Orbit classification in a disk galaxy model with a pseudo-Newtonian central black hole

¹ Department of Physics, School of Science, Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece
e-mail: evzotos@physics.auth.gr
² Facultad de Ciencias Humanas y de la Educación, Universidad de los Llanos, Villavicencio, Colombia
e-mail: fldubeibem@unal.edu.co
³ Academic Department of Mathematics, Universidade Tecnológica Federal do Paraná (UTFPR), Av. Sete de Setembro, 3165 Curitiba, Brazil
e-mail: steklain@utfpr.edu.br
⁴ Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, PO Box 80203, Jeddah 21589, Saudi Arabia

Received: 9 July 2020
Accepted: 31 August 2020

Abstract

We numerically investigate the motion of stars on the meridional plane of an axially symmetric disk galaxy model, containing a central supermassive black hole, represented by the Paczyński-Wiita potential. By using this pseudo-Newtonian potential we can replicate important relativistic properties such as the existence of the Schwarzschild radius. After classifying extensive samples of initial conditions of trajectories, we managed to distinguish between collisional, ordered, and chaotic motion. Besides all starting conditions of regular orbits were further classified into families of regular orbits. Our results are presented via color-coded basin diagrams on several types of two-dimensional planes. Our analysis reveals that both the mass of the black hole (in direct relation with the Schwarzschild radius) as well as angular momentum play an important role in the character of the orbits of stars. More specifically, the trajectories of low angular momentum stars are highly affected by the mass of the black hole, while high angular momentum stars seem to be unaffected by the central black hole. A comparison with previous related outcomes, using Newtonian potentials for the central region of the galaxy, is also made.