Complex statistics in Hamiltonian barred galaxy models

Abstract

We use probability density functions (pdfs) of sums of orbit coordinates, over time intervals of the order of one Hubble time, to distinguish weakly from strongly chaotic orbits in a barred galaxy model. We find that, in the weakly chaotic case, quasi-stationary states arise, whose pdfs are well approximated by $q$-Gaussian functions (with $1<q<3$), while strong chaos is identified by pdfs which quickly tend to Gaussians ($q=1$). Typical examples of weakly chaotic orbits are those that "stick" to islands of ordered motion. Their presence in rotating galaxy models has been investigated thoroughly in recent years due of their ability to support galaxy structures for relatively long time scales. In this paper, we demonstrate, on specific orbits of 2 and 3 degree of freedom barred galaxy models, that the proposed statistical approach can distinguish weakly from strongly chaotic motion accurately and efficiently, especially in cases where Lyapunov exponents and other local dynamic indicators appear to be inconclusive.

14 pages, 9 figures, submitted for publication

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• Chaotic motion and the evolution of morphological components in a time-dependent model of a barred galaxy within a dark matter halo
• Classifying orbits in galaxy models with a prolate or an oblate dark matter halo component
• Introducing a new 3D dynamical model for barred galaxies
• Distinguishing between order and chaos in a simple barred galaxy model
• Orbit classification of low and high angular momentum stars
• Determining the type of orbits in the central regions of barred galaxies
• Study of chaos in rotating galaxies using extended force-gradient symplectic methods
• Orbital dynamics in realistic galaxy models: NGC 3726, NGC 3877 and NGC 4010