Stability of power-law disks II. The global spiral modes (1997)

Author(s): Evans, N. W.; Read, J. C. A.

    Abstract: This paper reports on the in-plane normal modes in the self-consistent and the cut-out power-law disks. Although the cut-out disks are remarkably stable to bisymmetric perturbations, the are very susceptible to one-armed modes. For this harmonic, there is no inner Lindblad resonance, thus removing a powerful stabilising influence. A physical mechanism for the generation of the one-armed instabilities is put forward. Incoming trailing waves are reflected as leading waves at the inner cut-out, thus completing the feedback for the swing-amplifier. Growing three-armed and four-armed modes occur only at very low temperatures. However, neutral m=3 and m=4 modes are possible at higher temperatures for some disks. The rotation curve index, beta, has a marked effect on stability. For all azimuthal wavenumbers, any unstable modes persist to higher temperatures and grow more vigorously if the rotation curve is rising (beta<0) than if the rotation curve is falling (beta>0). If the central region or outer parts of the disk are carved out more abruptly, any instabilities become more virulent. The self-consistent power-law disks possess a number of unusual stability properties. There is no natural timescale in the self-consistent disks. If a mode is admitted at some pattern speed and growth rate, then it must be present at all pattern speeds and growth rates. Our analysis - although falling short of a complete proof - suggests that such a two-dimensional continuum of non-axisymmetric modes does not occur and that the self-consistent power-law disks admit no global non-axisymmetric normal modes whatsoever. Without reflecting boundaries or cut-outs, there is no resonant cavity and no possibility of unstable growing modes. The self-consistent power-law disks certainly admit equiangular spirals as neutral modes, together with a one-dimensional continuum of growing axisymmetric modes.

    Notes: Work done for my D.Phil. thesis; Evans was my supervisor.

      • Journal: Monthly Notices of the Royal Astronomical Society
      • Volume: 300
      • Pages: 106-130
      • Publication type: Article
      • Bibliographic status: Published

        Keywords: celestial mechanics, stellar dynamics galaxies, kinematics and dynamics galaxies, structure galaxies, spiral


        Professor Jennifer Read
        Professor of Vision Science