1.4 Dark Matter in Spiral Galaxies
The notion of dark matter in and around galaxies was only gradually developed, and became accepted during the 1970's. This slow development is due to the complexity of the problem : our knowledge of stellar populations in galaxies drastically improved due to new observational techniques and more systematic studies. Furthermore, the development of numerical simulations provided two very important concepts : the idea that dynamically hot matter is needed to stabilize disks (Ostriker & Peebles 1973), and the notion of merging of galaxies due to mutual interaction (Toomre & Toomre 1972, Toomre 1977).
If all the mass of a galaxy is in the center, and the ionized gas can be considered as orbiting test particles, one expects a Keplerian rotation curve (rotation velocity Vrot proportional to radius R-1/2). If the mass distribution follows the light distribution, i.e. the mass-to-light ratio is constant with radius, then, for an exponential light distribution (cf. Freeman 1970) one has a rotation curve which peaks at about 2.2 times the scalelength of the disk, and which thereafter slowly falls off towards the Keplerian behaviour. Note that for a rotation curve that just peaks at the edge of the optical disk, there is only 64% of the mass enclosed inside the radius of the disk. Hence a substantial fraction of mass is already outside the optical radius in that case. If no turnover is reached, more mass must be outside. This is the justification for the statement in Freeman (1970) that for M33 and NGC 300 a lot of mass must be outside the last measured point on the rotation curve.