Eccentricity Growth Rates of Tidally Distorted Discs

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.

11 pages, 15 figures to be published on MNRAS

References in corpus (6)

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• A mid-IR interferometric survey with MIDI/VLTI: resolving the second-generation protoplanetary disks around post-AGB binaries
• Spectral signatures of disk eccentricity in young binary systems: I. Circumprimary case
• Kozai-Lidov Disc Instability
• Planetary Rings
• Non-linear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure
• On the secular behavior of dust particles in an eccentric protoplanetary disk with an embedded massive gas giant planet
• Eccentric Modes in Disks With Pressure and Self-Gravity
• Investigating lack of accretion disk eccentricity growth in a global 3D MHD simulation of a superhump system
• HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. I. Hydrodynamic simulations
• Long-Lived Eccentricities in Accretion Disks
• Forced Eccentricity in Circumbinary Discs
• Tidal Instability and Superhump by a Wave-Wave Resonant Model