Three-dimensional evolution of radiative circumbinary discs: the size and shape of the inner cavity

The evolution of circumbinary discs and planets is often studied using two-dimensional (2D) numerical simulations, although recent work suggests that 3D effects may significantly alter the structure of the inner cavity created by the binary. In this study, we present the results of 3D hydrodynamical simulations of circumbinary discs that orbit around analogues of the Kepler-16 and Kepler-34 systems, including the effect of stellar heating and radiative cooling on the thermal disc structure. We find that compared to their 2D counterparts, the structures of the cavities in 3D circumbinary disc models appear to reach a quasi-stationary state more rapidly, and in a subset of our runs the evidence for this is unambiguous. Furthermore, the sizes and eccentricities of the inner cavity are smaller in 3D compared to 2D. We attribute this difference to enhanced spiral wave dissipation in disc regions above the midplane, where the cooling time is of the order of the dynamical timescale, resulting in smaller inner cavity sizes in 3D disc models. Our results suggest that migrating planets should park closer to the central binary in 3D models of circumbinary discs, and point to the importance of including the 3D structure when simulating circumbinary discs and planets.