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Zwicky (1933, 1937) 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. 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.

A certain discrepancy was detected between masses of individual galaxies and masses of pairs and groups of galaxies (Holmberg 1937, Page 1952, 1959, 1960). These determinations yield for the mass-to-light ratio (in blue light) the values M / LB = 1 ... 20 for spiral galaxy dominated pairs, and M / LB = 5 ... 90 for elliptical galaxy dominated pairs. These ratios are larger than found from local mass indicators of galaxies (velocity dispersions at the centre and rotation curves of spiral galaxies).

Kahn & Woltjer (1959) paid attention to the fact that most galaxies have positive redshifts, 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 form a physical system. 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 Mtot geq 1.8 × 1012 Modot. The conventional masses of the Galaxy and M31 were estimated to be of the order of 2 × 1011 Modot. In other words, the authors found evidence for the presence of additional mass in the Local Group of galaxies.

Information of masses of individual galaxies come from their rotation velocities. Roberts (1966) made a 21-cm hydrogen line survey of M31 using the National Radio Astronomy Observatory large 300-foot telescope. He found that the rotation velocity curve at large radii is flat, i.e., velocity is almost constant. From the comparison of the light distribution with the rotation curve the local value of the mass-to-luminosity can be calculated. He found in the outer regions a mass-to-light ratio ~ 250. A similar high value was found for the edge-on S0 galaxy NGC 3115 by Oort (1940). Rubin & Ford (1970) and Roberts & Rots (1973) derived the rotation curve of M31 up to a distance ~ 30 kpc, using optical and radio data, respectively. The rotation speed rises slowly with increasing distance from the centre of the galaxy and remains almost constant over radial distances of 16-30 kpc.

Two possibilities were suggested to explain flat rotation curves of galaxies. One possibility is to identify the observed rotation velocity with the circular velocity. In this case an explanation for a very high local M / L 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.

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