Title:	Secular instabilities of Keplerian stellar discs
Authors:	Kaur, Karamveer Kazandjian, Mher V Sridhar, S. Touma, Jihad R.
Keywords:	Galaxy Centre - galaxies Knematics and dynamics - galaxies Nuclei
Issue Date:	21-May-2018
Publisher:	Oxford University Press on behalf of the Royal Astronomical Society
Citation:	Monthly Notices of the Royal Astronomical Society, 2018, Vol. 476; p4104-4122
Abstract:	We present idealized models of a razor-thin, axisymmetric, Keplerian stellar disc around a massive black hole, and study non-axisymmetric secular instabilities in the absence of either counter-rotation or loss cones. These discs are prograde mono-energetic waterbags, whose phase-space distribution functions are constant for orbits within a range of eccentricities (e) and zero outside this range. The linear normal modes of waterbags are composed of sinusoidal disturbances of the edges of distribution function in phase space. Waterbags that include circular orbits (polarcaps) have one stable linear normal mode for each azimuthal wavenumber m. The m = 1 mode always has positive pattern speed and, for polarcaps consisting of orbits with e < 0.9428, only the m = 1 mode has positive pattern speed. Waterbags excluding circular orbits (bands) have two linear normal modes for each m, which can be stable or unstable. We derive analytical expressions for the instability condition, pattern speeds, growth rates, and normal mode structure. Narrow bands are unstable to modes with a wide range in m. Numerical simulations confirm linear theory and follow the non-linear evolution of instabilities. Long-time integration suggests that instabilities of different m grow, interact non-linearly, and relax collisionlessly to a coarse-grained equilibrium with a wide range of eccentricities.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/6884
ISSN:	0035-8711 1365-2966 - (online)
Alternative Location:	http://adsabs.harvard.edu/abs/2018MNRAS.476.4104K https://arxiv.org/abs/1710.11340 https://doi.org/10.1093/mnras/sty403
Copyright:	The Author(s)
Appears in Collections:	Research Papers (A&A)

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