Circumbinary discs for stellar population models

We develop a rapid algorithm for the evolution of stable, circular, circumbinary discs suitable for parameter estimation and population synthesis modelling. Our model includes disc mass and angular momentum changes, accretion on to the binary stars, and binary orbital eccentricity pumping. We fit our model to the post-asymptotic giant branch (post-AGB) circumbinary disc around IRAS 08544-4431, finding reasonable agreement despite the simplicity of our model. Our best-fitting disc has a mass of about $0.01\, \mathrm{M}_{\odot }$ and angular momentum $2.7\times 10^{52}\, \mathrm{g}\, \mathrm{cm}^{2}\, \mathrm{s}^{-1}\simeq 9 \,\mathrm{M}_{\odot }\, \mathrm{km}\, \mathrm{s}^{-1}\, \mathrm{au}$, corresponding to 0.0079 and 0.16 of the common-envelope mass and angular momentum, respectively. The best-fitting disc viscosity is $\alpha _\mathrm{disc} = 5 \times 10^{-3}$ and our tidal torque algorithm can be constrained such that the inner edge of the disc $R_{\mathrm{in}}\sim 2a$. The inner binary eccentricity reaches about 0.13 in our best-fitting model of IRAS 08544-4431, short of the observed 0.22. The circumbinary disc evaporates quickly when the post-AGB star reaches a temperature of $\sim \! 6\times 10^4\, \mathrm{K}$, suggesting that planetismals must form in the disc in about $10^{4}\, \mathrm{yr}$ if secondary planet formation is to occur, while accretion from the disc on to the stars at about 10 times the inner-edge viscous rate can double the disc lifetime.