Eccentricity Growth Rates of Tidally Distorted Discs

TL;DR

This paper investigates how tidally perturbed gaseous discs develop eccentric instabilities, analyzing the distribution of eccentricity and identifying modes like the superhump mode that influence instability growth rates.

Contribution

It applies a linear eccentricity evolution model to explore eccentricity distribution and growth in tidally perturbed discs, identifying dominant modes such as the superhump mode.

Findings

Identification of a superhump mode related to binary star systems.

Derivation of an analytic precession rate for cool discs.

Discovery that other eccentric modes can outgrow the superhump mode depending on disc properties.

Abstract

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 is not 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.