Linear Warping in Circumbinary Protoplanetary Disks

Evolution of linear warps in accretion discs and applications to protoplanetary discs in binaries

Authors:

Foucart et al

Abstract:

The existence of warped accretion discs is expected in a wide variety of astrophysical systems, including circumstellar discs in binaries and discs around binary protostars. A common feature of these discs is that they are perturbed by a misaligned external potential. In this paper, we study the long-term evolution of the disc warp and precession in the case of thick discs (with the dimensionless thickness H/r larger than the viscosity parameter α) in which bending waves can propagate. For small warps, such discs undergo approximately rigid-body precession with a coherent global frequency. We derive the analytical expressions for the warp/twist profiles of the disc and the alignment timescale for a variety of disc models/parameters. Applying our results to circumbinary discs, we find that these discs align with the orbital plane of the binary on a timescale comparable to the global precession time of the disc, and typically much smaller than its viscous timescale. The development of parametric instabilities associated with disc warp may further increase the inclination damping rate. We discuss the implications of our finding for the observations of misaligned circumbinary discs (such as KH 15D) and circumbinary planetary systems (such as Kepler-413); these observed misalignments provide useful constraints on the uncertain aspects of the disc warp theory. On the other hand, we find that circumstellar discs can maintain large misalignments with respect to the plane of the binary companion over their entire lifetime. Even when the enhanced damping effect due to parametric instabilities associated with the disc warp are taken into account, we estimate that inclination angles of ∼20∘ can be maintained for equal mass circular binaries and typical disc parameters (α=0.01, H/r=0.1). [Abridged]