AstroNuclPhysics ® Nuclear Physics - Astrophysics - Cosmology - Philosophy | Gravity, black holes and physics |
Chapter 4
BLACK HOLES
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" :
l 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).
Rotation in the 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).
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.
Magnetic field in space
A magnetic field of various intensities and
spatial extents is present everywhere in the universe, including
our earthly nature. In space, the magnetic field occurs inside
and around stars, planets, accretion disks, galaxies and nebulae,
and in interstellar and intergalactic space.
Here on Earth,
in nature, in laboratories, in technical applications, local weak
or moderately strong magnetic fields (fractions
of Tesla up to approx. 10 T) are mainly
used - to a lesser extent, permanent magnets, more often
electromagnets. In addition, we have a weak global geomagnetic
field (approx. 3x10-5 T) arising in the interior of the
Earth. This Earth's magnetic field cannot be generated by
ferromagnetic minerals (as previously
thought). Although the earth's core is
composed mainly of iron and nickel, due to the high temperatures (greater than 4000°C)
significantly exceeding the Curie temperature, they cannot form a
permanent magnet ("Geological significance..."). However, because the
outer part of the core is liquid, it can create a self-exciting
hydrodynamic geodynamo, as described below.
The primary mechanism of the
formation of a magnetic field is the movement of electric
charges (according to the
Biot-Savart-Laplace law), in co-production
with the phenomenon of electromagnetic induction (Faraday) - see, for example,
§1.5 "Electromagnetic field. Maxwell's equations.". So, in practice, it is primarily the movement
of electrons and ions, whether free or in metal conductors
or electrolytes, especially in ionized gases - the plasmatic
state in which more than 99% of baryonic
("atomic") matter in the universe is.
The genesis of
the existence of electric and magnetic fields in the universe was
born in the very early stages of the creation of the universe at
the end of the inflationary phase of the universe (.....) when
the electromagnetic and weak interactions separated. Since then,
electric and magnetic fields have been found in space and nature.
The electric field is practically not applied on large-scale
astronomical scales, as possible areas with different
representation of charges are automatically
"discharged" and neutralized by Coulombic attractive
forces. On the other hand, the accompanying magnetic
field, which is created by the effect of currents of
electric charges, electrons and positive ions in substances in
space, is significantly applied. Every movement - flow - of
ionized substances, plasmas, causes a magnetic field. And this is
a very widespread phenomenon in space.
Magnetohydrodynamic
dynamo
Many long-term and large-scale magnetic fields in space can arise
as a result of a "hydrodynamic self-exciting dynamo",
which is a liquid analogue of a classical electric dynamo without
a magnet. Movements of an electrically conductive fluid or plasma
in the presence of a magnetic field cause the creation of induced
currents, which in turn generate a magnetic field that amplifies
the original field. Under certain conditions, positive
feedback can occur, and even from an initial weak field, there
will be a gradual build-up, which can lead to the creation of a
permanent large-scale magnetic field that is constantly "regenerating"
(however, this field is not completely
permanent and stable, in fact it shows various dynamic changes ,
sometimes "reversal" or extinction; it is mentioned
below).
For this self-exciting dynamo to
work, three conditions must be met :
1. A sufficiently large volume of conductive
liquid or plasma that can freely move (rotate). This is fulfilled
in the liquid cores of the planets - Earth having an outer core
of liquid iron, Jupiter with a core of liquid metallic hydrogen;
Mars shows signs of past, now extinct, dynamo activity as the
core cooled and solidified. Stars (including the Sun) have cores,
and their entire interiors, of dense conductive plasma.
2. An energy source for driving a dynamo, needed
to maintain the induced electric currents against the ohmic
dissipation caused by the finite conductivity (electrical resistance) of the
fluid. Earth's core flows are probably driven by convection ....
Among the sources of heat driving convection may be even
radioactivity of uranium 235,238U, thorium 232Th, and potassium 40K ("Geological Significance of Natural Radioactivity").
3. Rotation, which through the Coriolis force
supplies kinetic energy to the movement of the liquid. It helps
direct the flow and feedback with the magnetic field.
For the planets, the magnetic field
generated in this way is quite weak, 3x10-5 T at Earth's equator,
4x10-4 T at Jupiter. Common solar-type stars have only about 10-3÷10-2 T, rare stars with a
high metal content (" chemically
peculiar") can reach up to Tesla
units. White dwarfs reach up to 1000 T, neutron stars up to 108 T, magnetars even up
to 1011÷12 Tesla. In these compact gravitationally collapsed objects,
very strong magnetic fields are caused by enormous compression
and rotational acceleration (up to several
hundreds of revolutions/second), while the
angular momentum remains conserved. This accelerates the
hydrodynamic dynamo and the original magnetic field can increase
more than 1000 times. The enormous intensity of the magnetic
field is also caused by shrinkage - a many times smaller radius
of the surface on which we measure the magnetic field. Black
holes, when alone in a vacuum, have no magnetic field ("a
black hole has no hair"). However, in the presence of
matter, an accretion disk is formed, which can have a very strong
magnetic field.
In the open universe, the weakest
magnetic field is in the intergalactic space: in
large empty regions it is only a tiny ~10-15 T, in extensive cosmological intergalactic
"filamentous" structures perhaps about 10-12 T. In the interstellar space in galaxies, the average
magnetic field is also very weak, of the order of only ~10-9-10-6 T; in nebulae ~10-4 T, in the very center
of galaxies in the vicinity of the accretion disk of the central
black hole, however, it can be significantly stronger, ~0.2 T, in
the interior of the accretion disks probably much stronger...?...
(but there we are not able to measure...)
The magnetic field created by a
hydrodynamic dynamo can be quite long-lasting under
favorable conditions, but it is not completely permanent and
stable. It shows various dynamic changes, fluctuations,
sometimes even "reversal of polarity", it can even disappear
if any of the above-mentioned conditions are violated. The time
scales of these changes depend (among other
local factors) on the evolution and size of
astronomical objects. For large, long-term stable main-sequence
stars, the time-averaged magnetic field is almost stable for many
millions to several billion years (if we
disregard short-term fluctuations caused by the rotation of the
star, eruptions of surface layers and other local influences,
e.g. the 11-year cycle of solar activity. ..). And likewise, the average magnetic field of galaxies
and intergalactic space remains stable.
For smaller objects such as planets,
however, it shows relatively significant changes and
instabilities, mostly irregularly (chaotic). It could be
caused by volcanic activity or an asteroid impact. Significant
changes, even a "reversal" of the magnetic dipole,
occurred at Earth's time intervals of roughly several tens to
hundreds of thousands of years. Short-term significant
fluctuations occur during geomagnetic storms, caused by the
eruption of particles from the Sun - see the passage "Stellar Wind" below, where the importance of the Earth's
geomagnetic field is also discussed. And for all planets in the
future, sooner or later, the magnetic field will
disappear due to the natural cooling and solidification
of their liquid core. On Mars it happened about 4 billion years
ago, on larger terrestrial planets like Earth, the duration of
the magnetic field is estimated at about 5-20x109 years.
Measurement of magnetic fields of
space objects
Classic laboratory magnetometers of various constructions (...)
are only of very limited use for measuring the magnetic field in
space, as it is necessary to transport them in a space probe to
the place where we want to measure the magnetic field. This is
available to us (and even to a limited
extent...) only within the solar system. In
special cases, highly sensitive SQUID quantum interference
magnetometers were tested in remote measurements of extremely
strong magnetic fields of neutron stars. However, such
measurements cannot be made for almost all astronomical objects.
We can therefore measure magnetic
fields in distant cosmic objects only indirectly - by spectrometric
analysis of the radiation coming from these places. The four
effects by which a magnetic field affects emitted or transmitted
electromagnetic radiation are most commonly used :
->
Zeeman effect - splitting of some
energy levels of atoms due to magnetic field. They are levels
that, without the presence of a magnetic field, have the same
energy and therefore create only a spectral line. In the presence
of a magnetic field, individual levels have slightly different
energies, so when radiation is emitted from these atoms, the
originally single spectral line splits into two or more lines.
This effect is suitable for measuring stronger magnetic fields >~10-2 T.
->
Polarization of radiation. ....
->
Synchrotron radiation. .......
->
Cyclotron resonance. .......
All measuring and analytical methods show us great
diversity in the intensity of the magnetic fields of space
objects and their systems.
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).
¨ Cepheids
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 :
¨ Quasars
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 astrophysical
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 GM2/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.").
Note: 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").
The 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, passing 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 :
a) 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.
Note: 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 "planétes" = "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...
Planets around stars. Left : The formation of planets by the gradual condensation of gas and dust in the protoplanetary disk around the nascent central star. Top right : A basic model of the planetary system, where the individual planets revolve around the central star in orbits with speed v according to the Newton-Kepler laws. Bottom right : A symbolic simplified representation of our planetary Solar System. |
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.
Left: Distribution of asteroids in the inner part of the Solar System. Right: Orbits of asteroids in the region around Earth and Mars. |
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.".
Exoplanets , 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.
l 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.
2. 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**/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 :
The nearest small open star cluster Pleiades | The open star cluster NGC 6705 | The Great Globular Cluster NGC 2210 |
Nebulae
In addition to stars and their groupings (in
galaxies and star clusters), there are also
sparse interstellar clouds of gases and dust particles,
called nebulae in astronomy *). The gas
of the current nebulae is mainly hydrogen, helium, nitrogen, ... Dust
is most often composed of carbon, silicon compounds, ice
particles, .... Primordial nebulae were formed already
in the early universe at the beginning of the era of matter, and
galaxies were gradually formed by their condensation ( .......)
and eventually stars were formed. The "nebulae" of that
time consisted only of hydrogen and helium and their condensates
(zero metallicity). Later nebulae, after the explosion of 1st
generation stars, were already enriched with carbon, nitrogen,
oxygen, silicon and other lighter elements.
*) The name "nebula"
comes from the resemblance to a cloud of condensed fog
in the Earth's atmosphere. Previously, until 1925, the name
"nebula" referred to all observed spread -
"blurred" astronomical objects. It was only with the
advent of large astronomical telescopes that it became clear that
a number of spreading clouds are actually very distant huge
systems of many millions of stars - galaxies. E. Hubble
in 1925 using photographic images discovered that the
"nebula" in Andromeda is not a cluster of gas and stars
in our Milky Way, but a large independent galaxy located
at a considerable distance from our Milky Way.
Most nebulae have a diffuse
spread shape, they have no well-defined boundaries. Nebulae are
usually quite large, with dimensions ranging from tens to
hundreds of light years. Although nebulae are denser than the
surrounding interstellar space (20-50
atoms/cm3,
intergalactic space only about 1 atom/cm3), the density of gas and dust
even in nebulae is very small, only 102-104 molecules/cm3; it is a far lower "vacuum"
than we can create in the laboratory so far (105-107 molecules/cm3)..!.. If we were
inside the nebula, we would practically not see it. Its
astronomical visibility is due to the summation of a large number
of photons from a huge volume, observed from a distance. It is a
general geometric-optical effect.
According to the radiation mechanism (or
absorption) of light, nebulae can be divided into three types :
Individual mechanisms of radiation emission and absorption in nebulae can be combined. In the often complex configuration of the distribution of gas-dust clouds around glowing structures, e.g. intense emission can take place in the inner part, weaker reflection from the surrounding material at a greater distance, and some parts can be shadowed by areas of unilluminated material.
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 ò 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) .
ägtt(r)a
ägrr(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/Ögtt = -ÖA(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) º 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
(4.3) |
(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 ³ 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 rs » 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[-Ö(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 = Ö(2kT/m), but from a physical
point of view the more important is the mean
square velocity of the particles vk
= Ö(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/m3,
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 º 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)
2. partial reaction: 2D1
+ 1H1 ® 3He2 + g (+ 5,49 MeV)
3. Partial reaction: 3He2 + 3He2 ® 4He2 + 2 1H1
(+ 12,85 MeV)
Helium 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 º 1H are gradually
converted into a helium nucleus :
1st partial reaction: 12 C + 1
H ® 13
N + g (
+ 1.95 MeV)
2nd 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. Here, too, in stages 2 and 5, the
transformation of the "u" -> "d" quark
takes place through a weak interaction - and thus with a very low
effective cross-section.
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.
The absorption of the inner planets, the extinction of life
The expanding red giant will gradually burn and absorb
the planets in the inner part of its planetary system.
In the Solar System, it will be Mercury and Venus, or even the
Earth will disappear in the heat of the Sun. If there was life on
some planet in the habitable zone, a life-giving star in the late
stages of its evolution would destroy all life,
in the creation and development of which it had previously played
a significant role..!.. Cf. also the passage "Astrophysics and cosmology - human hopelessness" in §5.6.
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 :
1. Basic state of beryllium-8 has an energy almost
exactly equal to the energy of two a-particles .
2. 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
+ g
, 16O8 + 4He2 ® 20Ne10 + g , 12C6
+ 12C6 ® 20Ne10 + 4He2 ,
12C6 + 12C6 ® 23Na11 + 1H1
, 12C6 + 12C6 ® 23Na12 + 1n0
, 12C6 + 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
2.109 °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 ® 32S16 , 32S16 + 4He2 ® 36Ar18 , 36Ar18 + 4He2 ® 40Ca20 , 40Ca20 + 4He2 ® 44Ti22 ,
44Ti22 + 4He2 ® 48Cr24 , 48Cr24 + 4He2 ® 52Fe26 , 52Fe26 + 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 108
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
In 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.
Note: 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
Light 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).
First-generation 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 | ||
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