Orbital dynamics in galactic potentials under mass transfer

TL;DR

This paper investigates the complex orbital dynamics in time-evolving galactic potentials with mass transfer, using ensemble methods and Poincaré sections to analyze chaos and stability in a system with changing parameters.

Contribution

It introduces a novel application of ensemble phase space analysis and a generalized Lyapunov exponent to study the effects of mass transfer on galactic orbital dynamics.

Findings

Phase space structure is significantly affected by mass transfer.

The generalized Lyapunov exponent effectively characterizes system stability.

Ensemble analysis reveals the emergence of chaos during mass transfer processes.

Abstract

Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show that an ensemble approach along with the so-called snapshot framework in dynamical system theory provide a powerful tool to analyze time dependent dynamics. In this work, we aim to explore and quantify the phase space structure and dynamical complexity in time-dependent galactic potentials consisting of multiple components. We apply the classical method of Poincar\'e-surface of section to analyze the phase space structure in a chaotic Hamiltonian system subjected to parameter drift. This, however, makes sense only when the evolution of a large ensemble of initial conditions is followed. Numerical simulations explore the phase space structure of such ensembles while the system undergoes a continuous parameter change. The pair-wise average distance of ensemble members allows us to define a generalized Lyapunov-exponent, that might also be time dependent, to describe the system stability. We provide a comprehensive dynamical analysis of the system under circumstances where linear mass transfer occurs between the disk and bulge components of the model.