Precessing ellipses as the building blocks of spiral arms

¹ Research center for Astronomy and Applied Mathematics, Academy of Athens, Soranou Efessiou 4, 115 27 Athens, Greece
e-mail: mharsoul@academyofathens.gr; gcontop@academyofathens.gr
² Department of Physics, Section of Astrophysics, Astronomy and Mechanics, University of Athens, Panepistimiopolis, 15784 Athens, Greece
e-mail: zouloukon@phys.uoa.gr
³ Department of Mathematics, Tullio Levi-Civita, University of Padua, Via Trieste, 63, 35121 Padova, Italy

Received: 2 April 2021
Accepted: 9 August 2021

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.