Forced Eccentricity in Circumbinary Discs

TL;DR

This paper investigates how a low mass circumbinary disc develops forced eccentricity due to secular tidal effects from an eccentric binary, highlighting the role of resonances and disc properties in shaping eccentricity distribution.

Contribution

It provides a detailed analysis of the conditions leading to global apsidal resonances and their impact on disc eccentricity, including differences between 2D and 3D discs.

Findings

Resonances occur at zero apsidal frequency allowing large eccentricities.

Eccentricity distribution varies with disc aspect ratio and resonance proximity.

3D discs show higher order free mode characteristics unless very cool.

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.