Linear Potentials and Galactic Rotation Curves

Abstract

We derive a simple, closed form expression for the potential of a thin exponential disk of stars interacting through gravitational potentials of the form $V(r)=-β/r+γr/2$, the potential associated with fundamental sources in the fourth order conformal invariant theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order Einstein theory. Using the model, we obtain a reasonable fit (flat to within $\pm3\%$) to the (prototypical) NGC3198 $HI$ rotation curve data without the need for any non-luminous or dark matter. Our study suggests that th observed flatness of rotation curves may only be an intermediate phenomenon, and an asymptotic one.