Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999apj...521..798e&link_type=abstract
The Astrophysical Journal, Volume 521, Issue 2, pp. 798-822.
Astronomy and Astrophysics
Astronomy
4
Accretion, Accretion Disks, Celestial Mechanics, Stellar Dynamics, Stars: Planetary Systems, Solar System: Formation, Stars: Pre-Main-Sequence
Scientific paper
We present an approach to the problem of particle disks in lopsided potentials-such as circumbinary dust or planetesimal disks-which focuses on planar and off-plane orbits in the restricted three-body problem. We show that several families of off-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 off-plane motion. When we include a dissipational term in our equations to mimic the effects of such forces as viscosity, gas drag, or Poynting-Robertson drag, disk particles spiral slowly inward. This allows us to test the effects of in-plane and vertical resonances on particle motion and to explore the effects of nonzero binary eccentricity. In the circular case, for mass ratios 0.02<~mu[=m_2/(m_1+m_2)]<~0.35, the 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 off-plane orbits. For slightly lower mass ratios (mu<~0.01), the corresponding k=Omega-Omega_B:kappa=-1:2 planar instability tends to dominate, and particles are forced onto orbits which escape from the binary before significant vertical excitation can occur; at very small mass ratios (mu<~0.001), neither of these outer resonances are strong enough to intercept a significant fraction of particles. Eccentricities of e>~0.01 effectively shut off this vertical excitation. But at e~0.1, we find 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 pre-main-sequence binaries and star-planet systems with dust disks and comment on the relevance of our results to circumbinary disks dominated by collective effects 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.
Erwin Peter
Sparke Linda S.
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