Celestial Mechanics and Dynamical Astronomy

, Volume 112, Issue 3, pp 235–251 | Cite as

Disintegration process of hierarchical triple systems. I. Small-mass planet orbiting equal-mass binary

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Abstract

The stability of hierarchical triple system is studied in the case of an extrasolar planet or a brown dwarf orbiting a pair of main sequence stars. The evolution of triple system is well modelled by random walk (RW) diffusion, particularly in the cases where the third body is small and tracing an orbit with a large eccentricity. A RW model neglects the fact that there are many periodic orbits accompanied by stability islands, and hence inherently overestimates the instability of the system. The present work is motivated by the hope to clarify how far the RW model is applicable. Escape time and the surface section technique are used to analyse the outcome of numerical integrations. The analysis shows that the RW-like model explains escape of the third body if the initial configuration is directly outside of the KAM tori. A small gap exists in (q 2/a 1, e 2)-plane between locations of the stability limit curves based on our numerical study and on RW-model (the former is shifted by –1.4 in q 2/a 1 direction from the latter).

Keywords

Hierarchical stability Triple system Random walk model KAM stability Hill-type stability Escape 
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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.The Institute of Statistical MathematicsTokyoJapan
  2. 2.National Astronomical Observatory of JapanTokyoJapan
  3. 3.Sobolev Astronomical InstituteSt. Petersburg State UniversitySt. PetersburgRussia
  4. 4.Main (Pulkovo) Astronomical Observatory of RASSt. PetersburgRussia

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