly.
- Chemical properties - different reactivity of elements and properties of emerging compounds. This is mainly the difference between dense and refractory compounds of silicon and many metals, as opposed to volatile compounds of hydrogen, carbon and other elements. As well as the inert properties of helium and other "rare" gases.
   In co-production with gravity, these three mechanisms act in the inner parts of the protoplanetary disk as a kind of "mass separators", separating light elements and molecules from heavier ones. In the inner parts of the protoplanetary disk, a relatively increased concentration of heavier elements and substances is formed, which are expelled more slowly by the pressure of radiation than light gases. In areas near the parent star (with smaller orbital radii), therefore, smaller planets with a higher content of heavier elements are formed - terrestrial planets (lat. Terra = Earth ; these are planets similar to Earth - earth type); in our system it is Mercury, Venus, Earth, Mars. A higher relative representation of heavier elements can be seen in the graph at the bottom of the figure. Terrestrial planets do not grow to large sizes and masses, as the proportion of the corresponding heavier elements in the germinal nebula is very small (<1%).
   At greater distances in the disk, the mass is already so cold that even volatile substances can be in a liquid and solid state. Germs made of ice materials (water-ice, carbon dioxide, methane, ammonia, ...) can condense here, which gravitationally capture hydrogen and helium from the surroundings during circulation in the protoplanetary nebula, of which there are a large amount. Thus, large planets are gradually forming in these areas composed mainly of light gases - gas giants; in our system it is Jupiter, Saturn, Uranus, Neptune.
   This was the situation at the origin of our solar system, where we have inner hot or warm small terrestrial planets and outer distant and therefore cold large planets
(they are cold only on the surface, there may be relatively high temperatures in their cores). These circumstances were very important for the possibility of the origin and evolution of life on Earth and in space - it is discussed in the work "Anthropic principle or cosmic God", part "Stars, planets, life" .
   If the protoplanetary disk is dense, the situation changes. On the one hand, large planets with a dominant representation of light gases can condense even relatively close to a star. Furthermore, large planets formed at greater distances can be slowed in their orbit by friction in a dense disk (and tidal forces), gradually getting closer ( migrating ) to the parent star. Dense protoplanetary disks can thus form large planets orbiting near a central star, heated by its radiation to high temperatures - these are a kind of "hot Jupiters ".
Gravitational instabilities of planets 
If only one planet orbited a star, its orbit would be long-term, theoretically eternal
(if we do not consider tidal phenomena and the emission of gravitational waves), stable. However, there are almost always more planets orbiting, so due to the mutual gravitational interaction of the planets, there are changes in the orbits and gravitational instabilities can occur in the planetary system. Particularly significant gravitational influences occur when the orbital periods of neighboring planets are in the ratio of small integers. In this situation, in regular time intervals, the planets will approach and move as close to each other as possible (at the same angle of orbit) - the so-called orbital resonance (also called Laplace resonance ) occurs. During repeated maximum approaches, there may be a greater gravitational influence, which gradually adds up.
   It is possible that during evolution, planetary systems may to lose some of their planets: by the gravitational action of other large planets, they can gradually get into a hyperbolic orbit and be "ejected" into interstellar space, or, conversely, absorbed by a central star, or in collisions, they may break into smaller fragments. Thus, "stray planets" may occur in interstellar space, within a few light-years of stars,
(see the section "Lone 'wandering' planets" below); some of them will hopefully be gradually discovered while improving astronomical observation techniques.
   The situation is even more complicated with close binary stars or multiple systems. Here we can expect a great diversity of planets with often very eccentric elliptical orbits, which are unstable due to the non-central time-varying gravitational field and tidal forces. Some of them may be absorbed by one of the stars or may be gravitationally ejected into interstellar space.
Radioactivity in the protoplanetary disk? Radioactive melting of planets ?
In 1st generation stars, no radionuclides were found in the protoplanetary disk, the entire system was made up of hydrogen and helium with a small admixture of deuterium, beryllium, and lithium. However, if a 2nd or 3rd generation star is formed from a cloud ejected by a supernova, it will contain a large amount of radioisotopes created during the supernova explosion. If star formation occurs shortly after the supernova explosion (approx. millions of years), the early protoplanetary disk will be a "radioactive fire" in which long-lived radioisotopes
(such as iodine 129I, aluminum 26Al, iron 60Fe, ...), now already decayed, in addition to radiation, they could also generate a large amount of heat that could melt smaller bodies. These processes may also have been involved in the differentiation of the planets.
   In the early stages of the formation of protoplanetary disks, there could therefore be a significantly greater representation of radioactive elements than in later periods. The large amount of heat from this radioactivity caused the melting of many early planets, causing the heavy iron to sink into the core while the lighter elements "floated" on the surface. This led to the differentiation of the composition of the terrestrial planets. These shorter-lived radioactive elements decayed over a few million years, and the upper layers of the terrestrial planets solidified.
Moons around the planets
Around a number of planets orbiting the Sun
(and no doubt even around the exoplanets of other stars) orbit other smaller bodies, called - by analogy with our Earth companion - the moons. The moons around the planets may have formed in different ways :
Some moons may form at the same time with planets in the protoplanetary disk. In the vicinity of the emerging planet, other smaller bodies could condense in the protoplanetary disk, which could be trapped in orbit around the planet.
Other moons (about a hundredths of the diameter or mass of the planet) were probably formed by gravitational capture of the asteroid, which got close to the planet as it moved.
Relatively larger moons (relative to the size of the planet) can form during catastrophic planetary collisions, when large amounts of material are ejected into the environment. If the collision occurred peripherally in the appropriate direction (with the appropriate angular momentum), part of the ejected material can be gravitationally bound and condense into an orbiting moon (this is probably how our Moon formed by the collision of an earlier Earth with another smaller planet called Theia) .
  If during the period of moon formation there were sufficiently high temperatures and stronger gravity
(which exceeded the strength of the material), the moon was divided - material differentiation - into layers according to density (and possibly other physical and chemical properties). This occurs mainly in larger months, which consist of the outer shell (water-ice, gases, ...), stone (silicate) shell and possibly the iron core. Small moons often remain undifferentiated.
Thermal energy of planets and moons
Thermal energy, heating the surface and interior of planets and their moons,
(except residual heat from the period of creation) basically has three origins :
The radiant energy (especially infrared radiation) of the parent star intensively heats the surface (and possible atmosphere) of the inner planets.
During the rotation and close orbit of the moons around the planets, tidal forces are significantly applied (see 1.2, passage "Gravitational gradients - tidal forces"), which can heat the subsurface layers by viscous "squeezing and kneading" of planet and moon material to such an extent, that volcanic activity (hot or cryovolcanic activity) and even in distant areas from the central star, there may be liquid water below the surface of planets and moons. Tidal forces from orbiting moons can thus contribute to the warming of the interior of planets, especially terrestrial ones, and their moons.
The natural radioactive decay of long-lived radionuclides (uranium 235,238U, thorium 232Th, potassium 40K) contained in the interior of planets and moons releases nuclear energy, which changes into heat - cf. passage "Geological significance of natural radioactivity" here on Earth in 1.4 of the monograph "Nuclear physics and physics of ionizing radiation" .

Small planets - Asteroids
In addition to the planets orbiting the sun, and no doubt around other stars, orbiting also a large number of smaller bodies called minor planets or asteroids *). These are bodies of much smaller masses than planets, mostly of irregular shape (their gravity is too weak to maintain a spherical shape). The bodies of this "cosmic garbage" have various sizes. The smallest are dust particles the size of micrometers. Furthermore, bodies the size of millimeters to tens of meters - these are sometimes called meteoroids, because when they collide with the Earth, this body flies into the atmosphere, where it heats up strongly and evaporates by friction, creating a light phenomenon - a meteor: a glowing trace of ionized and recombining air molecules and material evaporated from the surface of the flying body. Larger bodies (> tens of centimeters) do not completely evaporate in the atmosphere and hit the Earth's surface like meteorites. As asteroids are usually considered the bodies larger than 100 m. There are two hypotheses about the formation of asteroids in Sun system: 1. The desintegration (probably due to a collision) of an ancient planet orbiting somewhere between Mars and Jupiter; 2. These are the original formations formed by the condensation of dust grains (planetesimals), in which the gravitational accretion to the planet did not continue and thus remained small.
*) The name of the asteroid (Latin star similar; it was introduced by W.Herschel in 1802) comes from the fact that in the telescope these bodies appear as small points, similar to stars (while the planets appear as disks on which surface structures can be observed). However, they are characterized by rapid movement against the background of stars.
   The largest known asteroid in the solar system is Ceres with a diameter of almost 1000 km
(discovered in 1801 by G.Piazzi), other large asteroids are Pallas and Vesta with a diameter of about 500 km. The total number of smaller asteroids in the solar system is estimated at millions! The largest number of them orbit the belt between the orbits of Mars and Jupiter; it is assumed that due to the strong gravitational influence of Jupiter, a larger body could not have formed here in the protoplanetary disk.
  Many asteroids are also found in the outer parts of the solar system, behind Jupiter. They consist mostly of water ice, frozen carbon dioxide and solid methane, with admixtures of dust and minerals. They represent potential comet nuclei. Most comets probably form in areas far from the Sun (the so-called Oort cloud) by combining the remnants of the condensation of the protoplanetary nebula. Due to gravitational disturbances, some of these bodies can reach a very eccentric orbit, reaching the inner part of the solar system. As such a body approaches the Sun, heating its surface causes the outer ice layer to evaporate; the released gas and dust create a sparse "atmosphere" around the comet, called a coma. The pressure of the sun's rays (and the solar "wind") will cause a large tail to form away from the Sun. The dust in the tail reflects sunlight and the gases glow due to ionization and subsequent radiation deexcitation of the atoms. This causes a strong optical effect, some comets (their coma and tail) are visible to the naked eye. Although the comet's solid core is several kilometers to tens of kilometers in size, the coma reaches several hundred thousand kilometers and the tail can be up to hundreds of millions of kilometers long!
  The orbits of a number of asteroids cross the orbits of planets, which is why asteroids sometimes collide with planets. Due to the high kinetic energy, a very large impact crater is often formed on the planet's surface; the Moon and some other bodies (with a solid surface) in the solar system are directly "furrowed" by such craters from impacts in the distant past (in the past, the density of asteroids was higher and collisions was more frequent). Even the orbit of our Earth is crossed, or dangerously approached, by a number of asteroids - there is a danger of the Earth colliding with an asteroid (we live on a "space shooting range"!). In the past, such events have occurred repeatedly, impact craters have been found on Earth after ancient impacts of larger bodies several kilometers in diameter
(such as the large Chicxzulub crater in the Yucatan Peninsula, the remnant of an asteroid impact of about 10km that may have wiped out dinosaurs). On these and other dangers to humanity, see the passage "Astrophysics and cosmology: - human hopelessness?" in 5.6 "The Future of the Universe. Time arrow.".
, exon moons

Our solar system is not exceptional, the formation of planets around stars is an lawful phenomenon. Planets around stars outside the solar system, astronomers called extrasolar or short exoplanets. Direct observation of planets around distant stars is very difficult. However, among other things, the spectrometric analysis helps here: planets around stars shine by reflected light, which is "redder" than the light of the parent star. the presence of planets can be inferred from the presence of a dusty disk around the star, which absorbs part of the star's radiation and then re-emits it as infrared radiation.
There are basically three methods of indirect detection of exoplanets :
l Transit method - measures a slight decrease in the brightness of a star as the planet passes over the star disk, whereas these decreases in brightness are repeated regularly. However, the geometric condition here is that the elongated plane of the orbit of the exoplanet passes through the observer's location (ie the Earth). Based on the analysis of changes (fluctuations) in transit, long-term observation makes it possible to detect also some other planets (which do not pass through the star's disk from our point of view) and approximately determine the parameters of their orbit.
Fluctuations of the star's center of gravity - the planet and the star orbit the common center of gravity, causing regular small changes in the position of the star itself. Due to small deviations and large distances, this phenomenon cannot yet be observed directly (astrometrically) at the position of the star in the sky, but radial movements of the star towards us and away from us can be measured spectrometrically using the Doppler effect.
l Gravitational lens - when the analyzed star coincides with another more distant star, a bend of its light by a gravitational field, the effect of a gravitational lens can be expected (miniature similar to the phenomenon discussed in 4.3, passage "Gravitational lens. Optics of black holes"). Monitoring the course of this bending during the eclipse may reveal a possible planet near the star. This method is sensitive, but it is a rare and one-time event; from such a unique observation it is possible to conclude only on the existence of the planet, but it is not possible to determine the parameters of its orbit..
By these indirect methods have been proven several large planet with a few stars.
Exo moons
Like several planets in our solar system orbit the moons, is from the astrophysical point of view highly likely that around a series of exoplanets are orbiting a smaller body - exomoons. Their detection is even more difficult than the exoplanets. They may be manifested only by very slight anomalous fluctuations in the transit curves of the exoplanet passing through the disk of the central star.
Around some larger exoplanets could form a exo-terrestrial moon like Earth; could be interesting in terms of the possibility of life..?..
  For exoplanets and exomoons, the question of the possibility of the origin and presence of extraterrestrial life is often discussed ("
Anthropic principle or cosmic God", part "Stars, planets, life").
 Lonely "wandering" planets
In addition to planets orbiting stars, there is undoubtedly a large number of "homeless" planets (a bodies of planetary mass) in space that are not gravitationally bound to any star and move - "wander" - freely in interstellar space, only under the influence of the total gravitational field of surrounding stars, star systems and whole galaxy. Lone stray planets can basically have a dual origin :
1. Ejection from a planetary system around a star
These planets initially form in a cloud of gas and dust around the nascent star along with other planets, but are later ejected into space. It can be either giant gas planets (that will probably be the majority) or smaller terrestrial planets. This "desertion" from the planetary system can occur by three mechanisms :
--> As a result of the gravitational interaction with other large planets, the planet in question can gain a higher speed, is thrown out of its orbit and leaves the planetary system (cf. "Gravitational instabilities of the planets" above). This is probably the most common case of wandering planets.
--> The passage of a large body (e.g. a smaller star) around the planetary system can also disrupt the orbits of the planets, and in the resulting chaos some planets can leave their original orbital system. Unstable planetary systems certainly often occur around binaries or multiple star systems.
--> The unstable - explosive - behavior of the parent star, especially a supernova explosion, can destroy some planets and "drive" others away into interstellar space. Even with a more gradual loss of mass of the central star (stellar wind, red giant -> white dwarf), some more distant planets can be released from their orbital motion.
Independently formed bodies by gravitational contraction of small gas clouds
Huge gas-dust clouds break down into fragments of various sizes due to gravitational contraction due to inhomogeneities and turbulence. From the big ones, stars and star systems forms. Small globules can form into separate planets by gravitational contraction. They can be expected to be planets of a similar type to Jupiter. From slightly larger globules, transition types between stars and planets can form - brown dwarfs
(they are mentioned below) .
  Astronomically, it is estimated that there are many billions of lonely planets roaming in interstellar space in our galaxy. And it will be the same in all other galaxies...
  It is very difficult to observe solitary wandering planets in the bottomless depths of space. These bodies of relatively small dimensions (astronomically very small) do not glow with their own light; larger lone planets can only shine very faintly in the infrared. Some rare possibility of accidentally detecting a stray planet could be obscuring or observing the gravitational lensing effect mentioned above. Some wandering planets, as they travel through interstellar space for a long time, can find "their" new star to orbit - they can be gravitationally captured by the star they are currently flying around, mostly in distant or eccentric orbit. The more massive a star, the more likely it is to capture a stray planet (overall this probability is very small...).

Different masses of stars. Giant and dwarf stars
Gravity contraction and compaction of gas-dust clouds can in principle form stars and other formations of various sizes and masses. Indeed, astronomical observations show a wide range of stellar masses: from
dwarf stars with tenthss of a mass of M, through stars similar to our Sun, to massive stars of many tens of masses of the Sun M, called stellar giants. Especially in the first generation of stars in the early universe, stars with a mass of up to 300 M were also significantly represented.
   The resulting mass of the star is given by the amount of matter that the contracting cloud just needs to "pack" on itself until the ignition of the thermonuclear reaction; then the outer layers are "blown" into the space by the radiation pressure and no further accretion continues. This potential possibility depends on several factors :
The mass and density of the germinal cloud ,
limits the total mass of stars, planets and remaining material. In denser clouds, primarily more massive germs of star are formed, which condense more easily.

Chemical composition of the germinal cloud
In order for a protostar's gas to become a star, it must first be effectively cooled during condensation so that it can then be compressed by its own gravity. For a pure hydrogen protostar, cooling takes longer, the protostar only needs to "pack" more gas, so the resulting stars are more massive; in addition, the p-p thermonuclear reaction needs high temperature and pressure to run efficiently, so it ignites later. The presence of heavier elements helps to cool the hydrogen gas more efficiently
(more intense radiation). With a higher content of heavier elements, protostars collapse faster and ignite earlier thermonuclear reactions (CNO cycle can take place efficiently even at lower pressures), which blows away the remaining gas into the surrounding space; stars are not enough to grow into large masses. Roughly speaking, the mass of stars is inversely proportional to the stellar generation.
Rotation of the germinal cloud
- a cloud with a large rotational angular momentum during contraction due to centrifugal forces easily fragments into smaller parts, from which stars of smaller masses are formed.

Turbulence in the germinal cloud ,
as a result of which the original cloud is densely divided into a number of subregions-nuclei of different sizes, from which stars of various masses, mostly smaller ones, are formed.

Interaction of compacted areas in the germinal cloud ,
as a result of which some smaller germs can be ejected from the cloud and thus lose the supply of material - their growth stops.
Dwarf stars  
As a result of these circumstances, in addition to stars the mass of the Sun and higher, a large number of small dwarf stars with masses of several tenths of
M and probably even smaller formations are formed, which are no longer stars in the true sense of the word - so-called brown dwarfs.
A brown dwarf is a formation that is on the border between small stars and large planets. Their mass is estimated at tens of masses of Jupiter, ie several hundredths of the mass of the Sun
M. This weight is too small for the temperature inside them to reach the value necessary to ignite the usual nuclear fusion of hydrogen nuclei. By gravitational contraction, the brown dwarf is heated "into ore" to surface temperatures of several hundred to thousands of degrees and shines partly in a dark red color, but mostly in the infrared range of the spectrum. However, deuterium nuclei may coalesce inside larger brown dwarfs where the temperature is high. The newly formed brown dwarf may temporarily shine like a faint star, but the deuterium is soon consumed, the brown dwarf cools, and is then more like a large planet.
Giant stars

In a relatively lower number, "giant" stars are formed with a mass of about 20-60
M (rarely perhaps even higher), which have a massive and rapid course of thermonuclear reactions. Therefore, they have a high luminosity (a thousand to a million times higher than the Sun) and a very short lifespan - only millions of years. Upon completion of thermonuclear reactions, they explode as supernovae (4.2, section "Supernova explosion. Neutron star. Pulsars."). High-mass stars are relatively rare astronomically - partly because they form less often and partly because they live short.
   This group includes the so-called Wolf-Rayet stars (first observed by Ch.Wolf and G.Rayet in 1867 at the Paris Observatory), which, in addition to high luminosity and surface temperature of about 25-100 thousand degrees, are characterized by the presence of broad spectral lines of helium, nitrogen and carbon atoms (nitrogen is a product of the CNO fusion cycle). In the case of massive stars, in the final stages of development, the convective zone extends as close as possible to the star's core, thus mixing matter in the core and on the surface. Carbon (and other heavier elements) is therefore carried to the star's atmosphere and can be observed in the spectrum. These stars also observe a very intense ejection of matter into the surrounding universe - the stellar wind, which creates small emission nebulae around them. Wolf-Rayet stars are one of the final stages in the evolution of some very massive stars. After a short time, about hundreds of thousands of years, they explode as supernovae .

Interactions and "collisions" of stars
Interstellar space is basically very empty from an astronomical point of view, the stars are very sparsely distributed in it. The individual stars in galaxies and star clusters are spaced apart by units and decades of light years (approximately 30 million of their diameters), so the mutual influencing of their structure is virtually zero. The probability of a close approach or "collision" of two lonely stars can be practically ruled out. Even during collisions and intersections of galaxies, there are no direct collisions of stars (5.4, passage "Collisions of galaxies").
   The only situation, where such a phenomenon can, occur is that the stars formed together as a binary or multiple system. Such stars then orbit the common center of gravity at relatively close distances for a long time, so that their mutual gravitational influence can occur, which can lead to a slow gravitational approach, which can also result in a "collision" and fusion.
   In order for the two stars in the binary system to get close enough to orbit each other, the "excess" orbital energy and angular momentum must be removed. This can be done in principle by two mechanisms *) :
- A third body in a multiple system that can receive orbital energy from a tight binary system by mass exchange or tidal forces.
- A gaseous environment that inhibits and dissipates the kinetic energy of orbiting stars.
*) Note: The emission of gravitational waves, which is relatively very weak, cannot be applied here significantly. Unlike close systems of compact objects, neutron stars and black holes, where it is dominant - 4.8, passage "Binary gravitationally bound systems of black holes. Collisions and fusions of black holes and neutron stars".
   The decrease in orbital kinetic energy then leads to a decrease in the distance between the components of the binary, an acceleration of the mutual orbit, a spiral approach, and finally the fusion of the two stars into one. In the final phase of orbit, the two stars will share the mass of their outer layers, their envelopes will form an accretion disk, then the two nuclei of the stars will merge, which can ignite a new thermonuclear reaction - a large increase in radiation power - similar to the nova. The result is one more massive star.
The specific evolution of binary stars is discussed in more detail in the following passage :

Binary stars and multiple systems
When looking at the night sky, either with the naked eye or a telescope, in addition to a large number of individual "lonely" stars, we also observe a number of pairs of stars - stars lying very close to each other, or groups of several nearby stars. The cause of the observed close proximity of the stars can be twofold :
1. Apparent (optical) binary stars
The proximity here is only apparent, it is a mere optical illusion (sometimes referred to as optical binary stars) - they are formed by random projection of stars, which are in fact at very different distances in space behind each other and are not related to each other, into almost the same line of sight, resp. to a small angular distance from each other. When viewed from another place in the universe, we would see them far apart.
2. Real (physical) binary stars ,
which are bound to each other by gravity and orbit relatively close to each other according to Kepler's laws. As outlined above, stars usually form in groups. It often happens that two stars formed close to each other remain gravitationally bound to form a binary system or double star rotating around a common center of gravity. Possibly, several such gravitationally coupled stars will form a multiple system.
 Rotary fragmentation
The main reason for the frequent formation of binary stars and their multiple systems is the law of conservation of angular momentum. The cloud or region of gas from which the star is formed practically always rotates slowly at first. When the cloud shrinks, its moment of inertia decreases, so due to the law of conservation of momentum, the rotation of the cloud-protostar must accelerate
(the well-known "pirouette effect"). This results in centrifugal forces that can become strong enough to fragment the rotating cloud into two or several less gravitationally bound parts. If massive enough, these fragments can continue to contract and form separate stars that will orbit each other (around a common center of gravity) as binaries.
   Astronomical observations show, that only a minority of stars are single ("solitary", isolated), the majority form binary or multiple systems. Solitary stars are formed either in the case of very slow rotation of the protostellar cloud, asymmetric fragmentation, or even by the formation of an extensive protoplanetary disk, whose planets take away a large part of the rotational momentum of the central star. This is probably also the case with our Sun, where the planets of the solar system have roughly 90% of the total rotational angular momentum, while the Sun rotates slowly with 10% of the total angular momentum.

   Observation of a large number of separate and binary stars showed approximately logarithmic empirical relationship between the number N** of binary and the number N* of individual (separate) stars depending to their mass M :
/N*(M) 1/2 + 1/4 . log(M/M). This relationship is valid in the range of masses of M stars 0.1 <M/M <100 in relation to the mass of the Sun M .
   Such real, gravitationally coupled, star pairs are divided into three groups in terms of observation :

The astronomical significance of binary stars lies in the fact that by analyzing the periods and velocities of their orbits, the parameters of their orbits around a common center of gravity *) can be determined and the masses of these stars can be determined from there on the basis of Kepler's laws .
*) This is most reliable for visual binary stars, where the mass can be determined from the knowledge of the orbital time and the distance of the components from the center of gravity on the basis of the laws derived in 1.2. For spectroscopic binary stars, this encounters problems related to ignorance of orbital inclination and eccentricity.
   From an astrophysical point of view, the distance at which the two stars orbit the common center of gravity is important :

Evolution of stars in a close binary
A mass overflow between the components of a close binary can have a significant effect on the evolution of both stars. One of the possible scenarios is briefly as follows :
l The initial situation is a separate system of two nearby stars of different masses on the main sequence (H.-R. diagram), which (yet) do not fill the Roche limit.
l The more massive component previously exhausted the hydrogen in its interior, passes into the stage of the red giant (see the passage "Late Stages of Star Evolution" below), and fills the Roche limit with its increasing radius.
l Gases overflows from a more massive star to a less massive star, causing the mass ratio may be reversed.
l The interior of an originally massive star can become a white dwarf, the gas overflow will stop.
l The second star also reaches the stage of the red giant, fills Roche's limit, and begins to flow gas from it back in the opposite direction to the white dwarf.
l Accumulation of a certain critical amount of hydrogen on the surface of a white dwarf can trigger a chain thermonuclear fusion, which manifests itself as a nova explosion, that can be repeated several times. The process may eventually result in a supernova explosion (see 4.2, section "Types of supernovae ", or below section "Late stages of stellar evolution").

Extinction of binary and multiple systems
Binary and multiple *) stellar systems are not stable in terms of long-term evolution , but undergo evolution that inevitably leads to their extinction. The main mechanism leading to this scenario is the loss and taking away of mass (-energy) and especially the taking away of the orbital angular momentum out of the system. According to Kepler's laws, this leads to a shortening of the orbital period and to the mutual approaching of the two orbiting bodies, which eventually results in their fusion - the extinction of the binary system, which transforms them into one rotating star. The fusion of the two stars may be accompanied by an explosive effect reminiscent of a nova explosion. Further evolution of the newly formed star will already take place according to its mass, usually faster than the original stars; at higher masses, it can also result in a supernova explosion or the subsequent formation of a black hole.
*) The situation is more complicated with multiple systems, which we will not deal with in the next one. Some of the stars here, due to the gravitational interaction with other components, can gain a path along which they can escape from the system...
   The loss and carrying of the orbital angular momentum out of the binary system can basically take place by three mechanisms :
< - Ejection of gas clouds from the peripheral layers of the system due to rotational centrifugal force .
< - Dissipative friction in a dense gas cloud that may be contained in the system. This friction can brake the orbital speed of both components.
< - Thermoemission of particles - "stellar wind " - from the photosphere of both stars.
Emission of gravitational waves , which, however, can be applied more significantly only when the binary components are compact shapes - neutron stars and black holes orbiting at relatively close distances. The fusion of the two compact objects is then accompanied by a massive emission of gravitational waves. This mechanism is discussed in more detail in 2.7, section "Sources of gravitational waves in space".
   Thus, binary stars have a finite lifetime (the time until their extinction by fusion), although usually very long. Free binary solar mass systems can have a lifespan of more than 1012 years - that is, longer than the active lifespan of individual stars; in such a case, the two original stars will never actually merge, but possibly the resulting compact objects will merge due to gravitational radiation. However, in close binary stars (especially touch stars ) it can be shorter than 109 years, so the physical fusion of the two stars can really take place (it has not been observed yet...). In binary systems of massive stars (> 10 M), the gravitational collapse of each of the two components will occur relatively soon (as explained in 4.2 "Final phases of stellar evolution. Gravitational collapse"), so that possibly the merging of the resulting compact objects can take place only under the influence of gravitational radiation according to the relations 2.82b,c,d (in 2.7, part "Sources of gravitational waves in space"). The actual merger-collision-fusion of both components can be accompanied by significant electromagnetic radiation, depending on the nature of the objects. When neutron stars merge, the ejected neutron-rich material transforms into nuclei of heavy elements and glows intensely, manifests like nova explosion - produced gamma-flash followed by visual, infrared and then radio-wave radiation. At fusion black holes, but can not be expected photon radiation (if the system does not contain a gas, "has nothing" shine), only a massive emission of gravitational waves.
   The final product the fusion and extinction of a binary system can be a neutron star or a black hole, depending on the resulting weight after merging.

Groups of a large number of stars - star clusters, galaxies
Stars are not evenly distributed in space. Above all, they are part of large systems -
galaxies containing many billions of stars. The formation of galaxies at the beginning of the era of matter in the early universe, their structure and evolution, is discussed in more detail in 5.4 "Standard Cosmological Model. The Big Bang. Shaping the Structure of the Universe.", section "Structure and Evolution of Galaxies".
   The word "galaxy" comes from ancient Greek, where "galaxias kyklos" meant "milk circle" - then the only known large grouping observed in space - our Milky Way. At the time, however, it was not known that it was a huge grouping of billions of stars. Only a faint - "milky" - glowing nebula was observed, a strip stretching across the night sky..
   Within galaxies, the stars are concentrated most densely in the central part, then they are diffusely distributed in the spiral arms, the disk of the galaxy, and less frequently in the galactic "halo". They often form smaller or larger groups, usually of common origin and the same age. The above-mentioned binary stars and multiple gravitationally coupled systems represent the case of the smallest groups of stars. Larger groups of nearby stars are called star clusters - they are systems of a large number of relatively close stars, formed almost simultaneously during the fragmentation of a large gas cloud into individual protostars and then stars. Two types of star clusters are observed :

Variable stars
Most astronomically observed stars have a long-term virtually
constant luminosity *), the intensity of thermonuclear reactions inside them is perfectly regulated by gravity ( is discussed in more detail in the section "Evolution of stars") . However, stars are also observed that change their brightness over time, or variable stars. Since variable stars are a source of important information about the structure and especially the evolution of stars, we will make at least a brief mention of variable stars here.
*) In this physically oriented treatise, perhaps it is not necessary to recall that a certain "vibration" or "glitter" the stars, observed especially on clear summer nights, have nothing to do with the variability of the brightness of the stars. It is just an optical phenomenon caused by the bending of rays from stars as they pass through layers of different densely, turbulently flowing layers in the Earth's atmosphere - local fluctuations in the refractive index of air. This effect blurs images of stars in terestrial telescopes (the last time this undesirable phenomenon thrives corrected by the so-called. adaptive optics). When observing and photographing from space this phenomenon, of course not.
   The nature and causes of variability are different and depending of this the variable star are classified into different groups. The basic division is into two groups :

Eclipsing variable stars are astronomically important mainly because photometric analysis of their variability, together with spectrometric analysis (especially Doppler shifts of spectral lines), allows to determine the basic parameters of the star - especially the mass and diameter of the star. From the astrophysical point of view, the own (really) variable stars are more important, which we can again divide into two main categories :

   Irregularly variable stars are also known, in the atmosphere of which dust particles sometimes condense, forming an opaque cloud around the star. Due to its effect, the brightness of the star will decrease for some time. The cloud of dust then dissolves under the pressure of the radiation and the star brightens again. These changes occur randomly and irregularly, usually in a few years, the decrease in brightness lasts for a relatively short time (several tens of days). These are old, more massive stars (the longest known is R Coronae Borealis).
   In general, in "isolated" stars (which do not interact significantly with the surrounding matter and stars), instability, manifested by variability , is a characteristic feature of the initial stages after the star's formation and then the final stages evolution of the star. We will see this in more detail below in the second half of this 4.1 and the first half of the following 4.2 "The Final Phases of Stellar Evolution. The Gravitational Collapse.".

Hydrostatic equilibrium of the star
According to the findings of modern astrophysics, the star is a huge gaseous
thermonuclear reactor held together by its own gravity; gravity also maintains the reaction in balance. In the normal (relatively stable) phases of a star's life, the gravitational action trying to shrink the star is balanced by the pressure caused by heating and radiation during thermonuclear reactions taking place inside the star *). Conversely, it can be said that gravity seems to "hold the lid" (from the higher layers of colder gas) on the "high-pressure pot" which is the central core.
*) Gravitational energy
released during contraction is a source of stellar energy only during relatively short periods, which are the stage of the protostar and then again the final stages of evolution accompanied by gravitational collapse.
   For most of its life, the star is formed by a gas sphere that is in mechanical (hydrodynamic) and thermal equilibrium. Hydrodynamic balance indicates alignment gravitational forces and pressure forces acting on each element of the star's mass. Assuming a spherical star shape, then in the Newtonian approximation of the equilibrium equation is   

dp / dr =   - [G. m (r) / r 2 ]. r   , (4.1)

ie at each point the force of pressure acting per unit volume must be equal to the force by which the mass contained in it is attracted by the mass

m (r) = 4 p 0 r r r 2 dr ,        (4.2)

contained within the sphere of radius r .
   In the relativistic analysis of a spherical static star, it is necessary to apply Einstein's equations for spherically symmetric metrics with general shape (3.10)   

ds2 = - A(r).dt2 + B(r).dr2 + r2(dJ2 + sin2J dj2) .
gtt(r)a        grr(r)a                              

Assuming that the star is made up of an ideal liquid (or gas), the energy-momentum tensor (1.108) will appear on the right-hand side of Einstein's equations

T ik   = p. g ik + (p + r ) u i u k   ,

where p is the pressure, r is the density of its own total mass~energy and u i is the four-vector velocity. The assumption of staticity (liquid is at rest) and spherical symmetry leads to the fact that p i r are functions only radial coordinates r and ur= uj= uq= 0, ut= -l/gtt = -A(r); "Pascal's law" is fulfilled T11 = T22 = T33 = -p , T00 = rc2. From the law of conservation Tik;k = 0 follows the equation of hydrostatic equilibrium (dA/dr)/A = -[2/(p+r)].dp/dr. The Einstein equations for the components of the curvature tensor then have the form

Rtt = - 4pG (r + 3p) A ,  Rrr = - 4pG (r - p) B ,  Rqq = - 4pG (r - p) r2  .

With the boundary condition B(0) = 1, m(0) = 0 in the middle r = 0 we get the solution for B(r) g rr

g rr   =   [ 1 - 2 G m (r) / r) ] - 1   ,      

from which, by comparison with the Schwarzschild metric (3.13), it can be seen that m(R) = m (r> R) = M (R is the radius of the star) is actually the total mass of the star measured by its gravitational effects at great distances. The geometry of space-time is expressed here by the so-called inner Schwarzschild solution, in the surrounding space outside the star it is seamlessly followed by the standard Schwarzschild geometry (3.13) analyzed in 3.3. For the relationship between mass and radius (radial coordinate r ) the following applies

dm / dr  =  4 p r 2 r    .        

By combining the above simplified Einstein equations, an important equation can be obtained for the radial pressure gradient dp/dr


(Oppenheimer-Volkov-Landau equation) which determines the pressure p as a function of the radius r inside a static spherically symmetric body formed by an ideal fluid, if the equation of state between r and p is known. The mass m(r) contained within the intented sphere of radius r is again defined by relation (4.2). Equation (4.3) is a GTR generalization of the Newtonian equation of hydrostatic equilibrium (4.1); in the Newtonian limit the relation (4.3) really passes in (4.1).
   If we compare the relativistic and classical model of the star, it can be seen that the pressure gradient is larger in the relativistic model than in the Newtonian one. Towards the depth, the pressure increases faster than would correspond to Newton's theory: the higher the pressure, the greater the relativistic contribution in the numerator of equation (4.3). The general theory of relativity thus leads to the finding, that greater gravitational forces and higher pressures act inside the star than would correspond to Newton's theory. It turns out that sufficiently massive and dense stars, for which the Newtonian theory always predicts stable configurations in hydrostatic equilibrium, may in fact succumb to complete gravitational collapse; at first glance, it can be seen from equation (4.3) that, e.g. there cannot be a star in hydrostatic equilibrium, for which it would be 2.m(r)/r 1. The consequences of the general relativity for the late stages of evolution of massive stars will be discussed in the following 4.2 "Final phases of stellar evolution. Gravitational collapse".
   Further details on the astrophysics of stellar structures can be found in the relevant review literature, eg [285], [56], [227].

Evolution of stars
For a detailed understanding of the structure and evolution of stars, it is necessary to invite the latest knowledge from nuclear physics, thermodynamics, energy generation and transfer by radiation and convection, plasma physics, etc. However, as far as the force keeping this whole complex "reactor" in equilibrium, ie gravity, is concerned,
so far the old Newton's theory of gravity will suffice here. Relativistic influences may be more pronounced in ordinary stars only in the very final stages of their development. And just from these final stages, the evolution of stars will be the most interesting for us from the point of view of the relativistic conception of gravity!

Fig.4.l. The time course of some basic parameters of a star - diameter, temperature and luminosity - during its evolution.
The scale of the timeline is strongly nonlinear to capture both the very long equilibrium period and the shorter protostar period, as well as the very short final stage of evolution (shown in the "time magnifying glass").

Thermonuclear reactions inside stars
Some typical stages of stellar evolution are shown in Fig.4.1. The
basic "chemical composition" of the germinal cloud - protostar - 75% hydrogen and 25% helium, is the result of primordial cosmological nucleosynthesis (it is analyzed in more detail in 5.4, section "Lepton era. Initial nucleosynthesis"). As mentioned above in the "Star Formation" section, the initial collapse of the germinal cloud, replaced by a slower contraction, leads to an increase in density, pressure and temperature due to adiabatic compression. At high temperatures, the substance is ionized and the atomic nuclei acquire high kinetic energy that in collisions they can overcome mutually repulsive electrical (Coulomb) forces and approach each other at a distance of 10-13 cm, where attractive strong nuclear interactions begin to act . Nuclear forces then tie them together - the nuclei merge with each other, they fuse to form a new heavier nucleus and release nuclear binding energy. This is the mechanism of all thermonuclear reactions inside stars (their individual types will be described below).
The course of various types of thermonuclear reactions in stars is described in detail in the extensive work "Synthesis of elements in stars" [35].
Dynamics of thermonuclear reactions 
In order for a nuclear reaction to occur, the nuclei must approach each other at a distance r
s 10-13 cm, where attractive strong nuclear interactions begin to act. This requires a relatively high kinetic energy EC which overcomes electrostatic repulsion barrier (Coulomb potential "rampart") between two nuclei with charge Z1.e and Z2.e : EC = Z1.Z2.e2/rs. Between two hydrogen nuclei with the proton number Z1=Z2=1 will be the height of the barrier EC 1 MeV. A temperature higher than 1010 degrees would be required to thermally reach such a value of the mean kinetic energy of the nuclei. However, there are two favorable circumstances that significantly decreases the minimum temperature required for efficient formation of fusion reactions :
1. Tunnel effect , thanks to which there is always some non-zero probability that it will overcome the Coulomb barrier even particles whose energy is less than EC (this probability of overcoming for a particle with energy E is approximately PE ~ exp[-(EC/E)] ); see eg 1.1, section "Quantum nature of the microworld", passage "The quantum tunneling phenomenon"in the book "Nuclear Physics and Physics of Ionizing Radiation").
2. Maxwell's statistical distribution*) of the velocities of thermal motion of particles shows that there is always a number of particles moving at significantly higher velocities than the corresponding kinetic energy <ET> = 3/2.k.T.
Maxwell-Boltzmann statistical distribution of the thermal motion of the particles
Particles of idealized "gas", in our case the ion stellar substance of mass m, constantly move and collide, each having a different instantaneous velocity v, direction of motion and different kinetic energy E = m.v2/2, which randomly and chaotically changes due to mutual collisions. The distribution of velocities and energies of random motion of ideal gas particles is described by the so-called Maxwell-Boltzmann distribution function P , determining the probability of the number of particles in the state with velocity v : P(v) = 4p.(m/2pk.T)3/2.v2.exp(-mv2/2k,T), or equivalent with energy E : P(E) = 2p.(1/2pkT)3/2.v2.exp(-E/kT), where T is thermodynamic temperature and k is the Boltzmann constant (expressing the relationship between temperature and energy of gas particles: it is the amount of kinetic energy of one particle that corresponds to a change in gas temperature of 1 K; it has the value k = 1.38.10-23 J K-1). The graph of this distribution function is a wide "bell-shaped" (but asymmetrical) curve, the shape of which depends on the temperature: the higher the temperature, the wider the shape of the curve and its maximum is shifted towards higher energies and velocities. The maximum of the curve determines the most probable velocity vp = (2kT/m), but from a physical point of view the more important is the mean square velocity of the particles vk = (3kT/m), which corresponds mean kinetic energy particles at a temperature T: <ET > = 3/2 .kT. After converting to nuclear energy unit [eV] the mean particle energy 1eV corresponding to a temperature of 11600 K, so that the temperature of 1keV represents 11.6 million degrees. With temperature T , not only does the mean value of velocity or energy <ET> increase, but also the relative proportion of particles with high velocity and energy E >> <E T > increases.
   Due to these two circumstances (and due to the large volumes and high densities of gas-plasma), in stars, thermonuclear reactions between the lightest nuclei can take place sufficiently efficiently already from temperatures
   107 degrees.
   The heavier the nuclei (the higher their proton number Z), the higher the electrical repulsive barrier and the higher the threshold temperatures required for their thermonuclear fusion; as the temperature rises, so does the intensity of the reactions. The efficiency of fusion further depends on the internal mechanism of the nuclear reaction itself, depending on the configurations of proton and neutron energy levels of the participating nuclei, or co-production with weak interaction. Nuclear physics expresses it by the so-called effective cross section (see 1.3 "Nuclear reactions and nuclear energy" in the book "Nuclear physics and physics of ionizing radiation"), which is measured by the interaction of particles on accelerators. The study of these interactions has enabled nuclear astrophysics to understand the nature and course of nuclear interactions inside stars.
   Thus, for each type of thermonuclear reaction, a certain minimum threshold temperature is required at which the reaction begins. At this (or slightly higher) temperature, the reaction proceeds smoothly and very slowly, with low energy output. Due to the statistical distribution of the velocities of thermal motion of particles, only a small part of the nuclei has sufficient kinetic energy to overcome the Coulomb barrier (either directly or through the tunneling phenomenon). As the temperature T increases, the intensity of the reactions and the energy output increase sharply (at least as T4 ). In the equilibrium phases of the star's evolution, the intensity of the reactions and the energy output are regulated by gravity, the temperature being maintained at a value slightly above the minimum threshold. However, in the unstable phases of a star, it can happen that the stellar material heats up sharply, during which the temperature suddenly rises well above the threshold temperature. In this situation, an explosive thermonuclear fusion can occur, in which almost all the nuclei fuse in a short time and a huge amount of nuclear energy is released, accompanied by a massive explosion - see below "Late Stages of Star Evolution", passage "Explosion of Nova" or "Thermonuclear explosion of a star". Another mechanism is the explosion of a type I or II supernova, as will be explained in the following 4.2, section "Supernova explosion. Neutron star. Pulsars". Here, however, we will first deal with the peaceful succession of thermonuclear reactions, which occur as the temperature gradually increases by the gravitational contraction of stars.
The first nuclear reaction in the early development of stars
After the temperature reaches over one million degrees in the central regions of the protostar, the first thermonuclear reactions ignite, during which deuterium, lithium, beryllium and boron are converted into helium.
For example reactions: 2D1 + 1H1 3He2 + g ; 2D1 + 2D1 3He2 + n ; 6Li3 + 1H1 3He2 + 4He2 ;
                            6Li3 + 1H1 7Be4 ,7Be4 + e- 7Li3 + n, 7Li3 + 1H1 8Be4 2 4He2; 11B5 + 1H1 3 4He2; .....
Reactions of this kind, thanks to their larger effective cross-section, take place even at lower temperatures than the fusion of hydrogen itself.
   The released energy will temporarily stop the contraction of the protostar. However, the content of these elements in the interstellar gas (and thus in the core of the protostar) is small, so that a relatively small amount of energy is released and this stage lasts only a very short time *). By the "burnout" of a large part of these elements already in the early stages of stellar evolution is explained the relatively small representation of D, Li, Be and B in universe.
*) The stage of deuterium fusion is for the larger stars only a kind of temporary "stop" on the way from the protostar to the real star (max. tens of millions of years). However, for very small stars - brown dwarfs - deuterium fusion is the only source of energy (along with gravitational contraction); it can be slow take place even for a billion years.
   If the emerging star has a sufficiently high mass (at least tenths of M and higher), during its gradual gravitational shrinkage and heating, there will be a sequence of increasingly complex thermonuclear reactions, in which the binding nuclear energy is released and heavier elements are formed from lighter elements :

Hydrogen combustion
When the star's
interior reaches temperatures above 10 million K, the longest period of the star's active life begins - the "combustion" (nuclear fusion) of hydrogen to helium in the central part, with the star in a state of hydrodynamic and thermal equilibrium *). The gravitational weight of the outer layers is balanced by the pressure of radiation and the pressure of the thermal motion of the electrons and ions of the hot gas inside the star, heated by the released nuclear energy. From the point of view of nuclear physics, each star is a huge, perfectly functioning cosmic thermonuclear reactor, precisely regulated by gravity.
*) However, this equilibrium does not occur immediately after the ignition of thermonuclear reactions. On the contrary, the birth of a star is accompanied by significant instabilities, young stars are often variable. After the ignition of thermonuclear reactions in the central part, the surrounding gas expands sharply due to heating and radiation pressure. Part is "blown" out of the star, part falls back after cooling. It can reheat, expand and re-shrink the surrounding gas - the size and temperature of the star's surface change (partly regularly and irregularly), which appears as a variable star (type T Tauri). After a greater or lesser number of such cycles, most of the gaseous envelope of the protostar is finally "blown away" - the star "peeks out", brightens and shines undisturbed into space. From the gaseous envelope around the star, planets can gradually form, orbiting a star. In fast-rotating protostars, gas jets from "poles" in narrow cones along the axis of rotation can also be observed. Only after the initial instabilities have subsided, does the star "settle" between the stable stars of the main sequence on the HR diagram for a long time.
   Thermonuclear fusion is very sensitive to temperature, increasing it will speed it up, decreasing it will slow it down. If heat production decreases, the cooled star core shrinks by gravity, heating it up, accelerating fusion. This increases the production of energy, the star's core expands (against gravity) and cools by the resulting pressure, which dampens the fusion. This mechanism works like a kind of natural "thermostat", that the star always keeps the balance between shrinkage and expansion, heating and cooling. The disruption of stable equilibrium occurs only in the final stages of life stars after consuming thermonuclear" fuel "
(see "The late stages of the evolution of the stars") .
   Thermonuclear fusion inside stars is very slow. For ordinary stars the mass of the Sun, the power in the middle parts (with a diameter of about 350,000 km) is about 250 W/m
3, so the hydrogen "fuel" lasts for about 10 billion years. Inside our Sun, about 590 million tonnes of hydrogen are converted to 585 million tonnes of helium every second; the difference in mass of 5 million tonnes is converted into energy, which is gradually radiated outwards. During the combustion of hydrogen, which is the most abundant element in the universe, the star remains on  the main branch of the HR diagram.
   The basic thermonuclear reaction inside stars is the direct proton-proton reaction p-p (p 1 H), which takes place in three stages :
1. partial reaction:
1H1 + 1H1 2He2 + g ; 2He2 2D1 + e+ + n (+ 1,44 MeV) ; e+ + e- 2g (+ 1,02 MeV)
2nd partial reaction:
2D1 + 1H1 3He2 + g (+ 5,49 MeV)
3. Partial reaction: 3He2 + 3He2 4He2 + 2 1H1 (+ 12,85 MeV)
is formed as a result. Total energy balance: release 26.2 MeV = 4.2.10-12 J/(1 He nucleus).
   For massive stars of the 2nd and subsequent generations (which already contain heavier elements such as carbon, oxygen and nitrogen in their starting building material) at temperatures above 107 K is further approached by a reaction called CNO-cycle, where in the chain of reactions involving carbon (as a catalyst) 4 protons p 1H are gradually converted into a helium nucleus :
1st partial reaction:
12 C + 1 H 13 N + g ( + 1.95 MeV)
partial reaction: 13 N 13 C + e + + n (+ 2.22 MeV)
3rd partial reaction:
13 C + 1 H 14 N + g (+ 7.54 MeV )
4th partial reaction:
14 N + 1H 15 O + g (+ 7.35 MeV)
5th partial reaction: 15 O 15 N + e + + n (+ 2.71 MeV)
6th partial reaction: 15 N + 1 H 12 C + 4 He (+ 4.96 MeV)
   Total energy balance: release 25.0 MeV = 4.0.10-12 J/nucleus He. CNO cycle requires a slightly higher temperature than the p-p, because in the reactions are applied the nuclei with a higher proton number Z.
   In star second and subsequent generations on the main sequence, more massive than about 1.7
M, the CNO cycle is the main nuclear process, while in lighter stars (and of course in 1st generation stars) the p-p-reaction takes place.
   During the hydrogen combustion stage, about 12% of all hydrogen in the central parts of the star is converted to helium. Helium produced in the core is accumulated here, the hydrogen is depleted by gradual dilution with helium "ash" for fusion reactions
(ceased to be available for fusion), the reaction slows down, gravity prevails, and the star's core begins to compress.
The long path of energy and radiation from the interior to the star's surface
The nuclear binding energy of strong interactions is released inside the star during nuclear fusion in the form of kinetic energy of emitted particles and high-energy photons of g radiation (part is carried away by neutrinos flying out of the star). High-energy photons, if moved without obstacles (in a vacuum), could reach the star's surface in just a few seconds. In reality, however, this energy released by thermonuclear reactions from the star's core reaches the surface layers very slowly through a combination of multiple scattering, emission-absorption mechanisms, and finally convection.
   Inside the star is a fully ionized mixture (plasma) mainly of protons, electrons and helium nuclei, the temperature is more than 10 million degrees. In thermonuclear reactions (mentioned above) photons of high-energy radiation g are formed , in collisions of high-energy electrons and protons, additional hard braking gamma radiation is produced. These photons are further scattered on electrons by Compton, which reduces their energy and the accelerated electrons emit more photons with lower energies during collisions. From one original high-energy photon, two or more secondary photons with lower energies are created. By further and further interactions of photons with electrons, a large number of secondary photons with ever lower and lower energies are gradually formed - gradually X-rays, ultraviolet radiation and finally visible light and infrared radiation. Such division or "comminution" of one original high-energy gamma-photon ultimately produces up to 100,000 lower energy photons. Secondary photons radiate chaotically in different directions during interactions, once upwards, sometimes towards the inside of the star. However, the overall tendency is a slow transfer of energy from the inside out, in the direction of the temperature gradient of the star material. The speed of energy transfer from the interior of the star gradually increases from the center, because there is less pressure and density of matter and a larger mean free path of motion of photons and electrons.
   In the upper layers of the star, there is no longer (to that extend) such collisions and re-emissions of secondary photons, ie the division of photon energy. Radiation from the deeper layers is absorbed by electrons and converted into the kinetic energy of the particle's motion - into heat heating the outer part of the star. Near the surface of the star, convective energy transfer is applied - massive streams of hot gas rise to the surface, where they transfer heat, and the cooled ones fall deeper. The surface of stars typically has a temperature of several thousand degrees and emits electromagnetic radiation with a continuous spectrum, the higher the temperature, the shorter the wavelengths of the maximum and center of the energy spectrum (see HR diagram above). Hot stars with a surface temperature of about 30,000 C radiate most in the blue and UV part of the spectrum, Sun-like stars with a surface temperature of about 5000 C in yellow visible light, cold stars (red dwarfs, red giants) with a surface temperature of about 3000 C glows mainly in red light and infrared radiation. In the transition region between the upper layers of the star and the stellar atmosphere, radiation with a line spectrum characteristic of specific atoms is also emitted - bright emission lines arising from deexcitation of electron levels of atoms, excited by radiation and mutual thermal collisions. In the gas envelopes around the stars, dark absorption lines are formed in the spectrum, caused by the increased absorption of photons, whose energy corresponds to the energy differences between the electron shells of the gas atoms in these gas envelopes.
   Visible light from stars and other objects in space is thus many times transformed radiation originally from nuclear and subnuclear processes with much higher energies, corresponding primarily to g radiation. The energy released in the core of the star is thus "passed through the obstacle course" for hundreds of thousands of years to the surface, where from the photosphere is  finally emitted into the surrounding space in the form of photons, mainly visible and infrared light; these emitted photons are a kind of "great-great-great-great-grandchildren" of the original gamma-photons from the star's core. Only neutrinos pass almost freely through the star's material and are emitted almost immediately into the surrounding universe.

Combustion of helium
After the "burnout" of hydrogen in the central part
, for some time gravity prevails, the core of the star shrink, while the outer envelope expands due to the flow of energy from thermonuclear reaction, which moved into the hydrogen shell around the core. The outer radius of the star increases sharply and the temperature of the surface layers decreases - the star becomes a red giant. For sufficiently massive stars (M > 0.1 M), the temperature in the core increases to 108 K and the density to 108 kg/m3, when the helium nuclei begin to merge into carbon by "3-alpha" reactions, in which three helium-4 nuclei (a-particles) are converted to a carbon nucleus :
4 He 2 + 4 He 2 8 Be 4 + g  ,   8 Be 4 + 4 He 2 12 C 6 + g  .
Since there is no stable nucleus with nucleon number 5, heavier elements cannot be thermonuclear formed by simply trapping a proton in the helium nucleus or by fusing two helium nuclei. Up to three helium nuclei (3
a) can be synthetsized into a stable carbon nucleus. The direct triple synthesis of 3 a (= 4He ) 12C + g has a low probability, the reaction usually takes place gradually over beryllium 8Be. Although 8Be is very unstable (with a half time 6,7.10-17 seconds decays back into two alpha particles), there are two happy circumstances :
Basic state of beryllium-8 has an energy almost exactly equal to the energy of two
a-particles .
8Be + 4He has almost exactly the same energy as the excited state of the 12C nucleus .
This proximity of energies leads to resonances, which significantly increase the probability (effective cross section) of the respective reactions *) inside the star with a high concentration of helium. Therefore, the fusion of helium efficiently produces a large amount of beryllium-8, which has a high effective cross section for the capture of alpha particles. Thus, although
8Be is very unstable, under suitable conditions of high concentrations of helium in the interior of massive stars, 8Be is often not sufficient to decay before the capture of the third helium core, to form stable carbon-12. This significantly increases the probability of the resulting connection of the three helium nuclei and the formation of carbon.
*) If the energy of the excited state of carbon-12 were only slightly higher, the rate of its formation would be much lower, so that almost all beryllium-8 nuclei would decay back into helium nuclei before carbon could be formed. In addition to the original hydrogen and helium, very little carbon and other heavier elements necessary for life would be formed . Similarly, if the half-life of 8 Be was even shorter. Conversely, if beryium-8 were stable or long-lived, a large amount of carbon would be formed in the stars - perhaps the universe could be "swarming" with life..?..
 How finely must natural constants be "tuned" for life to form generally discussed in 5.7 "
Anthropic principle and existence of multiple universes" and in work "Anthropic principle or cosmic God"...
   Combining the three helium nuclei to carbon is released energy 7.2 MeV. Contraction core star it stops again and burning of helium for a certain time (but considerably shorter than that it was with the burning of hydrogen, less than 10% of life star) maintains the radiance and stability of the star.
   For stars of 1.generation with this thermonuclear fusion of helium for the first time discovered a new element - carbon, which was not in universe before !

Carbon Combustion
After most of the helium has been depleted, the
star core further shrinks by gravity, the temperature rising above 5.108 K, and the "ash" of the previous reactions - helium and carbon - becomes the "fuel" for subsequent reactions. The "burning" of carbon is an important stage in the thermonuclear evolution of medium and heavy stars (M > 0.8 M). Carbon combines with particles a (nuclei of helium 4He) and with the increase of temperature gradually ignites other reactions accompanied by the combustion of carbon, which produces other heavier elements - oxygen, neon, sodium, magnesium :
      12C6 + 4He2 16O8 + g16O8 + 4He2 20Ne10 + g12C6 + 12C6 20Ne10 + 4He2 ,
      12C6 + 12C6 23Na11 + 1H112C6 + 12C6 23Na12 + 1n012C6 + 12C6 24Mg12 + g , ... etc. ...
   The end result of burning carbon is a mixture of mostly oxygen, neon, sodium, magnesium. When the temperature rises above 1.2.109 K, the combustion of neon to magnesium continues, eg 20Ne10 + 4He2 24Mg12 + g .
Oxygen combustion
After depletion of most of the carbon, another gravitational contraction occurs inside the star, and at temperatures around 2.10
9 K inside the massive star (M > 8 M), oxygen nuclei can thermonuclear fuse to silicon and surrounding elements :
      16O8 + 16O8 28Si14 + 4He2 ,  resp. 31P15 + 1p1 ,  resp. 32S16 + g ,  24Mg12 + 4He2 ,  .... ... . etc. ...
Combustion of oxygen significantly enriches the inner part of the star with silicon.
Silicon combustion
The last and shortest stage in the sequence of thermonuclear reactions inside very massive stars (M >
10 M) is the fusion of silicon nuclei. It occurs after the burning of neon and oxygen, when the gravitational contraction raises the temperature of the star's interior above about 3.109 degrees. At these temperatures, protons and quantum g reach such a high energy that they break up the nuclei of heavier elements (photonuclear reactions), from which protons, neutrons, a-particles and other fragments of nuclei are ejected. The nuclei of silicon and other elements in the hot thermonuclear plasma capture neutrons, and protons, a-particles capable of, giving rise to other heavy elements, e.g. sequences a-processes :
28Si14 + 4He2 32S1632S16 + 4He2 36Ar1836Ar18 + 4He2 40Ca2040Ca20 + 4He2 44Ti22 ,
44Ti22 + 4He2 48Cr2448Cr24 + 4He2 52Fe2652Fe26 + 4He2 56Ni28  .
Silicon combustion is a source of energy for heavy stars only for a very short time (only a few days!), at the very end of their thermonuclear evolution.    
  In general, late thermonuclear reactions are becoming hotter and faster. And increasingly less effective in releasing nuclear energy. The active life of the star ends here very soon ..!..

Stellar nucleosynthesis - stable and radioactive nuclei
The above-mentioned sequences and cycles of thermonuclear reactions are often "unfinished", so that in addition to the "final" products, all intermediates are continuously formed. Many nuclei, synthesized by thermonuclear reactions in stars, are radioactive and one or more decays (mostly beta) give rise to stable isotopes of individual elements.

E.g. the above-mentioned
56Ni28 is decay to cobalt 56 Co27 with a half-life of 6 days of radioactivity b+ (or by electron capture EC) , and this is then further again by b+-radioactivity with a half-life of 77 days converts to stable iron 56Fe26 .
For the further chemical development of the universe, however, in addition to stable nuclei, only those radioactive nuclei will be preserved, whose half-life is sufficiently long, greater than about 10
8 years - natural so-called primary radionuclides (1.4 "Radionuclides" in the book "Nuclear Physics and Ionizing Radiation Physics").
   Due to the number of mentioned nuclear reactions of fusion and radioactive transformations - stellar nucleosynthesis - in the interior of massive stars, other heavier elements are gradually formed from hydrogen and helium, which can be summarized as follows :
- Helium 4He2 is formed by hydrogen combustion (in the original material was about 25% 4He from primordial cosmological nucleosynthesis and is enriched in the hydrogen combustion phase); the isotope 3He2 is formed by the incomplete p-p reaction.
- Carbon 12C6 is formed by thermonuclear fusion of three helium nuclei. Oxygen 16O8 and neon 20Ne10 are formed during the combustion of carbon with helium.
Isotopes of nitrogen 14N7, 15N7, carbon 13C6 and oxygen 17O8 are products of the unfinished CNO cycle.
- Magnesium 24Mg12, aluminum 27Al13, silicon 28Si14, phosphorus 31P15, sulfur 32S16, ..., are formed during the combustion of carbon and oxygen.
- Calcium 40Ca20, titanium 44Ti22, chromium 48Cr24, ..., finally iron 56Fe26 and nickel are formed at the end of a sequence of thermonuclear reactions by the gradual combustion of silicon and the resulting heavier elements with helium (a-processes).
- Elements heavier than iron and nickel were not formed by thermonuclear fusion, but by repeated neutron fusion followed by b- transformation (as will be discussed below - "Neutron capture and formation of heavy elements") . The synthesis of elements in stars is analyzed in detail in the extensive work "Synthesis of elements in stars" [35].
   In order for a star to synthesize heavier elements, it must have sufficient mass so that gravity induces the necessary high pressures and temperatures inside it. Small stars can only make helium from hydrogen, more massive stars like our Sun will form nuclei down to magnesium, and much larger stars will undergo a whole sequence of thermonuclear reactions. The implications of stellar nucleosynthesis for the chemical evolution of the universe will be discussed below in the section "
Alchemical Boilers of the Universe".
   Thus, stars go through successive stages of evolution accompanied by various thermonuclear reactions. As it transitions between stages, the star's interior shrinks and heats up until it begins to synthesize heavier atomic nuclei, whose fusion was previously impossible (due to temperature). The newly released energy again temporarily rebalances gravity and gas pressure. Later and "higher" stages are getting shorter.
   For each star, during its evolution, a sequence of thermonuclear reactions ends somewhere. When and where it ends depends on its initial mass, which determines the internal temperature inside the star and thus the type and speed of thermonuclear reactions. The star will end its thermonuclear evolution either because the temperature is not enough to continue the sequence of "higher" reactions, or because it has already exhausted all its available nuclear energy - its interior is composed mainly of iron and surrounding elements (nickel, cobalt, chromium), whose nuclei are so strongly bound, that they are already nuclear "non-flammable".

Neutron capture and formation of heavy elements
At high temperatures in the late stages of stellar evolution, neutrons are released (ejected) from nuclei
. This neutrons, because they do not have an electric charge, easily penetrate into the nuclei of heavier elements, where they can be captured by strong interaction. Such neutron capture makes the nucleus one nucleon heavier. The newly formed nucleus usually decays (transforms) by b- -radioactivity, emits an electron (and a neutrino) and forms an element with a proton number higher by "1", shifting by 1 to the right in Mendeleev's periodic table. This newly formed nucleus of the heavier element can capture the neutron again, and an even higher nucleus is formed by the b- conversion. Such processes of repeated neutron fusion with subsequent b- decays generate increasingly heavier and heavier nuclei up to lead and bismuth.
   During b- decay, the proton number increases by 1. With repeated absorption of the neutron and subsequent b- decay, the resulting nuclei constantly move to heavier and more complex nuclei :
      NAZ+n N+1AZ(b-) N+1BZ+1, N+1BZ+1+n N+2BZ+1(b-) N+2CZ+2 , ..... etc ..
   According to the ratio of the neutron capture rate and the subsequent
b- decay, nucleosynthesis of this type is divided into two types of processes :
At slow s-process ( slow ) undergoes beta conversion after the first capture, and the next neutron is captured by the nucleus until the b- decay occurs. In this way, medium-heavy nuclei up to N = 209 can be formed, but heavy nuclei in the uranium and transuranium region do not, because after neutron capture, there is a rapid decay a or the splitting of such a nucleus. These heavy nuclei can form in neutron-rich plasma during the so-called :
r-process (fast - rapid ), when another neutron is captured before b - decay occurs. This occurs in an environment where the density of free neutrons is so high that neutrons are captured by nuclei much faster than beta transformations take place. Thermonuclear plasma rich in neutrons occurs during a supernova explosion, which will be discussed in more detail in the next 4.2, passage "Astrophysical significance of supernovae". The rapid capture of neutrons creates unstable nuclei with an excess of neutrons, the subsequent repeated b--decays forms heavy nuclei in the expanding envelope of the supernova up to uranium and transurans. Many of them are radioactive. For further development, however, in addition to stable nuclei, only nuclei whose half-life of radioactive decay is sufficiently long, greater than about 108 years, will be preserved .
   During the "peaceful" thermonuclear reactions in the late stages of massive stars is released relatively few neutrons, so the nucleus after neutron capture has enough time to convert the beta- decay. Only then does in capture another neutron - it is the s-process by which heavy stars synthesize nuclei with numbers of nucleons from 60 to 209 at the end of their evolution. The thus formed in the universe of about half of nuclei heavier than iron, the other half (including heaviest elements) afforded r- process during a supernova explosions (discussed in 4.2, passage "Astrophysical significance of supernovae"). Significant amounts of heavy elements can also be created by nucleonization of neutron matter, ejected by the fusion of neutron stars in their binary systems - see 4.8, passage "Collisions and fusions of neutron stars".

Late stages of evolution of stars
the late stage at the evolution of the stars usually considered a period when the core of the star has already cease the last thermonuclear fusion - either because the lighter star's temperature is not enough to continue the more complex fusion, or because the heavier star has already exhausted all its nuclear energy. At what stage this occurs depends on the mass of the star (as discussed above). In any case, even in the case of heavy stars in iron core, the sequence of thermonuclear reactions, accompanied by shrinkage of the nucleus and expansion of the star's surface, ends because the elements around iron have the highest binding energy per nucleon, so the synthesis of heavier elements is no longer an exothermic reaction (energy must be supplied instead). However, these heavier elements are synthesized to a lesser extent by neutron capture - both by a slow process in thermonuclear reactions (as mentioned above) and by a fast process in a supernova explosion (see 4.2 below).
At temperatures above
3.109 K, a number of different reactions take place - both reactions in which heavier elements are formed and reactions in which the nuclei split. There is a certain dynamic equilibrium, in which the most stable nuclei are formed, which is a group of elements around iron (chromium, manganese, iron, cobalt, nickel).
The internal structure of a massive star in these late stages of evolution is already becoming quite complex - it resembles a somewhat shell structure of an onion *). Around the iron core is a layer where processes a at temperatures of 1-3.109 K burn carbon, oxygen and other elements. Above it, towards the periphery, is a layer of temperature 108 -109 K, in which helium is burned to carbon, and lastly there is a layer in which hydrogen is still burned to helium at a temperature of 7.106 K. This whole "hot furnace", in which the chemical elements are "boiled", is surrounded by a thick layer of plasma made of hydrogen and helium, through which the released energy gradually penetrates by convection, until it is finally the surface layers of temperature 104 K from which emitted in the form of electromagnetic radiation - in the infrared, visible and UV regions of the spectrum.
*) The stated depth distribution of elements of the shell ("onion") character can be expected only in non-rotating or slowly rotating stars. If the star rotates rapidly, centrifugal forces, magnetic and induced electric forces cause convective currents of matter from the interior to the surface, which can "mix" the chemical composition. Heavier elements such as nitrogen or carbon can thus reach the surface of the star.

A massive star in the final stages of its evolution (illustrative image - scales are not met) .
Left: In the final stage of its evolution, the star has a shell "onion-shaped" structure with a burnt core (in sufficiently massive stars it is formed mainly by iron), around which there are a number of zones in which individual types of thermonuclear reactions burn.
Right: In the final stages of evolution, the star sheds the envelope of the upper gas layers, which becomes a glowing so-called "planetary" nebula.

In the late stages of the star's evolution, energy sources appear in spherical layers, where various nuclear reactions ignite, a number of zones of radiant and convective energy transfer are created. At the same time, instabilities are beginning to manifest themselves significantly: the star pulsates (changes its size, brightness and temperature), eject the outer layers of matter or even explodes like a nova, at higher masses even like a supernova - see the following 4.2.
Nova explosion
We now know that it is not a "new star"
(cf. the following 4.2, section "Supernova explosion. Neutron star. Pulsars.", passage "Types of supernovae and their astronomical classification"), but a distant faint star - a white dwarf, hardly visible even with a large telescope, it suddenly increases its brightness about 100,000 times. The mechanism of the nova explosions is now explained by a thermonuclear explosion of hydrogen and helium that has accumulated on the surface of a white dwarf during the accretion of gases from a red giant, forming a tight binary star system with a white dwarf (4.2). The overflowing hydrogen and helium, forming a thin layer at the surface of the white dwarf, is compressed by strong gravity and heated to a high temperature. When a certain critical amount is reached, an explosive chain fusion (thermonuclear) reaction of an explosive nature is ignited, during which a large amount of energy is suddenly released. The increase in the brightness of the novae is sharp due to the thermonuclear explosion (several days until the maximum is reached), the decrease is significantly slower, months and years - the gradual radioactive decay of radioisotopes **), created during the thermonuclear explosion, also contributes to this.
**) During massive thermonuclear fusion of hydrogen nuclei, a large number of neutrons are releasedwhich can be absorbed by the cores of light and medium heavy elements. These nuclear reactions produce a large number of radioactive isotopes (eg Be-7, Na-22, ...) - see 1.3 "Nuclear reactions", passage "Neutron-induced reactions" in monograph "Nuclear physics and ionizing radiation physics".
The accumulated hydrogen fuses to helium by thermonuclear fusion, the energy radiates, the reaction stops and the white dwarf accumulates new material - for a possible further explosion. When the nova explodes, only surface layers are discarded (approx. 10-5 % of the star's mass) and after the explosion the brightness of the star returns in a few months or years to practically the same value as before the explosion. Gas from another binary partner may overflow again, and the nova explosion process may be repeated several times - the so-called recurrent nova. It turns out that the stronger the explosion of the nova, the longer the star "gains new strength" - the accumulation of sufficient hydrogen and helium. So far, only 8 recurrent novs have been observed, with somewhat irregular periods ranging from about 20-50 years. However, it is probable that a number of other novas are recurrent, but with a very long period of hundreds of thousands of years. It can be expected that after a certain number of cycles, Chandrasekhar's mass limit will eventually be exceeded and the white dwarf will definitely explode like a supernova.
 Nova - Kilonova - Supernova - Hypernova
From the name "nova" are also derived the names for significantly more powerful stellar explosions observed in space :
-> Kilonova is an explosion on the order of 1000 times stronger than a nova, but considerably weaker (about 10-100 times weaker) than a typical supernova. This explosion occurs during collisions and fusions of neutron stars - 4.8, passage "Collisions and fusions of neutron stars".
-> Supernova is a massive explosion of a star at the very end of its evolution, fatal for the star - the star disappears. It can be either a thermonuclear explosion of a star, or the gravitational collapse of the core of a massive star to form a neutron star or black hole - 4.2, section "Supernova explosion. Thermonuclear explosion. Core collapse - neutron star.". For less massive stars, at the end of their evolution, a supernova may not occur immediately, but only later: first, a white dwarf is formed, which accumulates mass from the stellar companion until it exceeds a critical value and only then explodes as a type Ia supernova.
-> Hypernova is sometimes called an even more powerful supernova explosion (about 10-100 times stronger), which occurs during the collapse of the rapidly rotating core of a very massive star, resulting in high-energy jets of matter and radiation from the accretion disk. Sometimes this name is also used for a hypothetical, as yet unobserved, thermonuclear explosion of a massive star due to e--e+- pair instability (4.2, passage "Formation of electron-positron pairs").
 The rapid final stages of stellar evolution
For the final stages of
stellar evolution are characterized by the fact that they proceed significantly faster than the main stages of hydrogen combustion to helium. This is because thermonuclear reactions between heavier nuclei have a much lower energy yield than between hydrogen nuclei, so that they "burn" very quickly at high temperatures and pressures.
   In the upper part of Fig.4.1 on the right, it can be seen that in the late stages of evolution, the inner part of the star shrinks, but the outer parts (and thus the "surface" of the star) expand - the star becomes a red giant. The kinetic energy of more and more hot gas and the increasing pressure of radiation expand the weakly bound surface layers towards the surrounding space - in the end the so-called planetary nebula *) is formed. As the glowing inner part of the star is gradually exposed, the effective wavelength of the emitted light decreases, changing color from orange to yellow, white and blue, until intense ultraviolet radiation is finally emitted, which excites and ionizes the ejected gas and causes it to fluoresce - the nebula glows in spectral colors.
*) Planetary nebulae, of course, have nothing to do with planets! This is what they mistakenly named at the beginning of the 19th century by the English astronomer W.Herschel, who in the telescope at the time reminded the disk of a distant planet. The name was maintained even later, when large telescopes revealed the true structure and nature of these nebulae. Planetary nebulae often have a very complex structure and are very beautiful in images from large telescopes. The details of the formation of these structures have not yet been fully elucidated - there are probably more influences such as rotation, gravitational action in multiple star systems and undoubtedly also the magnetic field.

Significance of stars for the chemical evolution of the universe
The starting material from which the first generation of stars formed was from the initial hot period of cosmological evolution of the universe
(analyzed in more detail in 5.4, "Lepton era. Initial nucleosynthesis") and consisted of about 75% hydrogen and 25% helium (helium is about 10% of all atoms). More complex (heavier) elements were practically absent. At the end of their evolution, however, these 1st generation stars already contained a certain percentage (approximately 1%) of heavier elements, created by thermonuclear fusion and other nuclear processes (discussed in detail above in the section "Thermonuclear reactions inside stars"). However, these heavier elements remain "trapped" by gravity for most of the star's life, with only a small portion leaving when the stellar "wind" emits.
    Only at the very end of the evolution of the star, when the nova and supernova explode
(see the following 4.2), these heavier elements are ejected and mix with the gas of the original interstellar matter, which they enrich with heavier nuclei *). Then, when new stars form in the clouds of this interstellar matter, they are enriched with heavier elements. Each subsequent generation of stars has more heavy elements than the previous ones (the Sun is considered a 3rd generation star). In terms of cosmic nucleogenesis, generations of stars metaphorically "pass the batton" in the formation of heavier elements (however, this "passage of the batton" takes millions and billions of years!) .
*) During the supernova explosion itself
(4.2, part "Supernova explosion. Neutron star. Pulsars."), even the heaviest elements up to uranium and transuranics can be effectively formed by the mechanism of repeated neutron fusion with the following b--transformation, in which the proton number always increases by 1. From "our parent supernova", however, only stable elements have been preserved to date, and of radioactive ones only those that have a very long half-life > ~108 years.
Metallicity, generation and population of stars
Relative proportion of the heavier elements with respect to hydrogen and helium is referred to as metallicity. In astronomy, however, this means not only the presence of metals, but a lump sum of all elements heavier than helium, especially carbon, oxygen, nitrogen, etc. A star or dust-gas cloud, containing a higher proportion of carbon, oxygen, nitrogen or neon, is referred to as "rich in metals" - with higher metallicity, although according to chemistry they are mostly non-metals
(after all, chemical metal bonds in ionized matter inside stars are not possible even with nuclei of metal elements..!..). Metallicity ZO of object O is quantitatively expressed as total mass share of mZ (Z>2) elements heavier than helium Z=2He in the total mass MO of the object: ZO = Z>2S(mZ/MO). For example, for the Sun the metallicity is Z 0.02, i.e. about 2% by weight. Of course, metallicity cannot be defined for neutron stars and black holes, because these compact objects are not composed of atomic nuclei of any elements. In stellar astronomy, the metallicity of stars is also sometimes expressed by the ratio of the iron in a given star compared to the Sun. In our Galaxy, metallicity increases slightly towards its center.
Note: Although the metallicity is mostly determined for stars, the metallicity even of other astronomical objects is sometimes discussed - nebulae, star clusters, galaxies, or and the whole universe...
    In connection with the mechanisms of cosmic nucleosynthesis, the metallicity of an astronomical object can indirectly provide information about its age. In the early stages when the Universe substance composed almost exclusively with hydrogen during the initial nucleosynthesis form a substantial proportion of helium and only trace amounts of lithium and beryllium, the heavier elements were absent (5.4, section "
Lepton era. Initial nucleosynthesis"). The metallicity of objects from a very early universe is Z = 0. During stellar nucleosynthesis, the metallicity gradually increases.
    In terms of the long-term evolution of stars and their interactions with interstellar matter, we have divided the stars into generations in our interpretation : in the early stages of the universe, soon after reionization and the onset of the matter era, massive 1st generation stars formed, composed practically only of hydrogen and helium (with zero initial metallicity). At the end of their lives, a supernova explosion made of gas-dust material, enriched by their nucleosynthesis with heavier elements, from which formed 2nd generation stars with higher metallicity (Z
0.001), which further enriched the space environment with heavier elements. And at the end of their lives, 3rd generation stars, such as our Sun, formed with even higher metallicity ( 0.02). Development will undoubtedly continue, towards future generations (see " Dynamics of stellar evolution " below) with increasing metallicity.
    This division of stars into generations considers the author to be logical from an astrophysical point of view and therefore we use it in principle in all our materials. In stellar astronomy, however, for historical reasons, the division into so-called stellar populations I, II and III was used in the order in which they were discovered. This is the opposite order to the time sequence of their formation
: the first stars in space (virtually free of heavier elements) according to this classification were population III, the current stars with high metallicity are population I. The first stars of the 1st generation, ie population III, so far remain hypothetical, have not yet been observed. Besides the large time offset is probably because that, due to their heavy weight (several hundreds M) is rapidly exhausted their fuel and in the violent explosion (possibly the mechanism "Formation of electron-positron pairs"in 4.2) has been full spreading and dispersion of all the material, which was then "used" to build the later stars that are now observed.

Relative abundance of elements in nature depending on their proton (atomic) number Z, related to hydrogen Z = 1.
Above: The current average abundance of elements in universe. Bottom: Occurrence of elements on Earth (in the Earth's crust) and in terrestrial planets.
Due to the large range of values, the relative abundance of the elements (relative to hydrogen Z = 1) on the vertical axis is plotted on a logarithmic scale; however, this can optically distort a large difference in the abundance of hydrogen and helium compared to heavier elements, especially in the upper graph.
The picture is taken from the monograph "
Nuclear physics and physics of ionizing radiation", 1.1 "Atoms and atomic nuclei", part "Origin of atomic nuclei and origin of elements - cosmic alchemy"

Cosmic nucleosynthesis - primordial cosmological and stellar - led to the current average representation of individual elements in universe according to the upper graph in the figure. By far the most abundant elements in the universe are hydrogen and helium. In principle, it can be said that the element is more abundant in the universe, the smaller the proton (atomic) number, ie the fewer protons it contains in the nucleus, the simpler it is - the easier it is to form in nuclear reactions. Exceptions are the light elements lithium (Li), beryllium (Be) and boron (B), the significantly lower occurrence of which is due to the fact that they "burn" to helium inside the stars before the main conversion of hydrogen to helium takes place. The opposite exception is a group of very stable elements (with high binding energy of nuclei, so it is easier to "survive" the final stages of stellar evolution) around iron (Fe), the content of which is increased. The very slight occurrence of elements that do not have stable isotopes - technetium (Tc), Pm and actinides such as polonium (Po) to palladium (Pa), is due to their radioactivity with a not too long half-life; these elements can be formed in trace amounts by neutron capture. Thorium (Th) and uranium (U) are also unstable (radioactive), but with very long half-lives (of the order of 108 -1010 years), so after their formation in supernovae it is sufficient to persist for a long time in interstellar clouds, stars and planets (even on Earth).
  The regular "oscillations" in the abundance between adjacent elements, which can be seen in the graph (especially in the areas between Z = 8-20, 30-40, 45-60 and 62-75), are related to the slightly higher binding energy of nuclei with an even proton number than nuclei with an odd number of protons. These even nuclei are therefore somewhat more stable - they are easier to form in nuclear reactions and are "more resistant" to destruction during the turbulent final stages of stellar evolution. Therefore, they occur a little more abundantly compared to their "odd" neighbors.
The chemical evolution of the universe is still ongoing, so the current representation of the elements will change in the distant future; there will be mainly a decrease in light elements, which will merge into heavier elements. See also 5.6 "
The Future of the Universe. The Arrow of Time. Hidden Matter."
  On Earth and terrestrial planets, the relative occurrence of elements is different than in the global universe (graph at the bottom of the figure). There are selection effects (gravitational, radiation, temporal, chemical)
"favoring" some elements and suppressing others - there is a differentiation of chemical composition (it was discussed in more detail above in the passage "Planets around stars") .
  Overall, however, only less than 10% of all atoms
(atomic nuclei and electrons) in the universe are part of stars, planets and other cosmic bodies. The majority, more than 90%, remains sparsely dispersed in interstellar matter - gases, dust, nebulae.

"Alchemical cauldrons of the universe"
The stars can therefore be described as a kind of "
alchemical cauldrons" of the universe, in which all other elements are synthesized from the original hydrogen and helium. Thus, every atom of carbon, oxygen or nitrogen in our body formed in the "fiery furnace" of some ancient star - "we are all descendants of stars", see "Cosmic Alchemy". From the point of view of nuclear physics, cosmic nucleosynthesis is described in the book "Nuclear physics and physics of ionizing radiation", 1.1 "Atoms and atomic nuclei", passage "Origin of atomic nuclei and origin of elements", general laws of thermonuclear reactions and possibilities of their energetic use in 1.3 "Nuclear reactions", passage "Fusion of atomic nuclei".
Note: Original opinion of G.Gamov that all elements of Mendeleev's periodic table were "cooked" in the earliest universe, proved erroneous. During the big Bang (in lepton era - see 5.4) only the lightest elements hydrogen and helium were formed, other heavier elements were (nuclear) synthesized only in the stars.
  However, if no other processes took place in the stars apart from thermonuclear nucleosynthesis, all the heavier elements "cooked" in this way would remain forever trapped in the interior of the stars by strong gravity and would not contribute in any way to the chemical evolution of the universe, not even life could arise. Fortunately, there are two processes that release the synthesized heavier elements from the gravitational grip of the stars and enrich the surrounding interstellar space with them :
--> Thermoemission of gases from the upper layers of the "atmosphere" of stars - the stellar wind (passage "Stellar wind" above), which continuously carries a small amount of the star's gas, with an admixture of synthesized heavy elements, into the surrounding space.
--> A supernova explosion that ejects a substantial amount of the star's material, including a large amount of thermonuclearly synthesized elements, into the surrounding space. And during its own explosion, it will create many other even heavier elements (see the section "Supernova explosion. Neutron star. Pulsars." in the following 4.2).
Nuclear astrophysics atomic astrochemistry
 atomic nuclei were formed according to the laws of nuclear astrophysics at the beginning of the universe by primordial cosmological nucleosynthesis, heavier nuclei by thermonuclear synthesis inside the stars. These nuclei are originally "bare", without electron shells - gamma radiation and sharp collisions at high temperatures will not allow the formation of a permanent electron shell, electrons are immediately ejected from the atomic sheath, complete ionization of atoms occurs. No chemical reactions and compound formation can occur here. In the ejected clouds, these nuclei enter cold interstellar space, where the nuclei, by their electrical attraction, capture free electrons to fill electron orbits to form complete atoms of elements. Chemical reactions may already occur between them.
  In terrestrial conditions (in nature, in a test tube or in a reactor), the concentration of atoms and molecules is very high and their movement is fast, depending on the temperature - collisions between atoms and molecules are frequent and violent, chemical reactions can take place efficiently. "Intermediates" of chemical reactions, highly reactive molecules - free radicals, under terrestrial conditions, they expire and disappear from the reaction mixture so quickly that they cannot even be demonstrated by conventional analytical methods. In outer space, on the contrary, in interstellar clouds, which are very sparse and cold, atoms are very far apart and move slowly. The probability of collision and merging of two or more atoms in the sparse gaseous state of cold interstellar clouds is very small. The chemical evolution of interstellar clouds therefore takes place over a time horizon of millions of years. More complex chemical reactions often take place here in several stages, as highly reactive molecules of intermediates (free radicals) are so isolated that they often do not find "partners" with whom they could react further; therefore, they can persist for a very long time. In the cosmic clouds we actually find a number of "bizarre" molecules that do not occur on Earth - intermediates that did not have enough time and opportunity to disappear in subsequent reactions...
However, there are two important mechanisms for faster chemical reactions in space :
"Cold" astrochemistry
Solid dust particles condensed in an ejected nebula are very important for the formation of molecules from atoms in space. There, the atoms are close to each other and can exchange electrons - chemical reactions and the synthesis of molecules from atoms in interstellar space take place on grains of dust. They can also be stimulated by radiation from surrounding stars and cosmic radiation. Neutral atoms interact with radiation to become ions, which, thanks to attractive electrical forces, are able to carry out reactions and bonds to molecules even at very low temperatures (at which normal chemical reactions do not take place).
"Hot" astrochemistry
As "space chemical laboratories", gaseous envelopes around some stars can function, especially around red giants rich in carbon and oxygen. There are large differences in temperature and pressure in the individual areas of the envelope and there is intense radiation. The kinetic energy of the thermal motion of atoms overcomes the repulsive electric forces, and the atoms can approach by sharing the valence electrons and merging them into molecules. Temperatures are higher in the interior and compounds of silicon, magnesium, aluminum, sodium, etc. may be formed. In the lower temperature, compounds with longer carbon chains may be formed.
Intense chemical reactions then occur in protoplanetary disks and the planets formed around them around stars, where there is sufficient density and often favorable temperature.
  Using radio astronomy spectrometry, a large number of molecules made up of the most abundant elements in the universe - hydrogen, carbon, oxygen, nitrogen, sulfur - were discovered in interstellar clouds. Not only inorganic molecules (water, carbon dioxide, ammonia, ...), but also more than 100 different types of "organic" molecules composed of hydrogen, carbon, oxygen, nitrogen. Some are composed of more than 10 atoms, in addition to methane, there are also polycyclic aromatic hydrocarbons, aldehydes, alcohols and the like.
As we originated here ?
One star giant (or several of these stars) on the inside of one of the spiral arms of the Milky Way, which exploded as a supernova about 7 billion years ago, was important to our Earth and solar system. From the cloud ejected by it, enriched with heavier and biogenic elements, condensed the germinal nebula for the Sun and our entire solar system, including the Earth. We do not know where the remnant of this previous star is, it probably ended up as a black hole...

Dynamics of stellar evolution
The primary and decisive variable for the properties and course of evolution of a star is its initial initial mass, which is already established when a protostar formed from a germinal cloud. The greater this mass, the brighter and hotter the star, and the faster its evolution.
It is clear that more massive stars require more radiation flux and a higher temperature inside to balance gravity, ie a much faster course of the thermonuclear reaction (the radiant power of the star on the main sequence of the HR diagram is proportional to approximately the 3th power of mass). Stellar nuclear astrophysics has come to the fundamental conclusion, that the more massive is star, the faster it consumes its nuclear fuel - the shorter its life *) and the more dramatic her "death". And thereby the more exotic object it will leave behind, as we will see in the next. The final fate of a star is then determined by the remaining mass M' at the end of its evolution (ie the initial mass minus the mass of all matter, particles and radiation that the star ejected during its evolution), after exhaustion of thermonuclear reactions.
*) In humans, obesity is only one of the risk factors for shortening life and premature death. In stars, "obesity" is a legal and fatal factor, overly massive stars always "live" for a much shorter tim than low-mass stars.

   The dynamics of stellar evolution can be summarized very briefly as follows
(a more detailed analysis for massive stars is in the following 4.2) :
Very massive stars (tens to hundreds of M) - the giants - are evolving very fast, consuming all available thermonuclear fuel after several tens of millions of years, and ceasing to generate enough energy inside to maintain balance against gravity. It collapses violently with a supernova explosion into a neutron star or black hole *).
*) Another possibility for very massive stars (hundreds of M) is the rapid ignition of thermonuclear fusion in the entire collapsing core of the star (one such mechanism is described in the section "Formation of electron-positron pairs", 4.2). At the same time, energy that is greater than the total gravitational binding energy of the star may suddenly be released - in which case it will occur a thermonuclear explosion of a star, in which the star is completely "scattered" and only a rapidly expanding cloud of gases remains.
Sun-like stars have burned hydrogen to helium for many billions of years. After the consumption of hydrogen and the onset of other thermonuclear reactions, they shed their outer layers (a "planet" nebula) and their core shrinks into a hot white dwarf composed (except for the remaining hydrogen and helium) of carbon and other heavier elements (which they were able to synthesize the fusion - according to the mass of the star) .
Light stars (0.1-0.5 M) - red dwarfs - they will shine for tens to hundreds of billions of years, the smallest even up to 10 trillion years! (many times longer than the current age of the universe) until it converts all hydrogen to helium; further thermonuclear reactions no longer proceed. The substance of smaller red dwarfs is fully convective - helium formed by burning hydrogen is continuously mixed with other substances, no "dead" helium core is formed. Therefore, hydrogen fuel is used more efficiently than in more massive stars, almost all hydrogen can be burned to helium (which also contributes to the very long life of the star). Eventually, this star turns into a white dwarf composed mostly of helium.
Brown dwarfs , the mass of which is less than the threshold for ignition of thermonuclear hydrogen fusion (hundredths of M), are initially heated by gravity shrinkage (and possibly the deuterium, lithium and boron fusion stage), but then slowly cooled and extinguished.

Long-term changes in the dynamics of stellar evolution
The processes of
star formation and evolution are influenced on a large time scale by the state of matter in space during global evolution - the different densities and chemical compositions of gas and dust from which stars form. In the early universe period of tens of millions to several billions of years, when large amounts of gas and dust were present (created during the expansion and cooling of the universe by condensation of hydrogen and helium from the Big Bang), large numbers of stars formed (hundreds of billions in our Galaxy alone).
stars that formed about 100-200 million years after the Big Bang from dense clouds hydrogen and helium (other elements were not yet in the universe at that time) probably often considerably large weight of about 100 to 300 M. Thus, according to the laws of stellar evolution, they evolved very rapidly - after about 3-5 million years, they exploded like supernovae and introduced heavier elements into the interstellar mass, which were formed in them by thermonuclear fusion. The next generation of stars, which formed from this substance enriched with heavier elements, no longer reached such masses *) and their lifetimes were hundreds of millions of years to several billion years. Our Sun was probably formed as a star of the 3rd generation from material enriched after the explosion of 2nd generation stars (and previously 1st generation); therefore, it has about 100 times the proportion of heavier elements than stars formed in the first few billion years after the beginning of the universe.
*) The presence of heavier elements causes the protostar to collapse faster and stimulates earlier ignition of thermonuclear reactions that "blow" the surrounding gas, so the star is not enough to "pack" so much matter in a sparse cloud (discussed above in "Different Star Masses") .
  Using spectrometric measurements of the radiation of distant stars and galaxies, one can in principle determine how many generations of stars were born and died there. The basic method of tracking metallicity is based on measuring the emission of nitrogen N relative to basic hydrogen H, the N/H ratio. Another criterion is the amount of nitrogen in relation to oxygen N/O, in confrontation with the ratio O/H. Nitrogen N is mainly ejected by low- and intermediate-mass stars, while oxygen O is ejected by massive stars. The study of the N/O ratio thus provides a certain clue to the formation history of stars of different masses, and thus to the refinement of the determination of metallicity.
  As stars form, the reserves of galactic gas and dust are gradually depleted. Material ejected by massive stars in the red giant phase and in supernova explosions, or the influx of fresh gas from intergalactic space, is unable to replace the gas that has been absorbed by the emerging stars. Sparse clouds form stars less often and have smaller masses. In most galaxies, "stellar birthrate" are steadily declining. Currently, the rate of star formation is about 10 times slower, about 1
M per year. In the distant future, the formation of new stars will gradually cease, pobably in a trillion years the formation of stars will end (or they will arise very rarely).
  Stellar nucleosynthesis using supernova explosions is constantly increasing the abundance of heavier elements in interstellar gas. Newly emerging stars (higher generations) therefore have, in addition to hydrogen and helium, higher proportion of heavier elements
(higher metallicity). Each subsequent generation of stars is formed with a larger "equipment" of heavy elements than the previous generation. This can (at the same initial mass) change the dynamics of stellar evolution somewhat by two opposing effects :
- The opacity (decreases the transparency) of the outer layers of the stars increases. Hydrogen and helium are practically transparent, but the admixture of heavier elements absorbs radiation and thus reduces the radiating power of the star. The star thus consumes its nuclear fuel more slowly and lasts longer on the main sequences. A star with a medium content of heavier elements will therefore shine less and live longer.
- The high proportion of heavy elements not involved in nuclear fusion will reduce the relative amount of hydrogen and increase the gravitational pressure. This means that the star has less fuel, which it must consume faster in order to balance the gravitational forces - this will shorten the life of the star.
  The first effect can be expected to apply to stars of the 3rd and several generations for many hundreds of billions of years, when the gradual growth of heavy elements in emerging stars reduces their luminosity and thus prolongs their age. In the late stages, however, in the case of stars of higher generations, heavy elements will represent a significant proportion of their material, which will shorten their lifespan (- the second effect).
(all these are only general assumptions, not verified by astronomical observations - it would be difficult to verify ...)
  A higher proportion of heavy elements is also likely to stimulate more abundant planetary formation around stars, including terrestrial planets
(- greater hope for the origin of life?). However, very few new stars will be formed in this late period ...

Compact objects
A common characteristic feature of the final stages of stellar evolution
(except for extinction by thermonuclear explosions) is the transformation of the inner parts of stars into compact objects (lat. Compactus = dense, continuous, integral, coherent, solid). Depending on the remaining mass M' of the star (after all thermonuclear reactions have died out), the resulting gravitationally collapsed object is a white dwarf, a neutron star or a black hole (will be discussed in more detail in the following 4.2 "Final Stages of Stellar Evolution. Gravitational Collapse"). By their nature, these compact objects differ from normal stars mainly by three aspects :

These properties give gravitationally collapsed compact objects a highly "exotic" character, completely unlike anything we know from our experience. Classical physics is no longer enough to understand them, but relativistic and quantum physics are fully applied here. In our book, we focus mainly on the effects of the general theory of relativity and the properties of spacetime in the vicinity (and possibly also inside) of compact objects.  
Note: Theoretically, there could be a possibility how very massive stars (>~100 M) can avoid the fate of compact objects: thermonuclear explosion of the entire interior of the star due to e- e+ -pair instability and "scattering" it into a rapidly expanding cloud, as described in 4.2, section "Electron-positron pair formation".

At the end of this chapter, we can say that gravity is the most important force with which the fate of each star is inextricably linked: in the beginning, gravity leads to the formation of the star, during its life maintains its balance, and finally causes its extinction. However, this demise does not mean destruction in the sense of "conversion into nothing" - disappearance, but the transformation of a star into a new compact object with very peculiar and interesting properties..!.. - as we will see in the next chapters.

3.9. Naked singularities and the
principle of cosmic censorship
  4.2. The final stages of stellar evolution.
Gravitational collapse

Gravity, black holes and space-time physics :
Gravity in physics General theory of relativity Geometry and topology
Black holes Relativistic cosmology Unitary field theory
Anthropic principle or cosmic God
Nuclear physics and physics of ionizing radiation
AstroNuclPhysics Nuclear Physics - Astrophysics - Cosmology - Philosophy

Vojtech Ullmann