Linear Potentials in Galaxies and Clusters of Galaxies

In a previous paper we presented a typical set of galactic rotation curves associated with the linear gravitational potential of the conformal invariant fourth order theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order NewtonEinstein theory. Reasonable agreement with data was obtained for four representative galaxies without the need for any non-luminous or dark matter. In this paper we present the associated formalism and compare and contrast the linear potential explanation of the general systematics of galactic rotation curves and the associated Tully-Fisher relation with that of the standard dark matter theory. Additionally, we show that the conformal gravity picture appears to have survived the recent round of microlensing observations unscathed. Finally, we make a first application of the conformal theory to the larger distance scale associated with a cluster of galaxies, with the theory being found to give a reasonable value for the mean velocity of the virialized core of the typical Coma cluster, again without the need to invoke dark matter. March, 1995 UCONN-95-2