Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred Galaxy Model

Abstract

We study the distinction and quantification of chaotic and regular motion in a time-dependent Hamiltonian barred galaxy model. Recently, a strong correlation was found between the strength of the bar and the presence of chaotic motion in this system, as models with relatively strong bars were shown to exhibit stronger chaotic behavior compared to those having a weaker bar component. Here, we attempt to further explore this connection by studying the interplay between chaotic and regular behavior of star orbits when the parameters of the model evolve in time. This happens for example when one introduces linear time dependence in the mass parameters of the model to mimic, in some general sense, the effect of self-consistent interactions of the actual N-body problem. We thus observe, in this simple time-dependent model also, that the increase of the bar's mass leads to an increase of the system's chaoticity. We propose a new way of using the Generalized Alignment Index (GALI) method as a reliable criterion to estimate the relative fraction of chaotic vs. regular orbits in such time-dependent potentials, which proves to be much more efficient than the computation of Lyapunov exponents. In particular, GALI is able to capture subtle changes in the nature of an orbit (or ensemble of orbits) even for relatively small time intervals, which makes it ideal for detecting dynamical transitions in time-dependent systems.

21 pages, 9 figures (minor typos fixed) to appear in J. Phys. A: Math. Theor

References in corpus (16)

• Numerical integration of variational equations
• Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi--Pasta--Ulam lattices by the Generalized Alignment Index method
• Regular and chaotic orbits in barred galaxies - I. Applying the SALI/GALI method to explore their distribution in several models
• Orbital structure in barred spiral galaxies
• Stability of Simple Periodic Orbits and Chaos in a Fermi -- Pasta -- Ulam Lattice
• Efficient integration of the variational equations of multi-dimensional Hamiltonian systems: Application to the Fermi-Pasta-Ulam lattice
• Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method
• Quantum chaos in the nuclear collective model: I. Classical-quantum correspondence
• The structure and evolution of confined tori near a Hamiltonian Hopf Bifurcation
• Scaling with system size of the Lyapunov exponents for the Hamiltonian Mean Field model
• Exploring the nature of orbits in a galactic model with a massive nucleus
• Chains of rotational tori and filamentary structures close to high multiplicity periodic orbits in a 3D galactic potential
• Complex statistics in Hamiltonian barred galaxy models
• Efficient control of accelerator maps
• Appropriate SCF basis sets for orbital studies of galaxies and a `quantum-mechanical' method to compute them
• The rate of secular evolution in elliptical galaxies with central masses

Cited by in corpus (15)

• Chaos and dynamical trends in barred galaxies: bridging the gap between N-body simulations and time-dependent analytical models
• Chaotic motion and the evolution of morphological components in a time-dependent model of a barred galaxy within a dark matter halo
• Boxy Orbital Structures in Rotating Bar Models
• Classifying orbits in galaxy models with a prolate or an oblate dark matter halo component
• Introducing a new 3D dynamical model for barred galaxies
• On the relevance of chaos for halo stars in the solar neighbourhood II
• Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method
• Performance of chaos diagnostics based on Lagrangian descriptors. Application to the 4D standard map
• Orbit evolution in growing stellar bars: Bar-supporting orbits at the vertical ILR region
• New phenomenons in the spatial isosceles three-body problem
• Distinguishing between order and chaos in a simple barred galaxy model
• Orbit classification of low and high angular momentum stars
• Orbital dynamics in galactic potentials under mass transfer
• How does the mass transport in disk galaxy models influence the character of orbits?
• Orbital dynamics in realistic galaxy models: NGC 3726, NGC 3877 and NGC 4010