de/dt in units of dlna/dt as a function of e (Eq. (9)) based on the model of Lubow & Artymowicz (1996, 2000), for a circumbinary disc with a viscosity parameter α = 0.1. The curve is divided in three regions. For eccentricities from 0 to 0.2, our model is strictly valid (red solid curve). For eccentricities from 0.2 to 0.7, the model is extrapolated outside its validity range according to an efficiency decreasing as 1/e (black dotted curve). At higher eccentricities, resonances that damp the eccentricity dominate, so de/dt = 0 (blue dashed curve).