Resolving the Sin(I) degeneracy in Low-Mass Multi-Planet Systems

TL;DR

This paper introduces a method to determine the true masses of planets in multi-planet systems by resolving the sin(I) degeneracy through analyzing their orbital states at the tidal fixed point, especially in systems with a hot, sub-Saturn mass planet.

Contribution

It provides a mathematical framework to directly measure the true masses and inclinations of planets in secular systems, enhancing exoplanet characterization capabilities.

Findings

Method resolves sin(I) degeneracy in multi-planet systems.

Application to 61 Vir system demonstrates practical utility.

Framework aids in determining planetary physical properties from orbital data.

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.