Dynamical dust traps in misaligned circumbinary discs: analytical theory and numerical simulations

Abstract

Recent observations have shown that circumbinary discs can be misaligned with respect to the binary orbital plane.The lack of spherical symmetry, together with the non-planar geometry of these systems, causes differential precession which might induce the propagation of warps. While gas dynamics in such environments is well understood, little is known about dusty discs. In this work, we analytically study the problem of dust traps formation in misaligned circumbinary discs. We find that pile-ups may be induced not by pressure maxima, as the usual dust traps, but by a difference in precession rates between the gas and dust. Indeed, this difference makes the radial drift inefficient in two locations, leading to the formation of two dust rings whose position depends on the system parameters. This phenomenon is likely to occur to marginally coupled dust particles (St ≳ 1) as both the effect of gravitational and drag force are considerable. We then perform a suite of three-dimensional SPH numerical simulations to compare the results with our theoretical predictions. We explore the parameter space, varying stellar mass ratio, disc thickness, radial extension, and we find a general agreement with the analytical expectations. Such dust pile-up prevents radial drift, fosters dust growth and may thus promote the planet formation in circumbinary discs.

Eccentric dust ring formation in Kozai-Lidov gas disks

“…Dipierro et al 2015) including disks in misaligned binaries (e.g. Aly & Lodato 2020;Longarini et al 2021).…”

“…Ring formation has been seen previously in misaligned circumbinary disk simulations as a result of nodal precession. Where the velocity difference between the dust and the gas is zero, there is no radial drift and so dust piles up (Longarini et al 2021).…”

Dust Traffic Jams in Inclined Circumbinary Protoplanetary Discs I. Morphology and Formation Theory

“…This difference in precession profiles alters the structure of the dust disc and forms rings. Longarini et al (2021) investigated this phenomenon analytically and numerically and showed that geometrical projections of the dust onto the gas plane leads to a prediction of two radii where the dust piles up. If the dust component is uncoupled from the gas, the effects of gas drag on the dust precession profile can be neglected and the dust will precess with the frequency of a test particle around a binary:…”

“…where 𝐿 g (𝑅) is the magnitude of the specific gas angular momentum density and can be evaluated from 𝐿 g (𝑅) = Σ g 𝑅 2 Ω. By equating the two above expressions, Longarini et al (2021) estimated the radius at which the gas and (uncoupled) dust share the same precession frequency. This co-precession radius 𝑅 cp can thus be computed from:…”

“…There exist two radii, inner and outer to the co-precession radius, where projection of the dust orbiting speed onto the gas plane will offset this reduction and the radial drift will vanish, forming dust rings. Longarini et al (2021) estimate these two radii assuming that the difference in the inclination angle between the gas and dust is minimum and can be neglected. Importantly, these dust rings do not occur at gas pressure maxima, and thus are different from classical dust traps.…”