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 and Bahcall) 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.
Another 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 neighbour 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 2 × 1012 M.
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 imposes 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 to determine 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 independently by Einasto et al. (1974a) and Ostriker et al. (1974), see Figs. 2 and 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."
Figure 2. The mean internal mass M(R) as a function of the radius R 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).
Figure 3. Masses (in units 1012 M) of local giant galaxies (Ostriker et al. 1974) (reproduced by permission of the AAS and authors).
The bottom line in both papers was: since the data suggest that all giant galaxies have massive halos/coronae, 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 galaxy whereas spiral and irregular (gaseous) companions of the same luminosity have larger distances from the primary galaxy; the distance of the segregation line from the primary galaxy depends on the luminosity of the satellite galaxy, 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 4. The distribution of luminosities of companion galaxies L(R) at various distances R from the main galaxy. Filled circles are for elliptical companions, open circles for spiral and irregular galaxies (Einasto et al. 1974b).
Additional arguments in favour 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).
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 summarised by Materne & Tammann (1976). Their most serious argument was: Big Bang nucleosynthesis suggests a low-density Universe with the density parameter 0.05; the smoothness of the Hubble flow also favours 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.
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 summarised 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 ~ 40 h-1 Mpc (we use in this paper the Hubble constant in the units of H0 = 100 h km s-1 Mpc-1), 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 M / L values Roberts assumed that late-type dwarf stars dominate the peripheral regions.
In mid-1970s 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. 5. Observations confirmed the general trend that the mean rotation curves remain flat over the whole observed range of distances from the center, up to ~ 40 kpc for several galaxies. The internal mass within the radius R increases over the whole distance interval.
Figure 5. The rotation curves of spiral galaxies of various morphological type according to Westerbork radio observations (Bosma 1978) (reproduced by permission of the author).
At the same time 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. 6.
Figure 6. 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).
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 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 M / L = 3, 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 M. These results showed that the mass-to-light ratios of stellar populations in spiral and elliptical galaxies are similar for a given colour, 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 favour of the new and 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 ~ 60 kpc from the study of ~ 2500 Blue Horizontal Branch stars from SDSS survey, and the rotation curves seems to be slightly falling from the 220 km s-1 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 ~ 14 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 1012 - 2.5 × 1012 M. The central density of dark matter halos of galaxies is surprisingly constant, about 0.1 M pc-3 (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, approximately comparable to the luminous mass in galaxies.
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 catalogue of X-ray clusters and galaxies. More than 1000 clusters up to a redshift ~ 0.5 were catalogued. Dark matter profiles have been determined in a number of cases (Humphrey et al. 2006).
The XMM and Chandra observatories allow 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 z = 1. The comparison of cluster properties at different redshifts allows to get more accurate information on the evolution of clusters which depend critically on the parameters of the cosmological model.
Chandra observations allow 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 × 1013 M. Local mass-to-light ratio profiles are flat within an optical half-light radius (Reff), rising more than an order of magnitude at ~ 10 Reff, which confirms the presence of dark matter. The baryon fraction (most baryons are in the hot X-ray emitting gas) in these galaxies is fb ~ 0.04 - 0.09. 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 M* / LK ~ 0.5 - 1.9 using the Salpeter IMF (for the infrared K-band, the ratios for the B-band are approximately 4 times higher). Interesting upper limits for the amount of 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 5 × 1015 cm-2. Assuming that the gaseous baryonic corona has the mass of order of ~ 6 × 1010 M, this measurement implies a very low metalicity of the corona plasma, below 3.7 percent of the solar value (York et al. 2000).
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:
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).
The strong lensing effect is observed in rich clusters, and allows 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 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 z = 0.45, the lensing mass estimate is almost twice as high as that determined from the X-ray data. The mass-to-light ratio is M / LB = 200 ± 50 in Solar units (Fischer & Tyson 1997, 1997 Fischer et al. ). For other recent work on weak lensing and X-ray clusters see Bradac et al. (2005), Dietrich et al. (2005), Clowe et al. (2006b), Massey et al. (2007).
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 baryonic 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 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).