A taxonomic algorithm for bar-building orbits

Abstract

Recently it has been realized that the major structures observed in rotating disc galaxies, i.e. bars and spirals, can be supported by regular as well as by chaotic orbits. The fact that the building of a structure cannot be attributed just to quasipe riodic orbits associated with a single orbital family, creates the need to classify the traject ories of the particles in structuresupporting and structure-non-supporting within a time interval of interest. Our goal is to present a simple algorithm that detects and classifies the or bits which reinforce the rectangularity of the outer envelope of a bar, independently of their regular or chaotic character. Our bar is a 2D response bar, formed when an external potential estimated from near-infrared observations of an early type barred-spiral galaxy, is impo sed to a set of initial conditions. For this purpose we use a method based on tracing patterns in sequences of characters, which indicate sign changes of the (Cartesian) coordinates. These sign changes occur when as integrate an orbit for a time t and we follow it in 2D subspaces of the phase space ((x, y), ( ˙, ˙ y), etc.). A sign change indicates crossing of an axis during the integration. In the case we describe in our paper the bar in the inner parts is supported by regular orbit s following the x1 flow, while the outer envelope of the bar is supported mainly by chaotic orbits at higher energies. With our method, at a given Jacobi constant, first we assess the contri bution to the local surface density of a large number of orbital segments. This is done by integrating their initial conditions for 10 pattern rotations. We depict this information on grey scale maps. We have realized, that this contribution is independent of the regular or chaotic chara cter of the integrated orbits. Then, by analyzing the arrays of sign changes we have registered during the orbital integrations, we separate the trajectories that shape the outer structure of the bar in two classes. They follow mainly boxy or/and diamond-like morphologies within the time of integration. By repeating the method at several Jacobi constants (EJ) we find that the majority of the orbits that support