Forced Eccentricity in Circumbinary Discs

Abstract

We analyze the eccentric response of a low mass coplanar circumbinary disc to secular tidal forcing by a Keplerian eccentric orbit central binary. The disc acquires a forced eccentricity whose magnitude depends on the properties of the binary and disc. The largest eccentricities occur when there is a global apsidal resonance in the disc. The driving frequency by the binary is its apsidal frequency that is equal to zero. A global resonance occurs when the disc properties permit the existence of a zero apsidal frequency free eccentric mode. Resonances occur for different free eccentric modes that differ in the number of radial nodes. For a disc not at resonance, the eccentricity distribution has somewhat similar form to the eccentricity distributions in discs at resonance that have the closest matching disc aspect ratios. For higher disc aspect ratios, the forced eccentricity distribution in a 2D disc is similar to that of the fundamental free mode. The forced eccentricity distribution in a 3D disc is similar to that of higher order free modes, not the fundamental mode, unless the disc is very cool. For parameters close to resonance, large phase shifts occur between the disc and binary eccentricities that are locked in phase. Forced eccentricity may play an important role in the evolution of circumbinary discs and their central binaries.

arXiv comment8 pages, 7 figures, accepted for publication in MNRAS

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Cited by in corpus (4)

• A Dynamical Systems Approach to the Theory of Circumbinary Orbits in the Circular Restricted Problem
• Tidal truncation of circumplanetary disks fails above a critical disk aspect ratio
• The influence of tight binaries on proto-planetary disk masses
• Insights from Analytical Theory of Eccentric Circumbinary Disks