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

TL;DR

This paper models the long-term evolution of warped accretion discs in binary systems, revealing that circumbinary discs tend to align with the binary plane quickly, while circumstellar discs can maintain large misalignments over their lifetime.

Contribution

It provides analytical solutions for warp profiles and alignment timescales, enhancing understanding of disc behavior in binary systems with applications to observed misaligned discs.

Findings

Circumbinary discs align with the binary plane on short timescales.

Circumstellar discs can sustain large misalignments for their entire lifetime.

Observations of misaligned discs support the theoretical predictions.

Abstract

Warped accretion discs are expected in many protostellar binary systems. In this paper, we study the long-term evolution of disc warp and precession for discs with dimensionless thickness $H/r$ larger than their viscosity parameter $\alpha$, such that bending waves can propagate and dominate the warp evolution. For small warps, these discs undergo approximately rigid-body precession. We derive analytical expressions for the warp/twist profiles of the disc and the alignment timescale for a variety of models. 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. 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. We estimate that inclination angles larger than $\sim 20^\circ$ can be maintained for typical disc parameters. Overall, our results suggest that while highly misaligned circumstellar discs in binaries are expected to be common, such misalignments should be rare for circumbinary discs. These expectations are consistent with current observations of protoplanetary discs and exoplanets in binaries, and can be tested with future observations.