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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 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 M / L 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. Dutch astronomer Jan HenrikOort (1932) analysed vertical motions of stars near the plane of the Galaxy and calculated from these data the vertical acceleration of matter. He also calculated the vertical acceleration due to all known stars near the Galactic plane. His result was alarming: the density due to known stars is not sufficient to explain vertical motions of stars - there must be some unseen matter near the Galactic plane.

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 expansion continues forever; if the mean density is larger than the critical, then after some time the expansion stops and thereafter the Universe starts to collapse. 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. The majority of 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 suggestion for the non-baryonic matter were particles well known at that time to physicists - neutrinos. However, this scenario soon lead 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 favoured 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) characterised 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), Tegmark et al. (2006), Frieman et al. (2008), see also proceedings by Longair & Einasto (1978), and Kormendy & Knapp (1987).

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