Forced eccentricity in circumbinary discs

We analyse 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, which 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, which 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.