A New Potential Formula Applicable to Flattened Systems

TL;DR

This paper introduces a modified gravitational potential formula tailored for flattened systems like exponential discs, improving rotation curve accuracy and reducing negative density issues.

Contribution

It proposes a new potential formula based on the Miyamoto-Nagai model, specifically designed for very flattened systems, enhancing modeling precision.

Findings

Rotation curves match well with those from special functions.

Total masses remain consistent with previous models.

Negative density effects are mitigated off the midplane.

Abstract

A new formula for the gravitational potential of flattened systems is proposed. It is a modification of the Miyamoto-Nagai potential and should be applied to very flattened systems, exponential discs as a typical example. The resulting rotation curve agrees sufficiently well with that obtained by using special functions and the total masses remain the same. The functions contained in the new term can improve the agreement for the rotation curve and also reduce the effect of negative density values which appear off the midplane.