Viscous circumbinary protoplanetary discs – I. Structure of the inner cavity

Many of the most intriguing features, including spirals and cavities, in the current disc observations are found in binary systems like GG Tau, HD 142527, or HD 100453. Such features are evidence of the dynamic interactions between binary stars and the viscous disc. Understanding these dynamic interactions and how they result in the structure and growth of asymmetric circumbinary discs is a difficult problem, for which there is no complete analytical solution, that predicts the shape of the observed disc accurately. We use numerical simulations to evolve circumbinary discs with varying disc viscosities and investigate the size and shape of the inner cavities in such protoplanetary discs. We have simulated over 140 locally isothermal 2D grid-based disc models for 3 × 104 binary orbits each and mapped out the parameter space relevant for protoplanetary discs. With this, it becomes possible to create parametrized profiles for individual discs to compare to observations and find limits to their binary eccentricity or internal viscosity from the simulation data. In the long-term simulations, larger cavity sizes than previously considered are possible within the parameter space (⁠ 6 binary separations). As an example, we find that the eccentricity of the disc around HD 142527 suggests the impact of the binary dynamics on the disc. However, even considering the larger cavity sizes, the large size of the cavity in HD 142527 remains unexplained by the simulations considering the most recent orbital constraints.