2008/08/14 by Mir Abbas Jalali
Physics and Astronomy · #Angular momentum #Angular momentum coupling #Astrophysics #Astrophysics and Star Formation Studies #Classical mechanics #Context (archaeology) #Galaxy #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Resonance (particle physics) #Specific relative angular momentum #Spiral galaxy #Stars #Stellar, planetary, and galactic studies #Total angular momentum quantum number #Wavenumber #astro-ph
paper · pdf · doi:10.1086/592556
15 Pages (emulateapj), 7 Figures, Accepted for Publication in The Astrophysical Journal
arxiv created 2008/08/14 · openalex publication_date 2008/11/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
I decompose the unstable growing modes of stellar disks to their Fourier components and present the physical mechanism of instabilities in the context of resonances. When the equilibrium distribution function is a nonuniform function of the orbital angular momentum, the capture of stars into the corotation resonance imbalances the disk angular momentum and triggers growing bar and spiral modes. The stellar disk can then recover its angular momentum balance through the response of nonresonant stars. I carry out a complete analysis of orbital structure corresponding to each Fourier component in the radial angle and present a mathematical condition for the occurrence of van Kampen modes, which constitute a continuous family. I discuss the discreteness and allowable pattern speeds of unstable modes and argue that the mode growth is saturated due to the resonance overlapping mechanism. An individual growing mode can also be suppressed if the corotation and inner Lindblad resonances coexist and compete to capture a group of stars. Based on this mechanism, I show that self-consistent scale-free disks with a sufficient distribution of noncircular orbits should be stable under perturbations of angular wavenumber m > 1. I also derive a criterion for the stability of stellar disks against nonaxisymmetric excitations.