DDA 2015 – Inclination Excitation in Compact Extrasolar Planetary Systems

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Juliette Becker (U. Michigan) (Duncombe prize winner)


The Kepler Mission has detected dozens of compact planetary systems with more than four transiting planets. This sample provides a collection of close-packed planetary systems with relatively liRle spread in the inclination angles of the inferred orbits. We have explored the effectiveness of dynamical mechanisms in exciting orbital inclination in this class of solar systems. The two mechanisms we discuss are self-excitation of orbital inclination in initially (nearly) coplanar planetary systems and perturbations by additional unseen larger bodies in the outer regions of the solar systems. For both of these scenarios, we determine the regimes of parameter space for which orbital inclination can be effectively excited. For compact planetary systems with the observed architectures, we find that the orbital inclination angles are not spread out appreciably through self-excitation, resulting in a negligible scaRer in impact parameter and a subsequently stable transiting system. In contrast, companions in the outer solar system can be effective in driving variations of the inclination angles of the inner planetary orbits, leading to significant scatter in impact parameter and resultantly non-transiting systems. We present the results of our study, the regimes in which each excitation method – self-excitation of inclination and excitation by a perturbing secondary – are relevant, and the magnitude of the effects.


  • Why so many multi-planet transiting system?
  • Ballard & Johnson 2014, Ballard 2014, Morton 2014, Morton & Winn 2014
  • Seems to be a “Kepler dichotomy”
  • $\rightarrow$ inclination excitation important
  • $2^{nd}$ order secular Laplace-Lagrange theory (Murray &Dermott)
    • inc. & ecc. decoupled
    • Inclination as function of time (analytical)
  • Use Kepler 4+ planets as model systems
  • Conclusions:
    • Self-excitation in compact solar system planets does not appear to be a significant mechanism
    • Current Kepler systems with non-transiting planets could have started out transiting but driven out of transit by self-excitation
    • Excitation by compact solar system planets themselves (smear their mass into a disk) does notappearto be a significant mechanism
      • It might be possible to see multi-transiting systems with Jovian masses (if they exist)
    • Dynamical transit duration variations due to secular interactions will be small ($10^{-4}$ to $10^{-7}$ sec) but potentially observable (via statistics on long time series)

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