Vertical Instabilities and Off‐Plane Orbits in Circumbinary Disks

Abstract

We present an approach to the problem of particle disks in lopsided potentialssuch as circumbinary dust or planetesimal diskswhich focuses on planar and oU-plane orbits in the restricted three-body problem. We show that several families of oU-plane orbits around a circular binary are stable, and at least one of these is easily accessible to particles orbiting in the plane of the binary motion (e.g., in a circumbinary accretion or protoplanetary disk). The presence of a vertical instability in the family of simple, periodic orbits that supports such disks suggests that particles in the disk should be excited into oU-plane motion. When we include a dissipational term in our equations to mimic the eUects of such forces as viscosity, gas drag, or Poynting-Robertson drag, disk particles spiral slowly inward. This allows us to test the eUects of in-plane and vertical resonances on particle motion and to explore the eUects of nonzero binary eccentricity. In the circular case, for mass ratios the 0.02 ( k( m 2 /(m 1 ) m 2 )) ( 0.35, vertical resonance located at a distance from the barycenter of just over twice the binary semimajor axis intercepts the majority of inbound particles and excites them onto the oU-plane orbits. For slightly lower mass ratios the corresponding planar instability tends to dominate, (k ( 0.01), k ) ( ) B : i \( 1:2 and particles are forced onto orbits which escape from the binary before signi—cant vertical excitation can occur; at very small mass ratios neither of these outer resonances are strong enough to (k ( 0.001), intercept a signi—cant fraction of particles. Eccentricities of eUectively shut oU this vertical exci- e Z 0.01 tation. But at e D 0.1, we —nd a new vertical excitation for particles on 1:3 planar orbits farther out, which branch from the main circumbinary orbits at the k \( 1:3 resonance (eccentric orbits at the Keplerian 4:1 mean-motion resonance). We discuss applications of these results to premain-sequence binaries and star-planet systems with dust disks and comment on the relevance of our results to circum- binary disks dominated by collective eUects such as gas pressure and self-gravity. A number of objects in the Kuiper Belt of the outer solar system may exist in highly inclined orbits as a result of the resonances discussed here. Subject headings: accretion, accretion diskscelestial mechanics, stellar dynamics ¨ planetary systemssolar system: formationstars: premain-sequence