Barker, AJ and Ogilvie, GI (2016) Nonlinear hydrodynamical evolution of eccentric Keplerian discs in two dimensions: validation of secular theory. Monthly Notices of the Royal Astronomical Society, 458 (4). pp. 3739-3751. ISSN 0035-8711
Abstract
We perform global two-dimensional hydrodynamical simulations of Keplerian discs with free eccentricity over thousands of orbital periods. Our aim is to determine the validity of secular theory in describing the evolution of eccentric discs, and to explore their nonlinear evolution for moderate eccentricities. Linear secular theory is found to correctly predict the structure and precession rates of discs with small eccentricities. However, discs with larger eccentricities (and eccentricity gradients) are observed to precess faster (retrograde relative to the orbital motion), at a rate that depends on their eccentricities (and eccentricity gradients). We derive analytically a nonlinear secular theory for eccentric gas discs, which explains this result as a modification of the pressure forces whenever eccentric orbits in a disc nearly intersect. This effect could be particularly important for highly eccentric discs produced in tidal disruption events, or for narrow gaseous rings; it might also play a role in causing some of the variability in superhump binary systems. In two dimensions, the eccentricity of a moderately eccentric disc is long-lived and persists throughout the duration of our simulations. Eccentric modes are however weakly damped by their interaction with non-axisymmetric spiral density waves (driven by the Papaloizou–Pringle instability, which occurs in our idealized setup with solid walls), as well as numerical diffusion.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | 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 Barker, AJ and Ogilvie, GI (2016) Nonlinear hydrodynamical evolution of eccentric Keplerian discs in two dimensions: validation of secular theory. Monthly Notices of the Royal Astronomical Society, 458 (4). pp. 3739-3751 is available online at: https://doi.org/10.1093/mnras/stw580 |
Keywords: | accretion, accretion discs; hydrodynamics; instabilities; waves; planetary systems |
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) |
Funding Information: | Funder Grant number Leverhulme Trust ECF-2014-216 |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Dec 2016 12:47 |
Last Modified: | 23 Jan 2018 12:15 |
Published Version: | https://doi.org/10.1093/mnras/stw580 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/mnras/stw580 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:108971 |