Stability of power-law discs - II. The global spiral modes

Details Stability of power-law discs - II. The global spiral modes Stability of power-law discs - II. The global spiral modes

Oct 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998mnras.300..106e&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Volume 300, Issue 1, pp. 106-130.

Astronomy and Astrophysics

Astronomy

43

Instabilities, Celestial Mechanics, Stellar Dynamics, Galaxies: Kinematics And Dynamics, Galaxies: Spiral, Galaxies: Structure

Scientific paper

This paper reports on the in-plane normal modes in the self-consistent and the cut-out power-law discs. Although the cut-out discs are remarkably stable to bisymmetric perturbations, they are very susceptible to one-armed modes. For this harmonic, there is no inner Lindblad resonance, thus removing a powerful stabilizing 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 discs. 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 regions or outer parts of the disc are carved out more abruptly, any instabilities become more virulent. The self-consistent power-law discs possess a number of unusual stability properties. There is no natural time-scale in the self-consistent disc. 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 discs 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 discs certainly admit equi-angular spirals as neutral modes, together with a one-dimensional continuum of growing axisymmetric modes.

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