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Vertical instability and inclination excitation during planetary migration

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Abstract

We consider a two-planet system migrating under the influence of dissipative forces that mimic the effects of gas-driven (Type II) migration. It has been shown that, in the planar case, migration leads to resonant capture after an evolution that forces the system to follow families of periodic orbits. Starting with planets that differ slightly from a coplanar configuration, capture can, also, occur and, additionally, excitation of planetary inclinations has been observed in some cases. We show that excitation of inclinations occurs, when the planar families of periodic orbits, which are followed during the initial stages of planetary migration, become vertically unstable. At these points, vertical critical orbits may give rise to generating stable families of \(3D\) periodic orbits, which drive the evolution of the migrating planets to non-coplanar motion. We have computed and present here the vertical critical orbits of the \(2/1\) and \(3/1\) resonances, for various values of the planetary mass ratio. Moreover, we determine the limiting values of eccentricity for which the “inclination resonance” occurs.

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Notes

  1. For \(\rho \gtrsim 6.5\), the vco enters the stable segment of \(S_4^{3/1}\).

  2. Particularly we used \(m_1=0.0005\) and \(m_2=0.005\). We remind that for \(\rho \gtrsim 6.5\), the vco belongs to the stable part of the family \(S_4^{3/1}\).

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Acknowledgments

This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) - Research Funding Program: Thales. Investing in knowledge society through the European Social Fund. The work of K.T. was supported by AUTh Research Committee’s “Action C: Support of Research Activities in Basic Research” (Contract Nr. 89406).

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  1. Department of Physics, Aristotle University of Thessaloniki, 54124 , Thessaloníki, Greece

    G. Voyatzis, K. I. Antoniadou & K. Tsiganis

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  1. G. Voyatzis
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  2. K. I. Antoniadou
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  3. K. Tsiganis
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Correspondence to K. I. Antoniadou.

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Voyatzis, G., Antoniadou, K.I. & Tsiganis, K. Vertical instability and inclination excitation during planetary migration. Celest Mech Dyn Astr 119, 221–235 (2014). https://doi.org/10.1007/s10569-014-9566-3

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  • DOI: https://doi.org/10.1007/s10569-014-9566-3

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