Volume 581, September 2015
|Number of page(s)||22|
|Published online||24 September 2015|
Secular diffusion in discrete self-gravitating tepid discs
I. Analytic solution in the tightly wound limit⋆
1 Institut d’Astrophysique de Paris and UPMC, CNRS (UMR 7095), 98bis boulevard Arago, 75014 Paris, France
e-mail: email@example.com; firstname.lastname@example.org
2 Institute of Astronomy & KICC, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
3 Laboratoire de Physique Théorique (IRSAMC), CNRS and UPS, Univ. de Toulouse, 31062 Toulouse, France
Received: 19 February 2015
Accepted: 2 May 2015
The secular evolution of an infinitely thin tepid isolated galactic disc made of a finite number of particles is described using the inhomogeneous Balescu-Lenard equation. Assuming that only tightly wound transient spirals are present in the disc, a WKB approximation provides a simple and tractable quadrature for the corresponding drift and diffusion coefficients. It provides insight into the physical processes at work during the secular diffusion of a self-gravitating discrete disc and makes quantitative predictions on the initial variations of the distribution function in action space. When applied to the secular evolution of an isolated stationary self-gravitating Mestel disc, this formalism predicts the initial importance of the corotation resonance in the inner regions of the disc leading to a regime involving radial migration and heating. It predicts in particular the formation of a ridge-like feature in action space, in agreement with simulations, but over-estimates the timescale involved in its appearance. Swing amplification is likely needed to resolve this discrepancy. In astrophysics, the inhomogeneous Balescu-Lenard equation and its WKB limit may also describe the secular diffusion of giant molecular clouds in galactic discs, the secular migration and segregation of planetesimals in proto-planetary discs, or even the long-term evolution of population of stars within the Galactic centre.
Key words: galaxies: evolution / galaxies: kinematics and dynamics / galaxies: spiral / diffusion / gravitation
Appendices are available in electronic form at http://www.aanda.org
© ESO, 2015
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