Orbital Classification in Rotating Bar Potentials Using an Empirical Proxy of the Second Integral of Motion

Journal article

We present a novel method for classifying two-dimensional orbits in rotating bar potentials based on an empirical proxy for the second integral of motion, calibrated angular momentum (CAM), which is defined as the ratio of the time-averaged angular momentum ( Lz¯ ) to its temporal dispersion ( σLz ) in the corotating frame. We show that CAM is determined by the ratio of the azimuthal to radial actions ( Jϕ′/Jr′ ) in the analytical Freeman bar model. We then construct a new parameter space defined by CAM versus the rms radius (Rrms) and apply this framework to orbits in several representative rotating bar potentials. In the CAM–Rrms plane, periodic orbits generate well-defined branches separating distinct regions corresponding to different orbital families. Several of these branches enclose isolated areas that can be associated with specific orbital families, such as the x2 orbital family. We further validate the method using orbits from test-particle simulations, which show a well-ordered and nonoverlapping distribution of orbital families in the CAM–Rrms plane. Since CAM is fundamentally linked to intrinsic orbital properties and readily applied to three-dimensional orbits in N-body simulations, our results establish the CAM–Rrms plane as a robust and efficient framework for orbit classification in rotating bars that complements conventional methods.

Authors: Xia, T; Shen, J; Magorrian, J; Qin, Y

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Astronomical Society
• Journal: The Astrophysical Journal
• Volume: 999
• Issue: 1
• Pages: 100
• Article number: 100
• Publication date: 2026-02-26
• Acceptance date: 2026-01-30
• DOI: 10.3847/1538-4357/ae4023
• EISSN: 1538-4357
• ISSN: 0004637X, 0004-637X
• Language: English
• Keywords: Galaxy dynamics; Orbits; Barred spiral galaxies