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Density waves in debris discs and galactic nuclei

Authors

  • Mir Abbas Jalali,

    Corresponding author
    1. Sharif University of Technology, Azadi Avenue, PO Box 11155-9567 Tehran, Iran
    2. School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
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  • Scott Tremaine

    Corresponding author
    1. School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
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E-mail: mjalali@sharif.edu (MAJ); tremaine@ias.edu (ST)

ABSTRACT

We study the linear perturbations of collisionless near-Keplerian discs. Such systems are models for debris discs around stars and the stellar discs surrounding supermassive black holes at the centres of galaxies. Using a finite-element method, we solve the linearized collisionless Boltzmann equation and Poisson’s equation for a wide range of disc masses and rms orbital eccentricities to obtain the eigenfrequencies and shapes of normal modes. We find that these discs can support large-scale ‘slow’ modes, in which the frequency is proportional to the disc mass. Slow modes are present for arbitrarily small disc mass so long as the self-gravity of the disc is the dominant source of apsidal precession. We find that slow modes are of two general types: parent modes and hybrid child modes, the latter arising from resonant interactions between parent modes and singular van Kampen modes. The most prominent slow modes have azimuthal wavenumbers m= 1 and m= 2. We illustrate how slow modes in debris discs are excited during a fly-by of a neighbouring star. Many of the non-axisymmetric features seen in debris discs (clumps, eccentricity, spiral waves) that are commonly attributed to planets could instead arise from slow modes; the two hypotheses can be distinguished by long-term measurements of the pattern speed of the features.

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