Dynamical friction in spherical clusters

The effect of dynamical friction on the density profile of the most massive galaxies in a cluster is calculated both for an isothermal model cluster and for Plummer's model. The resulting profiles show a depletion of massive objects near the centre, but this depletion appears unable to produce a secondary maximum. The application of the models to rich clusters of galaxies is discussed and it is found that the evolution should be at least strong enough to produce central objects the size of cD galaxies. Accurate luminosity profiles for clusters of galaxies are shown to be capable of putting constraints on the mass to light ratios of the member galaxies and to give an indication of the form and distribution of the 'missing mass'. (author)