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 postasymptotic giant branch (postAGB) circumbinary disc around IRAS 08544−4431, finding reasonable agreement despite the simplicity of our model. Our bestfitting 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 commonenvelope mass and angular momentum, respectively. The bestfitting disc viscosity is αdisc = 5 × 10−3 and our tidal torque algorithm can be constrained such that the inner edge of the disc Rin ∼ 2a. The inner binary eccentricity reaches about 0.13 in our bestfitting model of IRAS 08544−4431, short of the observed 0.22. The circumbinary disc evaporates quickly when the postAGB 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 ∼10 times the inneredge viscous rate can double the disc lifetime.
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ABSTRACT