Density waves in debris discs and galactic nuclei

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.

17 pages, 11 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society

References in corpus (12)

• Protoplanetary Disks and Their Evolution
• Optical Images of an Exosolar Planet 25 Light Years from Earth
• Direct Imaging of Fine Structures in Giant Planet Forming Regions of the Protoplanetary Disk around AB Aurigae
• Discovery of extreme asymmetry in the debris disk surrounding HD 15115
• VLT/NACO Polarimetric Differential Imaging of HD100546 - Disk Structure and Dust Grain Properties between 10-140 AU
• Resolved Submillimeter Observations of the HR 8799 and HD 107146 Debris Disks
• A 5 Micron Image of beta Pictoris b at a Sub-Jupiter Projected Separation: Evidence for a Misalignment Between the Planet and the Inner, Warped Disk
• Hubble and Spitzer Space Telescope Observations of the Debris Disk around the Nearby K Dwarf HD 92945
• A Resolved Ring of Debris Dust Around the Solar Analog HD 107146
• Planets of Beta Pictoris revisited
• Images of Vega Dust Ring at 350 and 450 microns: New Clues to the Trapping of Multiple-Sized Dust Particles in Planetary Resonances
• High-sensitivity search for clumps in the Vega Kuiper-belt. New PdBI 1.3mm observations

Cited by in corpus (19)

• Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
• Infrared Non-detection of Fomalhaut b -- Implications for the Planet Interpretation
• The SEEDS Direct Imaging Survey for Planets and Scattered Dust Emission in Debris Disk Systems
• A Primer on Unifying Debris Disk Morphologies
• Coplanar Circumbinary Debris Disks
• Formation of Gaps in Self-Gravitating Debris Disks by Secular Resonance in a Single-planet System I: A Simplified Model
• Fast Modes and Dusty Horseshoes in Transitional Disks
• Giant Impacts and Debris Disk Morphology
• The secular evolution of discrete quasi-Keplerian systems. I. Kinetic theory of stellar clusters near black holes
• Stellar Dynamics around a Massive Black Hole I: Secular Collisionless Theory
• The ALMA survey to Resolve exoKuiper belt Substructures (ARKS): VI. Asymmetries and offsets
• Global drag-induced instabilities in protoplanetary disks
• Constraints on the gas content of the Fomalhaut debris belt. Can gas-dust interactions explain the belt's morphology?
• The secular evolution of discrete quasi-Keplerian systems. II. Application to a multi-mass axisymmetric disc around a supermassive black hole
• Secular Instabilities of Keplerian Stellar Discs
• The ALMA survey to Resolve exoKuiper belt Substructures (ARKS). X. Interpreting the peculiar dust rings around HD 131835
• A modified WKB formulation for linear eigenmodes of a collisionless self-gravitating disc in the epicyclic approximation
• Modal analysis of gravitational instabilities in nearly Keplerian, counter-rotating collisionless discs
• Effect of dark matter halo on global spiral modes in a collisionless galactic disc