Ogilvie, GI and Barker, AJ (2014) Local and global dynamics of eccentric astrophysical discs. Monthly Notices of the Royal Astronomical Society, 445 (3). pp. 2621-2636. ISSN 0035-8711
Abstract
We formulate a local dynamical model of an eccentric disc in which the dominant motion consists of elliptical Keplerian orbits. The model is a generalization of the well-known shearing sheet, and is suitable for both analytical and computational studies of the local dynamics of eccentric discs. It is spatially homogeneous in the horizontal dimensions but has a time-dependent geometry that oscillates at the orbital frequency. We show how certain averages of the stress tensor in the local model determine the large-scale evolution of the shape and mass distribution of the disc. The simplest solutions of the local model are laminar flows consisting of a (generally non-linear) vertical oscillation of the disc. Eccentric discs lack vertical hydrostatic equilibrium because of the variation of the vertical gravitational acceleration around the eccentric orbit, and in some cases because of the divergence of the orbital velocity field associated with an eccentricity gradient. We discuss the properties of the laminar solutions, showing that they can exhibit extreme compressional behaviour for eccentricities greater than about 0.5, especially in discs that behave isothermally. We also derive the linear evolutionary equations for an eccentric disc that follow from the laminar flows in the absence of a shear viscosity. In a companion paper we show that these solutions are linearly unstable and we determine the associated growth rates and unstable modes.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2014, Oxford University Press. This is a pre-copyedited, author-produced PDF of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. The version of record Ogilvie, GI and Barker, AJ (2014) Local and global dynamics of eccentric astrophysical discs. Monthly Notices of the Royal Astronomical Society, 445 (3). pp. 2621-2636 is available online at: https://doi.org/10.1093/mnras/stu1795 |
Keywords: | accretion, accretion discs, hydrodynamics, celestial mechanics |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 Mar 2017 15:52 |
Last Modified: | 31 Jan 2018 11:45 |
Published Version: | https://doi.org/10.1093/mnras/stu1795 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/mnras/stu1795 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:108973 |