Modes of a stellar system II: non-ergodic systems. Issue 2 (29th July 2021)

• Record Type: Journal Article
• Authors: Lau, Jun Yan; Binney, James
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 507:Issue 2(2021)
• Page Start: 2562
• Page End: 2567
• Publication Date: 2021-07-29
• Subjects: methods: analytical -- Galaxy: kinematics and dynamics -- galaxies: kinematics and dynamics; Astronomy -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnras/stab2175
• Languages: English
• ISSNs: 0035-8711

Abstract

ABSTRACT: An equation is derived for the energy of a small disturbance in a system that is generated by a distribution function (DF) of the form f (J ) – most galaxies and star clusters can be closely approximated by such a DF. The theory of van Kampen modes is extended to such general systems. A bilinear form on the space of DFs is defined such that the energy of a disturbance is its norm under this form. It is shown that van Kampen modes which differ in frequency are then orthogonal, with the consequence that the energies of van Kampen modes are additive. Consequently, most of the insight into the dynamics of ergodic systems that was gained in a recent paper on the van Kampen modes of ergodic systems applies to real clusters and galaxies.