Inclinations of Circumbinary Planets: Assembly of Protoplanetary Discs and Secular Binary-Disc Interaction

Abstract

The Kepler satellite has discovered a number of transiting planets around close binary stars. These circumbinary systems have highly aligned planetary and binary orbits. In this paper, we explore how the mutual inclination between the planetary and binary orbits may reflect the physical conditions of the assembly of protoplanetary discs and the interaction between protostellar binaries and circumbinary discs. Given the turbulent nature of star-forming molecular clouds, it is possible that the infalling gas onto the outer region of a circumbinary disc rotates around a different axis compared to the central protostellar binary. Thus, the newly assembled circumbinary disc can be misaligned with respect to the binary. However, the gravitational torque from the binary produces warp and twist in the disc, and the back-reaction torque tends to align the disc and the binary orbital plane. We present a new, analytic calculation of this alignment torque, and show that the binary-disc inclination angle can be reduced appreciably after the binary accretes a few percent of its mass from the disc. Since mass accretion onto the proto-binary is very likely to occur, our calculation suggests that in the absence of other disturbances, circumbinary discs and planets around close (sub-AU) stellar binaries are highly aligned with the binary orbits, while discs and planets around wide binaries can be misaligned.