On the integration of an axially symmetric galaxy model

Abstract

A numerical exploration of the escape of a particle from a potential well modeling an axially symmetric galaxy requires the integration of millions of orbits over very long spans of time. In this paper, we propose an integration of the equations of motion of the system by recurrent power series. We prove the convergence of the method, compare the computational time of the recurrent series method against the Dormand‐Prince method, and study the propagation of the truncation errors in the numerical solutions.

Limiting curves in an axially symmetric galaxy

“…The numerical integration of the equations of motion has been performed by using recurrent power series, and the accuracy of the numerical solutions has been computed fixed to 10 −21 . 17 In Figure 2…”

“…Black points correspond to orbits that escape to infinity by the opening of the potential. In the right panel, W s, 17 ( )…”

“…If the particle stays inside the domain defined by the curve of zero velocity after T e units of time, we consider that the orbit is a non‐escaping orbit. The numerical integration of the equations of motion has been performed by using recurrent power series, and the accuracy of the numerical solutions has been computed fixed to 10 −21 17 …”

Orbital and Equilibrium Dynamics of a Multiwell Potential

“…The curves of zero velocity of this system present only one exit channel. The escape dynamics of this particular galactic system has been studied previously by Zotos [26] and Navarro [22,23]. Moreover, the escape from multichannel systems have been studied extensively (see e.g., [14,[16][17][18][19][20][21]25,27,28]).…”

Dependence of the escape from an axially symmetric galaxy on the energy

“…To this end, we study the escape from a galactic model with axial symmetry. This type of galactic system has been previously studied by Zotos 19 and Navarro 12 , 13 . In a companion paper, Navarro 13 investigates the geometry of the curves that delimite the escape domains by determining the intersection of the ingoing and outgoing asymptotic trajectories to the Lyapunov orbit with an apropiate surface of section, for a fixed value of the energy.…”