Dark Matter

Dark Matter

Jaan Einasto
Tartu Observatory, Estonia

Summary

We give a review of the development of the concept of dark matter. The dark matter story passed through several stages on its way from a minor observational puzzle to a major challenge for theory of elementary particles.

We begin the review with the description of the discovery of the mass paradox in our Galaxy and in clusters of galaxies. First hints of the problem appeared already in 1930s and later more observational arguments were brought up, but the issue of the mass paradox was mostly ignored by the astronomical community as a whole. In mid 1970s the amount of observational data was sufficient to suggest the presence of a massive and invisible population around galaxies and in clusters of galaxies. The nature of the dark population was not clear at that time, but the hypotheses of stellar as well as of gaseous nature of the new population had serious difficulties. These difficulties disappeared when non-baryonic nature of dark matter was suggested in early 1980s.

The final break through came in recent years. The systematic progress in the studies of the structure of the galaxies, the studies of the large scale structure based on galaxy surveys, the analysis of the structure formation after Big Bang, the chemical evolution of the Universe including the primordial nucleosynthesis, as well as observations of the microwave background showed practically beyond any doubt that the Universe actually contains more dark matter than baryonic matter! In addition to the presence of Dark Matter, recent observations suggest the presence of Dark Energy, which together with Dark Matter and ordinary baryonic matter makes the total matter/energy density of the Universe equal to the critical cosmological density. Both Dark Matter and Dark Energy are the greatest challenges for modern physics since their nature is unknown.

There are various hypotheses as for the nature of the dark matter particles, and generally some form of weakly interactive massive particles (WIMPs) are strongly favored. These particles would form a relatively cold medium thus named Cold Dark Matter (CDM). The realization that we do not know the nature of basic constituents of the Universe is a scientific revolution difficult to comprehend, and the plan to hunt for the dark matter particles is one of the most fascinating challenges for the future.

1 Dark Matter problem as a scientific revolution

Almost all information on celestial bodies comes to us via photons. Most objects are observed because they emit light. In other cases, like for example in some nebulae, we notice dark regions against otherwise luminous background which are due to absorption of light. Thus both light absorption and light emission allow us to trace the matter in the Universe, and the study goes nowadays well beyond the optical light. Modern instruments have first detected photon emission from astronomical bodies in the radio and infrared regions of the spectrum, and later also in the X-ray and gamma-ray band, with the use of detectors installed in space.

Presently available data indicate that astronomical bodies of different nature emit (or absorb) photons in very different ways, and with very different efficiency. At the one end there are extremely luminous supernovae, when a single star emits more energy than all other stars of the galaxy it belongs to, taken together. At the other extreme there are planetary bodies with a very low light emission per mass unit. The effectiveness of the emissivity can be conveniently described by the mass-to-light ratio of the object, usually expressed in Solar units in a fixed photometric system, say in blue (B) light. The examples above show that the mass-to-light ratio varies in very broad range. Thus a natural question arises: Do all astronomical bodies emit or absorb light? Observations carried out in the past century have led us to the conclusion that the answer is probably NO.

Astronomers frequently determine the mass by studying the object emission. However, the masses of astronomical bodies can be also determined directly, using motions of other bodies (considered as test particles) around or within the body under study. In many cases such direct total mass estimates exceed the estimated luminous masses of known astronomical bodies by a large fraction. It is customary to call the hypothetical matter, responsible for such mass discrepancy, Dark Matter.

The realization that the presence of dark matter is a serious problem which faces both modern astronomy and physics grew slowly but steadily. Early hints did not call much attention.

The first indication for the possible presence of dark matter came from the dynamical study of our Galaxy. British astronomer James Jeans (1922) reanalyzed vertical motions of stars near the plane of the Galaxy, studied by the Dutch astronomer Jacobus Kapteyn (1922). Both astronomers calculated from these data the density of matter near the Sun. They also estimated the density due to all stars near the Galactic plane. Kapteyn found that the spatial density of known stars is sufficient to explain the vertical motions. In contrast, Jeans results indicated the presence of two dark stars to each bright star.

The second observation was made by Fritz Zwicky (1933). He measured radial velocities of galaxies in the Coma cluster of galaxies, and calculated the mean random velocities in respect to the mean velocity of the cluster. Galaxies move in clusters along their orbits; the orbital velocities are balanced by the total gravity of the cluster, similar to the orbital velocities of planets moving around the Sun in its gravitation field. To his surprise Zwicky found that orbital velocities are almost a factor of ten larger than expected from the summed mass of all galaxies belonging to the cluster. Zwicky concluded that, in order to hold galaxies together in the cluster, the cluster must contain huge amounts of some Dark (invisible) matter.

The next hint of the dark matter existence came from cosmology.

One of the cornerstones of the modern cosmology is the concept of an expanding Universe. From the expansion speed it is possible to calculate the critical density of the Universe. If the mean density is less than the critical one, then the Universe has opened geometry; if the mean density is larger than the critical, the Universe is closed. If the density has exactly the critical value, the spatial geometry is flat. The mean density of the Universe can be estimated using masses of galaxies and of the gas between galaxies. These estimates show that the mean density of luminous matter (mostly stars in galaxies and interstellar or intergalactic gas) is a few per cent of the critical density. This estimate is consistent with the constraints from the primordial nucleosynthesis of the light elements.

Another cornerstone of the classical cosmological model is the smooth distribution of galaxies in space. There exist clusters of galaxies, but they contain only about one tenth of all galaxies. Most of the galaxies are more or less randomly distributed and are called field galaxies. This conclusion is based on counts of galaxies at various magnitudes and on the distribution of galaxies in the sky.

Almost all astronomical data fitted well to these classical cosmological paradigms until 1970s. Then two important analyses were made which did not match the classical picture. In mid 1970s first redshift data covering all bright galaxies were available. These data demonstrated that galaxies are not distributed randomly as suggested by earlier data, but form chains or filaments, and that the space between filaments is practically devoid of galaxies. Voids have diameters up to several tens of megaparsecs.

At this time it was already clear that structures in the Universe form by gravitational clustering, started from initially small fluctuations of the density of matter. Matter “falls” to places where the density is above the average, and “flows away” from regions where the density is below the average. This gravitational clustering is a very slow process. In order to form presently observed structures, the amplitude of density fluctuations must be at least one thousandth of the density itself at the time of recombination, when the Universe started to be transparent. The emission coming from this epoch was first detected in 1965 as a uniform cosmic microwave background. When finally the fluctuations of this background were measured by COBE satellite they appeared to be two orders of magnitude lower than expected from the density evolution of the luminous mass.

The solution of the problem was suggested independently by several theorists. In early 1980s the presence of dark matter was confirmed by many independent sources: the dynamics of the galaxies and stars in the galaxies, the mass determinations based on gravitational lensing, and X-ray studies of clusters of galaxies. If we suppose that the dominating population of the Universe – Dark Matter – is not made of ordinary matter but of some sort of non-baryonic matter, then density fluctuations can start to grow much earlier, and have at the time of recombination the amplitudes needed to form structures. The interaction of non-baryonic matter with radiation is much weaker than that of ordinary matter, and radiation pressure does not slow the early growth of fluctuations.

The first suggestions for the non-baryonic matter were particles well known at that time to physicists – neutrinos. However, this scenario soon led to major problems. Neutrinos move with very high velocities which prevents the formation of small structures as galaxies. Thus some other hypothetical non-baryonic particles were suggested, such as axions. The essential property of these particles is that they have much lower velocities. Because of this the new version of Dark Matter was called Cold, in contrast to neutrino-dominated Hot Dark Matter. Numerical simulations of the evolution of the structure of the Universe confirmed the formation of filamentary superclusters and voids in the Cold Dark Matter dominated Universe.

The suggestion of the Cold Dark Matter has solved most problems of the new cosmological paradigm. The actual nature of the CDM particles is still unknown. Physicists have attempted to discover particles which have properties needed to explain the structure of the Universe, but so far without success.

One unsolved problem remained. Estimates of the matter density (ordinary dark matter) yield values of about 0.3 of the critical density. This value – not far from unity but definitely smaller than unity – is neither favored by theorists nor by the data, including the measurements of the microwave background, the galaxy dynamics and the expansion rate of the Universe obtained from the study of supernovae. To fill the matter/energy density gap between unity and the observed matter density it was assumed that some sort of vacuum energy exists. This assumption is not new: already Einstein added to his cosmological equations a term called the Lambda-term. About ten years ago first direct evidence was found for the existence of the vacuum energy, presently called Dark Energy. This discovery has filled the last gap in the modern cosmological paradigm.

In the International Astronomical Union (IAU) symposium on Dark Matter in 1985 in Princeton, Tremaine (1987) characterized the discovery of the dark matter as a typical scientific revolution, connected with changes of paradigms. Kuhn (1970) in his book The Structure of Scientific Revolutions discussed in detail the character of scientific revolutions and paradigm changes. There are not so many areas in modern astronomy where the development of ideas can be described in these terms, thus we shall discuss the Dark Matter problem also from this point of view. Excellent reviews on the dark matter and related problems are given by Faber & Gallagher (1979), Trimble (1987), Srednicki (1990), Turner (1991), Silk (1992), van den Bergh (2001), Ostriker & Steinhardt (2003), Rees (2003), Turner (2003), Trimble (2010) and Sanders (2010), see also proceedings by Longair & Einasto (1978), and Kormendy & Knapp (1987).

2 Early evidence of the existence of dark matter

2.1 Local Dark Matter

The dynamical density of matter in the Solar vicinity can be estimated using vertical oscillations of stars around the galactic plane. The orbital motions of stars around the galactic center play a much smaller role in determining the local density. Ernst Öpik (1915) found that the summed contribution of all known stellar populations (and interstellar gas) is sufficient to explain the vertical oscillations of stars – in other words, there is no need to assume the existence of a dark population. Similar analyses were made by Kapteyn (1922) and Jeans (1922), who used the term “Dark Matter” to denote the invisible matter which existence is suggested by its gravity only. Kapteyn found for the dynamical density of matter near the Sun 0.099 , Jeans got 0.143 in the same units.

The next very careful determination of the matter density near the Sun was made by Jan Oort (1932). His analysis indicated that the total density, found from dynamical data, is 0.092 , and the density of stars, including expected number of white dwarfs, is approximately equal to the dynamical density. He concluded that the total mass of nebulous or meteoric dark matter near the Sun is very small.

The local density of matter has been re-determined by various authors many times. Grigori Kuzmin (1952b, 1955) and his students Heino Eelsalu (1959) and Mihkel Jõeveer (1972, 1974) confirmed the earlier results by Öpik, Kapteyn and Oort. A number of other astronomers, including more recently Oort (1960), John Bahcall & Soneira (1980); Bahcall (1984, 1987), found results in agreement with the Jeans result. Their results mean that the amount of invisible matter in the Solar vicinity should be approximately equal to a half of the amount of visible matter. This discussion was open until recently; we will describe the present conclusions below.

For long time no distinction between local and global dark matter was made. The realization, that these two types of dark matter have very different properties and nature came from the detailed study of galactic models, as we shall discuss below (Einasto, 1974).

2.2 Global Dark Matter – clusters, groups and galaxies

A different mass discrepancy was found by Fritz Zwicky (1933). He measured redshifts of galaxies in the Coma cluster and found that the velocities of individual galaxies with respect to the cluster mean velocity are much larger than those expected from the estimated total mass of the cluster, calculated from masses of individual galaxies. The only way to hold the cluster from rapid expansion is to assume that the cluster contains huge quantities of some invisible dark matter. According to his estimate the amount of dark matter in this cluster exceeds the total mass of cluster galaxies at least tenfold, probably even more.

Smith (1936) measured radial velocities of 30 galaxies in the Virgo cluster and confirmed the Zwicky result that the total dynamical mass of this cluster exceeds considerably the estimated total mass of galaxies. This conclusion was again confirmad by Zwicky (1937), who discussed masses of galaxies and clusters in detail. As characteristic in scientific revolutions, early indications of problems in current paradigms are ignored by the community, this happened also with the Zwicky’s discovery.

A certain discrepancy was detected between masses of individual galaxies and masses of pairs and groups of galaxies (Holmberg (1937), Page (1952, 1959, 1960)). The conventional approach for the mass determination of pairs and groups of galaxies is statistical. The method is based on the virial theorem and is almost identical to the procedure used to calculate masses of clusters of galaxies. Instead of a single pair or group often a synthetic group is used consisting of a number of individual pairs or groups. These determinations yield for the mass-to-light ratio (in blue light) the values for spiral galaxy dominated pairs, and for elliptical galaxy dominated pairs (for a review see Faber & Gallagher (1979)). These ratios are larger than found from local mass indicators of galaxies (velocity dispersions at the center and rotation curves of spiral galaxies). However, it was not clear how serious is the discrepancy between the masses found using global or local mass indicators.

A completely new approach in the study of masses of systems of galaxies was applied by Kahn & Woltjer (1959). They paid attention to the fact that most galaxies have positive redshifts as a result of the expansion of the Universe; only the Andromeda galaxy (M31) has a negative redshift of about 120 km/s, directed toward our Galaxy. This fact can be explained, if both galaxies, M31 and our Galaxy, form a physical system. A negative radial velocity indicates that these galaxies have already passed the apogalacticon of their relative orbit and are presently approaching each other. From the approaching velocity, the mutual distance, and the time since passing the perigalacticon (taken equal to the present age of the Universe), the authors calculated the total mass of the double system. They found that . The conventional masses of the Galaxy and M31 were estimated to be of the order of . In other words, the authors found evidence for the presence of additional mass in the Local Group of galaxies. The authors suggested that the extra mass is probably in the form of hot gas of temperature about K. Using more modern data Einasto & Lynden-Bell (1982) made a new estimate of the total mass of the Local Group, using the same method, and found the total mass of . This estimate is in good agreement with recent determinations of the sum of masses of M31 and the Galaxy including their dark halos (see below).

In 1961 during the International Astronomical Union (IAU) General Assembly a symposium on problems in extragalactic research was organised (G. C. McVittie, 1962), and a special meeting to discuss the stability of clusters of galaxies (Neyman et al., 1961). The last meeting was the first wide discussion of the mass discrepancy in clusters of galaxies. Here the hypothesis of Victor Ambartsumian (1961) on the stability and possible expansion of clusters was analysed in detail. Sidney van den Bergh (1961, 1962) drew attention to the fact that the dominating population in elliptical galaxies is the bulge consisting of old stars, indicating that cluster galaxies are old. It is very difficult to imagine how old cluster galaxies could form an instable and expanding system. These remarks did not find attention and the problem of the age and stability of clusters remained open. The background of this meeting and views of astronomers supporting these and some alternative solutions were described by Trimble (1995), van den Bergh (2001), Sanders (2010) and Trimble (2010).

Figure 1: The rotation curve of M31 by Roberts & Whitehurst (1975). The filled triangles show the optical data from Rubin & Ford (1970), the filled circles show the 21-cm measurements made with the 300-ft radio telescope (reproduced by permission of the AAS and the author).

2.3 Rotation curves of galaxies

Another problem with the distribution of mass and mass-to-light ratio was detected in spiral galaxies. Babcock (1939) obtained spectra of the Andromeda galaxy M31, and found that in the outer regions the galaxy is rotating with an unexpectedly high velocity, far above the expected Keplerian velocity. He interpreted this result either as a high mass-to-light ratio in the periphery or as a strong dust absorption. Oort (1940) studied the rotation and surface brightness of the edge-on S0 galaxy NGC 3115, and found in the outer regions a mass-to-light ratio .

After World War II there were numerous German radar dishes in the Dutch territory, and Oort and his colleagues understood that these devices can be used to detect radio waves from astronomical objects. His student van de Hulst has calculated that hydrogen emits radio waves in 21-cm, and this emission can be used to detect interstellar hydrogen and to measure its velocity. The first goal was to measure the radio emission from our own Galaxy (van de Hulst et al., 1954). The next goal was the Andromeda galaxy M31. van de Hulst et al. (1957) found that the neutral hydrogen emitting the 21-cm line extends much farther than the optical image. They were able to measure the rotation curve of M31 up to about 30 kpc from the center, confirming the global value of versus in the central region.

On the other hand, Schwarzschild (1954) analysed all available data on mass-to-luminosity ratio in galaxies, and found that within the optically visible disk is approximately constant, i.e. mass follows light. In elliptical galaxies this ratio is higher than in spiral galaxies.

About ten years later Morton Roberts (1966) made a new 21-cm hydrogen line survey of M31 using the National Radio Astronomy Observatory large 300-foot telescope. The flat rotation curve at large radii was confirmed with much higher accuracy. He constructed also a mass distribution model of M31.

Astronomers having access to large optical telescopes continued to collect dynamical data on galaxies. The most extensive series of optical rotation curves of galaxies was made by Margaret and Geoffrey Burbidge, starting from Burbidge & Burbidge (1959); Burbidge et al. (1959), and including normal and barred spirals as well as some ellipticals. For all galaxies authors calculated mass distribution models, for spiral galaxies rotation velocities were approximated by a polynom. They found that in most galaxies within visible images the mean .

Subsequently, Rubin & Ford (1970) and Roberts & Rots (1973) derived the rotation curve of M31 up to a distance kpc, using optical and radio data, respectively. The rotation speed rises slowly with increasing distance from the center of the galaxy and remains almost constant over radial distances of 16–30 kpc, see Fig. 1.

The rotation data allow us to determine the distribution of mass, and the photometric data – the distribution of light. Comparing both distributions one can calculate the local value of the mass-to-light ratio. In the periphery of M31 and other galaxies studied the local value of , calculated from the rotation and photometric data, increases very rapidly outwards, if the mass distribution is calculated directly from the rotation velocity. In the periphery old metal-poor halo-type stellar populations dominate. These metal-poor populations have a low (this value can be checked directly in globular clusters which contain similar old metal-poor stars as the halo). In the peripheral region the luminosity of a galaxy drops rather rapidly, thus the expected circular velocity should decrease according to the Keplerian law. In contrast, in the periphery the rotation speeds of galaxies are almost constant, which leads to very high local values of near the last points with a measured rotational velocity.

Two possibilities were suggested to solve this controversy. One possibility is to identify the observed rotation velocity with the circular velocity. But in this case an explanation for a very high local should be found. To explain this phenomenon it was suggested that in outer regions of galaxies low-mass dwarf stars dominate (Oort, 1940; Roberts, 1975). The other possibility is to assume that in the periphery of galaxies there exist non-circular motions which distort the rotation velocity.

To make a choice between the two possibilities for solving the mass discrepancy in galaxies more detailed models of galaxies were needed. In particular, it was necessary to take into account the presence of galactic stellar populations with different physical properties (age, metal content, colour, value, spatial and kinematical structure).

2.4 Mass paradox in galaxies from Galactic models

Classical models of elliptical galaxies were found from luminosity profiles and calibrated using either central velocity dispersions, or motions of companion galaxies. The luminosity profiles of disks were often approximated by an exponential law, and bulge and halo dominated ellipticals by the de Vaucouleurs (1953b) law.

Models of spiral galaxies were constructed using rotation velocities. As a rule, the rotation velocity was approximated by some simple formula, such as the Bottlinger (1933) law (Roberts, 1966), or a polynomial (Burbidge et al., 1959). The other possibility was to approximate the spatial density (calculated from the rotation data) by a sum of ellipsoids of constant density (the Schmidt (1956) model). In the first case there exists a danger that, if the velocity law is not chosen well, then the density in the periphery of the galaxy may have unrealistic values (negative density or too high density, leading to an infinite total mass). If the model is built by superposition of ellipsoids of constant density, then the density is not a smooth function of the distance from the center of the galaxy. To avoid these difficulties Kuzmin (1952a, 1956) developed models with a continuous change of the spatial density, and applied the new technique to M31 and our Galaxy. His method allows us to apply this approach also for galaxies consisting of several populations.

A natural generalization of classical galactic models is the use of all available observational data for spiral and elliptical galaxies, both photometric data on the distribution of color and light, and kinematical data on the rotation and/or velocity dispersion. Further, it is natural to apply identical methods for modeling of galaxies of different morphological type (including our own Galaxy), and to describe explicitly all major stellar populations, such as the bulge, the disk, the halo, as well as the flat population in spiral galaxies, consisting of young stars and interstellar gas.

All principal descriptive functions of galaxies (circular velocity, gravitational potential, projected density) are simple integrals of the spatial density. Therefore it is natural to apply for the spatial density of galactic populations a simple generalized exponential expression (Einasto, 1965):

(1)

where is the semi-major axis of the isodensity ellipsoid, is the effective radius of the population, and is a structural parameter, determining the shape of the density profile. This expression (called the Einasto profile) can be used for all galactic populations, including dark halos. The case corresponds to the de Vaucouleurs density law for spheroidal populations, corresponds to the exponential density law for disk. A similar profile has been used by Sersic (1968) for the projected density of galaxies and their populations; in this case the parameter is called the Sersic index.

Multi-component models for spiral and elliptical galaxies using photometric data were constructed by Freeman (1970). To combine photometric and kinematic data, mass-to-light ratios of galactic populations are needed. Luminosities and colors of galaxies in various photometric systems result from the physical evolution of stellar populations that can be modeled. The study of the chemical evolution of galaxies was pioneered by Schwarzschild & Spitzer (1953) and Cameron & Truran (1971). Detailed models of the physical and chemical evolution of galaxies were constructed by Tinsley (1968).

Combined population and physical evolution models were calculated for a representative sample of galaxies by Einasto (1972). It is natural to expect, that in similar physical conditions the mass-to-luminosity ratio of the population has similar values in different stellar systems (star clusters, galactic populations). Thus we can use compact stellar populations (star clusters and central cores of galaxies), to estimate values for the main galactic populations.

Results of these calculations were reported at the First European Astronomy Meeting in Athens in September 1972 by Einasto (1974). The main conclusion was: it is impossible to reproduce the rotation data by known stellar populations only. The only way to eliminate the conflict between photometric and rotational data was to assume the presence of an unknown almost spherical population with a very high value of the mass-to-light ratio, large radius and mass. To avoid confusion with the conventional stellar halo, the term “corona” was suggested for the massive population. Thus, the detailed modeling confirmed earlier results obtained by simpler models. But here we have one serious difficulty – no known stellar population has so large a value.

Additional arguments for the presence of a spherical massive population in spiral galaxies came from the stability criteria against bar formation, suggested by Ostriker & Peebles (1973). Their numerical calculations demonstrated that initially very flat systems become rapidly thicker (during one revolution of the system) and evolve to a bar-like body. In real spiral galaxies a thin population exists, and it has no bar-like form. In their concluding remarks the authors write: “Presumably even Sc and other relatively ’pure’ spirals must have some means of remaining stable, and the possibility exists that those systems also have very large, low-luminosity halos. The picture developed here agrees very well with the fact, noted by several authors (see, for example, Rogstad & Shostak (1972)), that the mass-to-light ratio increases rapidly with distance from the center in these systems; the increase may be due to the growing dominance of the high mass-to-light halo over the low mass-to-light ratio disk. It also suggests that the total mass of such systems has been severely underestimated. In particular, the finding of Roberts & Rots (1973) that the rotation curves of several nearby spirals become flat at large distances from the nucleus may indicate the presence of very extended halos having masses that diverge rapidly [M(r) prop to r] with distance.”

3 Dark Matter in astronomical data

Modern astronomical methods yield a variety of independent information on the presence and distribution of dark matter. For our Galaxy, the basic data are the stellar motions perpendicular to the plane of the Galaxy (for the local dark matter), the motions of star and gas streams and the rotation (for the global dark matter). Important additional data come from gravitational microlensing by invisible stars or planets. In nearby dwarf galaxies the basic information comes from stellar motions. In more distant and giant galaxies the basic information comes from the rotation curves and the X-ray emission of the hot gas surrounding galaxies. In clusters and groups of galaxies the gravitation field can be determined from relative motions of galaxies, the X-ray emission of hot gas and gravitational lensing. Finally, measurements of fluctuations of the Cosmic Microwave Background (CMB) radiation in combination with data from type Ia supernovae in nearby and very distant galaxies yield information on the curvature of the Universe that depends on the amount of Dark Matter and Dark Energy.

Now we shall discuss these data in more detail.

3.1 Stellar motions

The local mass density near the Sun can be derived from vertical oscillations of stars near the galactic plane, as was discussed before. Modern data by Kuijken & Gilmore (1989); Gilmore et al. (1989) have confirmed the results by Kuzmin and his collaborators. Thus we come to the conclusion that there is no evidence for the presence of large amounts of dark matter in the disk of the Galaxy. If there is some invisible matter near the galactic plane, then its amount is small, of the order of 15 percent of the total mass density. The local dark matter is probably baryonic (low–mass stars or jupiters), since non-baryonic matter is dissipationless and cannot form a highly flattened population. Spherical distribution of the local dark matter (in quantities suggested by Oort (1960) and Bahcall (1987)) is excluded since in this case the total mass of the dark population would be very large and would influence also the rotational velocity of the Galaxy at the location of the Solar System.

Additional information of the distribution of mass in the outer part of the Galaxy comes from streams of stars and gas. One of the streams discovered near the Galaxy is the Magellanic Stream of gas which forms a huge strip and connects the Large Magellanic Cloud (LMC) with the Galaxy (Mathewson et al., 1974). Model calculations emphasize that this stream is due to an encounter of the LMC with the Galaxy. Kinematical data for the stream are available and support the hypothesis on the presence of a massive halo surrounding the Galaxy (Einasto et al., 1976a). Recently, streams of stars have been discovered within the Galaxy as well as around our giant neighbor M31. Presently there are still few data on the kinematics of these streams.

Several measurements of the dark mass halo were also performed using the motion of the satellite galaxies or the globular clusters. Measurements indicate the mass of the dark halo of about .

However, significant progress is expected in the near future. The astronomical satellite GAIA (to fly in 2011) is expected to measure distances and photometric data for millions of stars in the Galaxy. When these data are available, more information on the gravitation field of the Galaxy can be found.

The motion of individual stars or gaseous clouds can be also studied in nearby dwarf galaxies. Determination of the dark halo was performed for over a dozen of them. Some of the newly discovered dwarfs, coming from the Sloan Digital Sky Survey, are very under-luminous but equally massive as the previously known dwarf galaxies in the Milky Way vicinity, which makes them good candidates for extreme examples of dark matter dominated objects. Also the studies of the disruption rate of these galaxies due to the interaction with the Milky Way impose limits to the amount of dark mass in these objects. The results indicate that the dark matter in these systems exceeds by a factor a few the mass of stars.

3.2 Dynamics and morphology of companion galaxies

The rotation data available in early 1970s allowed the determination the mass distribution in galaxies up to their visible edges. In order to find how large and massive galactic coronas or halos are, more distant test particles are needed. If halos are large enough, then in pairs of galaxies the companion galaxies are located inside the halo, and their relative velocities can be used instead of the galaxy rotation velocities to find the distribution of mass around giant galaxies. This test was made by Einasto et al. (1974a) (see Fig. 2 ), and reported in a cosmology winter-school near the Elbrus mountain on January 1974, organized by Yakov Zeldovich. Zeldovich and his group had been working over 15 years to find basic physical processes for the formation and evolution of the structure of the Universe. For them the presence of a completely new massive non-stellar population was a great surprise, and caused an avalanche of new studies to find its properties and physical nature (Ozernoi (1974), Jaaniste & Saar (1975), Komberg & Novikov (1975), Bobrova & Ozernoi (1975), Zeldovich (1975) among others).

Figure 2: The mean internal mass as a function of the radius from the main galaxy in 105 pairs of galaxies (dots). Dashed line shows the contribution of visible populations, dotted line the contribution of the dark corona, solid line the total distribution (Einasto et al., 1974a).

A similar study was made independently by Ostriker et al. (1974), see Fig. 3. The paper by Ostriker et al. begins with the statement: “There are reasons, increasing in number and quality, to believe that the masses of ordinary galaxies may have been underestimated by a factor of 10 or more”. The closing statement of the Einasto et al. paper is: “The mass of galactic coronas exceeds the mass of populations of known stars by one order of magnitude. According to new estimates the total mass density of matter in galaxies is 20% of the critical cosmological density.” The bottom line in both papers was: since the data suggest that all giant galaxies have massive halos/coronas, dark matter must be the dynamically dominating population in the whole Universe.

Results of these papers were questioned by Burbidge (1975), who noticed that satellites may be optical. To clarify if the companions are true members of the satellite systems, Einasto et al. (1974b) studied the morphology of companions. They found that companion galaxies are segregated morphologically: elliptical (non–gaseous) companions lie close to the primary (host) galaxy whereas spiral and irregular (gaseous) companions of the same luminosity have larger distances from the primary galaxy. The elliptical/spiral segregation line from the primary galaxy depends on the luminosity of the satellite galaxy, see Fig. 4. This result shows, first of all, that the companions are real members of these systems – random by-fliers cannot have such properties. Second, this result demonstrates that diffuse matter has an important role in the evolution of galaxy systems. Morphological properties of companion galaxies can be explained, if we assume that (at least part of) the corona is gaseous.

Figure 3: Masses (in units ) of local giant galaxies (Ostriker et al., 1974) (reproduced by permission of the AAS and authors).

Additional arguments in favor of physical connection of companions with their primary galaxies came from the dynamics of small groups. Their mass distribution depends on the morphology: in systems with a bright primary galaxy the density (found from kinematical data) is systematically higher, and in elliptical galaxy dominated systems it is also higher. The mass distribution found from the kinematics of group members smoothly continues the mass distribution of the primary galaxies, found from rotation data (Einasto et al., 1976b).

3.3 Extended rotation curves of galaxies

The dark matter problem was discussed in 1975 at two conferences, in January in Tallinn (Doroshkevich et al., 1975) and in July in Tbilisi. The central problems discussed in Tallinn were: Deuterium abundance and the mean density of the universe (Zeldovich, 1975), What is the physical nature of the dark matter? and: What is its role in the evolution of the Universe? Two basic models were suggested for coronas: faint stars or hot gas. It was found that both models have serious difficulties (Jaaniste & Saar, 1975; Komberg & Novikov, 1975). Neutrinos were also considered, but rejected since they can form only supercluster-scale halos, about 1000 times more massive than halos around galaxies are.

Figure 4: The distribution of luminosities of companion galaxies at various distances from the primary galaxy. Filled circles are for elliptical companions, open circles for spiral and irregular galaxies (Einasto et al., 1974b). Note the clear segregation of elliptical and spiral/irregular galaxies.

In Tbilisi the Third European Astronomical Meeting took place. Here the principal discussion was between the supporters of the classical paradigm with conventional mass estimates of galaxies, and of the new one with dark matter. The major arguments supporting the classical paradigm were summarized by Materne & Tammann (1976). Their most serious argument was: Big Bang nucleosynthesis suggests a low-density Universe with the density parameter ; the smoothness of the Hubble flow also favors a low-density Universe.

It was clear that by sole discussion the presence and nature of dark matter cannot be solved, new data and more detailed studies were needed. The first very strong confirmation of the dark matter hypothesis came from new extended rotation curves of galaxies.

Figure 5: The integral masses as a function of the distance from the nucleus for spiral galaxies of various morphological type (Rubin et al., 1978) (reproduced by permission of the AAS and authors).

In early 1970s optical data on rotation of galaxies were available only for inner bright regions of galaxies. Radio observations of the 21-cm line reached much longer rotation curves well beyond the Holmberg radius of galaxies. All available rotation data were summarized by Roberts (1975) in the IAU Symposium on Dynamics of Stellar Systems held in Besancon (France) in September 1974. Extended rotation curves were available for 14 galaxies; for some galaxies data were available until the galactocentric distance kpc (we use in this paper the Hubble constant in the units of km s Mpc), see Fig. 1 for M31. About half of galaxies had flat rotation curves, the rest had rotation velocities that decreased slightly with distance. In all galaxies the local mass-to-light ratio in the periphery reached values over 100 in Solar units. To explain such high values Roberts assumed that late-type dwarf stars dominate the peripheral regions.

Figure 6: The rotation curves of spiral galaxies of various morphological type according to Westerbork radio observations (Bosma, 1978) (reproduced by permission of the author).

In mid-1970s Vera Rubin and her collaborators developed new sensitive detectors to measure optically the rotation curves of galaxies at very large galactocentric distances. Their results suggested that practically all spiral galaxies have extended flat rotation curves (Rubin et al., 1978, 1980). The internal mass of galaxies rises with distance almost linearly, up to the last measured point, see Fig. 5.

At the same time measurements of a number of spiral galaxies with the Westerbork Synthesis Radio Telescope were completed, and mass distribution models were built, all-together for 25 spiral galaxies (Bosma, 1978), see Fig. 6. Observations confirmed the general trend that the mean rotation curves remain flat over the whole observed range of distances from the center, up to kpc for several galaxies. The internal mass within the radius increases over the whole distance interval.

These observational results confirmed the concept of the presence of dark halos of galaxies with a high confidence.

Another very important measurement was made by Sandra Faber and collaborators (Faber & Jackson, 1976; Faber et al., 1977; Faber & Gallagher, 1979). They measured the central velocity dispersions for 25 elliptical galaxies and the rotation velocity of the Sombrero galaxy, a S0 galaxy with a massive bulge and a very weak population of young stars and gas clouds just outside the main body of the bulge. Their data yielded for the bulge of the Sombrero galaxy a mass-to-light ratio , and for the mean mass-to-light ratios for elliptical galaxies about 7, close to the ratio for early type spiral galaxies. These observational data confirmed estimates based on the calculations of physical evolution of galaxies, made under the assumption that the lower mass limit of the initial mass function (IMF) is for all galactic populations of the order of 0.1 . These results showed that the mass-to-light ratios of stellar populations in spiral and elliptical galaxies are similar for a given color, and the ratios are much lower than those accepted in earlier studies based on the dynamics of groups and clusters. In other words, high mass-to-light ratios of groups and clusters of galaxies cannot be explained by visible galactic populations.

Earlier suggestions on the presence of mass discrepancy in galaxies and galaxy systems had been ignored by the astronomical community. This time new results were taken seriously. As noted by Kuhn, a scientific revolution begins when leading scientists in the field start to discuss the problem and arguments in favor of the new over the old paradigm.

More data are slowly accumulating (Sofue & Rubin, 2001). New HI measurements from Westerbork extend the rotation curves up to 80 kpc (galaxy UGC 2487) or even 100 kpc (UGC 9133 and UGC 11852) showing flat rotation curves (Noordermeer et al., 2005). The HI distribution in the Milky Way has been recently studied up to distances of 40 kpc by Kalberla (2003); Kalberla et al. (2007). The Milky Way rotation curve has been determined by Xue et al. (2008) up to kpc from the study of Blue Horizontal Branch stars from SDSS survey, and the rotation curves seems to be slightly falling from the 220 km s value at the Sun location. Earlier determinations did not extend so far and extrapolations were affected by the presence of the ring-like structure in mass distribution at kpc from the center. Implied values of the dark matter halo from different measurements still differ between themselves by a factor 2 - 3, being in the range from . The central density of dark matter halos of galaxies is surprisingly constant, about  pc (Einasto et al., 1974a; Gilmore et al., 2007). Smallest dwarf galaxies have half-light radius about 120 pc, largest star clusters of similar absolute magnitude have half-light radius up to 35 pc; this gap separates systems with and without dark halos (Gilmore et al., 2008).

3.4 X-ray data on galaxies and clusters of galaxies

Hot intra-cluster gas emitting X-rays was detected in almost all nearby clusters and in many groups of galaxies by the Einstein X-ray orbiting observatory. Observations confirmed that the hot gas is in hydrodynamical equilibrium, i.e. gas particles move in the general gravitation field of the cluster with velocities which correspond to the mass of the cluster (Forman & Jones, 1982; Sarazin, 1988; Rosati et al., 2002).

The distribution of the mass in clusters can be determined if the density and the temperature of the intra-cluster gas are known. This method of determining the mass has a number of advantages over the use of the virial theorem. First, the gas is a collisional fluid, and particle velocities are isotropically distributed, which is not true for galaxies as test particles of the cluster mass (uncertainties in the velocity anisotropy of galaxies affect mass determinations). Second, the hydrostatic method gives the mass as a function of radius, rather than the total mass alone as given by the virial method.

Using Einstein X-ray satellite data the method was applied to determine the mass of Coma, Perseus and Virgo clusters (Bahcall & Sarazin, 1977; Mathews, 1978). The results were not very accurate since the temperature profile was known only approximately. The results confirmed previous estimates of masses made with the virial method using galaxies as test particles. The mass of the hot gas itself is only about 0.1 of the total mass. The luminous mass in member galaxies is only a fraction of the X-ray emitting mass.

More recently clusters of galaxies have been observed in X-rays using the ROSAT satellite (operated in 1990–1999), and the XMM-Newton and Chandra observatories, launched both in 1999. The ROSAT satellite was used to compile an all-sky catalog of X-ray clusters and galaxies. More than 1000 clusters up to a redshift were cataloged. Dark matter profiles have been determined in a number of cases (Humphrey et al., 2006).

The XMM and Chandra observatories allow us to get detailed images of X-ray clusters, and to derive the density and temperature of the hot gas (Jordán et al., 2004; Rasia et al., 2006). Using the XMM observatory, a survey of X-ray clusters was initiated to find a representative sample of clusters at redshifts up to . The comparison of cluster properties at different redshifts allows the obtaining of more accurate information on the evolution of clusters which depend critically on the parameters of the cosmological model.

Chandra observations allow us to find the hot gas and total masses not only for groups and clusters, but also for nearby galaxies (Humphrey et al. (2006), see also Mathews et al. (2006), Lehmer et al. (2008)). For early-type (elliptical) galaxies the virial masses found were 0.7–9 M. Local mass-to-light ratio profiles are flat within an optical half-light radius (), rising more than an order of magnitude at , which confirms the presence of dark matter. The baryon fraction (most baryons are in the hot X-ray emitting gas) in these galaxies is . The gas mass profiles are similar to the profiles of dark matter shifted to lower densities. The stellar mass-to-light ratios in these old bulge dominated galaxies are using the Salpeter IMF (for the infrared K-band, the ratios for the B-band are approximately 4 times higher). Interesting information of the chemical composition of the hot plasma in the halo of the Milky Way were obtained in 2008 from the comparative study of the tiny absorption lines in a few Galactic and extragalactic X-ray sources, giving the total column density of O VII less than cm. Assuming that the gaseous baryonic corona has the mass of order of , as expected from the theory of galaxy formation, this measurement implies a very low metallicity of the corona plasma, below 3.7 percent of the solar value.

3.5 Galactic and extragalactic gravitational lensing

Clusters, galaxies and even stars are so massive that their gravity bends and focuses the light from distant galaxies, quasars and stars that lie far behind. There are three classes of gravitational lensing:

  • Strong lensing, where there are easily visible distortions such as the formation of Einstein rings, arcs, and multiple images, see Fig. 7.

  • Weak lensing, where the distortions of background objects are much smaller and can only be detected by analyzing the shape distortions of a large number of objects.

  • Microlensing, where no shape distortion can be seen, but the amount of light received from a background object changes in time. The background source and the lens may be stars in the Milky Way or in nearby galaxies (M31, Magellanic Clouds).

The strong lensing effect is observed in rich clusters, and allows us to determine the distribution of the gravitating mass in clusters. Massive galaxies can distort images of distant single objects, such as quasars: as a result we observe multiple images of the same quasar. The masses of clusters of galaxies determined using this method, confirm the results obtained by the virial theorem and the X-ray data.

Weak lensing allows us to determine the distribution of dark matter in clusters as well as in superclusters. For the most luminous X-ray cluster known, RXJ 1347.5-1145 at the redshift , the lensing mass estimate is almost twice as high as that determined from the X-ray data. The mass-to-light ratio is in Solar units (Fischer & Tyson, 1997; Fischer et al., 1997). For other recent work on weak lensing and X-ray clusters see Bradač et al. (2005); Dietrich et al. (2005); Clowe et al. (2006b); Massey et al. (2007).

Figure 7: The Hubble Space Telescope image of the cluster Abell 2218. This cluster is so massive that its gravity bends the light of more distant background galaxies. Images of background galaxies are distorted into stretched arcs (Astr. Pict. of the Day Jan. 11, 1998, Credit: W. Couch, R. Ellis).

A fraction of the invisible baryonic matter can lie in small compact objects – brown dwarf stars or Jupiter-like objects. To find the fraction of these objects in the cosmic balance of matter, special studies have been initiated, based on the microlensing effect.

Microlensing effects were used to find Massive Compact Halo Objects (MACHOs). MACHOs are small objects as planets, dead stars (white dwarfs) or brown dwarfs, which emit so little radiation that they are invisible most of the time. A MACHO may be detected when it passes in front of a star and the MACHOs gravity bends the light, causing the star to appear brighter. Several groups have used this method to search for the baryonic dark matter. Some authors claimed that up to 20 % of dark matter in our Galaxy can be in low-mass stars (white or brown dwarfs). However, observations using the Hubble Space Telescope’s (HST) NICMOS instrument show that only about 6% of the stellar mass is composed of brown dwarfs. This corresponds to a negligible fraction of the total matter content of the Universe (Graff & Freese, 1996; Najita et al., 2000).

4 The nature of Dark Matter

By the end of 1970s most objections against the dark matter hypothesis were rejected. In particular, luminous populations of galaxies have found to have lower mass-to-light ratios than expected previously, thus the need of extra dark matter both in galaxies and clusters is even stronger. However, there remained three problems:

  • It was not clear how to explain the Big Bang nucleosynthesis constraint on the low density of matter, and the smoothness of the Hubble flow.

  • If the massive halo (corona) is not stellar nor gaseous, of what stuff is it made of?

  • And a more general question: in Nature everything has its purpose. If 90 % of matter is dark, then there must be a reason for its presence. What is the role of dark matter in the history of the Universe?

First we shall discuss baryons as dark matter candidates.

Figure 8: The big-bang production of the light elements. The abundance of chemical elements is given as a function of the density of baryons, expressed in units of (horizontal axis). Predicted abundances are in agreement with measured primeval abundances in a narrow range of baryon density (Schramm & Turner, 1998).

4.1 Nucleosynthesis constraints on the amount of baryonic matter

According to the Big Bang model, the Universe began in an extremely hot and dense state. For the first second it was so hot that atomic nuclei could not form – space was filled with a hot soup of protons, neutrons, electrons, photons and other short-lived particles. Occasionally a proton and a neutron collided and stuck together to form a nucleus of deuterium (a heavy isotope of hydrogen), but at such high temperatures they were broken immediately by high-energy photons (Schramm & Turner, 1998).

When the Universe cooled off, these high-energy photons became rare enough that it became possible for deuterium to survive. These deuterium nuclei could keep sticking to more protons and neutrons, forming nuclei of helium-3, helium-4, lithium, and beryllium. This process of element-formation is called “nucleosynthesis”. The denser proton and neutron “gas” is at this time, the more of the total amount of light elements will be formed. As the Universe expands, the density of protons and neutrons decreases and the process slows down. Neutrons are unstable (with a lifetime of about 15 minutes) unless they are bound up inside a nucleus. After a few minutes the free neutrons will be gone and nucleosynthesis will stop. There is only a small window of time in which nucleosynthesis can take place, and the relationship between the expansion rate of the Universe (related to the total matter/radiation density) and the density of protons and neutrons (the baryonic matter density) determines how much of each of these light elements are formed in the early Universe.

According to nucleosynthesis data baryonic matter makes up 0.04 of the critical cosmological density, assuming (Fig. 8). Only a small fraction, less than 10%, of the baryonic matter is condensed to visible stars, planets and other compact objects. Most of the baryonic matter is in the intergalactic matter, it is concentrated also in hot X-ray coronas of galaxies and clusters.

Figure 9: The evolution of mass-to-light ratios of galactic populations of different metal abundance (Einasto, 1972).

4.2 Baryonic Dark Matter

Models of the galaxy evolution are based on stellar evolution tracks, star formation rates (as a function of time), and the initial mass function (IMF). For IMF the Salpeter (1955) law is usually used:

(2)

where is the mass of the forming star, and and are parameters. This law cannot be used for stars of arbitrary mass, because in this case the total mass of forming stars may be infinite. Thus we assume that this law is valid in the mass interval to (the lower and upper limit of the forming stars, respectively).

Early models of physical evolution of galaxies were constructed by Tinsley (1968) and Einasto (1972). These models show that the mass-to-light ratio of the population depends critically on the lower limit of the IMF, . Calculations by Einasto (1972) show, that even for rather different physical conditions the value of changes only moderately (Fig. 9). An independent check of the correctness of the lower limit is provided by homogeneous stellar populations, such as star clusters. Here we can assume that all stars were formed simultaneously, the age of the cluster can be estimated from the HR diagram, and the mass derived from the kinematics of stars in the cluster. Such data are available for old metal-poor globular clusters, for relatively young medium-metal-rich open clusters, as well as for metal-rich cores of galaxies. This check suggests that in the first approximation for all populations similar lower mass limits () can be used; in contracting gas clouds above this limit the hydrogen starts burning, below not. Using this mass lower limits we get for old metal-poor halo populations , and for extremely metal-rich populations in central regions of galaxies , as suggested by the central velocity dispersion in luminous elliptical galaxies. For intermediate populations (bulges and disks) one gets , see Fig. 9. Modern data yield for metal-rich populations lower values, due to more accurate measurements of velocity dispersions in the central regions of galaxies, as suggested in pioneering studies by Faber & Jackson (1976); Faber et al. (1977), and more accurate input data for evolution models.

To get very high values of , as suggested by the dynamics of companion galaxies or rotation data in the periphery of galaxies, one needs to use a very small value of the mass lower limit . All known stellar populations have much lower mass-to-light values, and form continuous sequences in color- and velocity dispersion- diagrams.

For this reason it is very difficult to explain the physical and kinematical properties of a stellar dark halo. Dark halo stars form an extended population around galaxies, and must have much higher velocity dispersion than the stars belonging to the ordinary halo. No fast-moving stars as possible candidates for stellar dark halos were found (Jaaniste & Saar, 1975). If the hypothetical population is of stellar origin, it must be formed much earlier than all known populations, because known stellar populations of different age and metallicity form a continuous sequence of kinematical and physical properties, and there is no place where to include this new population into this sequence. And, finally, it is known that star formation is not an efficient process – usually in a contracting gas cloud only about 1 %  of the mass is converted to stars. Thus we have a problem how to convert, in an early stage of the evolution of the Universe, a large fraction of the primordial gas into this population of dark stars. Numerical simulations suggest, that in the early universe only a very small fraction of gas condenses to stars which ionize the remaining gas and stop for a certain period further star formation (Cen, 2003; Gao et al., 2005b).

Stellar origin of dark matter in clusters was discussed by Napier & Guthrie (1975); they find that this is possible if the initial mass function of stars is strongly biased toward very low-mass stars. Thorstensen & Partridge (1975) discussed the suggestion made by Truran & Cameron (1971) that there may have been a pre-galactic generation of stars (population III), all of them more massive than the Sun, which are now present as collapsed objects. They conclude that the total mass of this population is negligible, thus collapsed stars cannot make up the dark matter.

Modern calculations suggests that metal-free population III stars are expected to be massive ( M) due to large Jeans mass during the initial baryonic collapse (for a discussion see Reed et al. (2005) and references therein). Thus population III stars are not suited to represent at the present epoch a high halo population.

Recently weak stellar halos have been detected around several nearby spiral galaxies at very large galactocentric distances. For instance, a very weak stellar halo is found in M31 up to distance of 165 kpc (Gilbert et al., 2006; Kalirai et al., 2006). The stars of this halo have very low metallicity, but have anomalously red color. The total luminosity and mass of these extended halos is, however, very small, thus these halos cannot be identified with the dark halo.

Gaseous coronas of galaxies and clusters were discussed in 1970s by Field (1972), Silk (1974), Tarter & Silk (1974), Komberg & Novikov (1975) and others. The general conclusion from these studies was that gaseous coronas of galaxies and clusters cannot consist of neutral gas since the intergalactic hot gas would ionize the coronal gas. On the other hand, a corona consisting of hot ionized gas would be observable. Modern data show that a fraction of the coronal matter around galaxies and in groups and clusters of galaxies consists indeed of the X-ray emitting hot gas, but the amount of this gas is not sufficient to explain the flat rotation curves of galaxies (Turner, 2003).

The results of early discussions of the nature of dark halos were inconclusive – no appropriate candidate was found. For many astronomers this was an argument against the presence of dark halos.

4.3 Non-baryonic Dark Matter and fluctuations of the CMB radiation

Already in 1970s suggestions were made that some sort of non-baryonic elementary particles, such as massive neutrinos, axions, photinos, etc., may serve as candidates for dark matter particles. There were several reasons to search for non-baryonic particles as a dark matter candidate. First of all, no baryonic matter candidate did fit the observational data. Second, the total amount of dark matter is of the order of 0.2–0.3 in units of the critical cosmological density, while the nucleosynthesis constraints suggest that the amount of baryonic matter cannot be higher than about 0.04 of the critical density.

A third very important observation was made which caused doubts to the baryonic matter as the dark matter candidate. In 1964 Cosmic Microwave Background (CMB) radiation was detected. This discovery was a powerful confirmation of the Big Bang theory. Initially the Universe was very hot and all density and temperature fluctuations of the primordial soup were damped by very intense radiation; the gas was ionized. But as the Universe expanded, the gas cooled and at a certain epoch called recombination the gas became neutral. From this time on, density fluctuations in the gas had a chance to grow by gravitational instability. Matter is attracted to the regions were the density is higher and it flows away from low-density regions. But gravitational clustering is a very slow process. Model calculations show that in order to have time to build up all observed structures as galaxies, clusters, and superclusters, the amplitude of initial density fluctuations at the epoch of recombination must be of the order of of the density itself. These calculations also showed that density fluctuations are of the same order as temperature fluctuations. Thus astronomers started to search for temperature fluctuations of the CMB radiation. None were found. As the accuracy of measurement increased, lower and lower upper limits for the amplitude of CMB fluctuations were obtained. In late 1970s it was clear that the upper limits are much lower than the theoretically predicted limit (see, for instance Parijskij (1978)).

Figure 10: Images of the merging ’bullet’ cluster 1E0657-558. The left panel shows a direct image of the cluster obtained with the 6.5-m Magellan telescope in the Las Campanas Observatory, the right panel is a X-ray satellite Chandra image of the cluster. Shock waves of the gas are visible, the gas of the smaller ’bullet’ cluster (right) lags behind the cluster galaxies. In both panels green contours are equidensity levels of the gravitational potential of the cluster, found using weak gravitational lensing of distant galaxies. The white bar has 200 kpc/h length at the distance of the cluster. Note that contours of the gravitational potential coincide with the location of visible galaxies, but not with the location of the X-ray gas (the dominant baryonic component of clusters) (Clowe et al., 2006a) (reproduced by permission of the AAS and authors).

Then astronomers recalled the possible existence of non-baryonic particles, such as heavy neutrinos. This suggestion was made independently by several astronomers (Cowsik & McClelland (1973); Szalay & Marx (1976); Tremaine & Gunn (1979); Doroshkevich et al. (1980b); Chernin (1981); Bond et al. (1983)) and others. They found that, if dark matter consists of heavy neutrinos, then this helps to explain the paradox of small temperature fluctuations of the cosmic microwave background radiation. This problem was discussed in a conference in Tallinn in April 1981. Recent experiments by a Moscow physicist Lyubimov were announced, which suggested that neutrinos have masses. If so, then the growth of perturbations in a neutrino-dominated medium can start much earlier than in a baryonic medium, and at the time of recombination perturbations may have amplitudes large enough for structure formation. The Lyubimov results were never confirmed, but it gave cosmologists an impulse to take non-baryonic dark matter seriously. In the conference banquet Zeldovich gave an enthusiastic speech: “Observers work hard in sleepless nights to collect data; theorists interpret observations, are often in error, correct their errors and try again; and there are only very rare moments of clarification. Today it is one of such rare moments when we have a holy feeling of understanding the secrets of Nature.” Non-baryonic dark matter is needed to start structure formation early enough. This example illustrates well the attitude of theorists to new observational discoveries – the Eddington’s test: “No experimental result should be believed until confirmed by theory” (cited by Turner (2000)). Dark matter condenses at early epoch and forms potential wells, the baryonic matter flows into these wells and forms galaxies (White & Rees, 1978).

The search of dark matter can also be illustrated with the words of Sherlock Holmes “When you have eliminated the impossible, whatever remains, however improbable, must be the truth” (cited by Binney & Tremaine (1987)). The non-baryonic nature of dark matter explains the role of dark matter in the evolution of the Universe, and the discrepancy between the total cosmological density of matter and the density of baryonic matter, as found from the nucleosynthesis constraint. Later studies have demonstrated that neutrinos are not the best candidates for the non-baryonic dark matter, see below.

4.4 Alternatives to Dark Matter

The presence of large amounts of matter of unknown origin has given rise to speculations on the validity of the Newton’s law of gravity at large distances. One of such attempts is the Modified Newtonian Dynamics (MOND), suggested by Milgrom & Bekenstein (1987), for a discussion see Sanders (1990). Another attempt is the Modified Gravity Theory (MOG), proposed by Moffat & Toth (2007). Indeed, MOND and MOG are able to represent a number of observational data without assuming the presence of some hidden matter. However, there exist several arguments which make these models unrealistic.

There exist numerous direct observations of the distribution of mass, visible galaxies and the hot X-ray gas, which cannot be explained in the MOND framework. One of such examples is the “bullet” cluster 1E 0657-558 (Clowe et al., 2004; Markevitch et al., 2004; Clowe et al., 2006a), shown in Fig. 10. This is a pair of galaxy clusters, where the smaller cluster (bullet) has passed the primary cluster almost tangentially to the line of sight. The hot X-ray gas has been separated by ram pressure-stripping during the passage. Weak gravitational lensing yields the distribution of mass in the cluster pair. Lensing observations show that the distribution of matter is identical with the distribution of galaxies. The dominant population of the baryonic mass is in X-ray gas which is well separated from the distribution of mass. This separation is only possible if the mass is in the collisionless component, i.e. in the non-baryonic dark matter halo, not in the baryonic X-ray gas.

Figure 11: The two-dimensional distribution of galaxies according to the Lick counts (Seldner et al., 1977). The north galactic pole is at the center, the galactic equator is at the edge. Superclusters are well seen, the Coma cluster is located near the center (reproduced by permission of the AAS and authors).

Another example of a merging cluster is the rich cluster Cl 0024+17 at redshift . This cluster has been observed using the Hubble Space Telescope Advanced Camera for Surveys (HST/ACS) data by Jee et al. (2007). The distribution of the hot intracluster medium (ICM) has been found using Chandra data. Jee et al. calculated the mass distribution, unifying both strong- and weak-lensing constraints. The mass reconstruction reveals a ringlike dark matter substructure at , which surrounds a dense core at . The redshift histogram of the cluster is bimodal, which is an indication of a high-speed line-of-sight collision of two massive clusters. Jee et al. (2007) interpret the mass distribution sub-structure as the result of the collision Gyr ago. The formation of a ringlike structure is analogous to that in ring galaxies (Lynds & Toomre, 1976). N-body simulation of a collision of two massive clusters confirmed the formation of temporary ringlike structures before the final merging of clusters. Hot ICM forms by collision of two separate approximately isothermal clouds. The distribution of galaxies in both colliding clusters also remains almost unchanged during the passage. Further analysis of the distribution of ICM using data obtained with the HST ACS and the Subaru telescope by Jee (2010) has confirmed the peculiar dark matter structure in this cluster. Jee et al. (2007) conclude: The ringlike mass structure surrounding the dense core not traced by the cluster ICM nor by the cluster galaxies serves as the most definitive evidence from gravitational lensing to date for the existence of dark matter. If there is no dark matter and the cluster ICM is the dominant source of gravity, the MONDian gravitational lensing mass should follow the ICM.

A more general argument in favour of the presence of non-baryonic dark matter comes from the CMB data. In the absence of large amounts of non-baryonic matter during the radiation domination era of the evolution of the Universe it would be impossible to get for the relative amplitude of density fluctuations a value of the order of , needed to form all observed structures.

It is fair to say that in comparison to the DM paradigm the consequences of the various modifications of the Newtonian gravity, that were mentioned above, have not been worked out in such a detail. Thus it still needs to be seen if any of those modified pictures could provide a viable alternative to the DM. However, one has to keep in mind that despite us having a good idea of what might make up a DM, the DM paradigm is remarkably simple: one just needs an additional cold collisionless component that interacts only through gravity. Once this component is accepted, a host of apparent problems, starting from galaxy and galaxy cluster scales and extending to the largest scales as probed by the large scale structure and CMB, get miraculously solved. So in that respect one might say that there is certainly some degree of elegance in the DM picture. On the other hand, taking into account the simplicity of the DM paradigm, it is quite hard to believe that any alternatives described above could achieve a similar level of agreement with observational data over such a large range of spatial and temporal scales. Indeed, it seems that for different scales one might need “a different MOND”.

5 Dark Matter and structure formation

It is clear that if dark matter dominates in the matter budget of the Universe, then the properties of dark matter particles determine the formation and evolution of the structure of the Universe. In this way the dark matter problem is related to the large-scale structure of the Universe.

5.1 The distribution of galaxies and clusters

Already in the New General Catalogue (NGC) of nebulae, composed from observations by William and John Herschel, a rich collection of nearby galaxies in the Virgo constellation was known. de Vaucouleurs (1953a) called this system the Local Super-galaxy, presently it is known as the Virgo or Local Supercluster. Detailed investigation of the distribution of galaxies became possible when Harlow Shapley started in the Harvard Observatory a systematic photographic survey of galaxies in selected areas, up to 18th magnitude (Shapley, 1935, 1937, 1940). Shapley discovered several other rich superclusters, one of them is presently named the Shapley Supercluster. These studies showed also that the mean spatial density of galaxies is approximately independent of the distance and of the direction in the sky. In other words, the Harvard survey indicated that galaxies are distributed in space more-or-less homogeneously, as expected from the general cosmological principle.

A complete photographic survey of galaxies was made in the Lick Observatory with the 20-inch Carnegie astrograph by Shane & Wirtanen (1967). Galaxy counts were made in cells of size , and the distribution of the number density of galaxies was studied. The general conclusion from this study was that galaxies are mostly located in clusters, the number of galaxies per cluster varying widely from pairs to very rich clusters of the Coma cluster type. The Lick counts were reduced by Jim Peebles and collaborators to exclude count limit irregularities; the resulting distribution of galaxies in the sky is shown in Fig. 11.

A much deeper photographic survey was made using the 48-inch Palomar Schmidt telescope. Fritz Zwicky used this survey to compile for the Northern hemisphere a catalogue of galaxies and clusters of galaxies (Zwicky et al., 1968). The galaxy catalogue is complete up to 15.5 photographic magnitude. George Abell used the same survey to compile a catalogue of rich clusters of galaxies for the Northern sky, later the catalogue was continued to the Southern sky (Abell, 1958; Abell et al., 1989). Using apparent magnitudes of galaxies approximate distances (distance classes) were estimated for clusters in both catalogues. Authors noticed that clusters of galaxies also show a tendency of clustering, similar to galaxies which cluster to form groups and clusters. Abell called these second order clusters superclusters, Zwicky – clouds of galaxies.

The Lick counts as well as galaxy and cluster catalogues by Zwicky and Abell were analyzed by Jim Peebles and collaborators (Peebles (1973), Hauser & Peebles (1973), Peebles & Hauser (1974), Peebles (1974)). To describe the distribution of galaxies Peebles introduced the two-point correlation (or covariance) function of galaxies (Peebles & Groth, 1975; Groth & Peebles, 1977; Fry & Peebles, 1978). This function describes the probability to find a neighbor at a given angular separation in the sky from a galaxy. At small separations the spatial galaxy correlation function can be approximated by a power law: , with the index . The distance , at which the correlation function equals unity, is called the correlation length. For galaxy samples its value is   Mpc, and for clusters of galaxies   Mpc. On scales times the correlation length the correlation function is very close to zero, i.e. the distribution of galaxies (clusters) is essentially random.

Figure 12: Wedge diagrams for two declination zones. Filled circles show rich clusters of galaxies, open circles – groups, dots – galaxies, crosses – Markarian galaxies. In the zone two rich clusters at RA about 12 h are the main clusters of the Coma supercluster, in the zone clusters at RA about 3 h belong to the main chain of clusters and galaxies of the Perseus-Pisces supercluster. Note the complete absence of galaxies in front of the Perseus-Pisces supercluster, and galaxy chains leading from the Local supercluster towards the Coma and Perseus-Oisces superclusters (Jõeveer & Einasto, 1978).

The conclusion from these studies, based on the apparent (2-dimensional) distribution of galaxies and clusters in the sky confirmed the picture suggested by Kiang (1967) and de Vaucouleurs (1970), among others, that galaxies are hierarchically clustered. However, this hierarchy does not continue to very large scales as this contradicts observations, which show that on very large scales the distribution is homogeneous. A theoretical explanation of this picture was given by Peebles in his hierarchical clustering scenario of structure formation (Peebles & Yu, 1970; Peebles, 1971).

5.2 Superclusters, filaments and voids

In 1970s new sensitive detectors were developed which allowed the measurement of redshifts of galaxies up to fainter magnitudes. Taking advance of this development several groups started to investigate the environment of relatively rich clusters of galaxies, such as the Coma cluster and clusters in the Hercules supercluster, with a limiting magnitude about 15.5. During this study Chincarini, Gregory, Rood, Thompson and Tifft noticed that the main clusters of the Coma supercluster, A1656 and A1367, are surrounded by numerous galaxies, forming a cloud around clusters at the redshift 7000 km/s. The Coma supercluster lies behind the Local supercluster, thus galaxies of the Local supercluster also form a condensation in the same direction at the redshift about 1000 km/s. In between there is a group of galaxies around NGC 4169 at the redshift 4000 km/s, and the space between these systems is completely devoid of galaxies (Chincarini & Rood, 1976; Gregory & Thompson, 1978). A similar picture was observed in front of the Hercules and Perseus superclusters.

In 1970s there were two main rivaling theories of structure formation: the “Moscow” pancake theory by Zeldovich (1970), and the “Princeton” hierarchical clustering theory by Peebles (1971).

In developing the structure formation scenario Zeldovich used his previous experience in studying explosive phenomena – he was a leading expert in the Soviet atomic bomb project. He knew that in the early phase of the evolution of the Universe, when density fluctuations are very small, the global velocities, determined by the gravitational potential field, play the dominant role. The development of the global velocity field leads to the formation of flat pancake-like systems. In this scenario the structure forms top-down: first matter collects into pancakes and then fragments to form smaller units.

The hierarchical clustering scenario is based on the Peebles experience of the study of galaxy clustering using Lick counts. The clustering can be described by the correlation function, which describes the local clustering of galaxies. According to this scenario the order of the formation of systems is the opposite: first small-scale systems (star-cluster sized objects) form, and by clustering systems of larger size (galaxies, clusters of galaxies) form; this is a bottom-up scenario.

In the Zeldovich team there were no experts on extragalactic astronomy, thus he asked Tartu astronomers for help in solving the question: Can we find observational evidence which can be used to discriminate between various theories of galaxy formation? In solving the Zeldovich question we started from the observational fact suggesting that random velocities of galaxies are of the order of several hundred km/s. Thus during the whole lifetime of the Universe galaxies have moved from their place of origin only by about 1  Mpc. In other words – if there exist some regularities in the distribution of galaxies, then these regularities must reflect the conditions in the Universe during the formation of galaxies.

In mid-1970s first all-sky complete redshift surveys of galaxies were just available: the de Vaucouleurs et al. (1976) Second Revised Catalogue of Galaxies, the Shapley-Adams revised catalogue by Sandage & Tammann (1981), complete up to the magnitude 13.5 (new redshifts were available earlier (Sandage, 1978)). For nearby clusters of galaxies and active (Markarian and radio) galaxies the redshift data were also available. The common practice to visualize the three-dimensional distribution of galaxies, groups and clusters of galaxies is the use of wedge-diagrams. In these diagrams, where galaxies as well as groups and clusters of galaxies were plotted, a regularity was clearly seen: galaxies and clusters are concentrated to identical essentially one-dimensional systems, and the space between these systems is practically empty (Jõeveer & Einasto, 1978). This distribution was quite similar to the distribution of test particles in a numerical simulation of the evolution of the structure of the Universe prepared by the Zeldovich group (Doroshkevich et al. (1980a), early results of simulation were available already in 1976). In this simulation a network of high- and low-density regions was seen: high-density regions form cells which surround large under-dense regions. Thus the observed high-density regions could be identified with Zeldovich pancakes (for a detailed description of the search of regularities in galaxy distribution see Einasto (2001)).

The Large Scale Structure of the Universe was discussed at the IAU symposium in Tallinn 1977, following an initiative by Zeldovich. The amazing properties of the distribution of galaxies were reported by four different groups: Tully & Fisher (1978) for the Local supercluster, Jõeveer & Einasto (1978) for the Perseus supercluster, Tarenghi et al. (1978) for the Hercules supercluster, and Tifft & Gregory (1978) for the Perseus supercluster; see also Gregory & Thompson (1978) for the Coma supercluster and Jõeveer et al. (1978) for the distribution of galaxies and clusters in the Southern galactic hemisphere. The presence of voids (holes) in galaxy distribution was suggested in all four reports. Tully & Fisher demonstrated a movie showing a filamentary distribution of galaxies in the Local supercluster.

Jõeveer and Einasto emphasized the presence of fine structure: groups and clusters of galaxies form chains in superclusters and connect superclusters to a continuous network, as seen from wedge diagrams in Fig. 12. They demonstrated also morphological properties of the structure of superclusters: clusters and groups within the chain are elongated along the chain, and main galaxies of clusters (supergiant galaxies of type cD) are also elongated along the chain. A long chain of clusters, groups and galaxies of the Perseus-Pisces supercluster is located almost perpendicular to the line of sight. The scatters of positions of clusters/groups along the chain in the radial (redshift) and tangential directions are practically identical. This demonstrates that the chain is essentially an one-dimensional structure.

Figure 13: A slice of the Universe according to the CfA Second redshift survey (de Lapparent et al., 1986). Galaxy chains connecting the Local and Coma superclusters are seen more clearly; the connection between the Hercules and Coma superclusters is also visible (reproduced by permission of the AAS and authors).

A direct consequence from this observation is that galaxies and groups/clusters of the chain are already formed within the chain. A later inflow from random locations to the chain is excluded, since in this case it would be impossible to stop galaxies and clusters in the chain after the inflow. The main results of the symposium were summarized by Malcolm Longair as follows: To me, some of the most exiting results presented at this symposium concerned the structure of the Universe on the largest scales. Everyone seemed to agree about the existence of superclusters on scales Mpc. But perhaps even more surprising are the great holes in the Universe. Peebles’ picture, Einasto’s analysis of the velocity distribution of galaxies which suggests a “cell-structure” and Tiffts’s similar analysis argue that galaxies are found in interlocking chains over scales Mpc forming pattern similar to a lace-tablecloth.

New data gave strong support to the pancake scenario by Zeldovich (1978). However, some important differences between the model and observations were evident. First of all, numerical simulations showed that there exists a rarefied population of test particles in voids absent in real data. This was the first indication for the presence of physical biasing in galaxy formation – there is primordial gas and dark matter in voids, but due to low density no galaxy formation takes place here. Theoretical explanation of the absence of galaxies in voids was given by Enn Saar (Einasto et al., 1980). In over-dense regions the density increases until the matter collapses to form compact objects (Zeldovich pancakes). In under-dense regions the density decreases substantially, but never reaches a zero value – gravity cannot evacuate voids completely.

The second difference lies in the structure of galaxy systems in high-density regions: in the original pancake model large-scale structures (superclusters) have rather diffuse forms, real superclusters consist of multiple intertwined filaments: Jõeveer & Einasto (1978), Zeldovich et al. (1982), Oort (1983). In the original pancake scenario small-scale perturbations were damped. This scenario corresponds to the neutrino-dominated dark matter. Neutrinos move with very high velocities which wash out small-scale fluctuations. Also, in the neutrino-dominated Universe superclusters and galaxies within them form relatively late, but the age of old stellar populations in galaxies suggests an early start of galaxy formation, soon after the recombination epoch. In other words, the original pancake scenario was in trouble (Bond et al., 1982; Peebles, 1982; Zeldovich et al., 1982; Bond & Szalay, 1983; White et al., 1983).

The presence of voids in galaxy distribution was initially met with skepticism, since 3-dimensional data were available only for bright galaxies, and faint galaxies could fill voids. However, independent evidence was soon found. A very large void was discovered in Bootes by Kirshner et al. (1981). The filamentary nature of galaxy distribution is very clearly seen in the 2nd Center for Astrophysics (Harvard) Redshift Survey by Huchra, Geller and collaborators (de Lapparent et al., 1986; Huchra et al., 1988), complete up to 15.5 apparent blue magnitude in the Northern Galactic hemisphere, see Fig. 13.

Huchra initiated a near-infrared survey of nearby galaxies, the Two Micron All-Sky Survey (2MASS) (Huchra, 2000; Skrutskie et al., 2006). Photometry in 3 near-infrared spectral bands is completed, it includes about half a million galaxies up to the limiting K magnitude 13.5. The redshifts are planned to be measured for all galaxies up to . The advantage of this survey is the coverage of low galactic latitudes up to 5 degrees from the Galactic equator. For the Southern sky the redshift survey of 2MASS galaxies is almost completed using the 6 degree Field Survey with the Australian large Schmidt telescope. The filamentary character of the distribution of galaxies is very well seen.

Figure 14: A wedge diagram of the luminosity density field of galaxies of the 2dFGRS Northern equatorial zone, degrees around the equator. The luminosity densities have been corrected for the incompleteness effect; the RA coordinate is shifted so that the plot is symmetrical around the vertical axis. The rich supercluster at the distance   Mpc from the observer is SCL126, according to the catalogue by Einasto et al. (2001); it is the richest condensation in the complex called Sloan Great Wall. This figure illustrates the structure of the cosmic web (the supercluster-void network). The density field shows that rich superclusters contain many rich clusters of galaxies, seen in picture as red dots. Filaments consisting of less luminous galaxies and located between superclusters and crossing large voids are also clearly seen (Einasto et al., 2007).

A much deeper redshift survey up to the blue magnitude 19.4 was recently completed using the Anglo-Australian 4-m telescope. This Two degree Field Galaxy Redshift Survey (2dFGRS) covers an equatorial strip in the Northern Galactic hemisphere and a contiguous area in the Southern hemisphere (Colless et al., 2001; Cross et al., 2001). Over 250 thousand redshifts have been measured, which allows us to see and measure the cosmic web (supercluster-void network) up to the redshift 0.2, corresponding to a co-moving distance about 575  Mpc. The luminosity density field calculated for the Northern equatorial slice of the 2dFGRS is shown in Fig. 14.

Presently the largest project to map the Universe, the Sloan Digital Sky Survey (SDSS) mentioned already before, has been initiated by a number of American, Japanese, and European universities and observatories (York et al., 2000; Stoughton et al., 2002; Zehavi et al., 2002; Abazajian et al., 2009). The goal is to map a quarter of the entire sky: to determine positions and photometric data in 5 spectral bands of galaxies and quasars of about 100 million objects down to the red magnitude r = 23, and redshifts of all galaxies down to r = 17.7 (about 1 million galaxies), as well as the redshifts of Luminous Red Galaxies (LRG, mostly central galaxies of groups and clusters) down to the absolute magnitude about . All 7 data releases have been made public. This has allowed the mapping of the largest volume of the Universe so far. LRGs have a spatial density about 10 times higher than rich Abell clusters of galaxies, which allows us to sample the cosmic web with sufficient details up to a redshift .

5.3 Structure formation in the Cold Dark Matter scenario

A consistent picture of the structure formation in the Universe slowly emerged from the advancement in the observational studies of the large scale structure and the Cosmic Microwave Background, and in the development of theory. The most important steps along the way were the following.

Motivated by the observational problems with neutrino dark matter, a new dark matter scenario was suggested by Blumenthal et al. (1982); Bond et al. (1982); Pagels & Primack (1982); Peebles (1982); Bond & Szalay (1983); Doroshkevich & Khlopov (1984) with hypothetical particles as axions, gravitinos, photinos or unstable neutrinos playing the role of dark matter. This model was called the Cold Dark Matter (CDM) model, in contrast to the neutrino-based Hot Dark Matter model. Newly suggested dark matter particles move slowly, thus small-scale perturbations are not suppressed, which allows an early start of the structure formation and the formation of fine structure. Advantages of this model were discussed by Blumenthal et al. (1984).

Next, the cosmological constant, , was incorporated into the scheme. Arguments favoring a model with the cosmological constant were suggested already by Gunn & Tinsley (1975); Turner et al. (1984); Kofman & Starobinskii (1985): combined constraints on the density of the Universe, ages of galaxies, and baryon nucleosynthesis.

Finally, there was a change in the understanding of the formation of initial perturbations which later lead to the observed structure. To explain the flatness of the Universe the inflation scenario was suggested by Starobinsky (1980), Guth (1981), Starobinsky (1982), Kofman et al. (1985) and others. According to the inflation model in the first stage the expansion of the Universe proceeded with accelerating rate (this early stage is called the inflation epoch). Such an evolutionary scenario allows the creation of the visible part of the Universe out of a small causally connected region and explains why in the large scale the Universe seems roughly uniform. Perturbations of the field are generated by small quantum fluctuations. These perturbations form a Gaussian random field, they are scale-invariant and have a purely adiabatic primordial power spectrum (Bardeen et al., 1986).

These ideas were progressively incorporated into the computer simulations of increasing complexity.

Pioneering numerical simulations of the evolution of the structure of the Universe were made in 1970s by Miller (1978), Aarseth et al. (1979) and the Zeldovich group (Doroshkevich et al., 1980a), using direct numerical integration. In early 1980s the Fourier transform was suggested to calculate the force field which allowed the increase of the number of test particles.

Numerical simulations of structure evolution for the hot and cold dark matter were compared by Melott et al. (1983), and by White et al. (1983, 1987) (standard CDM model with density parameter ). In contrast to the HDM model, in the CDM scenario the structure formation starts at an early epoch, and superclusters consist of a network of small galaxy filaments, similar to the observed distribution of galaxies. Thus CDM simulations reproduce quite well the observed structure with clusters, filaments and voids, including quantitative characteristics (percolation or connectivity, the multiplicity distribution of systems of galaxies, Melott et al. (1983)).

Models with the cosmological term were developed by Gramann (1988). Comparison of the SCDM and CDM models shows that the structure of the cosmic web is similar in both models. However, in order to get the correct amplitude of density fluctuations, the evolution of the SCDM model has to be stopped at an earlier epoch.

The largest so far simulation of the evolution of the structure – the Millennium Simulation – was made in the Max-Planck Institute for Astrophysics in Garching by Volker Springel and collaborators (Springel et al., 2005; Gao et al., 2005a; Springel et al., 2006). The simulation is assuming the CDM initial power spectrum. A cube of the comoving size of 500  Mpc was simulated using about 10 billion dark matter particles that allowed us to follow the evolution of small-scale features in galaxies. Using a semi-analytic model the formation and evolution of galaxies was also simulated (Di Matteo et al., 2005; Gao et al., 2005b; Croton et al., 2006). For simulated galaxies photometric properties, masses, luminosities and sizes of principal components (bulge, disk) were found. The comparison of this simulated galaxy catalogue with observations shows that the simulation was very successful. The results of the Millennium Simulation are frequently used as a starting point for further more detailed simulations of evolution of single galaxies.

One difficulty of the original pancake scenario by Zeldovich is the shape of objects formed during the collapse. It was assumed that forming systems are flat pancake-like objects, whereas dominant features of the cosmic web are filaments. This discrepancy has found an explanation by Bond et al. (1996). They showed that in most cases just essentially one-dimensional structures, i.e. filaments form.

The CDM model of structure formation and evolution combines all essential aspects of the original structure formation models, the pancake and the hierarchical clustering scenario. First structures form at very early epochs soon after the recombination in places where the primordial matter has the highest density. This occurs in the central regions of future superclusters. First objects to form are small dwarf galaxies, which grow by infall of primordial matter and other small galaxies. Thus, soon after the formation of the central galaxy other galaxies fall into the gravitational potential well of the supercluster. These clusters have had many merger events and have “eaten” all its nearby companions. During each merger event the cluster suffers a slight shift of its position. As merger galaxies come from all directions, the cluster sets more and more accurately to the center of the gravitational well of the supercluster. This explains the fact that very rich clusters have almost no residual motion in respect to the smooth Hubble flow. Numerous examples of the galaxy mergers are seen in the images of galaxies collected by the Hubble Space Telescope, see Fig. 10.

5.4 The density distribution of Dark Matter

Flat rotation curves of galaxies suggest, that the radial density distribution in galaxies, including stellar populations, interstellar gas and dark matter, is approximately isothermal: . As the dark matter is the dominating population, its density profile should also be close to an isothermal sphere. Thus, in the first approximation, one can use for the dark matter population a pseudo-isothermal profile

(3)

where is the semi-major axis of the isodensity ellipsoid, and is the effective radius of the population, called also the core radius. This law cannot be used at very large distances from the center, , since in this case the mass of the population would be infinite. This density law is an example of so-called cored profiles.

In the early 1990s, the results of high-resolution numerical N-body simulations of dark matter halos based on the collisionless CDM model became available. The simulations did not show the core-like behaviour in the inner halos, but were better described by a power-law density distribution, the so-called cusp. Navarro et al. (1997) investigated systematically simulated DM halos for many different sets of cosmological parameters. They found that the whole mass density distribution could be well described by an “universal density profile”

(4)

where is related to the density of the universe at the time of the halo collapse, and is the characteristic radius (semi-major axis) of the halo. This profile, known as the “NFW profile”, cannot be applied to the very center of the halo, since in this case the density would be infinite. Near the center of the halo the density rises sharply, forming a “cusp”.

The “core-cusp problem” has been a subject of many recent studies, based both on observational data as well as on results of very high-resolution numerical simulations. A review of these efforts is given by de Blok (2010). To find the DM-halo density profile de Blok (2010) used a collection of HI rotation curves of dwarf galaxies, which are dominated by dark matter. To get a better resolution near the center H long-slit rotation curves were analysed. These rotation curves indicate the presence of constant-density or mildly cuspy dark matter cores. Strongly cuspy central profiles as the NFW one are definitely excluded.

Navarro et al. (2010) performed a detailed numerical study of the distribution of the mass and velocity dispersion of DM halos in the framework of the Aquarius Project. The formation and evolution of 6 different galaxy-sized halos were simulated several times at varying numerical resolution, the highest resolution simulation had up to 4.4 billion particles per halo. Authors find that the mass profiles of halos are best represented by the Einasto profile (1). The radial dependence of the inner logarithmic slope, follows a power law, . The shape parameter varies slightly from halo to halo. Navarro et al. (2010) calculated also the pseudo-phase-space density, , where is the mean squared velocity dispersion, averaged in a spherical shell of radius . Authors find that pseudo-phase-density profiles of all halos follow an identical power law, . The origin of this behaviour is unclear, but its similarity for all halos may reflect a fundamental structural property of DM halos.

On cluster and supercluster scales the distribution of dark matter can be most accurately found by gravitational lensing. Gavazzi et al. (2003) used strong lensing data obtained with the ESO Very Large Telescope to analyse the radial mass profile of the galaxy cluster MS 2137.3-2353 at redshift . The mass density can be represented both with the isothermal model as well as the NFW model.

Massey et al. (2007) used 575 pointings of the HST SCS Wide Field Camera to cover a region of 1.637 square degrees, and measured shapes of half a million distant galaxies to calculate the density distribution around a rich cluster of galaxies at redshift . Additional information was obtained using the XMM-Newton X-ray satellite observations, and distribution of galaxies in and around the cluster. The most prominent peak in the distribution of matter using all tracers is the cluster itself. Weak lensing shows additionally the 3-dimensional distribution of matter around the cluster. The filamentary character of the mass distribution is clearly seen, the cluster lies at the connection of several filaments.

Heymans et al. (2008) applied weak lensing analysis of a HST STAGES survey to reconstruct dark matter distribution in the Abell 901/902 supercluster. Authors detect the four main structures of the supercluster. The distribution of dark matter is well traced by the cluster galaxies. The high number density of HST data allows us to produce a density map with sub-arcminute resolution. This allowed us to resolve the morphology of dark matter structures. Profiles of DM are far from the spherically symmetric NFW models. An extension of the dark matter distribution is in the direction of an in-falling X-ray group Abell 901, showing the filamentary character of the distribution of dark matter.

Humphrey et al. (2006); Humphrey & Buote (2010) used Chandra X-ray observatory data to investigate the mass profiles of samples of 7 and 10 galaxies, groups and clusters, respectively, spanning about 2 orders of magnitude in virial mass. They find that the total as well as DM mass density distributions can be well represented by a NFW/Einasto profile. For the projected density of baryonic stellar populations they use the Sersic (1968) profile. As shown by Einasto (1965, 1974), the generalized exponential expression (1) can be applied as well for the spatial density of galactic population. Thus the Humphrey & Buote (2010) study suggests that an identical expression (1) (Einasto profile) can be applied for the total mass density distribution, the baryonic and the DM mass density distribution.

The coincidence is remarkable, since the fraction of baryonic matter in the total mass distribution in clusters varies with radius considerably. This “galaxy-halo conspiracy” is similar to that which establishes flat rotation curves in galaxies – the “bulge-halo conspiracy”. These coincidences suggest the presence of some sort of interaction between the dominating stellar population (bulge) and the dark matter halo, both on galactic and cluster scales. We note that an analogous relation exists between the mass of the central black hole and the velocity dispersion of the bulge of elliptical galaxies (see Gültekin et al. (2009) for a review). Another interesting phenomenon is the almost constant central density of DM halos, as noted by Einasto et al. (1974a); Gilmore et al. (2007) and Donato et al. (2009).

These studies demonstrate that the density enhancements of the dark matter have a structure, which is very similar to the distribution of galaxies: both forms of matter follow the same pattern of the cosmic web, as expected (Bond et al., 1996).

6 Matter-energy content of the Universe

6.1 Dark Matter and Dark Energy

In early papers on dark matter the total density due to visible and dark matter was estimated to be about 0.2 of the critical cosmological density. These estimates were based on the dynamics of galaxies in groups and clusters. This density estimate can be interpreted in two different ways: either we live in an open Universe where the total density is less than the critical density, or there exists some additional form of matter/energy which allows the Universe to be flat, i.e. to have the critical total density. The additional term was identified with the Einstein -term, so that the total matter/energy density was taken to be equal to the critical cosmological density (Gunn & Tinsley (1975); Turner et al. (1984); Kofman & Starobinskii (1985)). Initially there was no direct observational evidence in favor of this solution and it was supported basically on general theoretical grounds. In its early evolution the size of the Universe increases very rapidly and any deviation from the exact critical density would lead to a rapid change of the relative density, either to zero, if the initial density was a bit less than the critical one, or to infinity, if it was greater than critical. In other words, some fine tuning is needed to keep the density at all times equal to the critical one. The fine tuning problem can be eliminated if one assumes an early accelerated epoch of expansion of the Universe (inflation).

Figure 15: Upper panel shows the acoustic peaks in the angular power spectrum of the CMB radiation according to the WMAP and other recent data, compared with the CDM model using all available data. The lower panel shows the signature of baryonic acoustic oscillations in the matter two-point correlation function (Eisenstein et al., 2005; Kolb, 2007) (reproduced by permission of the author)

.

In subsequent years several new independent methods were applied to estimate the cosmological parameters. Of these new methods two desire special attention. One of them is based on the measurements of small fluctuations of the Cosmic Microwave Background (CMB) radiation, and the other on the observation of distant supernovae.

According to the present cosmological paradigm the Universe was initially very hot and ionized. The photons provided high pressure and prevented baryons to cluster. Perturbations of baryons did not grow, but oscillated as sound waves. The largest possible amplitude of these oscillations is at the wavelength equal to the sound horizon size at the decoupling. This wavelength is seen as the first maximum in the angular power spectrum of the CMB radiation. The following maxima correspond to overtones of the first one. The fluctuations of CMB radiation were first detected by the COBE satellite. The first CMB data were not very accurate, since fluctuations are very small, of the order of . Subsequent experiments carried out using balloons, ground based instruments, and more recently the Wilkinson Microwave Anisotropy Probe (WMAP) satellite, allowed the measurement of the CMB radiation and its power spectrum with a much higher precision (Spergel et al., 2003). The position of the first maximum of the power spectrum depends on the total matter/energy density. Observations confirm the theoretically favored value 1 in units of the critical cosmological density, see Fig. 15.

The small initial overdensities of the primordial cosmic medium launch shock waves in the photon-baryon fluid. After some time photons completely decouple from baryons, and the baryons loose photon pressure support. The shock stops after traveling a distance of about 150 Mpc (in comoving coordinates). This leads to an overdensity of the baryonic medium on a distance scale of 150 Mpc. This overdensity has been recently detected in the correlation function of Luminous Red Galaxies of the SDSS survey (Eisenstein et al., 2005; Hütsi, 2006), see lower panel of Fig. 15. Baryonic acoustic oscillations depend on both the total matter/energy density and the baryon density, thus allowing us to estimate these parameters.

Another independent source of information on cosmological parameters comes from the distant supernova experiments. Two teams, led by Riess et al. (1998, 2007) (High-Z Supernova Search Team) and Perlmutter et al. (1999) (Supernova Cosmology Project), initiated programs to detect distant type Ia supernovae in the early stage of their evolution, and to investigate with large telescopes their properties. These supernovae have an almost constant intrinsic brightness (depending slightly on their evolution). By comparing the luminosities and redshifts of nearby and distant supernovae it is possible to calculate how fast the Universe was expanding at different times. The supernova observations give strong support to the cosmological model with the term, see Fig. 16.

Figure 16: Results of the Supernova Legacy Survey: apparent magnitudes of supernovae are normalized to the standard CDM model, shown as solid line. Dashed line shows the Einstein-de Sitter model with (Kolb, 2007) (reproduced by permission of the author).

Different types of dark energy affect the rate at which the Universe expands, depending on their effective equation of state. The cosmological constant is equivalent to the vacuum. The other possible candidate of dark energy is quintessence (a scalar field) that has a different and generally variable equation of state. Each variant of dark energy has its own equation of state that produces a signature in the Hubble diagram of the type Ia supernovae (Turner, 2000, 2003).

The combination of the CMB and supernova data allows us to estimate independently the matter density and the density due to dark energy, shown in Fig. 17. The results of this combined approach imply that the Universe is expanding at an accelerating rate. The acceleration is due to the existence of some previously unknown dark energy (or cosmological constant) which acts as a repulsive force (for reviews see Bahcall et al. (1999), Frieman et al. (2008)).

Figure 17: Combined constraints to cosmological densities and , using supernovae, CMB and cluster abundance data. The flat Universe with is shown with solid line (Knop et al., 2003).

Independently, the matter density parameter has been determined from clustering of galaxies in the 2-degree Field Redshift Survey and the Sloan Digital Sky Survey. The most accurate estimates of cosmological parameters are obtained using a combined analysis of the 2dFGRS, SDSS and the WMAP data (Spergel et al., 2003; Tegmark et al., 2004; Sánchez et al., 2006). According to these studies the matter density parameter is , not far from the value , suggested by Ostriker & Steinhardt (1995) as a concordant model. The combined method yields for the Hubble constant a value independent of other direct methods. From the same dataset authors get for the density of baryonic matter, . Comparing both density estimates we get for the dark matter density , and the dark energy density . These parameters imply that the age of the Universe is gigayears.

6.2 The role of dark energy in the evolution of the Universe

Studies of the Hubble flow in nearby space, using observations of type Ia supernovae with the Hubble Space Telescope (HST), were carried out by several groups. The major goal of the study was to determine the value of the Hubble constant. As a by-product also the smoothness of the Hubble flow was investigated. In this project supernovae were found up to the redshift (expansion speed) 20 000 km s. This project (Sandage et al., 2006) confirmed earlier results that the Hubble flow is very quiet over a range of scales from our Local Supercluster to the most distant objects observed. This smoothness in spite of the inhomogeneous local mass distribution requires a special agent. Dark energy as the solution has been proposed by several authors (Chernin (2001); Baryshev et al. (2001) and others). Sandage emphasizes that no viable alternative to dark energy is known at present, thus the quietness of the Hubble flow gives strong support for the existence of dark energy.

The vacuum dark energy has two important properties: its density is constant, i.e. the density does not depend not on time nor on location; and it acts as a repulsive force or antigravity (for detailed discussions see Chernin (2003), Chernin et al. (2006), Chernin (2008)).

The first property means that in an expanding universe in the earlier epoch the density of matter (ordinary + dark matter) exceeded the density of dark energy. As the universe expands the mean density of matter decreases and at a certain epoch the matter density and the absolute value of the dark energy effective gravitating density were equal. This happened at an epoch which corresponds to redshift . Before this epoch the gravity of matter decelerated the expansion, after this epoch the antigravity of the dark energy accelerated the expansion. This is a global phenomenon - it happened for the whole universe at once.

The density of the dark energy determines the expansion speed of the universe, expressed through the (vacuum energy defined) Hubble constant

(5)

This value is rather close to the actually observed value of the Hubble constant, given above, due to the dominance of the dark energy in the present epoch.

The dark energy influences also the local dynamics of astronomical bodies. Consider a virialised system as a group or cluster of galaxies. In the first approximation the dynamics of the system can be treated as a point of mass (index for matter). The total force to a test particle moving at a distance from the cluster center can be expressed as follows:

(6)

The first term is due to the gravity of the cluster, the second term is due to the antigravity of the dark energy in a sphere of radius around the cluster. The antigravity corresponds to the effective mass of the dark energy contained in the spherical volume of radius : . Near the cluster the gravity is larger and determines the movement of test bodies. At large distance the antigravity is larger, here stable orbits around the cluster are impossible. Both forces are equal at the distance ; this distance can be called the zero gravity distance (Chernin, 2008).

The local effect of the dark energy to the dynamics of bodies has been studied by Karachentsev, Chernin, Tully and collaborators. Using the Hubble Space Telescope and large ground-based telescopes Karachentsev determined accurate distances and redshifts of satellite galaxies in the Local group and several nearby groups of galaxies (Karachentsev et al. (2002), Karachentsev et al. (2003a), Karachentsev et al. (2003b), Karachentsev et al. (2006), Karachentsev et al. (2007), Karachentsev et al. (2009), Tully et al. (2008)). This study shows that near the group center up to distance   Mpc satellite galaxies have both positive and negative velocities in respect to the group center, at larger distance all relative velocities are positive and follow the Hubble flow. The distance 1.25  Mpc corresponds exactly to the expected zero gravity distance for groups of mass about solar masses. The new total mass estimates are 3–-5 times lower than old virial mass estimates of these groups, which leads to low density of matter associated with these galaxies, (Karachentsev (2005)). If confirmed, this result may indicate the presence of two types of dark matter: the matter associated with galaxies, and a more smoothly distributed dark matter.

This test demonstrates that the dark energy influences both the local and the global dynamics of astronomical systems. For rich clusters of galaxies the zero gravity distance is about 10  Mpc, for rich supercluster several tens  Mpc, which corresponds to the radius of cores of rich superclusters. The antigravity of the dark energy explains also the absence of extremely large superclusters: even the richest superclusters have characteristic radii of about 50  Mpc.

6.3 Searches of Dark Matter particles

In late 1970s and early 1980s it was clear that dark matter must be non-baryonic. The first natural candidate for DM particles was massive neutrino. Using astronomical constraints Szalay & Marx (1976) found upper mass limit of neutrinos as DM particles,  eV. However, as discussed above, massive neutrinos (Hot Dark Matter) cannot form the dominating population of DM particles, since the large-scale-structure of the cosmic web would be in this case completely different from the observed structure. For this reason hypothetical weakly interacting massive particles were suggested, which form the Cold Dark Matter. CDM model satisfies most known astronomical restrictions for the DM, as shown by Blumenthal et al. (1984) and many others.

Until recently it was thought that DM particles form a fully collisionless medium. The ringlike DM distribution in the merging cluster Cl 0024+17 suggests that DM “gas” may have some collisional properties. Jee et al. (2007) suggest that this cluster may serve as a very useful laboratory to address outstanding questions in DM physics.

This review has focused only on gravitational aspects of DM. However, it is natural to assume that in the arguably most realistic cases, where the DM is provided by some sort of an elementary particle (beyond the Standard Model of particle physics), those particles have other than only gravitational couplings to the rest of the matter. If this is the case, the phenomenology of DM could in principle be much richer. Indeed, there has been a lot of recent activity in trying to detect DM particles in high precision nuclear recoil experiments. DAMA/LIBRA collaboration has announced a possible detection of the DM induced signal visible as an expected annual modulation in the observational data, Bernabei et al. (2010).

Also, a multitude of astrophysical observations have been used to search for the indirect hints for the existence of the DM particles. Particularly interesting is the cosmic ray positron anomaly as revealed by the measurements of the PAMELA (Adriani et al., 2009), Fermi (Abdo et al., 2009), and HESS (Aharonian et al., 2009) experiments. This anomaly could be an indirect indication for the existence of the annihilating or decaying DM particle with a mass at the TeV scale.

Results from the neutrino oscillation experiments require at least one of the neutrinos to have a mass not less than eV (e.g. Dolgov (2002)). This immediately implies that the corresponding density parameter , i.e. approaching the density parameter of the baryons visible in the form of stars! Although neutrinos cannot form the dominant component of the DM, due to reasons discussed above, it shows that the general idea of the existence of DM in Nature is surely not a fiction.

For obvious reasons it is not possible here to give a full account of all the activities of DM searches that belong to the rapidly developing field of astroparticle physics. Instead we advise the reader to consult the excellent recent review papers by Bertone et al. (2005), Bergström (2009), Feng (2010), and Profumo & Ullio (2010).

7 Conclusions

The discoveries of dark matter and the cosmic web are two stages of a typical scientific revolution (Kuhn, 1970; Tremaine, 1987). As often in a paradigm shift, there was no single discovery, new concepts were developed step-by-step.

First of all, actually there are two dark matter problems – the local dark matter close to the plane of our Galaxy, and the global dark matter surrounding galaxies and clusters of galaxies. Dark matter in the Galactic disk is baryonic (faint stars or jupiters), since a collection of matter close to the galactic plane is possible, if it has formed by contraction of pre-stellar matter towards the plane and dissipation of the extra energy, that has conserved the flat shape of the population. The amount of local dark matter is low; it depends on the mass boundary between luminous stars and faint invisible stars.

The global dark matter is the dominating mass component in the Universe; it is concentrated in galaxies, clusters and superclusters, and populates also cosmic voids. Global dark matter must be non-baryonic, its density fluctuations start to grow much earlier than perturbations in the baryonic matter, and have at the recombination epoch the amplitude large enough to form all structures seen in the Universe. Initially neutrinos were suggested as particles of dark matter (hot dark matter), but presently some other weakly interacting massive particles, called cold dark matter, are preferred.

Recently direct observational evidence was found for the presence of Dark (or vacuum) Energy. New data suggest that the total matter/energy density of the Universe is equal to the critical cosmological density, the density of baryonic matter is about 0.04 of the critical density, the density of dark matter is about 0.23 of the critical density, and the rest is dark energy.

A number of current and future astronomical experiments have the aim to get additional data on the structure and evolution of the Universe and the nature and properties of dark matter and dark energy. Two astronomical space observatories were launched in 2009: the Planck CMB mission and the Herschel 3.5-m infrared telescope. The main goal of the Planck mission is to measure the CMB radiation with a precision and sensitivity about ten times higher than those of the WMAP satellite. This allows us to estimate the values of the cosmological parameters with a very high accuracy. The Herschel telescope covers the spectral range from the far-infrared to sub-millimeter wavelengths and allows us to study very distant redshifted objects, i.e young galaxies and clusters (Cooray et al., 2010).

Very distant galaxies are the target of the joint project GOODS – The Great Observatories Origins Deep Survey. Observations are made at different wavelengths with various telescopes: the Hubble Space Telescope, the Chandra X-ray telescope, the Spitzer infrared space telescope, and by great ground-based telescopes (the 10-m Keck telescope in Hawaii, the 8.2-m ESO VLT-telescopes in Chile). Distant cluster survey is in progress in ESO (White et al., 2005).

NASA and U.S. Department of Energy formed the Joint Dark Energy Mission (JDEM) and proposed a space observatory SNAP (the SuperNova Acceleration Probe) to detect and obtain precision photometry, light-curves and redshifts of over 2000 type Ia supernovae over the redshift range to constrain the nature of dark energy.

The largest so far planned space telescope is The James Webb Space Telescope (JWSP) – a 6.5-m infrared optimized telescope, scheduled for launch in 2013. The main goal is to observe first galaxies that formed in the early Universe.

To investigate the detailed structure of our own Galaxy the space mission GAIA will be launched in 2011. It will measure positions, proper motions, distances and photometric data for 1 billion stars, repeatedly. Its main goal is to clarify the origin and evolution of our Galaxy and to probe the distribution of dark matter within the Galaxy.

The story of the dark matter and dark energy is not over yet – we still do not know of what non-baryonic particles the dark matter is made of, and the nature of dark energy is also unknown. We even do not know is a radical change in our understanding of the Newton and Einstein theories of gravitation needed. All these problems are challenges for physics. So far the direct information of both dark components of the Universe comes solely from astronomical observations.

Acknowledgments

The study of dark matter and large-scale structure of the Universe in Tartu Observatory is supported by Estonian Science Foundation grant 6104, and Estonian Ministry for Education and Science grant TO 0060058S98. The author thanks Astrophysikalisches Institut Potsdam (using DFG-grant MU 1020/11-1), ICRANet and the Aspen Center for Physics for hospitality, where part of this study was performed, and Elmo Tempel and Triin Einasto for help in preparing the bibliography. Fruitful discussions with Arthur Chernin, Maret Einasto, Gert Hütsi, Enn Saar, Alar Toomre, Virginia Trimble, Sidney van den Bergh, and the editor of the series Bozena Czerny helped to improve the quality of the review.

Glossary

Acoustic peaks: features in the angular spectrum of the CMB radiation (and corresponding peak in the correlation function of galaxies) due to the acoustic oscillations of the hot gas in the young universe before the recombination (sound waves driven by cosmic perturbations of the hot plasma).

Baryonic dark matter: dark matter composed of baryons - protons, neutrons and bodies made of baryons. Candidates for baryonic dark matter are MACHOs, brown dwarfs, Jupiters and non-luminous gas.

Biased galaxy formation: a model of galaxy formation suggesting that galaxies form only in high-density regions, whereas in low-density regions the matter remains in gaseous (pre-galactic) form.

Big Bang: a model of the formation of the Universe from an extremely dense and hot state with followed by very rapid expansion (inflation) and more moderate expansion today.

Bulge: a spheroidal population of galaxies consisting of old medium metal-rich stars.

Clusters of galaxies: largest gravitationally bound aggregates of galaxies, containing typically more than 30 galaxies and having diameters up to 5 megaparsecs. They consist of visible galaxies, hot intracluster medium and invisible dark matter

CMB fluctuations: fluctuations of the temperature of the CMB radiation, seen on the sky as small anisotropies - deviations from the mean temperature. Temperature fluctuations are related to fluctuations of the density of matter, from overdense regions of the primordial plasma due to gravitational clustering all large astronomical objects formed, such as galaxies, clusters of galaxies.

CMB radiation - Cosmic microwave background radiation: electromagnetic radiation filling the universe, and formed during the hot stage of the evolution of the universe just before recombination of light chemical elements which makes the universe transparent for radiation. As the universe expanded both the plasma and radiation cooled, so the temperature of the CMB radiation is presently about 2.7 K, seen in the microwave range of the spectrum.

Cold dark matter (CDM): a variety of dark matter which consists of particles having small velocities relative to the speed of light, which allows these particles to form density enhancements called dark halos. Candidate CDM particles, such as axions, or supersymmetric particles are proposed, none of those experimentally detected yet.

Corona: an extended and nearly spherical population surrounding galaxies and clusters of galaxies, consisting of hot X-ray emitting gas and dark matter.

Cosmic inflation: theoretically predicted period in the evolution of the Universe during which the whole Universe expanded exponentially after the Big Bang, driven by the negative-pressure (antigravity) of the vacuum energy.

Cosmic web: a spider-web-like distribution of galaxies in the universe along filaments and superclusters, also called supercluster-void network.

Critical density of the universe: the density of matter/energy in the universe that separates the two spatial geometries - opened and closed; with the dividing line providing flat geometry.

Dark ages: the period in time evolution of the Universe after the recombination and before the formation of first stars and galaxies.

Dark halo (often shortly halo): an extended and nearly spherical population surrounding galaxies and clusters of galaxies, consisting of dark matter.

Dark matter: hypothetical matter, whose presence can be detected from its gravity only.

Disk: a relatively flat population in galaxies, consisting of stars of various age and metallicity.

Elliptical galaxies: galaxies consisting mainly of old populations, having an approximately ellipsoidal shape (bulge, halo).

Filament: a chain of galaxies and galaxy systems (groups or clusters).

Galactic evolution: the change of physical parameters of galaxies and their populations in time. As parameters such quantities are considered as age, stellar content, chemical composition, photometric properties (color), mass-to-luminosity ratios etc.

Galactic models: mathematical models which describe quantitatively the structure of galaxies and their populations - spatial density, rotation, physical properties (colors, luminosities, mean ages of stars etc).

Galactic populations: populations of stars or gas of similar age, composition (metallicity), spatial distribution and kinematical properties (velocity dispersion of stars, rotation velocity around the galactic center). Main galactic populations are nucleus, disk, young population, bulge, stellar halo, dark halo (or corona).

Galaxies: large systems of stars and interstellar matter, consisting of one or more galactic populations.

Global dark matter: dark matter surrounding galaxies and clusters of galaxies and populating voids between galaxy systems. Most, if not all, global dark matter is non-baryonic.

Gravitational clustering: the clustering of matter due to gravity - matter concentrates toward overdense regions and flows away from underdense regions in space.

Gravitational lensing: the bending of the light from a distant source around a massive object like a cluster of galaxies.

Gravitational microlensing: gravitational lensing where the amount of light received from a background object changes in time. Microlensing allows us to study low-mass objects (brown and red dwarfs, planets) that emit little or no light.

Groups of galaxies: smallest gravitationally bound systems of galaxies, containing typically fewer than 30 galaxies and having diameters of 1 to 2 megaparsecs.

Hot dark matter (HDM): a variety of dark matter which consists of fast moving particles, close to the speed of light. Neutrinos are the only experimentally confirmed HDM particles.

Hubble’s law: the equation stating that the recession velocity of galaxies from the earth is proportional to their distance from us; the constant of proportionality is called the Hubble constant. Recent data suggest a value of the Hubble constant (km/s)/Mpc.

Initial mass function (IMF): an empirical function that describes the mass distribution of a population of stars at the epoch of star formation.

Jupiter: in cosmology a giant planet-type body with mass less than a critical value needed to start nuclear reactions inside the body.

Lambda CDM model: (Lambda-Cold Dark Matter) model or the concordant model is a model of the universe which has critical cosmological density and contains three main components of the matter/energy: baryonic matter, dark matter and dark energy; the last component is also called the cosmological constant Lambda.

Large scale structure of the Universe: the characterization of the distribution of large-scale structures (galaxies and systems of galaxies) in space. Galaxies are concentrated to filaments forming superclusters, the space between filaments contains no galaxies (cosmic voids).

Local dark matter: dark matter in the Solar vicinity near the plane of the Galaxy. Local dark matter is baryonic since collisionless non-baryonic dark matter cannot form a flattened disk.

MACHO - massive compact halo object: astronomical body that emits little or no radiation and can be detected by its gravitation only. MACHO’s were suggested as an alternative to non-baryonic dark matter candidate in galactic dark halos.

Megaparsec (Mpc): a measurement of distance in the Universe, equal to one million parsecs or 3.26 million light years ( meters).

MOND - modified Newtonian dynamics: a theory that proposes a modification of the Newton’s Law of Gravity to explain flat rotation curves of galaxies.

Morphology of galaxies: structural properties of galaxies, like the presence of different stellar or gaseous populations, their color, metal content, age, as well as size and shape, kinematical properties etc. Morphological properties of galaxies are explained by formation and evolution of their populations.

N-body simulation: simulation of the formation and evolution of structures of the universe using massive particles under the influence of gravity, sometimes also other forces to take into account the evolution of the gas to stars.

Non-baryonic dark matter: dark matter composed of non-baryonic particles, i.e. it has no atoms and bodies composed of atoms, such as various chemical elements.

Primordial nucleosynthesis: the process of forming nuclei of light elements from protons and neutrons. This process happens in a short time interval when the temperature of the universe and its density are in limits which allows this process to occur (between 3 and 20 minutes after the Big Bang).

Paradigm: the set of ideas and practices that define a scientific discipline during a particular period of time.

Recombination: the period in the evolution of the universe when temperature was low enough to allow nuclei of light elements (hydrogen, helium, lithium) bound electrons around the nucleus and to form neutral atoms of these elements.

Scientific revolution: a period in the history of science when new observations or experiments led to a rejection of older doctrines (paradigms) and formation of new ideas (paradigms), also called paradigm shift.

Spiral galaxies: galaxies containing a flat disk of young stars and interstellar matter, which form spiral arms.

Standard cosmological model (LCDM model): currently accepted cosmological model with parameters: Hubble constant 71 km/s per Mpc, baryonic matter density 0.04, dark matter density 0.23, and dark energy (or cosmological constant) density 0.73, all in units of the critical cosmological density.

Stellar halo: a population of old metal-poor stars in galaxies.

Structure formation: the formation of the structure of the universe in the process of gravitational clustering which attracts matter to higher density regions (superclusters) and makes voids emptier.

Supercluster: density enhancement in the cosmic web, consisting of one or more clusters of galaxies and galaxy/cluster filaments with voids between them. Superclusters can be defined as the largest non-percolating systems of galaxies and clusters/groups in the Universe.

Supernova: an explosion of a star which causes a burst of radiation that for some time (from weeks to months) outshines an entire galaxy.

Universe: everything that physically exists - all forms of matter, energy, space and time, governed by physical laws and constants. An alternative definition is “our Universe”, which means the Universe we live in and postulates the presence of many disconnected “universes” as the multiverse.

Virial theorem: a theorem in mechanics that provides an equation that relates the average over time of the total kinetic energy with that of the total potential energy.

Void: a region between galaxies and systems of galaxies devoid of visible objects.

WIMP - weakly interacting massive particles: hypothetical particles, serving as candidates to non-baryonic dark matter. They interact through gravity and possible through nuclear force no stronger than the weak force. Thus their interaction with electromagnetic radiation is so weak that their density evolution can start much earlier than for baryonic particles.

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