Journal Article

Eccentricity growth rates of tidally distorted discs

Stephen H. Lubow

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 406, issue 4, pages 2777-2786
Published in print August 2010 | ISSN: 0035-8711
Published online August 2010 | e-ISSN: 1365-2966 | DOI:
Eccentricity growth rates of tidally distorted discs

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We consider discs that orbit a central object and are tidally perturbed by a circular orbit companion. Such discs are sometimes subject to an eccentric instability due to the effects of certain resonances. Eccentric instabilities may be present in planetary rings perturbed by satellites, protostellar discs perturbed by planets and discs in binary star systems. Although the basic mechanism for eccentric instability is well understood, the detailed response of a gaseous disc to such an instability has not been understood. We apply a linear eccentricity evolution equation developed by Goodchild and Ogilvie. We explore how the eccentricity is distributed in such a disc and how the distribution in turn affects the instability growth rate for a range of disc properties. We identify a disc mode, termed the superhump mode, that is likely at work in the superhump binary star case. The mode results from the excitation of the fundamental free precession mode. We determine an analytic expression for the fundamental free mode precession rate that is applicable to a sufficiently cool disc. Depending on the disc sound speed and disc edge location, other eccentric modes can grow faster than the superhump mode and dominate.

Keywords: accretion, accretion discs; instabilities; methods: numerical; planets and satellites: rings; planet–disc interactions; binaries: close

Journal Article.  7586 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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