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Published April 1, 2011 | Accepted Version + Published
Journal Article Open

Resolving the sin(I) Degeneracy in Low-mass Multi-planet Systems

Abstract

Long-term orbital evolution of multi-planet systems under tidal dissipation often converges to a stationary state, known as the tidal fixed point. The fixed point is characterized by a lack of oscillations in the eccentricities and apsidal alignment among the orbits. Quantitatively, the nature of the fixed point is dictated by mutual interactions among the planets as well as non-Keplerian effects. We show that if a roughly coplanar system hosts a hot, sub-Saturn mass planet, and is tidally relaxed, separation of planet-planet interactions and non-Keplerian effects in the equations of motion leads to a direct determination of the true masses of the planets. Consequently, a "snap-shot" observational determination of the orbital state resolves the sin(I) degeneracy and opens up a direct avenue toward identification of the true lowest-mass exoplanets detected. We present an approximate, as well as a general, mathematical framework for computation of the line-of-sight inclination of secular systems, and apply our models illustratively to the 61 Vir system. We conclude by discussing the observability of planetary systems to which our method is applicable and we set our analysis into a broader context by presenting a current summary of the various possibilities for determining the physical properties of planets from observations of their orbital states.

Additional Information

© 2011 American Astronomical Society. Received 2011 January 18; accepted 2011 January 27; published 2011 March 9. We are grateful to Y. Wu, D. J. Stevenson, J. A. Johnson, and M. E. Brown for carefully reviewing the manuscript and for useful discussions. We thank the anonymous referee for useful suggestions. This work was funded by NASA grant NNX08AY38A and NASA/Spitzer/JPL grant 1368434 to G.L.

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Published - Batygin2011p13397Astrophys_J.pdf

Accepted Version - 1102.0274.pdf

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August 22, 2023
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