Analytical potential-density pairs from complex-shifted Kuzmin-Toomre discs

TL;DR

This paper introduces a novel method using complex shifts on Kuzmin-Toomre discs to generate non-axisymmetric matter distributions and rings, extending to triaxial systems and exploring the imaginary component of potentials.

Contribution

It presents a new application of the complex-shift technique to create non-axisymmetric and triaxial potential-density pairs from known disc models.

Findings

Generated non-axisymmetric flat distributions and rings.

Constructed triaxial potential-density pairs.

Discussed the role of the imaginary part of potentials.

Abstract

The complex-shift method is applied to the Kuzmin-Toomre family of discs to generate a family of non-axisymmetric flat distributions of matter. These are then superposed to construct non-axisymmetric flat rings. We also consider triaxial potential-density pairs obtained from these non-axisymmetric flat systems by means of suitable transformations. The use of the imaginary part of complex-shifted potential-density pairs is also discussed.