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 towards identification of the true lowest-mass exo-planets 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.

9 pages, 7 figures, 1 table, Accepted to the Astrophysical Journal

References in corpus (5)

• Migration and the formation of systems of hot super-Earths and Neptunes
• Long-term tidal evolution of short-period planets with companions
• Chaotic diffusion in the Solar System
• The Value of Systems with Multiple Transiting Planets
• Secular dynamics of coplanar, non-resonant planetary system under the general relativity and quadrupole moment perturbations

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• Dynamical Constraints on the Core Mass of Hot Jupiter HAT-P-13b
• A dynamical study on the habitability of terrestrial exoplanets II: The super Earth HD 40307 g
• Onset of Secular Chaos in Planetary Systems: Period Doubling & Strange Attractors
• Dynamical Measurements of the Interior Structure of Exoplanets
• Aligned Major Axes in a Planetary System without Tidal Evolution: The 61 Virginis example
• The effects of viewing angle on the mass distribution of exoplanets
• The tidal parameters of TRAPPIST-1 b and c
• The Role of Kozai Cycles in Near-Earth Binary Asteroids