Mir Abbas Jalali, Scott Tremaine
We study the linear perturbations of collisionless near-Keplerian discs that
have a ring-like structure. 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.
View original:
http://arxiv.org/abs/1110.4551
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