Precessing ellipses as the building blocks of spiral arms

TL;DR

This paper investigates how stable precessing elliptical orbits in galactic models can generate spiral density waves, revealing correlations between spiral arm properties and orbital dynamics.

Contribution

It introduces a framework linking precessing elliptical orbits to spiral density wave formation and quantifies parameter ranges for stable spiral structures.

Findings

Correlation between pitch angle and spiral perturbation amplitude

Relationship between pitch angle and pattern speed

Precessing ellipses support ordered spiral density waves

Abstract

Stable periodic orbits in spiral galactic models that form families of precessing ellipses can create spiral density waves similar to those that are observed in real grand-design galaxies. We study the range in parameter space for which the amplitude of the spiral perturbation, the pattern speed, and the pitch angle collaborate so as to lead to the creation of density waves that are supported by precessing ellipses and their surrounding matter in ordered motion. Quantitative estimates lead to a correlation between the pitch angle and the amplitude of the spiral perturbation and also between the pitch angle and the pattern speed of the spiral arms. These correlations can be regarded as an orbital analog of a nonlinear dispersion relation in density wave theory.