Dark Matter and Cosmic Web Story

by Jaan Einasto

  The presence of various populations (sub-systems) of stars with different kine-matical and spatial properties was clarified gradually. Stromberg (1924) noticed that there exists an asymmetric drift of velocity centroids with respect to the Sun’s motion: the centroid motion of a certain class of stars is larger the higher the velocity dispersion of stars of this class. This phenomenon is known as the Strömberg asymmetric drift. Lindblad (1927) and Oort (1927, 1928) interpreted this phenomenon as evidence for the rotation of the Galaxy. The sub-systems rotate around their common axis, and each one has a different speed of rotation. “The system of globular clusters has the lowest rotation velocity, it is not excluded that this population is not rotating at all. Bright stars in solar vicinity have the smallest velocity dispersion, these stars can be considered as moving very nearly in circular orbits around the centre” (Oort, 1927).

  Lindblad (1927) and Oort (1927) noticed also that the sub-system of globular clusters has an almost spherical shape, whereas subsystems of stars in the solar vicinity form a rather flattened system. According to Lindblad (1927) the gravitational field of the Galaxy can be expressed as a superposition of a spherical mass, and a mass of a flattened spheroidal population. He found that the mass of the spheroidal components exceeds the mass of the spherical population by a factor of about 5.

  This concept of the presence in the Galaxy of a number of stellar populations with various kinematical, spatial distribution and morphological properties has been further developed by many astronomers. At the Sternberg Astronomical Institute Boris Kukarkin and Pavel Parenago suggested using variable stars as markers of different populations to investigate the kinematical and spatial structure of populations in Galaxy. They divided galactic populations into three main classes: spherical, flat, and intermediate, which correspond approximately to halos, disks, and bulges of external galaxies.

  Already early studies of stellar dynamics (Eddington, 1914) suggested that kinematical and spatial properties of stellar populations change very slowly. Thus galactic populations contain information on their formation and evolution. This property was used in Tartu Observatory by Taavet Rootsmäe, who started in the mid 1930’s a study of the kinematics of various stellar populations in the hope of finding the direction of evolution of stars. He assumed that stellar populations of various age were formed during the collapsing proto-Galaxy. Unfortunately the study proceeded rather slowly, and was published only posthumously (Rootsmäe, 1961). A similar task was realized by Eggen et al. (1962), who found evidence from the motion of old stars that the Galaxy collapsed during its formation.

  It is generally accepted that star clusters, both open and globular, formed from a single gas cloud. For this reason all stars of a given cluster have similar age and chemical composition. Eggen (1950) performed accurate photoelectric studies of star clusters of various type and found that the colour-magnitude (or HR-) diagram of clusters is very narrow, if binary stars are excluded. This suggests that HR-diagrams can be used to derive the age of the cluster if star evolution tracks are known with sufficient accuracy. This property of clusters is widely used; see Eggen & Sandage (1964) as an example.

  The modern concept of stellar populations was generally accepted after the review talk by Oort (1958) at the Vatican Conference.

  2.1.6 The evolution of stars

  The evolution of galaxies and the Universe as a whole depends on the evolution of stars. The understanding of sources of stellar energy and the path of the evolution of stars are important elements of the classical cosmological paradigm.

  In the early years of the 20th century astronomers adopted the Russell hypothesis on stellar evolution: stars are born as red giants, they contract to form blue giants, and then cool and move along the dwarf branch (main sequence) towards red dwarfs. The dominating source of energy according to Russell was gravitation or radioactive decay.

  It is well known that the mean mass of stars in the main sequence is not constant — O and A type stars have masses 10–30 solar masses, whereas the masses of red dwarfs are only a fraction of the solar mass. Stellar evolution was one of the topics of interest to Ernst Öpik. He concluded that, if the Russell hypothesis is correct, stellar evolution should be accompanied with mass loss. If mass loss occurs in double stars, the distance between components must increase from blue to red double stars of the main sequence — the expected increase is approximately 20 times. To check this result Öpik (1923, 1924) studied double stars, and found that contrary to the expectation, the mean distance between components of double stars decreases about 2 times when moving from blue to red main sequence stars.

  Another fact contrary to the Russell hypothesis comes from geological data which indicate that the mean temperature on the Earth surface has been almost constant during its whole geological history. If the Sun evolved according to the Russell hypothesis its luminosity must decrease along the main sequence by a factor of a thousand, and it is impossible to avoid similar changes of the temperature on Earth.

  The first conclusion from these calculations was: the Hertzsprung–Russell diagram is not an evolutionary diagram, but a diagram of various initial conditions in mass and chemical composition. The same conclusion was made by Eddington (1924). The energy production per unit mass of blue giants is much higher than that of red dwarfs, thus the energy production must depend on physical conditions in the star. In faint companions of double stars (i.e. on main sequence stars) the luminosity per unit mass is proportional to the 9th power of the mass (Öpik, 1923). The basic physical parameter which changes among the main sequence stars of different mass is the temperature, thus a similar dependence must be valid also for the temperature. Since the temperature rises inwards, the energy source of stars must be located near the centre (Öpik, 1922b). Öpik (1922b) and Eddington (1924, 1926) concluded that stars obtained their energy from nuclear reactions.

  In order to find more accurately the energy source and stellar evolution Öpik waited until more data on the structure of atoms became available. He continued to think on these problems, and immediately after basic facts of atomic transmutations were available suggested a new, much more accurate theory of stellar evolution. In the Introduction to his major paper on the stellar structure and evolution Öpik (1938) explains his approach to the problem as follows: “stellar structure is a physical, not a mathematical problem. What matters are the premises, not the exact mathematical deductions from given premises; we want to know the actual physical conditions determining stellar structure and evolution; a correct mathematical theory may then easily follow. We believe that a mere qualitative picture, taking into account all the complexity of the conditions in stellar interiors, is still a better approximation to the truth than an exact mathematical theory based on simplifications which do not take into account certain most important factors of stellar structure and evolution”.

  The first important factor to be taken into account is convection. Since the energy source is located in the centre of the star, this leads to convection, similar to the formation of convection in boiling water in a kettle heated from below. Due to convection the active matter is continuously replaced. The source of energy was found — nucleosynthesis, mainly the transmutation of the hydrogen into helium. The energy output of this process was known, and Öpik was able to calculate models of stellar interiors taking into account energy production and transport.

  Öpik’s calculations suggested that the star is convective only in the central parts. In this case its structure is a composite one — the convective core is surrounded by a radiative envelope. There exists no mixing of stellar matter between the core and envelope, and the chemical composition of the core is not constant. This process continues until all the hydrogen is used. Öpik (1938) concludes: “A core devoid of hydrogen, thus presumably devoid of subatomic sources of energy, is doomed to collapse on a ‘Kelvin’ time scale, high densities can be attained, and a super-dense core may be formed. The contraction of the core is a gradual one; instead of blowing up, the
envelope gradually expands and adjusts itself to such low values of the effective density and temperature that the release of subatomic energy remains more or less normal…. A typical giant structure results, consisting of a vast extended envelope of low density in radiative equilibrium, an intermediate zone in adiabatic (convective) equilibrium,… and a contracting superdense core of zero hydrogen content”, see Fig. 2.1.

  The amount of energy which is produced during the burning of hydrogen to helium is well-known, thus Öpik was able to calculate the maximal age of stars of different mass. For highly luminous early type main sequence stars this age is very short — about 10 million years. “Thus, the presence of massive and luminous main sequence stars in the Galactic System we ascribe to stars being continually formed in the place of those which become giants” (Öpik, 1938). The idea of a recent origin for blue main sequence stars was commonly accepted after Ambartsumian’s discovery of stellar associations (Ambartsumian, 1958).

  Fig. 2.1 A scheme of a giant star structure. C is the nucleus of radius r, exhausted of nuclear energy; A is the region of release of the subatomic energy, of radius R1; B is the region of undisturbed radiative equilibrium without energy sources (Öpik, 1938).

  The chemical inhomogeneity and composite structure were omitted by previous investigators, but they are the most important factors determining the structure of giants.

  Öpik’s theory of the evolution of main sequence stars toward giants was not accepted immediately. Alar Toomre recently gave an interview to the Estonian magazine “Horisont”, and told a story about Öpik: “When the famous astrophysicist Chandrasekhar was 65, I was in a conference in Chicago, where one lecture was given by Martin Schwarzschild, a famous astronomer who studied the structure of stars. Remembering Chandrasekhar he told, that the first person who understood the structure of red giants was Ernst Öpik in 1930s, but for personal reasons they decided not to believe him. After the lecture I asked Martin, what kind of personal reasons were. It appears that Öpik was a self-confident person and told to everybody, if you do not believe me, you are fool, you are idiot. Their personal reason not to believe was the unwillingness to believe that Öpik was right. But he was.”

  Öpik’s theory is now fully accepted. The only basic difference between his theory and modern data concerns the energy source of the giants. According to modern data giants also burn chemical elements to produce energy, first helium to carbon, and thereafter other heavier elements until iron. Only after using all atomic fuel does the core of a giant star collapse under gravity to form white dwarfs or neutron stars depending on the mass.

  The modern theory of stellar evolution and the synthesis of the elements in stars was elaborated by Schwarzschild and coauthors (Härm & Schwarzschild, 1955; Hoyle & Schwarzschild, 1955; Oke & Schwarzschild, 1952; Sandage & Schwarzschild, 1952; Schwarzschild et al., 1953), and Burbidge et al. (1957). This theory is well supported by the relative distribution of chemical elements in stars, Earth’s core and other cosmic objects. According to this theory all elements heavier than hydrogen, helium and lithium are synthesised in stellar interiors by stellar nucleosynthesis.

  In the first stage a main sequence star burns hydrogen to helium. When all hydrogen in the convecting core is exhausted, the core contracts and heats up, and the envelope expands — the star becomes a red giant. As the temperature in the inner region of the star increases, nuclear reactions demanding higher temperature start. Thus a red giant looks like an onion: an outer shell of hydrogen burning, while in inner sheets heavier elements burn to form carbon, neon, oxygen, silicon etc. In the very central zone, where the temperature is high enough, iron is produced. But this is the end of energy releasing nuclear reactions. All previous nuclear reactions produce energy, but when iron fuses into heavier elements, it absorbs energy out of the reaction, slowing it down. The central region of the star no longer produces energy and its gravity pulls outer layers inward. The star collapses quickly and explodes as a supernova.

  During supernova explosions large amounts of energy are released and the temperature rises, thus in a short timescale all elements heavier than iron are synthesised. During the explosion outer layers are expelled and enrich the interstellar matter with heavier elements. Thus the next generations of stars form from a medium which already contains elements heavier than hydrogen, helium and lithium. Expanding shock waves from a supernova explosion can trigger the formation of new stars. All atoms in our bodies were formed in stellar interiors, and expelled from a supernova. From remnants of this supernova our Sun and all its planets formed about 4.5 billion years ago.

  With the explanation of sources of stellar energy and the evolution of stars the development of the classical cosmological paradigm culminated. This paradigm can be described shortly as follows:

  • The Universe formed as a result of the Big Bang about 15–19 billion years ago. Big Bang itself was considered as a mathematical singularity.

  • The Universe is presently expanding with a rate which corresponds to the Hubble parameter in the range of 50–100 km/s/Mpc.

  • The expansion of the Universe is spatially very uniform.

  • The mean density of the Universe is about 0.04 of the critical cosmological density. This density concerns only baryonic matter, but this was recognised later.

  • Galaxies are distributed in space almost randomly. About 10% of galaxies form clusters and superclusters of galaxies.

  • During the early phase of the evolution of the Universe only light chemical elements formed via the Big Bang nucleosynthesis; all heavier elements formed inside stars by stellar and supernova nucleosynthesis. Nucleosynthesis is the basic source of energy in stars.

  • Galaxies consist of populations of various age, composition, kinematics, and spatial structure. HR-diagrams of homogeneous populations (as star clusters) can be used to determine the ages of populations, and to reconstruct the history of the formation and evolution of galaxies.

  Almost all observations known in the early 1970’s supported this paradigm. There were only a few clouds on the horizon which did not fit into this paradigm. One of these facts was the mass paradox in clusters of galaxies found by Zwicky (1933, 1937). A related theoretical problem was: the Universe has expanded enormously, thus even small deviations from the critical density should increase during this time. How is it possible that the present density is smaller than the critical one, but only by a factor on the order of ten?

  From these small clouds and new observational data a new cosmological paradigm formed. But there was a long way to go. In the following chapters I discuss some of these steps which led to the paradigm change in cosmology.

  2.2 History of Estonia, my family roots, and Tartu Observatory

  2.2.1 A short history of Estonia

  The Estonian language belongs to the Finno-Ugric family of languages, which covers Northern Europe east of the Baltic Sea to the Ural Mountains and beyond. Finno-Ugric tribes populated this area from the Arctic Ocean to the Southern edge of the forested region. Finno-Ugric languages differ from Indo-European languages in several fundamental aspects. They lack grammatical gender and use one pronoun for both he and she. Second, Finno-Ugric languages are agglutinative languages, by adding suffixes (parts of the word) instead of prepositions (separate words). There is a smooth transition from languages near the Baltic Sea (Estonian, Finnish) towards the Ural mountains, and further to Samoyedic languages in Siberia.

  During the Ice Age most of Northern Europe was covered with ice and only several regions were free of ice, suitable for people to live. These regions had tundra features; there was enough rainfall only near the ice sheets. Regions free from ice are called Last Glacial Maximum refugia. One is today in the Don river region, it reached in the North-East direction almost to the Pechora river near the Ural Mountains. At this time the climate was very dry and tundra type vegetation was available only near the ice sheet. Stone Age people during the Ice Age were nomadic; they travelled to gather and hunt for food, mostly Northe
rn elks, polar bears, possibly also mammoths. When ice melted, animals moved Northwards, and people followed them. Present-day Estonia was populated about 10 thousand years ago. The Finnish Gulf was a hindrance, and people stayed here. Another hindrance was the Peipus lake, one of the largest in Europe. East of the lake there is a continuous transition of Baltic Ugro-Finnish languages from South-East Estonian (Setu) dialect, to Ingrian, towards Karelian.

  The Estonian mythology is very similar to the Finnish one, and has many similar features with other Finno-Ugric nations. The mythology is animalistic: animals and trees had souls. Ancient Estonians knew the sky well; constellations had names of everyday life and instruments. The Milky Way is in Estonian Linnutee, i.e. “the path of the birds”, because birds were believed to use it as a guide during spring and autumn migration.

  A meteorite passed over the populated region in North Estonia and landed on the island Saaremaa around 3 thousand years ago, creating a lake, called “Kaali”. This cataclysmic event may have influenced Estonian and Finnish mythology, since a “sun” flew over the sky in a wrong direction, and seemed to set in the East. The Kaali lake was considered by ancient Estonians as a sacred place, where the Sun went to rest. According to a theory, proposed by the ethnologist and the first afterwar Estonian president Lennart Meri, it is possible that Saaremaa was the legendary “Thule island”, mentioned by ancient Greek geographer Pytheas, where the name “Thule” could have been connected to the Finnish/Estonian word tule/tuli (fire).

  Genetically the closest relatives of Estonians are Swedes, Latvians, and Russians. The genetic close links to Russians seem surprising, but it stems from the colonisation history of Russiaby Slavs. DNA analysis shows that along the maternal line, ancestors of Russians in the whole Northern region took wives from the local Finno-Ugric nations. Along the paternal line only in the North-Western region are the majority of Russians relatives of Finno-Ugric nations. This means that in these regions almost the whole population was originally Finno-Ugric, and a language transfer happened.