Precession and accretion in circumbinary discs: the case of HD 104237

We present the results of smoothed particle hydrodynamics (SPH) simulations of the disc around the young, eccentric stellar binary HD 104237. We find that the binary clears out a large cavity in the disc, driving a significant eccentricity at the cavity edge. This then precesses around the binary at a rate of dot{\varpi } = 0.48°T_b^{-1}, which for HD 104237 corresponds to a precession period of 40 years. We find that the accretion pattern into the cavity and on to the binary changes with this precession, resulting in a periodic accretion variability driven purely by the physical parameters of the binary and its orbit. For each star we find that this results in order of magnitude changes in the accretion rate. We also find that the accretion variability allows the primary to accrete gas at a higher rate than the secondary for approximately half of each precession period. Using a large number of three-body integrations of test particles orbiting different binaries, we find good agreement between the precession rate of a test particle and our SPH disc precession. These rates also agree very well with the precession rates predicted by the analytic theory of Leung & Lee, showing that their prescription can be accurately used to predict long-term accretion variability time-scales for eccentric binaries accreting from a disc. We discuss the implications of our result, and suggest that this process provides a viable way of preserving unequal-mass ratios in accreting eccentric binaries in both the stellar and supermassive black hole regimes.