Orbital classification in an N-body bar

Abstract

The dynamics and evolution of any galactic structure are strongly influenced by the properties of the orbits that constitute it. In this paper, we compare two orbit classification schemes, one by Laskar (NAFF) , and the other by Carpintero and Aguilar (CA), by applying both of them to orbits obtained by following individual particles in a numerical simulation of a barred galaxy. We find that, at least for our case and some provisos, the main frequencies calculated by the two methods are in good agreement: for $80\%$ of the orbits the difference between the results of the two methods is less than $5\%$ for all three main frequencies. However, it is difficult to evaluate the amount of regular or chaotic bar orbits in a given system. The fraction of regular orbits obtained by the NAFF method strongly depends on the critical frequency drift parameter, while in the CA method the number of fundamental frequencies strongly depends on the frequency difference parameter $L_{\rm r}$ and the maximum integer used for searching the linear independence of the fundamental frequencies. We also find that, for a given particle, in general the projection of its motion along the bar minor axis is more regular than the other two projections, while the projection along the intermediate axis is the least regular.