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A circumbinary disc model for the variability of the eclipsing binary CoRoT 223992193

We calculate the flux received from a binary system obscured by a circumbinary disc. The disc is modelled using two dimensional hydrodynamical simulations, and the vertical structure is derived by assuming it is isothermal. The gravitational torque from the binary creates a cavity in the disc's inner parts. If the line of sight along which the system is observed has a high inclination $I$, it intersects the disc and some absorption is produced. As the system is not axisymmetric, the resulting light curve displays variability. We calculate the absorption and produce light curves for different values of the dust disc aspect ratio $H/r$ and mass of dust in the cavity $M_{\rm dust}$. This model is applied to the high inclination ($I=85^{\circ}$) eclipsing binary CoRoT 223992193, which shows 5-10% residual photometric variability after the eclipses and a spot model are subtracted. We find that such variations for $I \sim 85^{\circ}$ can be obtained for $H/r=10^{-3}$ and $M_{\rm dust} \ge 10^{-12}$ M$_{\odot}$. For higher $H/r$, $M_{\rm dust}$ would have to be close to this lower value and $I$ somewhat less than $85^{\circ}$. Our results show that such variability in a system where the stars are at least 90% visible at all phases can be obtained only if absorption is produced by dust located inside the cavity. If absorption is dominated by the parts of the disc located close to or beyond the edge of the cavity, the stars are significantly obscured.