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Kozai Lidov disc instability

Monthly Notices of the Royal Astronomical Society, ISSN: 1365-2966, Vol: 469, Issue: 4, Page: 4292-4305
2017
  • 33
    Citations
  • 0
    Usage
  • 11
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    33
    • Citation Indexes
      33
  • Captures
    11

Article Description

Recent results by Martin et al. showed in 3D smoothed particle hydrodynamics simulations that tilted discs in binary systems can be unstable to the development of global, damped Kozai Lidov (KL) oscillations in which the discs exchange tilt for eccentricity. We investigate the linear stability of KL modes for tilted inviscid discs under the approximations that the disc eccentricity is small and the disc remains flat. By using 1D equations, we are able to probe regimes of large ratios of outer to inner disc edge radii that are realistic for binary systems of hundreds of astronomical unit separations and are not easily probed by multidimensional simulations. For order unity binary mass ratios, KL instability is possible for a window of disc aspect ratios H/r in the outer parts of a disc that roughly scale as (nb/n)2 H /r nb/n, for binary orbital frequency nb and orbital frequency n at the disc outer edge. We present a framework for understanding the zones of instability based on the determination of branches of marginally unstable modes. In general, multiple growing eccentric KL modes can be present in a disc. Coplanar apsidal nodal precession resonances delineate instability branches. We determine the range of tilt angles for unstable modes as a function of disc aspect ratio. Unlike the KL instability for free particles that involves a critical (minimum) tilt angle, disc instability is possible for any non-zero tilt angle depending on the disc aspect ratio.

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