Linear analysis of the evolution of nearly polar low-mass circumbinary discs

Abstract

Martin & Lubow (2017) showed through simulations that an initially tilted disc around an eccentric binary can evolve to polar alignment in which the disc lies perpendicular to the binary orbital plane. We apply linear theory to show both analytically and numerically that a nearly polar aligned low mass circumbinary disc evolves to polar alignment and determine the alignment timescale. Significant disc evolution towards the polar state around moderately eccentric binaries can occur for typical protostellar disc parameters in less than a typical disc lifetime for binaries with orbital periods of order 100 years or less. Resonant torques are much less effective at truncating the inner parts of circumbinary polar discs than the inner parts of coplanar discs.For polar discs, they vanish for a binary eccentricity of unity. The results agree with the simulations in showing that discs can evolve to a polar state.Circumbinary planets may then form in such discs and reside on polar orbits.

A circumbinary protoplanetary disk in a polar configuration

“…While the timescale for this evolution depends on the specific assumptions made for the simulations (e.g. the disc scale height and viscosity), and may be longer than found by our simulations, theory suggests that discs will typically become aligned within a few million years 4,10 .…”

“…For small initial misalignments the angular momentum vector of circumbinary orbits L c precesses about the binary angular momentum vector L b (a 'coplanar' family of orbits), but for larger misalignments L c precesses about a vector in the binary's pericentre direction b (a 'polar' family) 7 . Because the discs that orbit young stars are gas-rich and hence dissipative, an initially misaligned circumbinary disc will generally evolve to an end state that belongs to one of these two families 3,4,[8][9][10][11] . The expected timescale for this reorientation is generally shorter than the typical ∼3 million-year disc lifetime 12 , meaning that young gas-rich circumbinary discs are most likely to be observed to be in one of the two possible orientations, rather than at an intermediate orientation.…”

Dusty clumps in circumbinary discs

“…Within this context, polar circumbinary discs are of particular interest since we have shown they form stable and prominent dusty clumps (e50-i90 and e75-i90). Theoretical models first predicted the existence of this kind of polar discs (Aly et al 2015;Martin & Lubow 2017;Zanazzi & Lai 2018;Lubow & Martin 2018), as the one very recently discovered in HD 98800 by Kennedy et al (2019). It seems reasonable to think that planets will eventually form in these polar circumbinary discs.…”

Effects of disc warping on the inclination evolution of star–disc–binary systems

“…6), γ sd depends strongly on the surface density and sound-speed power-law indices p and q. The alignment rate of a circumbinary disk with its binary orbital plane has a similarly strong dependence on p and q (Foucart & Lai 2013, 2014Lubow & Martin 2018). This strong dependence arises because the torque on the inner part of a disk from an oblate star or binary is strongest near rin.…”