Title:	Stellar dynamics around a massive black hole III: Resonant relaxation of axisymmetric discs.
Authors:	Sridhar, S. Touma, Jihad R.
Keywords:	Centre galaxies Kinematics and dynamics galaxies
Issue Date:	Feb-2017
Publisher:	Oxford University Press for the Royal Astronomical Society
Citation:	Monthly Notices of the Royal Astronomical Society, 2017, Vol. 465, p1856-1878
Abstract:	We study the resonant relaxation (RR) of an axisymmetric, low-mass (or Keplerian) stellar disc orbiting a more massive black hole (MBH). Our recent work on the general kinetic theory of RR is simplified in the standard manner by the neglect of ‘gravitational polarization’ and applied to a razor-thin axisymmetric disc. The wake of a stellar orbit is expressed in terms of the angular momenta exchanged with other orbits, and used to derive a kinetic equation for RR under the combined actions of self-gravity, 1 PN and 1.5 PN general relativistic effects of the MBH and an arbitrary external axisymmetric potential. This is a Fokker–Planck equation for the stellar distribution function (DF), wherein the diffusion coefficients are given self-consistently in terms of contributions from apsidal resonances between pairs of stellar orbits. The physical kinetics is studied for the two main cases of interest. (1) ‘Lossless’ discs in which the MBH is not a sink of stars, and disc mass, angular momentum and energy are conserved: we prove that general H-functions can increase or decrease during RR, but the Boltzmann entropy is (essentially) unique in being a non-decreasing function of time. Therefore, secular thermal equilibria are maximum entropy states, with DFs of the Boltzmann form; the two-ring correlation function at equilibrium is computed. (2) Discs that lose stars to the MBH through an ‘empty loss cone’: we derive expressions for the MBH feeding rates of mass, angular momentum and energy in terms of the diffusive fluxes at the loss-cone boundaries.
Description:	Open Access
URI:	http://hdl.handle.net/2289/6679
ISSN:	0035-8711 1365-2966 - (online)
Alternative Location:	http://adsabs.harvard.edu/abs/2017MNRAS.465.1856S http://arxiv.org/abs/1602.05763 http://dx.doi.org/10.1093/mnras/stw2765
Copyright:	2016 The authors & the Royal Astronomical Society
Appears in Collections:	Research Papers (A&A)

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