A new family of potential-density pairs for flattened systems with flat rotation curves

Abstract

ABSTRACT We present a new family of field-density pairs that may be used to model highly flattened systems like spiral galaxies. The rotation curves are asymptotically flat and the density is positive within the domain of a disc that is highly constricted near the centre. We used a member of the family to show that it may reproduce the observed rotation curves of a sample of Sc galaxies. We also computed its surface density and found that it initially reproduced the observed exponential variation, but fell-off more slowly at large R. A subsequent member of the family yielded an exponential surface density. The effective potentials within both models were shown to have minima throughout the systems, thus admitting stable bounded orbits. To justify the existence of a disc with exponentially decreasing surface density and flat rotation curve, we proved that a deviation from Keplerian fall-off is intrinsic to cylindrically symmetric potentials.