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1.3 Dark Matter in Groups and Clusters

An analysis of 21 radial velocities of galaxies in the Coma cluster, assuming virial equilibrium, led Zwicky (1933) to conclude that the integrated mass-to-light ratio Upsilon of those galaxies must be of order 100-500. This result has been confirmed in more recent studies of clusters of galaxies (cf. sec. 4.2).

A classical paper on dark matter in the Local Group is Kahn & Woltjer (1959). Several notions still of interest are introduced in this paper. One is on the persistence of warps. A warp in the outer HI layer of the Milky Way had been discovered by the work of Burke (1957) and Kerr (1957). Kahn & Woltjer note that for any non-spherical distribution of mass a warp will suffer from differential precession. Thus a tidally pulled warp, with an integral sign warp shape, will wrap up and corrugate the disk in at most a few Gyr. It is clear that warps suffer from a similar persistence problem as do spiral arms.

The most interesting argument in Kahn & Woltjer (1959) is called the ``timing argument'', and is based on the notion that M31 approaches our Galaxy with a relative speed of 119 km s-1. Such a local deviation from the Hubble flow can only be due to the presence of mass in the Local Group. If M31 approaches us for the first time, a total mass for the Local Group of ~ 3 1012 Msmsun follows. In principle the mass could reside in each of the two principal galaxies, or else it could be much more spread out in the entire volume of the Local Group. In fact Kahn & Woltjer (1959) propose a much more spread out distribution in gaseous form, and study the potential effect of magnetic forces due to an intergalactic wind blowing on the outer gas layer of our Galaxy thereby causing the warped shape. (The notion that gravity is the dominant force in the dynamics of galaxies, including interactions between them, was firmly established only with the article of Toomre & Toomre (1972) on galactic bridges and tails).