Complex statistics in Hamiltonian barred galaxy models

TL;DR

This paper introduces a statistical method using probability density functions of orbit coordinate sums to distinguish weakly from strongly chaotic orbits in barred galaxy models, providing a more reliable classification than traditional indicators.

Contribution

The study demonstrates that analyzing the PDFs of orbit coordinate sums effectively differentiates weakly and strongly chaotic orbits in galaxy models, especially when other indicators are inconclusive.

Findings

Weakly chaotic orbits exhibit q-Gaussian PDFs with 1<q<3.

Strong chaos corresponds to PDFs tending to Gaussian (q=1).

The method accurately identifies chaos levels in specific 2 and 3 degree of freedom 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.